0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : purification_ext
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	  --ho-purify ext \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --restrict-hidden-sup-at-vars \
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   : n122.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 08:17:54 CST 2018
1.04/1.29	% done 891 iterations in 1.081s
1.04/1.29	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
1.04/1.29	% SZS output start Refutation
1.04/1.29	tff(conj_0, conjecture,
1.04/1.29	  (power_power(int,
1.04/1.29	               minus_minus(int,
1.04/1.29	                           plus_plus(int,
1.04/1.29	                                     times_times(int,
1.04/1.29	                                                 number_number_of(int,
1.04/1.29	                                                                  bit0(
1.04/1.29	                                                                  bit0(
1.04/1.29	                                                                  bit1(pls)))),
1.04/1.29	                                                 m),
1.04/1.29	                                     one_one(int)),
1.04/1.29	                           one_one(int)),
1.04/1.29	               number_number_of(nat,bit0(bit1(pls)))) =
1.04/1.29	   minus_minus(int,
1.04/1.29	               times_times(int,
1.04/1.29	                           plus_plus(int,
1.04/1.29	                                     times_times(int,
1.04/1.29	                                                 number_number_of(int,
1.04/1.29	                                                                  bit0(
1.04/1.29	                                                                  bit0(
1.04/1.29	                                                                  bit1(pls)))),
1.04/1.29	                                                 m),
1.04/1.29	                                     one_one(int)),
1.04/1.29	                           minus_minus(int,
1.04/1.29	                                       plus_plus(int,
1.04/1.29	                                                 times_times(int,
1.04/1.29	                                                             number_number_of(
1.04/1.29	                                                             int,
1.04/1.29	                                                             bit0(bit0(
1.04/1.29	                                                                  bit1(pls)))),
1.04/1.29	                                                             m),
1.04/1.29	                                                 one_one(int)),
1.04/1.29	                                       one_one(int))),
1.04/1.29	               times_times(int,one_one(int),
1.04/1.29	                           minus_minus(int,
1.04/1.29	                                       plus_plus(int,
1.04/1.29	                                                 times_times(int,
1.04/1.29	                                                             number_number_of(
1.04/1.29	                                                             int,
1.04/1.29	                                                             bit0(bit0(
1.04/1.29	                                                                  bit1(pls)))),
1.04/1.29	                                                             m),
1.04/1.29	                                                 one_one(int)),
1.04/1.29	                                       one_one(int)))))).
1.04/1.29	tff(zf_stmt_0, negated_conjecture,
1.04/1.29	  (power_power(int,
1.04/1.29	               minus_minus(int,
1.04/1.29	                           plus_plus(int,
1.04/1.29	                                     times_times(int,
1.04/1.29	                                                 number_number_of(int,
1.04/1.29	                                                                  bit0(
1.04/1.29	                                                                  bit0(
1.04/1.29	                                                                  bit1(pls)))),
1.04/1.29	                                                 m),
1.04/1.29	                                     one_one(int)),
1.04/1.29	                           one_one(int)),
1.04/1.29	               number_number_of(nat,bit0(bit1(pls)))) !=
1.04/1.29	   minus_minus(int,
1.04/1.29	               times_times(int,
1.04/1.29	                           plus_plus(int,
1.04/1.29	                                     times_times(int,
1.04/1.29	                                                 number_number_of(int,
1.04/1.29	                                                                  bit0(
1.04/1.29	                                                                  bit0(
1.04/1.29	                                                                  bit1(pls)))),
1.04/1.29	                                                 m),
1.04/1.29	                                     one_one(int)),
1.04/1.29	                           minus_minus(int,
1.04/1.29	                                       plus_plus(int,
1.04/1.29	                                                 times_times(int,
1.04/1.29	                                                             number_number_of(
1.04/1.29	                                                             int,
1.04/1.29	                                                             bit0(bit0(
1.04/1.29	                                                                  bit1(pls)))),
1.04/1.29	                                                             m),
1.04/1.29	                                                 one_one(int)),
1.04/1.29	                                       one_one(int))),
1.04/1.29	               times_times(int,one_one(int),
1.04/1.29	                           minus_minus(int,
1.04/1.29	                                       plus_plus(int,
1.04/1.29	                                                 times_times(int,
1.04/1.29	                                                             number_number_of(
1.04/1.29	                                                             int,
1.04/1.29	                                                             bit0(bit0(
1.04/1.29	                                                                  bit1(pls)))),
1.04/1.29	                                                             m),
1.04/1.29	                                                 one_one(int)),
1.04/1.29	                                       one_one(int)))))).
