0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : supatvars_int
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --sup-at-vars \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n119.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 14:12:10 CST 2018
294.63/294.87	% done 29573 iterations in 294.664s
294.63/294.87	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
294.63/294.87	% SZS output start Refutation
294.63/294.87	tff(fact_9__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096, axiom,
294.63/294.87	  (?[N1:nat]:
294.63/294.87	     (member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
294.63/294.87	             product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),
294.63/294.87	             aa(fun(arrow_159774573e_indi,
294.63/294.87	                    fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                     arrow_411405190le_alt),
294.63/294.87	                        bool)),
294.63/294.87	                fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
294.63/294.87	                    bool),
294.63/294.87	                f,
294.63/294.87	                combc(arrow_159774573e_indi,
294.63/294.87	                      fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                       arrow_411405190le_alt),
294.63/294.87	                          bool),
294.63/294.87	                      fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                       arrow_411405190le_alt),
294.63/294.87	                          bool),
294.63/294.87	                      combc(arrow_159774573e_indi,
294.63/294.87	                            fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                             arrow_411405190le_alt),
294.63/294.87	                                bool),
294.63/294.87	                            fun(fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                 arrow_411405190le_alt),
294.63/294.87	                                    bool),
294.63/294.87	                                fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                 arrow_411405190le_alt),
294.63/294.87	                                    bool)),
294.63/294.87	                            combb(bool,
294.63/294.87	                                  fun(fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                       arrow_411405190le_alt),
294.63/294.87	                                          bool),
294.63/294.87	                                      fun(fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                           arrow_411405190le_alt),
294.63/294.87	                                              bool),
294.63/294.87	                                          fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                           arrow_411405190le_alt),
294.63/294.87	                                              bool))),
294.63/294.87	                                  arrow_159774573e_indi,
294.63/294.87	                                  if(fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                      arrow_411405190le_alt),
294.63/294.87	                                         bool)),
294.63/294.87	                                  combc(arrow_159774573e_indi,nat,bool,
294.63/294.87	                                        combb(nat,fun(nat,bool),
294.63/294.87	                                              arrow_159774573e_indi,
294.63/294.87	                                              ord_less(nat),h),
294.63/294.87	                                        plus_plus(nat,N1,one_one(nat)))),
294.63/294.87	                            lab),
294.63/294.87	                      lba))) & 
294.63/294.87	      (![M3:nat]:
294.63/294.87	         (ord_less_eq(nat,M3,N1) =>
294.63/294.87	          member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
294.63/294.87	                 product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),
294.63/294.87	                 aa(fun(arrow_159774573e_indi,
294.63/294.87	                        fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                         arrow_411405190le_alt),
294.63/294.87	                            bool)),
294.63/294.87	                    fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                     arrow_411405190le_alt),
294.63/294.87	                        bool),
294.63/294.87	                    f,
294.63/294.87	                    combc(arrow_159774573e_indi,
294.63/294.87	                          fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                           arrow_411405190le_alt),
294.63/294.87	                              bool),
294.63/294.87	                          fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                           arrow_411405190le_alt),
294.63/294.87	                              bool),
294.63/294.87	                          combc(arrow_159774573e_indi,
294.63/294.87	                                fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                 arrow_411405190le_alt),
294.63/294.87	                                    bool),
294.63/294.87	                                fun(fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                     arrow_411405190le_alt),
294.63/294.87	                                        bool),
294.63/294.87	                                    fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                     arrow_411405190le_alt),
294.63/294.87	                                        bool)),
294.63/294.87	                                combb(bool,
294.63/294.87	                                      fun(fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                           arrow_411405190le_alt),
294.63/294.87	                                              bool),
294.63/294.87	                                          fun(fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                               arrow_411405190le_alt),
294.63/294.87	                                                  bool),
294.63/294.87	                                              fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                               arrow_411405190le_alt),
294.63/294.87	                                                  bool))),
294.63/294.87	                                      arrow_159774573e_indi,
294.63/294.87	                                      if(fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                          arrow_411405190le_alt),
294.63/294.87	                                             bool)),
294.63/294.87	                                      combc(arrow_159774573e_indi,nat,bool,
294.63/294.87	                                            combb(nat,fun(nat,bool),
294.63/294.87	                                                  arrow_159774573e_indi,
294.63/294.87	                                                  ord_less(nat),h),
294.63/294.87	                                            M3)),
294.63/294.87	                                lab),
294.63/294.87	                          lba))))) & 
294.63/294.87	      pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),N1),
294.63/294.87	            finite_card(arrow_159774573e_indi,
294.63/294.87	                        top_top(fun(arrow_159774573e_indi,bool)))))))).
