0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : original
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : kbo
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n138.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 08:16:38 CST 2018
96.10/96.30	% done 50231 iterations in 96.091s
96.10/96.30	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
96.10/96.30	% SZS output start Refutation
96.10/96.30	tff(conj_0, conjecture,
96.10/96.30	  (ord_less(int,
96.10/96.30	            times_times(int,
96.10/96.30	                        plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),
96.10/96.30	                        minus_minus(int,
96.10/96.30	                                    times_times(int,
96.10/96.30	                                                number_number_of(int,
96.10/96.30	                                                                 bit0(
96.10/96.30	                                                                 bit1(pls))),
96.10/96.30	                                                plus_plus(int,one_one(int),
96.10/96.30	                                                          semiring_1_of_nat(
96.10/96.30	                                                          int,n))),
96.10/96.30	                                    times_times(int,
96.10/96.30	                                                number_number_of(int,
96.10/96.30	                                                                 bit0(
96.10/96.30	                                                                 bit0(
96.10/96.30	                                                                 bit1(pls)))),
96.10/96.30	                                                m1))),
96.10/96.30	            zero_zero(int)))).
96.10/96.30	tff(zf_stmt_0, negated_conjecture,
96.10/96.30	  (~
96.10/96.30	    ord_less(int,
96.10/96.30	             times_times(int,
96.10/96.30	                         plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),
96.10/96.30	                         minus_minus(int,
96.10/96.30	                                     times_times(int,
96.10/96.30	                                                 number_number_of(int,
96.10/96.30	                                                                  bit0(
96.10/96.30	                                                                  bit1(pls))),
96.10/96.30	                                                 plus_plus(int,one_one(int),
96.10/96.30	                                                           semiring_1_of_nat(
96.10/96.30	                                                           int,n))),
96.10/96.30	                                     times_times(int,
96.10/96.30	                                                 number_number_of(int,
96.10/96.30	                                                                  bit0(
96.10/96.30	                                                                  bit0(
96.10/96.30	                                                                  bit1(pls)))),
96.10/96.30	                                                 m1))),
96.10/96.30	             zero_zero(int)))).
96.10/96.30	tff('0', plain,
96.10/96.30	    ~ ord_less(int, 
96.10/96.30	        times_times(int, 
96.10/96.30	          plus_plus(int, one_one(int), semiring_1_of_nat(int, n)), 
96.10/96.30	          minus_minus(int, 
96.10/96.30	            times_times(int, number_number_of(int, bit0(bit1(pls))), 
96.10/96.30	              plus_plus(int, one_one(int), semiring_1_of_nat(int, n))), 
96.10/96.30	            times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), 
96.10/96.30	              m1))), zero_zero(int)),
96.10/96.30	    inference('cnf', [status(esa)], [zf_stmt_0])).
96.10/96.30	tff(fact_97_number__of__is__id, axiom,
96.10/96.30	  (![K:int]: (number_number_of(int,K) = K))).
96.10/96.30	tff('1', plain, ![X215 : int]: number_number_of(int, X215) = X215,
96.10/96.30	    inference('cnf', [status(esa)], [fact_97_number__of__is__id])).
96.10/96.30	tff(fact_14_numeral__1__eq__1, axiom,
96.10/96.30	  (![A:$tType]:
96.10/96.30	     (number_ring(A) => (number_number_of(A,bit1(pls)) = one_one(A))))).
96.10/96.30	tff('2', plain,
96.10/96.30	    ![X19 : $tType]:
96.10/96.30	      (number_number_of(X19, bit1(pls)) = one_one(X19) | ~ number_ring(X19)),
96.10/96.30	    inference('cnf', [status(esa)], [fact_14_numeral__1__eq__1])).
96.10/96.30	tff('3', plain, (bit1(pls) = one_one(int) | ~ number_ring(int)),
96.10/96.30	    inference('sup+', [status(thm)], ['1', '2'])).
96.10/96.30	tff(arity_Int_Oint___Int_Onumber__ring, axiom, (number_ring(int))).
96.10/96.30	tff('4', plain, number_ring(int),
96.10/96.30	    inference('cnf', [status(esa)], [arity_Int_Oint___Int_Onumber__ring])).
96.10/96.30	tff('5', plain, (bit1(pls) = one_one(int) | ~ $true),
96.10/96.30	    inference('demod', [status(thm)], ['3', '4'])).
96.10/96.30	tff('6', plain, bit1(pls) = one_one(int),
96.10/96.30	    inference('simplify', [status(thm)], ['5'])).
96.10/96.30	tff(fact_37_mult__Bit0, axiom,
96.10/96.30	  (![L1:int,K:int]:
96.10/96.30	     (times_times(int,bit0(K),L1) = bit0(times_times(int,K,L1))))).
96.10/96.30	tff('7', plain,
96.10/96.30	    ![X59 : int, X60 : int]:
96.10/96.30	      times_times(int, bit0(X59), X60) = bit0(times_times(int, X59, X60)),
96.10/96.30	    inference('cnf', [status(esa)], [fact_37_mult__Bit0])).
96.10/96.30	tff(fact_36_mult__Pls, axiom, (![W:int]: (times_times(int,pls,W) = pls))).
96.10/96.30	tff('8', plain, ![X58 : int]: times_times(int, pls, X58) = pls,
96.10/96.30	    inference('cnf', [status(esa)], [fact_36_mult__Pls])).
96.10/96.30	tff(fact_13_mult__Bit1, axiom,
96.10/96.30	  (![L1:int,K:int]:
96.10/96.30	     (times_times(int,bit1(K),L1) =
96.10/96.30	      plus_plus(int,bit0(times_times(int,K,L1)),L1)))).
96.10/96.30	tff('9', plain,
96.10/96.30	    ![X17 : int, X18 : int]:
96.10/96.30	      times_times(int, bit1(X17), X18)
96.10/96.30	       = plus_plus(int, bit0(times_times(int, X17, X18)), X18),
96.10/96.30	    inference('cnf', [status(esa)], [fact_13_mult__Bit1])).
96.10/96.30	tff('10', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      times_times(int, bit1(pls), X0) = plus_plus(int, bit0(pls), X0),
96.10/96.30	    inference('sup+', [status(thm)], ['8', '9'])).
96.10/96.30	tff(fact_29_Bit0__Pls, axiom, (bit0(pls) = pls)).
96.10/96.30	tff('11', plain, bit0(pls) = pls,
96.10/96.30	    inference('cnf', [status(esa)], [fact_29_Bit0__Pls])).
96.10/96.30	tff('12', plain,
96.10/96.30	    ![X0 : int]: times_times(int, bit1(pls), X0) = plus_plus(int, pls, X0),
96.10/96.30	    inference('demod', [status(thm)], ['10', '11'])).
96.10/96.30	tff(fact_39_diff__bin__simps_I7_J, axiom,
96.10/96.30	  (![L1:int,K:int]:
96.10/96.30	     (minus_minus(int,bit0(K),bit0(L1)) = bit0(minus_minus(int,K,L1))))).
