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    : fo
0.00/0.00	% Ordering    : rpo6
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-ho \
0.00/0.00	  --no-avatar \
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	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n159.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:50:54 CST 2018
1.86/2.06	% done 898 iterations in 1.859s
1.86/2.06	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
1.86/2.06	% SZS output start Refutation
1.86/2.06	tff(conj_0, conjecture,
1.86/2.06	  (minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),
1.86/2.06	               number_number_of(int,min)) =
1.86/2.06	   plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),
1.86/2.06	             one_one(int)))).
1.86/2.06	tff(zf_stmt_0, negated_conjecture,
1.86/2.06	  (minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),
1.86/2.06	               number_number_of(int,min)) !=
1.86/2.06	   plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),
1.86/2.06	             one_one(int)))).
1.86/2.06	tff('0', plain,
1.86/2.06	    minus_minus(int, 
1.86/2.06	      power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), 
1.86/2.06	      number_number_of(int, min))
1.86/2.06	     != plus_plus(int, 
1.86/2.06	          power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), 
1.86/2.06	          one_one(int)),
1.86/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.86/2.06	tff(fact_41_Bit0__def, axiom, (![K:int]: (bit0(K) = plus_plus(int,K,K)))).
1.86/2.06	tff('1', plain, ![X63 : int]: bit0(X63) = plus_plus(int, X63, X63),
1.86/2.06	    inference('cnf', [status(esa)], [fact_41_Bit0__def])).
1.86/2.06	tff(arity_Int_Oint___Int_Onumber, axiom, (number(int))).
1.86/2.06	tff('2', plain, number(int),
1.86/2.06	    inference('cnf', [status(esa)], [arity_Int_Oint___Int_Onumber])).
1.86/2.06	tff(fact_63_power2__eq__square__number__of, axiom,
1.86/2.06	  (![B1:$tType]:
1.86/2.06	     ((number(B1) & monoid_mult(B1)) =>
1.86/2.06	      (![W:int]:
1.86/2.06	         (power_power(B1,number_number_of(B1,W),
1.86/2.06	                      number_number_of(nat,bit0(bit1(pls)))) =
1.86/2.06	          times_times(B1,number_number_of(B1,W),number_number_of(B1,W))))))).
1.86/2.06	tff('3', plain,
1.86/2.06	    ![X106 : $tType, X107 : int]:
1.86/2.06	      (power_power(X106, number_number_of(X106, X107), 
1.86/2.06	         number_number_of(nat, bit0(bit1(pls))))
1.86/2.06	        = times_times(X106, number_number_of(X106, X107), 
1.86/2.06	            number_number_of(X106, X107))
1.86/2.06	       | ~ monoid_mult(X106)
1.86/2.06	       | ~ number(X106)),
1.86/2.06	    inference('cnf', [status(esa)], [fact_63_power2__eq__square__number__of])).
1.86/2.06	tff('4', plain,
1.86/2.06	    ![X106 : $tType, X107 : int]:
1.86/2.06	      (power_power(X106, number_number_of(X106, X107), 
1.86/2.06	         number_number_of(nat, plus_plus(int, bit1(pls), bit1(pls))))
1.86/2.06	        = times_times(X106, number_number_of(X106, X107), 
1.86/2.06	            number_number_of(X106, X107))
1.86/2.06	       | ~ monoid_mult(X106)
1.86/2.06	       | ~ number(X106)),
1.86/2.06	    inference('demod', [status(thm)], ['3', '1'])).
1.86/2.06	tff('5', plain,
1.86/2.06	    ![X0 : int]:
1.86/2.06	      (~ $true
1.86/2.06	       | ~ monoid_mult(int)
1.86/2.06	       | power_power(int, number_number_of(int, X0), 
1.86/2.06	           number_number_of(nat, plus_plus(int, bit1(pls), bit1(pls))))
1.86/2.06	          = times_times(int, number_number_of(int, X0), 
1.86/2.06	              number_number_of(int, X0))),
1.86/2.06	    inference('sup-', [status(thm)], ['2', '4'])).
1.86/2.06	tff(arity_Int_Oint___Groups_Omonoid__mult, axiom, (monoid_mult(int))).
1.86/2.06	tff('6', plain, monoid_mult(int),
1.86/2.06	    inference('cnf', [status(esa)], [arity_Int_Oint___Groups_Omonoid__mult])).
1.86/2.06	tff(fact_38_number__of__is__id, axiom,
1.86/2.06	  (![K:int]: (number_number_of(int,K) = K))).
1.86/2.06	tff('7', plain, ![X60 : int]: number_number_of(int, X60) = X60,
1.86/2.06	    inference('cnf', [status(esa)], [fact_38_number__of__is__id])).