1.04/1.29	tff('0', plain,
1.04/1.29	    power_power(int, 
1.04/1.29	      minus_minus(int, 
1.04/1.29	        plus_plus(int, 
1.04/1.29	          times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), 
1.04/1.29	          one_one(int)), one_one(int)), 
1.04/1.29	      number_number_of(nat, bit0(bit1(pls))))
1.04/1.29	     != minus_minus(int, 
1.04/1.29	          times_times(int, 
1.04/1.29	            plus_plus(int, 
1.04/1.29	              times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), 
1.04/1.29	                m), one_one(int)), 
1.04/1.29	            minus_minus(int, 
1.04/1.29	              plus_plus(int, 
1.04/1.29	                times_times(int, 
1.04/1.29	                  number_number_of(int, bit0(bit0(bit1(pls)))), m), 
1.04/1.29	                one_one(int)), one_one(int))), 
1.04/1.29	          times_times(int, one_one(int), 
1.04/1.29	            minus_minus(int, 
1.04/1.29	              plus_plus(int, 
1.04/1.29	                times_times(int, 
1.04/1.29	                  number_number_of(int, bit0(bit0(bit1(pls)))), m), 
1.04/1.29	                one_one(int)), one_one(int)))),
1.04/1.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.04/1.29	tff(fact_48_number__of__is__id, axiom,
1.04/1.29	  (![K1:int]: (number_number_of(int,K1) = K1))).
1.04/1.29	tff('1', plain, ![X97 : int]: number_number_of(int, X97) = X97,
1.04/1.29	    inference('cnf', [status(esa)], [fact_48_number__of__is__id])).
1.04/1.29	tff(fact_24_mult__Bit0, axiom,
1.04/1.29	  (![L1:int,K1:int]:
1.04/1.29	     (times_times(int,bit0(K1),L1) = bit0(times_times(int,K1,L1))))).
1.04/1.29	tff('2', plain,
1.04/1.29	    ![X43 : int, X44 : int]:
1.04/1.29	      times_times(int, bit0(X43), X44) = bit0(times_times(int, X43, X44)),
1.04/1.29	    inference('cnf', [status(esa)], [fact_24_mult__Bit0])).
1.04/1.29	tff(fact_23_mult__Pls, axiom, (![W:int]: (times_times(int,pls,W) = pls))).
1.04/1.29	tff('3', plain, ![X42 : int]: times_times(int, pls, X42) = pls,
1.04/1.29	    inference('cnf', [status(esa)], [fact_23_mult__Pls])).
1.04/1.29	tff(fact_6_mult__Bit1, axiom,
1.04/1.29	  (![L1:int,K1:int]:
1.04/1.29	     (times_times(int,bit1(K1),L1) =
1.04/1.29	      plus_plus(int,bit0(times_times(int,K1,L1)),L1)))).
1.04/1.29	tff('4', plain,
1.04/1.29	    ![X8 : int, X9 : int]:
1.04/1.29	      times_times(int, bit1(X8), X9)
1.04/1.29	       = plus_plus(int, bit0(times_times(int, X8, X9)), X9),
1.04/1.29	    inference('cnf', [status(esa)], [fact_6_mult__Bit1])).
1.04/1.29	tff('5', plain,
1.04/1.29	    ![X0 : int]:
1.04/1.29	      times_times(int, bit1(pls), X0) = plus_plus(int, bit0(pls), X0),
1.04/1.29	    inference('sup+', [status(thm)], ['3', '4'])).