294.63/294.87	tff('0', plain,
294.63/294.87	    ![X0 : nat]:
294.63/294.87	      (member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	         product_Pair(arrow_411405190le_alt, arrow_411405190le_alt, b, a), 
294.63/294.87	         aa(
294.63/294.87	           fun(arrow_159774573e_indi, 
294.63/294.87	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	               bool)), 
294.63/294.87	           fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	             bool), f, 
294.63/294.87	           combc(arrow_159774573e_indi, 
294.63/294.87	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	               bool), 
294.63/294.87	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	               bool), 
294.63/294.87	             combc(arrow_159774573e_indi, 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool), 
294.63/294.87	               fun(
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool)), 
294.63/294.87	               combb(bool, 
294.63/294.87	                 fun(
294.63/294.87	                   fun(
294.63/294.87	                     product_prod(arrow_411405190le_alt, 
294.63/294.87	                       arrow_411405190le_alt), bool), 
294.63/294.87	                   fun(
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool), 
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool))), 
294.63/294.87	                 arrow_159774573e_indi, 
294.63/294.87	                 if(
294.63/294.87	                   fun(
294.63/294.87	                     product_prod(arrow_411405190le_alt, 
294.63/294.87	                       arrow_411405190le_alt), bool)), 
294.63/294.87	                 combc(arrow_159774573e_indi, nat, bool, 
294.63/294.87	                   combb(nat, fun(nat, bool), arrow_159774573e_indi, 
294.63/294.87	                     ord_less(nat), h), X0)), lab), lba)))
294.63/294.87	       | ~ ord_less_eq(nat, X0, sk_N1)),
294.63/294.87	    inference('cnf', [status(esa)],
294.63/294.87	              [fact_9__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096])).
294.63/294.87	tff('1', plain,
294.63/294.87	    member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	      product_Pair(arrow_411405190le_alt, arrow_411405190le_alt, a, b), 
294.63/294.87	      aa(
294.63/294.87	        fun(arrow_159774573e_indi, 
294.63/294.87	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	            bool)), 
294.63/294.87	        fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), bool), 
294.63/294.87	        f, 
294.63/294.87	        combc(arrow_159774573e_indi, 
294.63/294.87	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	            bool), 
294.63/294.87	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	            bool), 
294.63/294.87	          combc(arrow_159774573e_indi, 
294.63/294.87	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	              bool), 
294.63/294.87	            fun(
294.63/294.87	              fun(
294.63/294.87	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                bool), 
294.63/294.87	              fun(
294.63/294.87	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                bool)), 
294.63/294.87	            combb(bool, 
294.63/294.87	              fun(
294.63/294.87	                fun(
294.63/294.87	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                  bool), 
294.63/294.87	                fun(
294.63/294.87	                  fun(
294.63/294.87	                    product_prod(arrow_411405190le_alt, 
294.63/294.87	                      arrow_411405190le_alt), bool), 
294.63/294.87	                  fun(
294.63/294.87	                    product_prod(arrow_411405190le_alt, 
294.63/294.87	                      arrow_411405190le_alt), bool))), 
294.63/294.87	              arrow_159774573e_indi, 
294.63/294.87	              if(
294.63/294.87	                fun(
294.63/294.87	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                  bool)), 
294.63/294.87	              combc(arrow_159774573e_indi, nat, bool, 
294.63/294.87	                combb(nat, fun(nat, bool), arrow_159774573e_indi, 
294.63/294.87	                  ord_less(nat), h), plus_plus(nat, sk_N1, one_one(nat)))), 
294.63/294.87	            lab), lba))),
294.63/294.87	    inference('cnf', [status(esa)],
294.63/294.87	              [fact_9__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096])).
294.63/294.87	tff(conj_0, axiom,
294.63/294.87	  (![N:nat]:
294.63/294.87	     (pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),N),
294.63/294.87	            finite_card(arrow_159774573e_indi,
294.63/294.87	                        top_top(fun(arrow_159774573e_indi,bool))))) =>
294.63/294.87	      ((![M:nat]:
294.63/294.87	          (ord_less_eq(nat,M,N) =>
294.63/294.87	           member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
294.63/294.87	                  product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,
294.63/294.87	                               a),
294.63/294.87	                  aa(fun(arrow_159774573e_indi,
294.63/294.87	                         fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                          arrow_411405190le_alt),
294.63/294.87	                             bool)),
294.63/294.87	                     fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                      arrow_411405190le_alt),
294.63/294.87	                         bool),
294.63/294.87	                     f,
294.63/294.87	                     combc(arrow_159774573e_indi,
294.63/294.87	                           fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                            arrow_411405190le_alt),
294.63/294.87	                               bool),
294.63/294.87	                           fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                            arrow_411405190le_alt),
294.63/294.87	                               bool),
294.63/294.87	                           combc(arrow_159774573e_indi,
294.63/294.87	                                 fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                  arrow_411405190le_alt),
294.63/294.87	                                     bool),
294.63/294.87	                                 fun(fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                      arrow_411405190le_alt),
294.63/294.87	                                         bool),
294.63/294.87	                                     fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                      arrow_411405190le_alt),
294.63/294.87	                                         bool)),
294.63/294.87	                                 combb(bool,
294.63/294.87	                                       fun(fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                            arrow_411405190le_alt),
294.63/294.87	                                               bool),
294.63/294.87	                                           fun(fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                                arrow_411405190le_alt),
294.63/294.87	                                                   bool),
294.63/294.87	                                               fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                                arrow_411405190le_alt),
294.63/294.87	                                                   bool))),
294.63/294.87	                                       arrow_159774573e_indi,
294.63/294.87	                                       if(fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                           arrow_411405190le_alt),
294.63/294.87	                                              bool)),
294.63/294.87	                                       combc(arrow_159774573e_indi,nat,bool,