96.10/96.30	tff('13', plain,
96.10/96.30	    ![X63 : int, X64 : int]:
96.10/96.30	      minus_minus(int, bit0(X63), bit0(X64))
96.10/96.30	       = bit0(minus_minus(int, X63, X64)),
96.10/96.30	    inference('cnf', [status(esa)], [fact_39_diff__bin__simps_I7_J])).
96.10/96.30	tff(fact_43_number__of__Pls, axiom,
96.10/96.30	  (![A:$tType]: (number_ring(A) => (number_number_of(A,pls) = zero_zero(A))))).
96.10/96.30	tff('14', plain,
96.10/96.30	    ![X73 : $tType]:
96.10/96.30	      (number_number_of(X73, pls) = zero_zero(X73) | ~ number_ring(X73)),
96.10/96.30	    inference('cnf', [status(esa)], [fact_43_number__of__Pls])).
96.10/96.30	tff('15', plain, (pls = zero_zero(int) | ~ number_ring(int)),
96.10/96.30	    inference('sup+', [status(thm)], ['1', '14'])).
96.10/96.30	tff('16', plain, (pls = zero_zero(int) | ~ $true),
96.10/96.30	    inference('demod', [status(thm)], ['15', '4'])).
96.10/96.30	tff('17', plain, pls = zero_zero(int),
96.10/96.30	    inference('simplify', [status(thm)], ['16'])).
96.10/96.30	tff('18', plain,
96.10/96.30	    ~ ord_less(int, 
96.10/96.30	        times_times(int, 
96.10/96.30	          plus_plus(int, bit1(pls), semiring_1_of_nat(int, n)), 
96.10/96.30	          bit0(
96.10/96.30	            minus_minus(int, 
96.10/96.30	              plus_plus(int, pls, 
96.10/96.30	                plus_plus(int, bit1(pls), semiring_1_of_nat(int, n))), 
96.10/96.30	              bit0(plus_plus(int, pls, m1))))), pls),
96.10/96.30	    inference('demod', [status(thm)],
96.10/96.30	              ['0', '6', '1', '6', '7', '12', '1', '7', '7', '12', '13', '17'])).
96.10/96.30	tff(fact_61_add__Bit0__Bit1, axiom,
96.10/96.30	  (![L1:int,K:int]:
96.10/96.30	     (plus_plus(int,bit0(K),bit1(L1)) = bit1(plus_plus(int,K,L1))))).
96.10/96.30	tff('19', plain,
96.10/96.30	    ![X124 : int, X125 : int]:
96.10/96.30	      plus_plus(int, bit0(X124), bit1(X125))
96.10/96.30	       = bit1(plus_plus(int, X124, X125)),
96.10/96.30	    inference('cnf', [status(esa)], [fact_61_add__Bit0__Bit1])).
96.10/96.30	tff('20', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      plus_plus(int, pls, bit1(X0)) = bit1(plus_plus(int, pls, X0)),
96.10/96.30	    inference('sup+', [status(thm)], ['11', '19'])).
96.10/96.30	tff(fact_6_add__special_I3_J, axiom,
96.10/96.30	  (![A:$tType]:
96.10/96.30	     (number_ring(A) =>
96.10/96.30	      (![V:int]:
96.10/96.30	         (plus_plus(A,number_number_of(A,V),one_one(A)) =
96.10/96.30	          number_number_of(A,plus_plus(int,V,bit1(pls)))))))).
96.10/96.30	tff('21', plain,
96.10/96.30	    ![X2 : $tType, X3 : int]:
96.10/96.30	      (plus_plus(X2, number_number_of(X2, X3), one_one(X2))
96.10/96.30	        = number_number_of(X2, plus_plus(int, X3, bit1(pls)))
96.10/96.30	       | ~ number_ring(X2)),
96.10/96.30	    inference('cnf', [status(esa)], [fact_6_add__special_I3_J])).
96.10/96.30	tff('22', plain,
96.10/96.30	    ![X0 : $tType]:
96.10/96.30	      (plus_plus(X0, number_number_of(X0, pls), one_one(X0))
96.10/96.30	        = number_number_of(X0, bit1(plus_plus(int, pls, pls)))
96.10/96.30	       | ~ number_ring(X0)),
96.10/96.30	    inference('sup+', [status(thm)], ['20', '21'])).
96.10/96.30	tff(fact_22_double__eq__0__iff, axiom,
96.10/96.30	  (![A:$tType]:
96.10/96.30	     (linord219039673up_add(A) =>
96.10/96.30	      (![A2:A]: ((plus_plus(A,A2,A2) = zero_zero(A)) <=> (A2 = zero_zero(A))))))).
96.10/96.30	tff('23', plain,
96.10/96.30	    ![X33 : $tType, X34 : X33]:
96.10/96.30	      (X34 != zero_zero(X33)
96.10/96.30	       | plus_plus(X33, X34, X34) = zero_zero(X33)
96.10/96.30	       | ~ linord219039673up_add(X33)),
96.10/96.30	    inference('cnf', [status(esa)], [fact_22_double__eq__0__iff])).
96.10/96.30	tff('24', plain,
96.10/96.30	    ![X33 : $tType]:
96.10/96.30	      (~ linord219039673up_add(X33)
96.10/96.30	       | plus_plus(X33, zero_zero(X33), zero_zero(X33)) = zero_zero(X33)),
96.10/96.30	    inference('simplify', [status(thm)], ['23'])).
96.10/96.30	tff('25', plain,
96.10/96.30	    (plus_plus(int, zero_zero(int), pls) = zero_zero(int)
96.10/96.30	     | ~ linord219039673up_add(int)),
96.10/96.30	    inference('sup+', [status(thm)], ['17', '24'])).
96.10/96.30	tff(arity_Int_Oint___Groups_Olinordered__ab__group__add, axiom,
96.10/96.30	  (linord219039673up_add(int))).
96.10/96.30	tff('26', plain, linord219039673up_add(int),
96.10/96.30	    inference('cnf', [status(esa)],
96.10/96.30	              [arity_Int_Oint___Groups_Olinordered__ab__group__add])).
96.10/96.30	tff('27', plain, (plus_plus(int, pls, pls) = pls | ~ $true),
96.10/96.30	    inference('demod', [status(thm)], ['25', '17', '17', '26'])).
96.10/96.30	tff('28', plain, plus_plus(int, pls, pls) = pls,
96.10/96.30	    inference('simplify', [status(thm)], ['27'])).
96.10/96.30	tff('29', plain,
96.10/96.30	    ![X0 : $tType]:
96.10/96.30	      (plus_plus(X0, number_number_of(X0, pls), one_one(X0))
96.10/96.30	        = number_number_of(X0, bit1(pls))
96.10/96.30	       | ~ number_ring(X0)),
96.10/96.30	    inference('demod', [status(thm)], ['22', '28'])).
96.10/96.30	tff(fact_50_add__number__of__left, axiom,
96.10/96.30	  (![A:$tType]:
96.10/96.30	     (number_ring(A) =>
96.10/96.30	      (![Z:A,W:int,V:int]:
96.10/96.30	         (plus_plus(A,number_number_of(A,V),
96.10/96.30	                    plus_plus(A,number_number_of(A,W),Z)) =
96.10/96.30	          plus_plus(A,number_number_of(A,plus_plus(int,V,W)),Z)))))).