1.86/2.06	tff('8', plain,
1.86/2.06	    ![X0 : int]:
1.86/2.06	      (~ $true
1.86/2.06	       | ~ $true
1.86/2.06	       | power_power(int, X0, 
1.86/2.06	           number_number_of(nat, plus_plus(int, bit1(pls), bit1(pls))))
1.86/2.06	          = times_times(int, X0, X0)),
1.86/2.06	    inference('demod', [status(thm)], ['5', '6', '7', '7', '7'])).
1.86/2.06	tff('9', plain,
1.86/2.06	    ![X0 : int]:
1.86/2.06	      power_power(int, X0, 
1.86/2.06	        number_number_of(nat, plus_plus(int, bit1(pls), bit1(pls))))
1.86/2.06	       = times_times(int, X0, X0),
1.86/2.06	    inference('simplify', [status(thm)], ['8'])).
1.86/2.06	tff(fact_39_add__Pls__right, axiom, (![K:int]: (plus_plus(int,K,pls) = K))).
1.86/2.06	tff('10', plain, ![X61 : int]: plus_plus(int, X61, pls) = X61,
1.86/2.06	    inference('cnf', [status(esa)], [fact_39_add__Pls__right])).
1.86/2.06	tff(arity_Int_Oint___Int_Onumber__ring, axiom, (number_ring(int))).
1.86/2.06	tff('11', plain, number_ring(int),
1.86/2.06	    inference('cnf', [status(esa)], [arity_Int_Oint___Int_Onumber__ring])).
1.86/2.06	tff(fact_53_add__number__of__diff1, axiom,
1.86/2.06	  (![A:$tType]:
1.86/2.06	     (number_ring(A) =>
1.86/2.06	      (![C:A,W:int,V:int]:
1.86/2.06	         (plus_plus(A,number_number_of(A,V),
1.86/2.06	                    minus_minus(A,number_number_of(A,W),C)) =
1.86/2.06	          minus_minus(A,number_number_of(A,plus_plus(int,V,W)),C)))))).
1.86/2.06	tff('12', plain,
1.86/2.06	    ![X82 : $tType, X83 : int, X84 : int, X85 : X82]:
1.86/2.06	      (plus_plus(X82, number_number_of(X82, X83), 
1.86/2.06	         minus_minus(X82, number_number_of(X82, X84), X85))
1.86/2.06	        = minus_minus(X82, number_number_of(X82, plus_plus(int, X83, X84)), 
1.86/2.06	            X85)
1.86/2.06	       | ~ number_ring(X82)),
1.86/2.06	    inference('cnf', [status(esa)], [fact_53_add__number__of__diff1])).
1.86/2.06	tff('13', plain,
1.86/2.06	    ![X0 : int, X1 : int, X2 : int]:
1.86/2.06	      (~ $true
1.86/2.06	       | plus_plus(int, number_number_of(int, X2), 
1.86/2.06	           minus_minus(int, number_number_of(int, X1), X0))
1.86/2.06	          = minus_minus(int, number_number_of(int, plus_plus(int, X2, X1)), 
1.86/2.06	              X0)),
1.86/2.06	    inference('sup-', [status(thm)], ['11', '12'])).
1.86/2.06	tff('14', plain,
1.86/2.06	    ![X0 : int, X1 : int, X2 : int]:
1.86/2.06	      (~ $true
1.86/2.06	       | plus_plus(int, X2, minus_minus(int, X1, X0))
1.86/2.06	          = minus_minus(int, plus_plus(int, X2, X1), X0)),
1.86/2.06	    inference('demod', [status(thm)], ['13', '7', '7', '7'])).
1.86/2.06	tff('15', plain,
1.86/2.06	    ![X0 : int, X1 : int, X2 : int]:
1.86/2.06	      plus_plus(int, X2, minus_minus(int, X1, X0))
1.86/2.06	       = minus_minus(int, plus_plus(int, X2, X1), X0),
1.86/2.06	    inference('simplify', [status(thm)], ['14'])).
1.86/2.06	tff('16', plain,
1.86/2.06	    ![X0 : int, X1 : int]:
1.86/2.06	      plus_plus(int, X0, minus_minus(int, pls, X1))
1.86/2.06	       = minus_minus(int, X0, X1),
1.86/2.06	    inference('sup+', [status(thm)], ['10', '15'])).
1.86/2.06	tff(fact_91_zmult__eq__1__iff, axiom,
1.86/2.06	  (![N1:int,Ma:int]:
1.86/2.06	     ((times_times(int,Ma,N1) = one_one(int)) <=>
1.86/2.06	      (((N1 = number_number_of(int,min)) & (Ma = number_number_of(int,min))) | 
1.86/2.06	       ((N1 = one_one(int)) & (Ma = one_one(int))))))).
1.86/2.06	tff('17', plain,
1.86/2.06	    ![X187 : int, X189 : int]:
1.86/2.06	      (times_times(int, X189, X187) = one_one(int)
1.86/2.06	       | X187 != number_number_of(int, min)
1.86/2.06	       | X189 != number_number_of(int, min)),
1.86/2.06	    inference('cnf', [status(esa)], [fact_91_zmult__eq__1__iff])).