294.63/294.87	                                             combb(nat,fun(nat,bool),
294.63/294.87	                                                   arrow_159774573e_indi,
294.63/294.87	                                                   ord_less(nat),h),
294.63/294.87	                                             M)),
294.63/294.87	                                 lab),
294.63/294.87	                           lba))))) =>
294.63/294.87	       (member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),
294.63/294.87	               product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),
294.63/294.87	               aa(fun(arrow_159774573e_indi,
294.63/294.87	                      fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                       arrow_411405190le_alt),
294.63/294.87	                          bool)),
294.63/294.87	                  fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                   arrow_411405190le_alt),
294.63/294.87	                      bool),
294.63/294.87	                  f,
294.63/294.87	                  combc(arrow_159774573e_indi,
294.63/294.87	                        fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                         arrow_411405190le_alt),
294.63/294.87	                            bool),
294.63/294.87	                        fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                         arrow_411405190le_alt),
294.63/294.87	                            bool),
294.63/294.87	                        combc(arrow_159774573e_indi,
294.63/294.87	                              fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                               arrow_411405190le_alt),
294.63/294.87	                                  bool),
294.63/294.87	                              fun(fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                   arrow_411405190le_alt),
294.63/294.87	                                      bool),
294.63/294.87	                                  fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                   arrow_411405190le_alt),
294.63/294.87	                                      bool)),
294.63/294.87	                              combb(bool,
294.63/294.87	                                    fun(fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                         arrow_411405190le_alt),
294.63/294.87	                                            bool),
294.63/294.87	                                        fun(fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                             arrow_411405190le_alt),
294.63/294.87	                                                bool),
294.63/294.87	                                            fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                             arrow_411405190le_alt),
294.63/294.87	                                                bool))),
294.63/294.87	                                    arrow_159774573e_indi,
294.63/294.87	                                    if(fun(product_prod(arrow_411405190le_alt,
294.63/294.87	                                                        arrow_411405190le_alt),
294.63/294.87	                                           bool)),
294.63/294.87	                                    combc(arrow_159774573e_indi,nat,bool,
294.63/294.87	                                          combb(nat,fun(nat,bool),
294.63/294.87	                                                arrow_159774573e_indi,
294.63/294.87	                                                ord_less(nat),h),
294.63/294.87	                                          plus_plus(nat,N,one_one(nat)))),
294.63/294.87	                              lab),
294.63/294.87	                        lba))) =>
294.63/294.87	        thesis))))).
294.63/294.87	tff('2', plain,
294.63/294.87	    ![X340 : nat]:
294.63/294.87	      (thesis
294.63/294.87	       | ~ pp(
294.63/294.87	             aa(nat, bool, aa(nat, fun(nat, bool), ord_less(nat), X340), 
294.63/294.87	               finite_card(arrow_159774573e_indi, 
294.63/294.87	                 top_top(fun(arrow_159774573e_indi, bool)))))
294.63/294.87	       | ~ member(
294.63/294.87	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt, a, b), 
294.63/294.87	             aa(
294.63/294.87	               fun(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool)), 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool), f, 
294.63/294.87	               combc(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 combc(arrow_159774573e_indi, 
294.63/294.87	                   fun(
294.63/294.87	                     product_prod(arrow_411405190le_alt, 
294.63/294.87	                       arrow_411405190le_alt), bool), 
294.63/294.87	                   fun(
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool), 
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool)), 
294.63/294.87	                   combb(bool, 
294.63/294.87	                     fun(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool), 
294.63/294.87	                       fun(
294.63/294.87	                         fun(
294.63/294.87	                           product_prod(arrow_411405190le_alt, 
294.63/294.87	                             arrow_411405190le_alt), bool), 
294.63/294.87	                         fun(
294.63/294.87	                           product_prod(arrow_411405190le_alt, 
294.63/294.87	                             arrow_411405190le_alt), bool))), 
294.63/294.87	                     arrow_159774573e_indi, 
294.63/294.87	                     if(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool)), 
294.63/294.87	                     combc(arrow_159774573e_indi, nat, bool, 
294.63/294.87	                       combb(nat, fun(nat, bool), arrow_159774573e_indi, 
294.63/294.87	                         ord_less(nat), h), 
294.63/294.87	                       plus_plus(nat, X340, one_one(nat)))), lab), lba)))
294.63/294.87	       | ~ member(
294.63/294.87	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt, b, a), 
294.63/294.87	             aa(
294.63/294.87	               fun(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool)), 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool), f, 
294.63/294.87	               combc(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 combc(arrow_159774573e_indi, 
294.63/294.87	                   fun(
294.63/294.87	                     product_prod(arrow_411405190le_alt, 
294.63/294.87	                       arrow_411405190le_alt), bool), 
294.63/294.87	                   fun(
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool), 
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool)), 
294.63/294.87	                   combb(bool, 
294.63/294.87	                     fun(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool), 
294.63/294.87	                       fun(
294.63/294.87	                         fun(
294.63/294.87	                           product_prod(arrow_411405190le_alt, 
294.63/294.87	                             arrow_411405190le_alt), bool), 
294.63/294.87	                         fun(
294.63/294.87	                           product_prod(arrow_411405190le_alt, 
294.63/294.87	                             arrow_411405190le_alt), bool))), 
294.63/294.87	                     arrow_159774573e_indi, 
294.63/294.87	                     if(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool)), 
294.63/294.87	                     combc(arrow_159774573e_indi, nat, bool, 
294.63/294.87	                       combb(nat, fun(nat, bool), arrow_159774573e_indi, 
294.63/294.87	                         ord_less(nat), h), sk_M1(X340))), lab), lba)))),
294.63/294.87	    inference('cnf', [status(esa)], [conj_0])).