96.10/96.30	tff('30', plain,
96.10/96.30	    ![X97 : $tType, X98 : int, X99 : int, X100 : X97]:
96.10/96.30	      (plus_plus(X97, number_number_of(X97, X98), 
96.10/96.30	         plus_plus(X97, number_number_of(X97, X99), X100))
96.10/96.30	        = plus_plus(X97, number_number_of(X97, plus_plus(int, X98, X99)), 
96.10/96.30	            X100)
96.10/96.30	       | ~ number_ring(X97)),
96.10/96.30	    inference('cnf', [status(esa)], [fact_50_add__number__of__left])).
96.10/96.30	tff('31', plain,
96.10/96.30	    ![X0 : int, X1 : int, X2 : int]:
96.10/96.30	      (plus_plus(int, X0, plus_plus(int, number_number_of(int, X2), X1))
96.10/96.30	        = plus_plus(int, number_number_of(int, plus_plus(int, X0, X2)), X1)
96.10/96.30	       | ~ number_ring(int)),
96.10/96.30	    inference('sup+', [status(thm)], ['1', '30'])).
96.10/96.30	tff('32', plain,
96.10/96.30	    ![X0 : int, X1 : int, X2 : int]:
96.10/96.30	      (plus_plus(int, X0, plus_plus(int, X2, X1))
96.10/96.30	        = plus_plus(int, plus_plus(int, X0, X2), X1)
96.10/96.30	       | ~ $true),
96.10/96.30	    inference('demod', [status(thm)], ['31', '1', '1', '4'])).
96.10/96.30	tff('33', plain,
96.10/96.30	    ![X0 : int, X1 : int, X2 : int]:
96.10/96.30	      plus_plus(int, X0, plus_plus(int, X2, X1))
96.10/96.30	       = plus_plus(int, plus_plus(int, X0, X2), X1),
96.10/96.30	    inference('simplify', [status(thm)], ['32'])).
96.10/96.30	tff('34', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      (plus_plus(int, number_number_of(int, pls), 
96.10/96.30	         plus_plus(int, one_one(int), X0))
96.10/96.30	        = plus_plus(int, number_number_of(int, bit1(pls)), X0)
96.10/96.30	       | ~ number_ring(int)),
96.10/96.30	    inference('sup+', [status(thm)], ['29', '33'])).
96.10/96.30	tff('35', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      (plus_plus(int, pls, plus_plus(int, bit1(pls), X0))
96.10/96.30	        = plus_plus(int, bit1(pls), X0)
96.10/96.30	       | ~ $true),
96.10/96.30	    inference('demod', [status(thm)], ['34', '1', '6', '1', '4'])).
96.10/96.30	tff('36', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      plus_plus(int, pls, plus_plus(int, bit1(pls), X0))
96.10/96.30	       = plus_plus(int, bit1(pls), X0),
96.10/96.30	    inference('simplify', [status(thm)], ['35'])).
96.10/96.30	tff('37', plain,
96.10/96.30	    ~ ord_less(int, 
96.10/96.30	        times_times(int, 
96.10/96.30	          plus_plus(int, bit1(pls), semiring_1_of_nat(int, n)), 
96.10/96.30	          bit0(
96.10/96.30	            minus_minus(int, 
96.10/96.30	              plus_plus(int, bit1(pls), semiring_1_of_nat(int, n)), 
96.10/96.30	              bit0(plus_plus(int, pls, m1))))), pls),
96.10/96.30	    inference('demod', [status(thm)], ['18', '36'])).
96.10/96.30	tff(fact_2__096_I1_A_L_Aint_An_J_A_K_A_I2_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_J_A_060_A_I1_A_L_Aint_An_J_A_K_A0_096, axiom,
96.10/96.30	  (ord_less(int,
96.10/96.30	            times_times(int,
96.10/96.30	                        plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),
96.10/96.30	                        minus_minus(int,
96.10/96.30	                                    times_times(int,
96.10/96.30	                                                number_number_of(int,
96.10/96.30	                                                                 bit0(
96.10/96.30	                                                                 bit1(pls))),
96.10/96.30	                                                plus_plus(int,one_one(int),
96.10/96.30	                                                          semiring_1_of_nat(
96.10/96.30	                                                          int,n))),
96.10/96.30	                                    times_times(int,
96.10/96.30	                                                number_number_of(int,
96.10/96.30	                                                                 bit0(
96.10/96.30	                                                                 bit0(
96.10/96.30	                                                                 bit1(pls)))),
96.10/96.30	                                                m1))),
96.10/96.30	            times_times(int,
96.10/96.30	                        plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),
96.10/96.30	                        zero_zero(int))))).
96.10/96.30	tff('38', plain,
96.10/96.30	    ord_less(int, 
96.10/96.30	      times_times(int, 
96.10/96.30	        plus_plus(int, one_one(int), semiring_1_of_nat(int, n)), 
96.10/96.30	        minus_minus(int, 
96.10/96.30	          times_times(int, number_number_of(int, bit0(bit1(pls))), 
96.10/96.30	            plus_plus(int, one_one(int), semiring_1_of_nat(int, n))), 
96.10/96.30	          times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m1))), 
96.10/96.30	      times_times(int, 
96.10/96.30	        plus_plus(int, one_one(int), semiring_1_of_nat(int, n)), 
96.10/96.30	        zero_zero(int))),
96.10/96.30	    inference('cnf', [status(esa)],
96.10/96.30	              [fact_2__096_I1_A_L_Aint_An_J_A_K_A_I2_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_J_A_060_A_I1_A_L_Aint_An_J_A_K_A0_096])).
96.10/96.30	tff('39', plain,
96.10/96.30	    ord_less(int, 
96.10/96.30	      times_times(int, 
96.10/96.30	        plus_plus(int, one_one(int), semiring_1_of_nat(int, n)), 
96.10/96.30	        minus_minus(int, 
96.10/96.30	          times_times(int, bit0(bit1(pls)), 
96.10/96.30	            plus_plus(int, one_one(int), semiring_1_of_nat(int, n))), 
96.10/96.30	          times_times(int, bit0(bit0(bit1(pls))), m1))), 
96.10/96.30	      times_times(int, 
96.10/96.30	        plus_plus(int, one_one(int), semiring_1_of_nat(int, n)), 
96.10/96.30	        zero_zero(int))),
96.10/96.30	    inference('demod', [status(thm)], ['38', '1', '1'])).
96.10/96.30	tff('40', plain,
96.10/96.30	    ord_less(int, 
96.10/96.30	      times_times(int, 
96.10/96.30	        plus_plus(int, one_one(int), semiring_1_of_nat(int, n)), 
96.10/96.30	        minus_minus(int, 
96.10/96.30	          bit0(
96.10/96.30	            times_times(int, bit1(pls), 
96.10/96.30	              plus_plus(int, one_one(int), semiring_1_of_nat(int, n)))), 
96.10/96.30	          bit0(bit0(times_times(int, bit1(pls), m1))))), 
96.10/96.30	      times_times(int, 
96.10/96.30	        plus_plus(int, one_one(int), semiring_1_of_nat(int, n)), 
96.10/96.30	        zero_zero(int))),
96.10/96.30	    inference('demod', [status(thm)], ['39', '7', '7', '7'])).