1.04/1.29	tff(fact_22_Bit0__Pls, axiom, (bit0(pls) = pls)).
1.04/1.29	tff('6', plain, bit0(pls) = pls,
1.04/1.29	    inference('cnf', [status(esa)], [fact_22_Bit0__Pls])).
1.04/1.29	tff('7', plain,
1.04/1.29	    ![X0 : int]: times_times(int, bit1(pls), X0) = plus_plus(int, pls, X0),
1.04/1.29	    inference('demod', [status(thm)], ['5', '6'])).
1.04/1.29	tff(fact_51_add__Pls, axiom, (![K1:int]: (plus_plus(int,pls,K1) = K1))).
1.04/1.29	tff('8', plain, ![X102 : int]: plus_plus(int, pls, X102) = X102,
1.04/1.29	    inference('cnf', [status(esa)], [fact_51_add__Pls])).
1.04/1.29	tff('9', plain, ![X0 : int]: times_times(int, bit1(pls), X0) = X0,
1.04/1.29	    inference('demod', [status(thm)], ['7', '8'])).
1.04/1.29	tff(fact_72_one__is__num__one, axiom,
1.04/1.29	  (one_one(int) = number_number_of(int,bit1(pls)))).
1.04/1.29	tff('10', plain, one_one(int) = number_number_of(int, bit1(pls)),
1.04/1.29	    inference('cnf', [status(esa)], [fact_72_one__is__num__one])).
1.04/1.29	tff('11', plain, one_one(int) = bit1(pls),
1.04/1.29	    inference('demod', [status(thm)], ['10', '1'])).
1.04/1.29	tff(fact_37_add__Bit0__Bit1, axiom,
1.04/1.29	  (![L1:int,K1:int]:
1.04/1.29	     (plus_plus(int,bit0(K1),bit1(L1)) = bit1(plus_plus(int,K1,L1))))).
1.04/1.29	tff('12', plain,
1.04/1.29	    ![X81 : int, X82 : int]:
1.04/1.29	      plus_plus(int, bit0(X81), bit1(X82)) = bit1(plus_plus(int, X81, X82)),
1.04/1.29	    inference('cnf', [status(esa)], [fact_37_add__Bit0__Bit1])).
1.04/1.29	tff(fact_50_add__Pls__right, axiom,
1.04/1.29	  (![K1:int]: (plus_plus(int,K1,pls) = K1))).
1.04/1.29	tff('13', plain, ![X101 : int]: plus_plus(int, X101, pls) = X101,
1.04/1.29	    inference('cnf', [status(esa)], [fact_50_add__Pls__right])).
1.04/1.29	tff(fact_38_diff__bin__simps_I10_J, axiom,
1.04/1.29	  (![L1:int,K1:int]:
1.04/1.29	     (minus_minus(int,bit1(K1),bit1(L1)) = bit0(minus_minus(int,K1,L1))))).
1.04/1.29	tff('14', plain,
1.04/1.29	    ![X83 : int, X84 : int]:
1.04/1.29	      minus_minus(int, bit1(X83), bit1(X84))
1.04/1.29	       = bit0(minus_minus(int, X83, X84)),
1.04/1.29	    inference('cnf', [status(esa)], [fact_38_diff__bin__simps_I10_J])).
1.04/1.29	tff(fact_54_diff__bin__simps_I1_J, axiom,
1.04/1.29	  (![K1:int]: (minus_minus(int,K1,pls) = K1))).
1.04/1.29	tff('15', plain, ![X106 : int]: minus_minus(int, X106, pls) = X106,
1.04/1.29	    inference('cnf', [status(esa)], [fact_54_diff__bin__simps_I1_J])).
1.04/1.29	tff(fact_1_power2__eq__square__number__of, axiom,
1.04/1.29	  (![B1:$tType]:
1.04/1.29	     ((number(B1) & monoid_mult(B1)) =>
1.04/1.29	      (![W:int]:
1.04/1.29	         (power_power(B1,number_number_of(B1,W),
1.04/1.29	                      number_number_of(nat,bit0(bit1(pls)))) =
1.04/1.29	          times_times(B1,number_number_of(B1,W),number_number_of(B1,W))))))).