294.63/294.87	tff(help_COMBC_1_1_U, axiom,
294.63/294.87	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun(A,fun(B,C))]:
294.63/294.87	     (aa(A,C,combc(A,B,C,P,Q),R) = aa(B,C,aa(A,fun(B,C),P,R),Q)))).
294.63/294.87	tff('3', plain,
294.63/294.87	    ![X330 : $tType, X331 : $tType, X332 : $tType, 
294.63/294.87	      X333 : fun(X332, fun(X330, X331)), X334 : X332, X335 : X330]:
294.63/294.87	      aa(X332, X331, combc(X332, X330, X331, X333, X335), X334)
294.63/294.87	       = aa(X330, X331, aa(X332, fun(X330, X331), X333, X334), X335),
294.63/294.87	    inference('cnf', [status(esa)], [help_COMBC_1_1_U])).
294.63/294.87	tff('4', plain,
294.63/294.87	    ![X340 : nat]:
294.63/294.87	      (thesis
294.63/294.87	       | ~ pp(
294.63/294.87	             aa(nat, bool, 
294.63/294.87	               combc(nat, nat, bool, ord_less(nat), 
294.63/294.87	                 finite_card(arrow_159774573e_indi, 
294.63/294.87	                   top_top(fun(arrow_159774573e_indi, bool)))), X340))
294.63/294.87	       | ~ member(
294.63/294.87	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt, a, b), 
294.63/294.87	             aa(
294.63/294.87	               fun(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool)), 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool), f, 
294.63/294.87	               combc(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 combc(arrow_159774573e_indi, 
294.63/294.87	                   fun(
294.63/294.87	                     product_prod(arrow_411405190le_alt, 
294.63/294.87	                       arrow_411405190le_alt), bool), 
294.63/294.87	                   fun(
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool), 
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool)), 
294.63/294.87	                   combb(bool, 
294.63/294.87	                     fun(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool), 
294.63/294.87	                       fun(
294.63/294.87	                         fun(
294.63/294.87	                           product_prod(arrow_411405190le_alt, 
294.63/294.87	                             arrow_411405190le_alt), bool), 
294.63/294.87	                         fun(
294.63/294.87	                           product_prod(arrow_411405190le_alt, 
294.63/294.87	                             arrow_411405190le_alt), bool))), 
294.63/294.87	                     arrow_159774573e_indi, 
294.63/294.87	                     if(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool)), 
294.63/294.87	                     combc(arrow_159774573e_indi, nat, bool, 
294.63/294.87	                       combb(nat, fun(nat, bool), arrow_159774573e_indi, 
294.63/294.87	                         ord_less(nat), h), 
294.63/294.87	                       plus_plus(nat, X340, one_one(nat)))), lab), lba)))
294.63/294.87	       | ~ member(
294.63/294.87	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt, b, a), 
294.63/294.87	             aa(
294.63/294.87	               fun(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool)), 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool), f, 
294.63/294.87	               combc(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 combc(arrow_159774573e_indi, 
294.63/294.87	                   fun(
294.63/294.87	                     product_prod(arrow_411405190le_alt, 
294.63/294.87	                       arrow_411405190le_alt), bool), 
294.63/294.87	                   fun(
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool), 
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool)), 
294.63/294.87	                   combb(bool, 
294.63/294.87	                     fun(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool), 
294.63/294.87	                       fun(
294.63/294.87	                         fun(
294.63/294.87	                           product_prod(arrow_411405190le_alt, 
294.63/294.87	                             arrow_411405190le_alt), bool), 
294.63/294.87	                         fun(
294.63/294.87	                           product_prod(arrow_411405190le_alt, 
294.63/294.87	                             arrow_411405190le_alt), bool))), 
294.63/294.87	                     arrow_159774573e_indi, 
294.63/294.87	                     if(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool)), 
294.63/294.87	                     combc(arrow_159774573e_indi, nat, bool, 
294.63/294.87	                       combb(nat, fun(nat, bool), arrow_159774573e_indi, 
294.63/294.87	                         ord_less(nat), h), sk_M1(X340))), lab), lba)))),
294.63/294.87	    inference('demod', [status(thm)], ['2', '3'])).