96.10/96.30	tff('41', plain,
96.10/96.30	    ord_less(int, 
96.10/96.30	      times_times(int, plus_plus(int, bit1(pls), semiring_1_of_nat(int, n)), 
96.10/96.30	        bit0(
96.10/96.30	          minus_minus(int, 
96.10/96.30	            plus_plus(int, pls, 
96.10/96.30	              plus_plus(int, bit1(pls), semiring_1_of_nat(int, n))), 
96.10/96.30	            bit0(plus_plus(int, pls, m1))))), 
96.10/96.30	      times_times(int, plus_plus(int, bit1(pls), semiring_1_of_nat(int, n)), 
96.10/96.30	        pls)),
96.10/96.30	    inference('demod', [status(thm)],
96.10/96.30	              ['40', '6', '6', '12', '12', '13', '6', '17'])).
96.10/96.30	tff('42', plain,
96.10/96.30	    ord_less(int, 
96.10/96.30	      times_times(int, plus_plus(int, bit1(pls), semiring_1_of_nat(int, n)), 
96.10/96.30	        bit0(
96.10/96.30	          minus_minus(int, 
96.10/96.30	            plus_plus(int, bit1(pls), semiring_1_of_nat(int, n)), 
96.10/96.30	            bit0(plus_plus(int, pls, m1))))), 
96.10/96.30	      times_times(int, plus_plus(int, bit1(pls), semiring_1_of_nat(int, n)), 
96.10/96.30	        pls)),
96.10/96.30	    inference('demod', [status(thm)], ['41', '36'])).
96.10/96.30	tff(fact_44_left__diff__distrib__number__of, axiom,
96.10/96.30	  (![B:$tType]:
96.10/96.30	     ((ring(B) & number(B)) =>
96.10/96.30	      (![V:int,B1:B,A1:B]:
96.10/96.30	         (times_times(B,minus_minus(B,A1,B1),number_number_of(B,V)) =
96.10/96.30	          minus_minus(B,times_times(B,A1,number_number_of(B,V)),
96.10/96.30	                      times_times(B,B1,number_number_of(B,V)))))))).
96.10/96.30	tff('43', plain,
96.10/96.30	    ![X74 : $tType, X75 : X74, X76 : int, X77 : X74]:
96.10/96.30	      (times_times(X74, minus_minus(X74, X75, X77), 
96.10/96.30	         number_number_of(X74, X76))
96.10/96.30	        = minus_minus(X74, 
96.10/96.30	            times_times(X74, X75, number_number_of(X74, X76)), 
96.10/96.30	            times_times(X74, X77, number_number_of(X74, X76)))
96.10/96.30	       | ~ number(X74)
96.10/96.30	       | ~ ring(X74)),
96.10/96.30	    inference('cnf', [status(esa)], [fact_44_left__diff__distrib__number__of])).
96.10/96.30	tff('44', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      (times_times(int, minus_minus(int, bit1(pls), X1), 
96.10/96.30	         number_number_of(int, X0))
96.10/96.30	        = minus_minus(int, plus_plus(int, pls, number_number_of(int, X0)), 
96.10/96.30	            times_times(int, X1, number_number_of(int, X0)))
96.10/96.30	       | ~ ring(int)
96.10/96.30	       | ~ number(int)),
96.10/96.30	    inference('sup+', [status(thm)], ['12', '43'])).
96.10/96.30	tff(arity_Int_Oint___Rings_Oring, axiom, (ring(int))).
96.10/96.30	tff('45', plain, ring(int),
96.10/96.30	    inference('cnf', [status(esa)], [arity_Int_Oint___Rings_Oring])).
96.10/96.30	tff(arity_Int_Oint___Int_Onumber, axiom, (number(int))).
96.10/96.30	tff('46', plain, number(int),
96.10/96.30	    inference('cnf', [status(esa)], [arity_Int_Oint___Int_Onumber])).
96.10/96.30	tff('47', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      (times_times(int, minus_minus(int, bit1(pls), X1), X0)
96.10/96.30	        = minus_minus(int, plus_plus(int, pls, X0), times_times(int, X1, X0))
96.10/96.30	       | ~ $true
96.10/96.30	       | ~ $true),
96.10/96.30	    inference('demod', [status(thm)], ['44', '1', '1', '1', '45', '46'])).
96.10/96.30	tff('48', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      times_times(int, minus_minus(int, bit1(pls), X1), X0)
96.10/96.30	       = minus_minus(int, plus_plus(int, pls, X0), times_times(int, X1, X0)),
96.10/96.30	    inference('simplify', [status(thm)], ['47'])).
96.10/96.30	tff('49', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      times_times(int, minus_minus(int, bit1(pls), bit1(pls)), X0)
96.10/96.30	       = minus_minus(int, plus_plus(int, pls, X0), plus_plus(int, pls, X0)),
96.10/96.30	    inference('sup+', [status(thm)], ['12', '48'])).
96.10/96.30	tff(fact_62_diff__bin__simps_I10_J, axiom,
96.10/96.30	  (![L1:int,K:int]:
96.10/96.30	     (minus_minus(int,bit1(K),bit1(L1)) = bit0(minus_minus(int,K,L1))))).
96.10/96.30	tff('50', plain,
96.10/96.30	    ![X126 : int, X127 : int]:
96.10/96.30	      minus_minus(int, bit1(X126), bit1(X127))
96.10/96.30	       = bit0(minus_minus(int, X126, X127)),
96.10/96.30	    inference('cnf', [status(esa)], [fact_62_diff__bin__simps_I10_J])).
96.10/96.30	tff(fact_15_diff__bin__simps_I3_J, axiom,
96.10/96.30	  (![L1:int]: (minus_minus(int,pls,bit0(L1)) = bit0(minus_minus(int,pls,L1))))).
96.10/96.30	tff('51', plain,
96.10/96.30	    ![X20 : int]:
96.10/96.30	      minus_minus(int, pls, bit0(X20)) = bit0(minus_minus(int, pls, X20)),
96.10/96.30	    inference('cnf', [status(esa)], [fact_15_diff__bin__simps_I3_J])).
96.10/96.30	tff('52', plain,
96.10/96.30	    minus_minus(int, pls, pls) = bit0(minus_minus(int, pls, pls)),
96.10/96.30	    inference('sup+', [status(thm)], ['11', '51'])).
96.10/96.30	tff('53', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      (times_times(int, minus_minus(int, pls, X1), number_number_of(int, X0))
96.10/96.30	        = minus_minus(int, pls, 
96.10/96.30	            times_times(int, X1, number_number_of(int, X0)))
96.10/96.30	       | ~ ring(int)
96.10/96.30	       | ~ number(int)),
96.10/96.30	    inference('sup+', [status(thm)], ['8', '43'])).