1.04/1.29	tff('16', plain,
1.04/1.29	    ![X0 : $tType, X1 : int]:
1.04/1.29	      (power_power(X0, number_number_of(X0, X1), 
1.04/1.29	         number_number_of(nat, bit0(bit1(pls))))
1.04/1.29	        = times_times(X0, number_number_of(X0, X1), number_number_of(X0, X1))
1.04/1.29	       | ~ monoid_mult(X0)
1.04/1.29	       | ~ number(X0)),
1.04/1.29	    inference('cnf', [status(esa)], [fact_1_power2__eq__square__number__of])).
1.04/1.29	tff('17', plain,
1.04/1.29	    ![X0 : int]:
1.04/1.29	      (power_power(int, X0, number_number_of(nat, bit0(bit1(pls))))
1.04/1.29	        = times_times(int, number_number_of(int, X0), 
1.04/1.29	            number_number_of(int, X0))
1.04/1.29	       | ~ number(int)
1.04/1.29	       | ~ monoid_mult(int)),
1.04/1.29	    inference('sup+', [status(thm)], ['1', '16'])).
1.04/1.29	tff(arity_Int_Oint___Int_Onumber, axiom, (number(int))).
1.04/1.29	tff('18', plain, number(int),
1.04/1.29	    inference('cnf', [status(esa)], [arity_Int_Oint___Int_Onumber])).
1.04/1.29	tff(arity_Int_Oint___Groups_Omonoid__mult, axiom, (monoid_mult(int))).
1.04/1.29	tff('19', plain, monoid_mult(int),
1.04/1.29	    inference('cnf', [status(esa)], [arity_Int_Oint___Groups_Omonoid__mult])).
1.04/1.29	tff('20', plain,
1.04/1.29	    ![X0 : int]:
1.04/1.29	      (power_power(int, X0, number_number_of(nat, bit0(bit1(pls))))
1.04/1.29	        = times_times(int, X0, X0)
1.04/1.29	       | ~ $true
1.04/1.29	       | ~ $true),
1.04/1.29	    inference('demod', [status(thm)], ['17', '1', '1', '18', '19'])).
1.04/1.29	tff('21', plain,
1.04/1.29	    ![X0 : int]:
1.04/1.29	      power_power(int, X0, number_number_of(nat, bit0(bit1(pls))))
1.04/1.29	       = times_times(int, X0, X0),
1.04/1.29	    inference('simplify', [status(thm)], ['20'])).
1.04/1.29	tff('22', plain,
1.04/1.29	    ![X0 : int]:
1.04/1.29	      power_power(int, bit0(X0), number_number_of(nat, bit0(bit1(pls))))
1.04/1.29	       = bit0(times_times(int, X0, bit0(X0))),
1.04/1.29	    inference('sup+', [status(thm)], ['21', '2'])).
1.04/1.29	tff(fact_55_int__distrib_I1_J, axiom,
1.04/1.29	  (![W:int,Z2:int,Z1:int]:
1.04/1.29	     (times_times(int,plus_plus(int,Z1,Z2),W) =
1.04/1.29	      plus_plus(int,times_times(int,Z1,W),times_times(int,Z2,W))))).
1.04/1.29	tff('23', plain,
1.04/1.29	    ![X107 : int, X108 : int, X109 : int]:
1.04/1.29	      times_times(int, plus_plus(int, X107, X109), X108)
1.04/1.29	       = plus_plus(int, times_times(int, X107, X108), 
1.04/1.29	           times_times(int, X109, X108)),
1.04/1.29	    inference('cnf', [status(esa)], [fact_55_int__distrib_I1_J])).
1.04/1.29	tff(fact_28_right__distrib__number__of, axiom,
1.04/1.29	  (![B1:$tType]:
1.04/1.29	     ((semiring(B1) & number(B1)) =>
1.04/1.29	      (![C:B1,B:B1,V:int]:
1.04/1.29	         (times_times(B1,number_number_of(B1,V),plus_plus(B1,B,C)) =
1.04/1.29	          plus_plus(B1,times_times(B1,number_number_of(B1,V),B),
1.04/1.29	                    times_times(B1,number_number_of(B1,V),C))))))).