294.63/294.87	tff(conj_1, conjecture, (thesis)).
294.63/294.87	tff(zf_stmt_0, negated_conjecture, (~thesis)).
294.63/294.87	tff('5', plain, ~ thesis, inference('cnf', [status(esa)], [zf_stmt_0])).
294.63/294.87	tff('6', plain,
294.63/294.87	    ![X340 : nat]:
294.63/294.87	      (~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	           product_Pair(arrow_411405190le_alt, arrow_411405190le_alt, b, a), 
294.63/294.87	           aa(
294.63/294.87	             fun(arrow_159774573e_indi, 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool)), 
294.63/294.87	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	               bool), f, 
294.63/294.87	             combc(arrow_159774573e_indi, 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool), 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool), 
294.63/294.87	               combc(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 fun(
294.63/294.87	                   fun(
294.63/294.87	                     product_prod(arrow_411405190le_alt, 
294.63/294.87	                       arrow_411405190le_alt), bool), 
294.63/294.87	                   fun(
294.63/294.87	                     product_prod(arrow_411405190le_alt, 
294.63/294.87	                       arrow_411405190le_alt), bool)), 
294.63/294.87	                 combb(bool, 
294.63/294.87	                   fun(
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool), 
294.63/294.87	                     fun(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool), 
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool))), 
294.63/294.87	                   arrow_159774573e_indi, 
294.63/294.87	                   if(
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool)), 
294.63/294.87	                   combc(arrow_159774573e_indi, nat, bool, 
294.63/294.87	                     combb(nat, fun(nat, bool), arrow_159774573e_indi, 
294.63/294.87	                       ord_less(nat), h), sk_M1(X340))), lab), lba)))
294.63/294.87	       | ~ member(
294.63/294.87	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt, a, b), 
294.63/294.87	             aa(
294.63/294.87	               fun(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool)), 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool), f, 
294.63/294.87	               combc(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 combc(arrow_159774573e_indi, 
294.63/294.87	                   fun(
294.63/294.87	                     product_prod(arrow_411405190le_alt, 
294.63/294.87	                       arrow_411405190le_alt), bool), 
294.63/294.87	                   fun(
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool), 
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool)), 
294.63/294.87	                   combb(bool, 
294.63/294.87	                     fun(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool), 
294.63/294.87	                       fun(
294.63/294.87	                         fun(
294.63/294.87	                           product_prod(arrow_411405190le_alt, 
294.63/294.87	                             arrow_411405190le_alt), bool), 
294.63/294.87	                         fun(
294.63/294.87	                           product_prod(arrow_411405190le_alt, 
294.63/294.87	                             arrow_411405190le_alt), bool))), 
294.63/294.87	                     arrow_159774573e_indi, 
294.63/294.87	                     if(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool)), 
294.63/294.87	                     combc(arrow_159774573e_indi, nat, bool, 
294.63/294.87	                       combb(nat, fun(nat, bool), arrow_159774573e_indi, 
294.63/294.87	                         ord_less(nat), h), 
294.63/294.87	                       plus_plus(nat, X340, one_one(nat)))), lab), lba)))
294.63/294.87	       | ~ pp(
294.63/294.87	             aa(nat, bool, 
294.63/294.87	               combc(nat, nat, bool, ord_less(nat), 
294.63/294.87	                 finite_card(arrow_159774573e_indi, 
294.63/294.87	                   top_top(fun(arrow_159774573e_indi, bool)))), X340))),
294.63/294.87	    inference('clc', [status(thm)], ['4', '5'])).
294.63/294.87	tff('7', plain,
294.63/294.87	    (~ $true
294.63/294.87	     | ~ pp(
294.63/294.87	           aa(nat, bool, 
294.63/294.87	             combc(nat, nat, bool, ord_less(nat), 
294.63/294.87	               finite_card(arrow_159774573e_indi, 
294.63/294.87	                 top_top(fun(arrow_159774573e_indi, bool)))), sk_N1))
294.63/294.87	     | ~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	           product_Pair(arrow_411405190le_alt, arrow_411405190le_alt, b, a), 
294.63/294.87	           aa(
294.63/294.87	             fun(arrow_159774573e_indi, 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool)), 
294.63/294.87	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	               bool), f, 
294.63/294.87	             combc(arrow_159774573e_indi, 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool), 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool), 
294.63/294.87	               combc(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 fun(
294.63/294.87	                   fun(
294.63/294.87	                     product_prod(arrow_411405190le_alt, 
294.63/294.87	                       arrow_411405190le_alt), bool), 
294.63/294.87	                   fun(
294.63/294.87	                     product_prod(arrow_411405190le_alt, 
294.63/294.87	                       arrow_411405190le_alt), bool)), 
294.63/294.87	                 combb(bool, 
294.63/294.87	                   fun(
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool), 
294.63/294.87	                     fun(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool), 
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool))), 
294.63/294.87	                   arrow_159774573e_indi, 
294.63/294.87	                   if(
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool)), 
294.63/294.87	                   combc(arrow_159774573e_indi, nat, bool, 
294.63/294.87	                     combb(nat, fun(nat, bool), arrow_159774573e_indi, 
294.63/294.87	                       ord_less(nat), h), sk_M1(sk_N1))), lab), lba)))),
294.63/294.87	    inference('sup-', [status(thm)], ['1', '6'])).