96.10/96.30	tff('54', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      (times_times(int, minus_minus(int, pls, X1), X0)
96.10/96.30	        = minus_minus(int, pls, times_times(int, X1, X0))
96.10/96.30	       | ~ $true
96.10/96.30	       | ~ $true),
96.10/96.30	    inference('demod', [status(thm)], ['53', '1', '1', '45', '46'])).
96.10/96.30	tff('55', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      times_times(int, minus_minus(int, pls, X1), X0)
96.10/96.30	       = minus_minus(int, pls, times_times(int, X1, X0)),
96.10/96.30	    inference('simplify', [status(thm)], ['54'])).
96.10/96.30	tff('56', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      times_times(int, minus_minus(int, pls, pls), X0)
96.10/96.30	       = minus_minus(int, pls, pls),
96.10/96.30	    inference('sup+', [status(thm)], ['8', '55'])).
96.10/96.30	tff('57', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      minus_minus(int, pls, pls)
96.10/96.30	       = minus_minus(int, plus_plus(int, pls, X0), plus_plus(int, pls, X0)),
96.10/96.30	    inference('demod', [status(thm)], ['49', '50', '52', '56'])).
96.10/96.30	tff(fact_45_right__diff__distrib__number__of, axiom,
96.10/96.30	  (![B:$tType]:
96.10/96.30	     ((ring(B) & number(B)) =>
96.10/96.30	      (![C:B,B1:B,V:int]:
96.10/96.30	         (times_times(B,number_number_of(B,V),minus_minus(B,B1,C)) =
96.10/96.30	          minus_minus(B,times_times(B,number_number_of(B,V),B1),
96.10/96.30	                      times_times(B,number_number_of(B,V),C))))))).
96.10/96.30	tff('58', plain,
96.10/96.30	    ![X78 : $tType, X79 : int, X80 : X78, X81 : X78]:
96.10/96.30	      (times_times(X78, number_number_of(X78, X79), 
96.10/96.30	         minus_minus(X78, X80, X81))
96.10/96.30	        = minus_minus(X78, 
96.10/96.30	            times_times(X78, number_number_of(X78, X79), X80), 
96.10/96.30	            times_times(X78, number_number_of(X78, X79), X81))
96.10/96.30	       | ~ number(X78)
96.10/96.30	       | ~ ring(X78)),
96.10/96.30	    inference('cnf', [status(esa)],
96.10/96.30	              [fact_45_right__diff__distrib__number__of])).
96.10/96.30	tff('59', plain,
96.10/96.30	    ![X0 : int, X1 : int, X2 : int]:
96.10/96.30	      (times_times(int, minus_minus(int, X2, X1), number_number_of(int, X0))
96.10/96.30	        = minus_minus(int, times_times(int, X2, X0), 
96.10/96.30	            times_times(int, X1, number_number_of(int, X0)))
96.10/96.30	       | ~ ring(int)
96.10/96.30	       | ~ number(int)),
96.10/96.30	    inference('sup+', [status(thm)], ['1', '43'])).
96.10/96.30	tff('60', plain,
96.10/96.30	    ![X0 : int, X1 : int, X2 : int]:
96.10/96.30	      (times_times(int, minus_minus(int, X2, X1), X0)
96.10/96.30	        = minus_minus(int, times_times(int, X2, X0), 
96.10/96.30	            times_times(int, X1, X0))
96.10/96.30	       | ~ $true
96.10/96.30	       | ~ $true),
96.10/96.30	    inference('demod', [status(thm)], ['59', '1', '1', '45', '46'])).
96.10/96.30	tff('61', plain,
96.10/96.30	    ![X0 : int, X1 : int, X2 : int]:
96.10/96.30	      times_times(int, minus_minus(int, X2, X1), X0)
96.10/96.30	       = minus_minus(int, times_times(int, X2, X0), times_times(int, X1, X0)),
96.10/96.30	    inference('simplify', [status(thm)], ['60'])).
96.10/96.30	tff('62', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      (times_times(int, 
96.10/96.30	         minus_minus(int, number_number_of(int, X1), 
96.10/96.30	           number_number_of(int, X1)), X0)
96.10/96.30	        = times_times(int, number_number_of(int, X1), 
96.10/96.30	            minus_minus(int, X0, X0))
96.10/96.30	       | ~ ring(int)
96.10/96.30	       | ~ number(int)),
96.10/96.30	    inference('sup+', [status(thm)], ['58', '61'])).
96.10/96.30	tff('63', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      (times_times(int, minus_minus(int, X1, X1), X0)
96.10/96.30	        = times_times(int, X1, minus_minus(int, X0, X0))
96.10/96.30	       | ~ $true
96.10/96.30	       | ~ $true),
96.10/96.30	    inference('demod', [status(thm)], ['62', '1', '1', '1', '45', '46'])).
96.10/96.30	tff('64', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      times_times(int, minus_minus(int, X1, X1), X0)
96.10/96.30	       = times_times(int, X1, minus_minus(int, X0, X0)),
96.10/96.30	    inference('simplify', [status(thm)], ['63'])).
96.10/96.30	tff('65', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      minus_minus(int, pls, pls)
96.10/96.30	       = times_times(int, pls, minus_minus(int, X0, X0)),
96.10/96.30	    inference('sup+', [status(thm)], ['56', '64'])).
96.10/96.30	tff('66', plain, minus_minus(int, pls, pls) = pls,
96.10/96.30	    inference('demod', [status(thm)], ['65', '8'])).
96.10/96.30	tff('67', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      pls
96.10/96.30	       = minus_minus(int, plus_plus(int, pls, X0), plus_plus(int, pls, X0)),
96.10/96.30	    inference('demod', [status(thm)], ['57', '66'])).
96.10/96.30	tff('68', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      times_times(int, minus_minus(int, X0, X0), pls)
96.10/96.30	       = times_times(int, X0, pls),
96.10/96.30	    inference('sup+', [status(thm)], ['66', '64'])).
96.10/96.30	tff('69', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      times_times(int, pls, pls)
96.10/96.30	       = times_times(int, plus_plus(int, pls, X0), pls),
96.10/96.30	    inference('sup+', [status(thm)], ['67', '68'])).
96.10/96.30	tff(fact_41_left__distrib__number__of, axiom,
96.10/96.30	  (![B:$tType]:
96.10/96.30	     ((semiring(B) & number(B)) =>
96.10/96.30	      (![V:int,B1:B,A1:B]:
96.10/96.30	         (times_times(B,plus_plus(B,A1,B1),number_number_of(B,V)) =
96.10/96.30	          plus_plus(B,times_times(B,A1,number_number_of(B,V)),
96.10/96.30	                    times_times(B,B1,number_number_of(B,V)))))))).
96.10/96.30	tff('70', plain,
96.10/96.30	    ![X65 : $tType, X66 : X65, X67 : int, X68 : X65]:
96.10/96.30	      (times_times(X65, plus_plus(X65, X66, X68), number_number_of(X65, X67))
96.10/96.30	        = plus_plus(X65, times_times(X65, X66, number_number_of(X65, X67)), 
96.10/96.30	            times_times(X65, X68, number_number_of(X65, X67)))
96.10/96.30	       | ~ number(X65)
96.10/96.30	       | ~ semiring(X65)),
96.10/96.30	    inference('cnf', [status(esa)], [fact_41_left__distrib__number__of])).