1.04/1.29	tff('24', plain,
1.04/1.29	    ![X53 : $tType, X54 : int, X55 : X53, X56 : X53]:
1.04/1.29	      (times_times(X53, number_number_of(X53, X54), plus_plus(X53, X55, X56))
1.04/1.29	        = plus_plus(X53, times_times(X53, number_number_of(X53, X54), X55), 
1.04/1.29	            times_times(X53, number_number_of(X53, X54), X56))
1.04/1.29	       | ~ number(X53)
1.04/1.29	       | ~ semiring(X53)),
1.04/1.29	    inference('cnf', [status(esa)], [fact_28_right__distrib__number__of])).
1.04/1.29	tff('25', plain,
1.04/1.29	    ![X0 : int, X1 : int]:
1.04/1.29	      (times_times(int, number_number_of(int, X1), plus_plus(int, X0, X0))
1.04/1.29	        = times_times(int, 
1.04/1.29	            plus_plus(int, number_number_of(int, X1), 
1.04/1.29	              number_number_of(int, X1)), X0)
1.04/1.29	       | ~ semiring(int)
1.04/1.29	       | ~ number(int)),
1.04/1.29	    inference('sup+', [status(thm)], ['23', '24'])).
1.04/1.29	tff(fact_52_Bit0__def, axiom, (![K1:int]: (bit0(K1) = plus_plus(int,K1,K1)))).
1.04/1.29	tff('26', plain, ![X103 : int]: bit0(X103) = plus_plus(int, X103, X103),
1.04/1.29	    inference('cnf', [status(esa)], [fact_52_Bit0__def])).
1.04/1.29	tff(arity_Int_Oint___Rings_Osemiring, axiom, (semiring(int))).
1.04/1.29	tff('27', plain, semiring(int),
1.04/1.29	    inference('cnf', [status(esa)], [arity_Int_Oint___Rings_Osemiring])).
1.04/1.29	tff('28', plain,
1.04/1.29	    ![X0 : int, X1 : int]:
1.04/1.29	      (times_times(int, X1, bit0(X0)) = bit0(times_times(int, X1, X0))
1.04/1.29	       | ~ $true
1.04/1.29	       | ~ $true),
1.04/1.29	    inference('demod', [status(thm)],
1.04/1.29	              ['25', '1', '26', '1', '1', '26', '2', '27', '18'])).
1.04/1.29	tff('29', plain,
1.04/1.29	    ![X0 : int, X1 : int]:
1.04/1.29	      times_times(int, X1, bit0(X0)) = bit0(times_times(int, X1, X0)),
1.04/1.29	    inference('simplify', [status(thm)], ['28'])).
1.04/1.29	tff('30', plain,
1.04/1.29	    ![X0 : int]:
1.04/1.29	      power_power(int, bit0(X0), number_number_of(nat, bit0(bit1(pls))))
1.04/1.29	       = bit0(bit0(times_times(int, X0, X0))),
1.04/1.29	    inference('demod', [status(thm)], ['22', '29'])).
1.04/1.29	tff(fact_26_diff__bin__simps_I7_J, axiom,
1.04/1.29	  (![L1:int,K1:int]:
1.04/1.29	     (minus_minus(int,bit0(K1),bit0(L1)) = bit0(minus_minus(int,K1,L1))))).
1.04/1.29	tff('31', plain,
1.04/1.29	    ![X47 : int, X48 : int]:
1.04/1.29	      minus_minus(int, bit0(X47), bit0(X48))
1.04/1.29	       = bit0(minus_minus(int, X47, X48)),
1.04/1.29	    inference('cnf', [status(esa)], [fact_26_diff__bin__simps_I7_J])).