294.63/294.87	tff('8', plain,
294.63/294.87	    pp(
294.63/294.87	      aa(nat, bool, aa(nat, fun(nat, bool), ord_less(nat), sk_N1), 
294.63/294.87	        finite_card(arrow_159774573e_indi, 
294.63/294.87	          top_top(fun(arrow_159774573e_indi, bool))))),
294.63/294.87	    inference('cnf', [status(esa)],
294.63/294.87	              [fact_9__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096])).
294.63/294.87	tff(help_If_3_1_T, axiom, (![P:bool]: ((P = fFalse) | (P = fTrue)))).
294.63/294.87	tff('9', plain, ![X323 : bool]: (X323 = fFalse | X323 = fTrue),
294.63/294.87	    inference('cnf', [status(esa)], [help_If_3_1_T])).
294.63/294.87	tff(help_pp_1_1_U, axiom, (~pp(fFalse))).
294.63/294.87	tff('10', plain, ~ pp(fFalse),
294.63/294.87	    inference('cnf', [status(esa)], [help_pp_1_1_U])).
294.63/294.87	tff('11', plain, ![X0 : bool]: (~ pp(X0) | X0 = fTrue),
294.63/294.87	    inference('sup-', [status(thm)], ['9', '10'])).
294.63/294.87	tff('12', plain,
294.63/294.87	    (~ $true
294.63/294.87	     | aa(nat, bool, aa(nat, fun(nat, bool), ord_less(nat), sk_N1), 
294.63/294.87	         finite_card(arrow_159774573e_indi, 
294.63/294.87	           top_top(fun(arrow_159774573e_indi, bool))))
294.63/294.87	        = fTrue),
294.63/294.87	    inference('sup-', [status(thm)], ['8', '11'])).
294.63/294.87	tff('13', plain,
294.63/294.87	    aa(nat, bool, aa(nat, fun(nat, bool), ord_less(nat), sk_N1), 
294.63/294.87	      finite_card(arrow_159774573e_indi, 
294.63/294.87	        top_top(fun(arrow_159774573e_indi, bool))))
294.63/294.87	     = fTrue,
294.63/294.87	    inference('simplify', [status(thm)], ['12'])).
294.63/294.87	tff('14', plain,
294.63/294.87	    aa(nat, bool, 
294.63/294.87	      combc(nat, nat, bool, ord_less(nat), 
294.63/294.87	        finite_card(arrow_159774573e_indi, 
294.63/294.87	          top_top(fun(arrow_159774573e_indi, bool)))), sk_N1)
294.63/294.87	     = fTrue,
294.63/294.87	    inference('demod', [status(thm)], ['13', '3'])).
294.63/294.87	tff(help_pp_2_1_U, axiom, (pp(fTrue))).
294.63/294.87	tff('15', plain, pp(fTrue), inference('cnf', [status(esa)], [help_pp_2_1_U])).
294.63/294.87	tff('16', plain,
294.63/294.87	    (~ $true
294.63/294.87	     | ~ $true
294.63/294.87	     | ~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	           product_Pair(arrow_411405190le_alt, arrow_411405190le_alt, b, a), 
294.63/294.87	           aa(
294.63/294.87	             fun(arrow_159774573e_indi, 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool)), 
294.63/294.87	             fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	               bool), f, 
294.63/294.87	             combc(arrow_159774573e_indi, 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool), 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool), 
294.63/294.87	               combc(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 fun(
294.63/294.87	                   fun(
294.63/294.87	                     product_prod(arrow_411405190le_alt, 
294.63/294.87	                       arrow_411405190le_alt), bool), 
294.63/294.87	                   fun(
294.63/294.87	                     product_prod(arrow_411405190le_alt, 
294.63/294.87	                       arrow_411405190le_alt), bool)), 
294.63/294.87	                 combb(bool, 
294.63/294.87	                   fun(
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool), 
294.63/294.87	                     fun(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool), 
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool))), 
294.63/294.87	                   arrow_159774573e_indi, 
294.63/294.87	                   if(
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool)), 
294.63/294.87	                   combc(arrow_159774573e_indi, nat, bool, 
294.63/294.87	                     combb(nat, fun(nat, bool), arrow_159774573e_indi, 
294.63/294.87	                       ord_less(nat), h), sk_M1(sk_N1))), lab), lba)))),
294.63/294.87	    inference('demod', [status(thm)], ['7', '14', '15'])).