96.10/96.30	tff('71', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      (times_times(int, plus_plus(int, pls, X1), number_number_of(int, X0))
96.10/96.30	        = plus_plus(int, pls, 
96.10/96.30	            times_times(int, X1, number_number_of(int, X0)))
96.10/96.30	       | ~ semiring(int)
96.10/96.30	       | ~ number(int)),
96.10/96.30	    inference('sup+', [status(thm)], ['8', '70'])).
96.10/96.30	tff(arity_Int_Oint___Rings_Osemiring, axiom, (semiring(int))).
96.10/96.30	tff('72', plain, semiring(int),
96.10/96.30	    inference('cnf', [status(esa)], [arity_Int_Oint___Rings_Osemiring])).
96.10/96.30	tff('73', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      (times_times(int, plus_plus(int, pls, X1), X0)
96.10/96.30	        = plus_plus(int, pls, times_times(int, X1, X0))
96.10/96.30	       | ~ $true
96.10/96.30	       | ~ $true),
96.10/96.30	    inference('demod', [status(thm)], ['71', '1', '1', '72', '46'])).
96.10/96.30	tff('74', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      times_times(int, plus_plus(int, pls, X1), X0)
96.10/96.30	       = plus_plus(int, pls, times_times(int, X1, X0)),
96.10/96.30	    inference('simplify', [status(thm)], ['73'])).
96.10/96.30	tff('75', plain,
96.10/96.30	    ![X0 : int]: pls = plus_plus(int, pls, times_times(int, X0, pls)),
96.10/96.30	    inference('demod', [status(thm)], ['69', '8', '74'])).
96.10/96.30	tff(fact_89_int__0, axiom,
96.10/96.30	  (semiring_1_of_nat(int,zero_zero(nat)) = zero_zero(int))).
96.10/96.30	tff('76', plain, semiring_1_of_nat(int, zero_zero(nat)) = zero_zero(int),
96.10/96.30	    inference('cnf', [status(esa)], [fact_89_int__0])).
96.10/96.30	tff('77', plain, semiring_1_of_nat(int, zero_zero(nat)) = pls,
96.10/96.30	    inference('demod', [status(thm)], ['76', '17'])).
96.10/96.30	tff(fact_86_zle__iff__zadd, axiom,
96.10/96.30	  (![Z1:int,Wa:int]:
96.10/96.30	     (ord_less_eq(int,Wa,Z1) <=>
96.10/96.30	      (?[N:nat]: (Z1 = plus_plus(int,Wa,semiring_1_of_nat(int,N))))))).
96.10/96.30	tff('78', plain,
96.10/96.30	    ![X192 : int, X193 : int, X194 : nat]:
96.10/96.30	      (ord_less_eq(int, X193, X192)
96.10/96.30	       | X192 != plus_plus(int, X193, semiring_1_of_nat(int, X194))),
96.10/96.30	    inference('cnf', [status(esa)], [fact_86_zle__iff__zadd])).
96.10/96.30	tff('79', plain,
96.10/96.30	    ![X193 : int, X194 : nat]:
96.10/96.30	      ord_less_eq(int, X193, 
96.10/96.30	        plus_plus(int, X193, semiring_1_of_nat(int, X194))),
96.10/96.30	    inference('simplify', [status(thm)], ['78'])).
96.10/96.30	tff('80', plain, ![X0 : int]: ord_less_eq(int, X0, plus_plus(int, X0, pls)),
96.10/96.30	    inference('sup+', [status(thm)], ['77', '79'])).
96.10/96.30	tff(fact_75_less__int__def, axiom,
96.10/96.30	  (![Wa:int,Z1:int]:
96.10/96.30	     (ord_less(int,Z1,Wa) <=> ((Z1 != Wa) & ord_less_eq(int,Z1,Wa))))).
96.10/96.30	tff('81', plain,
96.10/96.30	    ![X162 : int, X164 : int]:
96.10/96.30	      (ord_less(int, X164, X162)
96.10/96.30	       | ~ ord_less_eq(int, X164, X162)
96.10/96.30	       | X164 = X162),
96.10/96.30	    inference('cnf', [status(esa)], [fact_75_less__int__def])).
96.10/96.30	tff(fact_80_le__number__of__eq__not__less, axiom,
96.10/96.30	  (![A:$tType]:
96.10/96.30	     ((linorder(A) & number(A)) =>
96.10/96.30	      (![Wa:int,Va:int]:
96.10/96.30	         (ord_less_eq(A,number_number_of(A,Va),number_number_of(A,Wa)) <=>
96.10/96.30	          (~ord_less(A,number_number_of(A,Wa),number_number_of(A,Va)))))))).
96.10/96.30	tff('82', plain,
96.10/96.30	    ![X175 : $tType, X176 : int, X178 : int]:
96.10/96.30	      (~ ord_less_eq(X175, number_number_of(X175, X178), 
96.10/96.30	           number_number_of(X175, X176))
96.10/96.30	       | ~ ord_less(X175, number_number_of(X175, X176), 
96.10/96.30	             number_number_of(X175, X178))
96.10/96.30	       | ~ number(X175)
96.10/96.30	       | ~ linorder(X175)),
96.10/96.30	    inference('cnf', [status(esa)], [fact_80_le__number__of__eq__not__less])).
96.10/96.30	tff('83', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      (~ $true
96.10/96.30	       | number_number_of(int, X1) = number_number_of(int, X0)
96.10/96.30	       | ~ ord_less_eq(int, number_number_of(int, X1), 
96.10/96.30	             number_number_of(int, X0))
96.10/96.30	       | ~ linorder(int)
96.10/96.30	       | ~ number(int)
96.10/96.30	       | ~ ord_less_eq(int, number_number_of(int, X0), 
96.10/96.30	             number_number_of(int, X1))),
96.10/96.30	    inference('sup-', [status(thm)], ['81', '82'])).
96.10/96.30	tff(arity_Int_Oint___Orderings_Olinorder, axiom, (linorder(int))).
96.10/96.30	tff('84', plain, linorder(int),
96.10/96.30	    inference('cnf', [status(esa)], [arity_Int_Oint___Orderings_Olinorder])).
96.10/96.30	tff('85', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      (~ $true
96.10/96.30	       | X1 = X0
96.10/96.30	       | ~ ord_less_eq(int, X1, X0)
96.10/96.30	       | ~ $true
96.10/96.30	       | ~ $true
96.10/96.30	       | ~ ord_less_eq(int, X0, X1)),
96.10/96.30	    inference('demod', [status(thm)],
96.10/96.30	              ['83', '1', '1', '1', '1', '84', '46', '1', '1'])).
96.10/96.30	tff('86', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      (~ ord_less_eq(int, X0, X1) | ~ ord_less_eq(int, X1, X0) | X1 = X0),
96.10/96.30	    inference('simplify', [status(thm)], ['85'])).