1.04/1.29	tff(fact_30_right__diff__distrib__number__of, axiom,
1.04/1.29	  (![B1:$tType]:
1.04/1.29	     ((ring(B1) & number(B1)) =>
1.04/1.29	      (![C:B1,B:B1,V:int]:
1.04/1.29	         (times_times(B1,number_number_of(B1,V),minus_minus(B1,B,C)) =
1.04/1.29	          minus_minus(B1,times_times(B1,number_number_of(B1,V),B),
1.04/1.29	                      times_times(B1,number_number_of(B1,V),C))))))).
1.04/1.29	tff('32', plain,
1.04/1.29	    ![X61 : $tType, X62 : int, X63 : X61, X64 : X61]:
1.04/1.29	      (times_times(X61, number_number_of(X61, X62), 
1.04/1.29	         minus_minus(X61, X63, X64))
1.04/1.29	        = minus_minus(X61, 
1.04/1.29	            times_times(X61, number_number_of(X61, X62), X63), 
1.04/1.29	            times_times(X61, number_number_of(X61, X62), X64))
1.04/1.29	       | ~ number(X61)
1.04/1.29	       | ~ ring(X61)),
1.04/1.29	    inference('cnf', [status(esa)],
1.04/1.29	              [fact_30_right__diff__distrib__number__of])).
1.04/1.29	tff(fact_58_int__distrib_I3_J, axiom,
1.04/1.29	  (![W:int,Z2:int,Z1:int]:
1.04/1.29	     (times_times(int,minus_minus(int,Z1,Z2),W) =
1.04/1.29	      minus_minus(int,times_times(int,Z1,W),times_times(int,Z2,W))))).
1.04/1.29	tff('33', plain,
1.04/1.29	    ![X115 : int, X116 : int, X117 : int]:
1.04/1.29	      times_times(int, minus_minus(int, X115, X117), X116)
1.04/1.29	       = minus_minus(int, times_times(int, X115, X116), 
1.04/1.29	           times_times(int, X117, X116)),
1.04/1.29	    inference('cnf', [status(esa)], [fact_58_int__distrib_I3_J])).
1.04/1.29	tff('34', plain,
1.04/1.29	    ![X0 : int, X1 : int]:
1.04/1.29	      (times_times(int, 
1.04/1.29	         minus_minus(int, number_number_of(int, X1), 
1.04/1.29	           number_number_of(int, X1)), X0)
1.04/1.29	        = times_times(int, number_number_of(int, X1), 
1.04/1.29	            minus_minus(int, X0, X0))
1.04/1.29	       | ~ ring(int)
1.04/1.29	       | ~ number(int)),
1.04/1.29	    inference('sup+', [status(thm)], ['32', '33'])).
1.04/1.29	tff(arity_Int_Oint___Rings_Oring, axiom, (ring(int))).
1.04/1.29	tff('35', plain, ring(int),
1.04/1.29	    inference('cnf', [status(esa)], [arity_Int_Oint___Rings_Oring])).
1.04/1.29	tff('36', plain,
1.04/1.29	    ![X0 : int, X1 : int]:
1.04/1.29	      (times_times(int, minus_minus(int, X1, X1), X0)
1.04/1.29	        = times_times(int, X1, minus_minus(int, X0, X0))
1.04/1.29	       | ~ $true
1.04/1.29	       | ~ $true),
1.04/1.29	    inference('demod', [status(thm)], ['34', '1', '1', '1', '35', '18'])).
1.04/1.29	tff('37', plain,
1.04/1.29	    ![X0 : int, X1 : int]:
1.04/1.29	      times_times(int, minus_minus(int, X1, X1), X0)
1.04/1.29	       = times_times(int, X1, minus_minus(int, X0, X0)),
1.04/1.29	    inference('simplify', [status(thm)], ['36'])).
1.04/1.29	tff('38', plain,
1.04/1.29	    ![X0 : int]:
1.04/1.29	      times_times(int, minus_minus(int, bit1(pls), bit1(pls)), X0)
1.04/1.29	       = minus_minus(int, X0, X0),
1.04/1.29	    inference('sup+', [status(thm)], ['9', '37'])).