294.63/294.87	tff('17', plain,
294.63/294.87	    ~ member(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	        product_Pair(arrow_411405190le_alt, arrow_411405190le_alt, b, a), 
294.63/294.87	        aa(
294.63/294.87	          fun(arrow_159774573e_indi, 
294.63/294.87	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	              bool)), 
294.63/294.87	          fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	            bool), f, 
294.63/294.87	          combc(arrow_159774573e_indi, 
294.63/294.87	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	              bool), 
294.63/294.87	            fun(product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	              bool), 
294.63/294.87	            combc(arrow_159774573e_indi, 
294.63/294.87	              fun(
294.63/294.87	                product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                bool), 
294.63/294.87	              fun(
294.63/294.87	                fun(
294.63/294.87	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                  bool), 
294.63/294.87	                fun(
294.63/294.87	                  product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                  bool)), 
294.63/294.87	              combb(bool, 
294.63/294.87	                fun(
294.63/294.87	                  fun(
294.63/294.87	                    product_prod(arrow_411405190le_alt, 
294.63/294.87	                      arrow_411405190le_alt), bool), 
294.63/294.87	                  fun(
294.63/294.87	                    fun(
294.63/294.87	                      product_prod(arrow_411405190le_alt, 
294.63/294.87	                        arrow_411405190le_alt), bool), 
294.63/294.87	                    fun(
294.63/294.87	                      product_prod(arrow_411405190le_alt, 
294.63/294.87	                        arrow_411405190le_alt), bool))), 
294.63/294.87	                arrow_159774573e_indi, 
294.63/294.87	                if(
294.63/294.87	                  fun(
294.63/294.87	                    product_prod(arrow_411405190le_alt, 
294.63/294.87	                      arrow_411405190le_alt), bool)), 
294.63/294.87	                combc(arrow_159774573e_indi, nat, bool, 
294.63/294.87	                  combb(nat, fun(nat, bool), arrow_159774573e_indi, 
294.63/294.87	                    ord_less(nat), h), sk_M1(sk_N1))), lab), lba))),
294.63/294.87	    inference('simplify', [status(thm)], ['16'])).
294.63/294.87	tff('18', plain, (~ $true | ~ ord_less_eq(nat, sk_M1(sk_N1), sk_N1)),
294.63/294.87	    inference('sup-', [status(thm)], ['0', '17'])).
294.63/294.87	tff('19', plain,
294.63/294.87	    ![X340 : nat]:
294.63/294.87	      (thesis
294.63/294.87	       | ~ pp(
294.63/294.87	             aa(nat, bool, aa(nat, fun(nat, bool), ord_less(nat), X340), 
294.63/294.87	               finite_card(arrow_159774573e_indi, 
294.63/294.87	                 top_top(fun(arrow_159774573e_indi, bool)))))
294.63/294.87	       | ~ member(
294.63/294.87	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt, a, b), 
294.63/294.87	             aa(
294.63/294.87	               fun(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool)), 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool), f, 
294.63/294.87	               combc(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 combc(arrow_159774573e_indi, 
294.63/294.87	                   fun(
294.63/294.87	                     product_prod(arrow_411405190le_alt, 
294.63/294.87	                       arrow_411405190le_alt), bool), 
294.63/294.87	                   fun(
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool), 
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool)), 
294.63/294.87	                   combb(bool, 
294.63/294.87	                     fun(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool), 
294.63/294.87	                       fun(
294.63/294.87	                         fun(
294.63/294.87	                           product_prod(arrow_411405190le_alt, 
294.63/294.87	                             arrow_411405190le_alt), bool), 
294.63/294.87	                         fun(
294.63/294.87	                           product_prod(arrow_411405190le_alt, 
294.63/294.87	                             arrow_411405190le_alt), bool))), 
294.63/294.87	                     arrow_159774573e_indi, 
294.63/294.87	                     if(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool)), 
294.63/294.87	                     combc(arrow_159774573e_indi, nat, bool, 
294.63/294.87	                       combb(nat, fun(nat, bool), arrow_159774573e_indi, 
294.63/294.87	                         ord_less(nat), h), 
294.63/294.87	                       plus_plus(nat, X340, one_one(nat)))), lab), lba)))
294.63/294.87	       | ord_less_eq(nat, sk_M1(X340), X340)),
294.63/294.87	    inference('cnf', [status(esa)], [conj_0])).
294.63/294.87	tff('20', plain,
294.63/294.87	    ![X340 : nat]:
294.63/294.87	      (thesis
294.63/294.87	       | ~ pp(
294.63/294.87	             aa(nat, bool, 
294.63/294.87	               combc(nat, nat, bool, ord_less(nat), 
294.63/294.87	                 finite_card(arrow_159774573e_indi, 
294.63/294.87	                   top_top(fun(arrow_159774573e_indi, bool)))), X340))
294.63/294.87	       | ~ member(
294.63/294.87	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt, a, b), 
294.63/294.87	             aa(
294.63/294.87	               fun(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool)), 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool), f, 
294.63/294.87	               combc(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 combc(arrow_159774573e_indi, 
294.63/294.87	                   fun(
294.63/294.87	                     product_prod(arrow_411405190le_alt, 
294.63/294.87	                       arrow_411405190le_alt), bool), 
294.63/294.87	                   fun(
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool), 
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool)), 
294.63/294.87	                   combb(bool, 
294.63/294.87	                     fun(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool), 
294.63/294.87	                       fun(
294.63/294.87	                         fun(
294.63/294.87	                           product_prod(arrow_411405190le_alt, 
294.63/294.87	                             arrow_411405190le_alt), bool), 
294.63/294.87	                         fun(
294.63/294.87	                           product_prod(arrow_411405190le_alt, 
294.63/294.87	                             arrow_411405190le_alt), bool))), 
294.63/294.87	                     arrow_159774573e_indi, 
294.63/294.87	                     if(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool)), 
294.63/294.87	                     combc(arrow_159774573e_indi, nat, bool, 
294.63/294.87	                       combb(nat, fun(nat, bool), arrow_159774573e_indi, 
294.63/294.87	                         ord_less(nat), h), 
294.63/294.87	                       plus_plus(nat, X340, one_one(nat)))), lab), lba)))
294.63/294.87	       | ord_less_eq(nat, sk_M1(X340), X340)),
294.63/294.87	    inference('demod', [status(thm)], ['19', '3'])).