96.10/96.30	tff('87', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      (~ $true
96.10/96.30	       | plus_plus(int, X0, pls) = X0
96.10/96.30	       | ~ ord_less_eq(int, plus_plus(int, X0, pls), X0)),
96.10/96.30	    inference('sup-', [status(thm)], ['80', '86'])).
96.10/96.30	tff('88', plain,
96.10/96.30	    ![X0 : int, X1 : $tType]:
96.10/96.30	      (plus_plus(X1, number_number_of(X1, bit0(X0)), one_one(X1))
96.10/96.30	        = number_number_of(X1, bit1(plus_plus(int, X0, pls)))
96.10/96.30	       | ~ number_ring(X1)),
96.10/96.30	    inference('sup+', [status(thm)], ['19', '21'])).
96.10/96.30	tff(fact_87_int__1, axiom,
96.10/96.30	  (semiring_1_of_nat(int,one_one(nat)) = one_one(int))).
96.10/96.30	tff('89', plain, semiring_1_of_nat(int, one_one(nat)) = one_one(int),
96.10/96.30	    inference('cnf', [status(esa)], [fact_87_int__1])).
96.10/96.30	tff('90', plain, semiring_1_of_nat(int, one_one(nat)) = bit1(pls),
96.10/96.30	    inference('demod', [status(thm)], ['89', '6'])).
96.10/96.30	tff('91', plain,
96.10/96.30	    ![X0 : int]: ord_less_eq(int, X0, plus_plus(int, X0, bit1(pls))),
96.10/96.30	    inference('sup+', [status(thm)], ['90', '79'])).
96.10/96.30	tff('92', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      ord_less_eq(int, plus_plus(int, X1, X0), 
96.10/96.30	        plus_plus(int, X1, plus_plus(int, X0, bit1(pls)))),
96.10/96.30	    inference('sup+', [status(thm)], ['33', '91'])).
96.10/96.30	tff('93', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      (ord_less_eq(int, 
96.10/96.30	         number_number_of(int, bit1(plus_plus(int, X0, pls))), 
96.10/96.30	         plus_plus(int, number_number_of(int, bit0(X0)), 
96.10/96.30	           plus_plus(int, one_one(int), bit1(pls))))
96.10/96.30	       | ~ number_ring(int)),
96.10/96.30	    inference('sup+', [status(thm)], ['88', '92'])).
96.10/96.30	tff(fact_5_add__special_I2_J, axiom,
96.10/96.30	  (![A:$tType]:
96.10/96.30	     (number_ring(A) =>
96.10/96.30	      (![W:int]:
96.10/96.30	         (plus_plus(A,one_one(A),number_number_of(A,W)) =
96.10/96.30	          number_number_of(A,plus_plus(int,bit1(pls),W))))))).
96.10/96.30	tff('94', plain,
96.10/96.30	    ![X0 : $tType, X1 : int]:
96.10/96.30	      (plus_plus(X0, one_one(X0), number_number_of(X0, X1))
96.10/96.30	        = number_number_of(X0, plus_plus(int, bit1(pls), X1))
96.10/96.30	       | ~ number_ring(X0)),
96.10/96.30	    inference('cnf', [status(esa)], [fact_5_add__special_I2_J])).
96.10/96.30	tff('95', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      (plus_plus(int, one_one(int), X0)
96.10/96.30	        = number_number_of(int, plus_plus(int, bit1(pls), X0))
96.10/96.30	       | ~ number_ring(int)),
96.10/96.30	    inference('sup+', [status(thm)], ['1', '94'])).
96.10/96.30	tff('96', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      (plus_plus(int, one_one(int), X0) = plus_plus(int, bit1(pls), X0)
96.10/96.30	       | ~ $true),
96.10/96.30	    inference('demod', [status(thm)], ['95', '1', '4'])).
96.10/96.30	tff('97', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      plus_plus(int, one_one(int), X0) = plus_plus(int, bit1(pls), X0),
96.10/96.30	    inference('simplify', [status(thm)], ['96'])).
96.10/96.30	tff(fact_9_one__add__one__is__two, axiom,
96.10/96.30	  (![A:$tType]:
96.10/96.30	     (number_ring(A) =>
96.10/96.30	      (plus_plus(A,one_one(A),one_one(A)) =
96.10/96.30	       number_number_of(A,bit0(bit1(pls))))))).
96.10/96.30	tff('98', plain,
96.10/96.30	    ![X10 : $tType]:
96.10/96.30	      (plus_plus(X10, one_one(X10), one_one(X10))
96.10/96.30	        = number_number_of(X10, bit0(bit1(pls)))
96.10/96.30	       | ~ number_ring(X10)),
96.10/96.30	    inference('cnf', [status(esa)], [fact_9_one__add__one__is__two])).
96.10/96.30	tff('99', plain,
96.10/96.30	    (plus_plus(int, bit1(pls), one_one(int))
96.10/96.30	      = number_number_of(int, bit0(bit1(pls)))
96.10/96.30	     | ~ number_ring(int)),
96.10/96.30	    inference('sup+', [status(thm)], ['97', '98'])).
96.10/96.30	tff('100', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      (plus_plus(int, X0, one_one(int))
96.10/96.30	        = number_number_of(int, plus_plus(int, X0, bit1(pls)))
96.10/96.30	       | ~ number_ring(int)),
96.10/96.30	    inference('sup+', [status(thm)], ['1', '21'])).
96.10/96.30	tff('101', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      (plus_plus(int, X0, one_one(int)) = plus_plus(int, X0, bit1(pls))
96.10/96.30	       | ~ $true),
96.10/96.30	    inference('demod', [status(thm)], ['100', '1', '4'])).
96.10/96.30	tff('102', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      plus_plus(int, X0, one_one(int)) = plus_plus(int, X0, bit1(pls)),
96.10/96.30	    inference('simplify', [status(thm)], ['101'])).
96.10/96.30	tff('103', plain,
96.10/96.30	    (plus_plus(int, bit1(pls), bit1(pls)) = bit0(bit1(pls)) | ~ $true),
96.10/96.30	    inference('demod', [status(thm)], ['99', '102', '1', '4'])).
96.10/96.30	tff('104', plain, plus_plus(int, bit1(pls), bit1(pls)) = bit0(bit1(pls)),
96.10/96.30	    inference('simplify', [status(thm)], ['103'])).
96.10/96.30	tff(fact_38_add__Bit0__Bit0, axiom,
96.10/96.30	  (![L1:int,K:int]:
96.10/96.30	     (plus_plus(int,bit0(K),bit0(L1)) = bit0(plus_plus(int,K,L1))))).
96.10/96.30	tff('105', plain,
96.10/96.30	    ![X61 : int, X62 : int]:
96.10/96.30	      plus_plus(int, bit0(X61), bit0(X62)) = bit0(plus_plus(int, X61, X62)),
96.10/96.30	    inference('cnf', [status(esa)], [fact_38_add__Bit0__Bit0])).