1.04/1.29	tff('39', plain, ![X0 : int]: pls = minus_minus(int, X0, X0),
1.04/1.29	    inference('demod', [status(thm)], ['38', '14', '15', '6', '3'])).
1.04/1.29	tff(fact_71_add__number__of__diff1, axiom,
1.04/1.29	  (![A:$tType]:
1.04/1.29	     (number_ring(A) =>
1.04/1.29	      (![C:A,W:int,V:int]:
1.04/1.29	         (plus_plus(A,number_number_of(A,V),
1.04/1.29	                    minus_minus(A,number_number_of(A,W),C)) =
1.04/1.29	          minus_minus(A,number_number_of(A,plus_plus(int,V,W)),C)))))).
1.04/1.29	tff('40', plain,
1.04/1.29	    ![X143 : $tType, X144 : int, X145 : int, X146 : X143]:
1.04/1.29	      (plus_plus(X143, number_number_of(X143, X144), 
1.04/1.29	         minus_minus(X143, number_number_of(X143, X145), X146))
1.04/1.29	        = minus_minus(X143, 
1.04/1.29	            number_number_of(X143, plus_plus(int, X144, X145)), X146)
1.04/1.29	       | ~ number_ring(X143)),
1.04/1.29	    inference('cnf', [status(esa)], [fact_71_add__number__of__diff1])).
1.04/1.29	tff('41', plain,
1.04/1.29	    ![X0 : int, X1 : int]:
1.04/1.29	      (plus_plus(int, number_number_of(int, X1), pls)
1.04/1.29	        = minus_minus(int, number_number_of(int, plus_plus(int, X1, X0)), 
1.04/1.29	            number_number_of(int, X0))
1.04/1.29	       | ~ number_ring(int)),
1.04/1.29	    inference('sup+', [status(thm)], ['39', '40'])).
1.04/1.29	tff(arity_Int_Oint___Int_Onumber__ring, axiom, (number_ring(int))).
1.04/1.29	tff('42', plain, number_ring(int),
1.04/1.29	    inference('cnf', [status(esa)], [arity_Int_Oint___Int_Onumber__ring])).
1.04/1.29	tff('43', plain,
1.04/1.29	    ![X0 : int, X1 : int]:
1.04/1.29	      (X1 = minus_minus(int, plus_plus(int, X1, X0), X0) | ~ $true),
1.04/1.29	    inference('demod', [status(thm)], ['41', '1', '13', '1', '1', '42'])).
1.04/1.29	tff('44', plain,
1.04/1.29	    ![X0 : int, X1 : int]: X1 = minus_minus(int, plus_plus(int, X1, X0), X0),
1.04/1.29	    inference('simplify', [status(thm)], ['43'])).
1.04/1.29	tff('45', plain,
1.04/1.29	    ![X0 : int, X1 : int]:
1.04/1.29	      bit0(times_times(int, X1, X0))
1.04/1.29	       = minus_minus(int, times_times(int, bit1(X1), X0), X0),
1.04/1.29	    inference('sup+', [status(thm)], ['4', '44'])).
1.04/1.29	tff('46', plain,
1.04/1.29	    bit0(bit0(bit0(bit0(times_times(int, m, m)))))
1.04/1.29	     != bit0(bit0(bit0(bit0(times_times(int, m, m))))),
1.04/1.29	    inference('demod', [status(thm)],
1.04/1.29	              ['0', '1', '2', '2', '9', '11', '12', '13', '11', '14', '15', 
1.04/1.29	               '30', '2', '29', '1', '2', '2', '9', '11', '12', '13', '1', 
1.04/1.29	               '2', '2', '9', '11', '12', '13', '11', '14', '15', '29', 
1.04/1.29	               '29', '11', '1', '2', '2', '9', '11', '12', '13', '11', '14', 
1.04/1.29	               '15', '9', '31', '31', '45', '2'])).
1.04/1.29	tff('47', plain, $false, inference('simplify', [status(thm)], ['46'])).
1.04/1.29	
1.04/1.29	% SZS output end Refutation
1.04/1.29	EOF