294.63/294.87	tff('21', plain,
294.63/294.87	    ![X340 : nat]:
294.63/294.87	      (ord_less_eq(nat, sk_M1(X340), X340)
294.63/294.87	       | ~ member(
294.63/294.87	             product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	             product_Pair(arrow_411405190le_alt, arrow_411405190le_alt, a, b), 
294.63/294.87	             aa(
294.63/294.87	               fun(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool)), 
294.63/294.87	               fun(
294.63/294.87	                 product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                 bool), f, 
294.63/294.87	               combc(arrow_159774573e_indi, 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 fun(
294.63/294.87	                   product_prod(arrow_411405190le_alt, arrow_411405190le_alt), 
294.63/294.87	                   bool), 
294.63/294.87	                 combc(arrow_159774573e_indi, 
294.63/294.87	                   fun(
294.63/294.87	                     product_prod(arrow_411405190le_alt, 
294.63/294.87	                       arrow_411405190le_alt), bool), 
294.63/294.87	                   fun(
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool), 
294.63/294.87	                     fun(
294.63/294.87	                       product_prod(arrow_411405190le_alt, 
294.63/294.87	                         arrow_411405190le_alt), bool)), 
294.63/294.87	                   combb(bool, 
294.63/294.87	                     fun(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool), 
294.63/294.87	                       fun(
294.63/294.87	                         fun(
294.63/294.87	                           product_prod(arrow_411405190le_alt, 
294.63/294.87	                             arrow_411405190le_alt), bool), 
294.63/294.87	                         fun(
294.63/294.87	                           product_prod(arrow_411405190le_alt, 
294.63/294.87	                             arrow_411405190le_alt), bool))), 
294.63/294.87	                     arrow_159774573e_indi, 
294.63/294.87	                     if(
294.63/294.87	                       fun(
294.63/294.87	                         product_prod(arrow_411405190le_alt, 
294.63/294.87	                           arrow_411405190le_alt), bool)), 
294.63/294.87	                     combc(arrow_159774573e_indi, nat, bool, 
294.63/294.87	                       combb(nat, fun(nat, bool), arrow_159774573e_indi, 
294.63/294.87	                         ord_less(nat), h), 
294.63/294.87	                       plus_plus(nat, X340, one_one(nat)))), lab), lba)))
294.63/294.87	       | ~ pp(
294.63/294.87	             aa(nat, bool, 
294.63/294.87	               combc(nat, nat, bool, ord_less(nat), 
294.63/294.87	                 finite_card(arrow_159774573e_indi, 
294.63/294.87	                   top_top(fun(arrow_159774573e_indi, bool)))), X340))),
294.63/294.87	    inference('clc', [status(thm)], ['20', '5'])).
294.63/294.87	tff('22', plain,
294.63/294.87	    (~ $true
294.63/294.87	     | ~ pp(
294.63/294.87	           aa(nat, bool, 
294.63/294.87	             combc(nat, nat, bool, ord_less(nat), 
294.63/294.87	               finite_card(arrow_159774573e_indi, 
294.63/294.87	                 top_top(fun(arrow_159774573e_indi, bool)))), sk_N1))
294.63/294.87	     | ord_less_eq(nat, sk_M1(sk_N1), sk_N1)),
294.63/294.87	    inference('sup-', [status(thm)], ['1', '21'])).
294.63/294.87	tff('23', plain, (~ $true | ~ $true | ord_less_eq(nat, sk_M1(sk_N1), sk_N1)),
294.63/294.87	    inference('demod', [status(thm)], ['22', '14', '15'])).
294.63/294.87	tff('24', plain, ord_less_eq(nat, sk_M1(sk_N1), sk_N1),
294.63/294.87	    inference('simplify', [status(thm)], ['23'])).
294.63/294.87	tff('25', plain, (~ $true | ~ $true),
294.63/294.87	    inference('demod', [status(thm)], ['18', '24'])).
294.63/294.87	tff('26', plain, $false, inference('simplify', [status(thm)], ['25'])).
294.63/294.87	
294.63/294.87	% SZS output end Refutation
294.63/294.88	EOF