96.10/96.30	tff('106', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      (ord_less_eq(int, bit1(plus_plus(int, X0, pls)), 
96.10/96.30	         bit0(plus_plus(int, X0, bit1(pls))))
96.10/96.30	       | ~ $true),
96.10/96.30	    inference('demod', [status(thm)],
96.10/96.30	              ['93', '1', '1', '6', '104', '105', '4'])).
96.10/96.30	tff('107', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      ord_less_eq(int, bit1(plus_plus(int, X0, pls)), 
96.10/96.30	        bit0(plus_plus(int, X0, bit1(pls)))),
96.10/96.30	    inference('simplify', [status(thm)], ['106'])).
96.10/96.30	tff(fact_65_rel__simps_I33_J, axiom,
96.10/96.30	  (![L:int,K3:int]:
96.10/96.30	     (ord_less_eq(int,bit1(K3),bit0(L)) <=> ord_less(int,K3,L)))).
96.10/96.30	tff('108', plain,
96.10/96.30	    ![X132 : int, X133 : int]:
96.10/96.30	      (ord_less(int, X132, X133) | ~ ord_less_eq(int, bit1(X132), bit0(X133))),
96.10/96.30	    inference('cnf', [status(esa)], [fact_65_rel__simps_I33_J])).
96.10/96.30	tff('109', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      (~ $true
96.10/96.30	       | ord_less(int, plus_plus(int, X0, pls), 
96.10/96.30	           plus_plus(int, X0, bit1(pls)))),
96.10/96.30	    inference('sup-', [status(thm)], ['107', '108'])).
96.10/96.30	tff('110', plain,
96.10/96.30	    ![X0 : int]:
96.10/96.30	      ord_less(int, plus_plus(int, X0, pls), plus_plus(int, X0, bit1(pls))),
96.10/96.30	    inference('simplify', [status(thm)], ['109'])).
96.10/96.30	tff(fact_67_zle__add1__eq__le, axiom,
96.10/96.30	  (![Z1:int,Wa:int]:
96.10/96.30	     (ord_less(int,Wa,plus_plus(int,Z1,one_one(int))) <=>
96.10/96.30	      ord_less_eq(int,Wa,Z1)))).
96.10/96.30	tff('111', plain,
96.10/96.30	    ![X138 : int, X139 : int]:
96.10/96.30	      (ord_less_eq(int, X138, X139)
96.10/96.30	       | ~ ord_less(int, X138, plus_plus(int, X139, one_one(int)))),
96.10/96.30	    inference('cnf', [status(esa)], [fact_67_zle__add1__eq__le])).
96.10/96.30	tff('112', plain,
96.10/96.30	    ![X138 : int, X139 : int]:
96.10/96.30	      (ord_less_eq(int, X138, X139)
96.10/96.30	       | ~ ord_less(int, X138, plus_plus(int, X139, bit1(pls)))),
96.10/96.30	    inference('demod', [status(thm)], ['111', '6'])).
96.10/96.30	tff('113', plain,
96.10/96.30	    ![X0 : int]: (~ $true | ord_less_eq(int, plus_plus(int, X0, pls), X0)),
96.10/96.30	    inference('sup-', [status(thm)], ['110', '112'])).
96.10/96.30	tff('114', plain, ![X0 : int]: ord_less_eq(int, plus_plus(int, X0, pls), X0),
96.10/96.30	    inference('simplify', [status(thm)], ['113'])).
96.10/96.30	tff('115', plain,
96.10/96.30	    ![X0 : int]: (~ $true | plus_plus(int, X0, pls) = X0 | ~ $true),
96.10/96.30	    inference('demod', [status(thm)], ['87', '114'])).
96.10/96.30	tff('116', plain, ![X0 : int]: plus_plus(int, X0, pls) = X0,
96.10/96.30	    inference('simplify', [status(thm)], ['115'])).
96.10/96.30	tff('117', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      plus_plus(int, X0, plus_plus(int, pls, X1)) = plus_plus(int, X0, X1),
96.10/96.30	    inference('sup+', [status(thm)], ['116', '33'])).
96.10/96.30	tff('118', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      plus_plus(int, X1, pls) = plus_plus(int, X1, times_times(int, X0, pls)),
96.10/96.30	    inference('sup+', [status(thm)], ['75', '117'])).
96.10/96.30	tff('119', plain,
96.10/96.30	    ![X0 : int, X1 : int]: X1 = plus_plus(int, X1, times_times(int, X0, pls)),
96.10/96.30	    inference('demod', [status(thm)], ['118', '116'])).
96.10/96.30	tff('120', plain,
96.10/96.30	    ![X0 : int, X1 : int, X2 : int]:
96.10/96.30	      (times_times(int, plus_plus(int, X2, X1), number_number_of(int, X0))
96.10/96.30	        = plus_plus(int, times_times(int, X2, X0), 
96.10/96.30	            times_times(int, X1, number_number_of(int, X0)))
96.10/96.30	       | ~ semiring(int)
96.10/96.30	       | ~ number(int)),
96.10/96.30	    inference('sup+', [status(thm)], ['1', '70'])).
96.10/96.30	tff('121', plain,
96.10/96.30	    ![X0 : int, X1 : int, X2 : int]:
96.10/96.30	      (times_times(int, plus_plus(int, X2, X1), X0)
96.10/96.30	        = plus_plus(int, times_times(int, X2, X0), times_times(int, X1, X0))
96.10/96.30	       | ~ $true
96.10/96.30	       | ~ $true),
96.10/96.30	    inference('demod', [status(thm)], ['120', '1', '1', '72', '46'])).
96.10/96.30	tff('122', plain,
96.10/96.30	    ![X0 : int, X1 : int, X2 : int]:
96.10/96.30	      times_times(int, plus_plus(int, X2, X1), X0)
96.10/96.30	       = plus_plus(int, times_times(int, X2, X0), times_times(int, X1, X0)),
96.10/96.30	    inference('simplify', [status(thm)], ['121'])).
96.10/96.30	tff('123', plain,
96.10/96.30	    ![X0 : int, X1 : int]:
96.10/96.30	      times_times(int, plus_plus(int, X0, X1), pls)
96.10/96.30	       = times_times(int, X0, pls),
96.10/96.30	    inference('sup+', [status(thm)], ['119', '122'])).
96.10/96.30	tff('124', plain,
96.10/96.30	    ord_less(int, 
96.10/96.30	      times_times(int, plus_plus(int, bit1(pls), semiring_1_of_nat(int, n)), 
96.10/96.30	        bit0(
96.10/96.30	          minus_minus(int, 
96.10/96.30	            plus_plus(int, bit1(pls), semiring_1_of_nat(int, n)), 
96.10/96.30	            bit0(plus_plus(int, pls, m1))))), pls),
96.10/96.30	    inference('demod', [status(thm)], ['42', '123', '12', '116'])).
96.10/96.30	tff('125', plain, ~ $true, inference('demod', [status(thm)], ['37', '124'])).
96.10/96.30	tff('126', plain, $false, inference('simplify', [status(thm)], ['125'])).
96.10/96.30	
96.10/96.30	% SZS output end Refutation
96.10/96.31	EOF