1.86/2.06	tff('18', plain,
1.86/2.06	    times_times(int, number_number_of(int, min), number_number_of(int, min))
1.86/2.06	     = one_one(int),
1.86/2.06	    inference('simplify', [status(thm)], ['17'])).
1.86/2.06	tff(fact_54_one__is__num__one, axiom,
1.86/2.06	  (one_one(int) = number_number_of(int,bit1(pls)))).
1.86/2.06	tff('19', plain, one_one(int) = number_number_of(int, bit1(pls)),
1.86/2.06	    inference('cnf', [status(esa)], [fact_54_one__is__num__one])).
1.86/2.06	tff('20', plain, one_one(int) = bit1(pls),
1.86/2.06	    inference('demod', [status(thm)], ['19', '7'])).
1.86/2.06	tff('21', plain, times_times(int, min, min) = bit1(pls),
1.86/2.06	    inference('demod', [status(thm)], ['18', '7', '7', '20'])).
1.86/2.06	tff(fact_67_mult__number__of__left, axiom,
1.86/2.06	  (![A:$tType]:
1.86/2.06	     (number_ring(A) =>
1.86/2.06	      (![Z:A,W:int,V:int]:
1.86/2.06	         (times_times(A,number_number_of(A,V),
1.86/2.06	                      times_times(A,number_number_of(A,W),Z)) =
1.86/2.06	          times_times(A,number_number_of(A,times_times(int,V,W)),Z)))))).
1.86/2.06	tff('22', plain,
1.86/2.06	    ![X114 : $tType, X115 : int, X116 : int, X117 : X114]:
1.86/2.06	      (times_times(X114, number_number_of(X114, X115), 
1.86/2.06	         times_times(X114, number_number_of(X114, X116), X117))
1.86/2.06	        = times_times(X114, 
1.86/2.06	            number_number_of(X114, times_times(int, X115, X116)), X117)
1.86/2.06	       | ~ number_ring(X114)),
1.86/2.06	    inference('cnf', [status(esa)], [fact_67_mult__number__of__left])).
1.86/2.06	tff('23', plain,
1.86/2.06	    ![X0 : int, X1 : int, X2 : int]:
1.86/2.06	      (~ $true
1.86/2.06	       | times_times(int, number_number_of(int, X2), 
1.86/2.06	           times_times(int, number_number_of(int, X1), X0))
1.86/2.06	          = times_times(int, 
1.86/2.06	              number_number_of(int, times_times(int, X2, X1)), X0)),
1.86/2.06	    inference('sup-', [status(thm)], ['11', '22'])).
1.86/2.06	tff('24', plain,
1.86/2.06	    ![X0 : int, X1 : int, X2 : int]:
1.86/2.06	      (~ $true
1.86/2.06	       | times_times(int, X2, times_times(int, X1, X0))
1.86/2.06	          = times_times(int, times_times(int, X2, X1), X0)),
1.86/2.06	    inference('demod', [status(thm)], ['23', '7', '7', '7'])).
1.86/2.06	tff('25', plain,
1.86/2.06	    ![X0 : int, X1 : int, X2 : int]:
1.86/2.06	      times_times(int, X2, times_times(int, X1, X0))
1.86/2.06	       = times_times(int, times_times(int, X2, X1), X0),
1.86/2.06	    inference('simplify', [status(thm)], ['24'])).
1.86/2.06	tff('26', plain,
1.86/2.06	    ![X0 : int]:
1.86/2.06	      times_times(int, min, times_times(int, min, X0))
1.86/2.06	       = times_times(int, bit1(pls), X0),
1.86/2.06	    inference('sup+', [status(thm)], ['21', '25'])).
1.86/2.06	tff(fact_72_mult__Bit1, axiom,
1.86/2.06	  (![L:int,K:int]:
1.86/2.06	     (times_times(int,bit1(K),L) =
1.86/2.06	      plus_plus(int,bit0(times_times(int,K,L)),L)))).
1.86/2.06	tff('27', plain,
1.86/2.06	    ![X134 : int, X135 : int]:
1.86/2.06	      times_times(int, bit1(X134), X135)
1.86/2.06	       = plus_plus(int, bit0(times_times(int, X134, X135)), X135),
1.86/2.06	    inference('cnf', [status(esa)], [fact_72_mult__Bit1])).
1.86/2.06	tff(fact_65_mult__Bit0, axiom,
1.86/2.06	  (![L:int,K:int]: (times_times(int,bit0(K),L) = bit0(times_times(int,K,L))))).
1.86/2.06	tff('28', plain,
1.86/2.06	    ![X109 : int, X110 : int]:
1.86/2.06	      times_times(int, bit0(X109), X110) = bit0(times_times(int, X109, X110)),
1.86/2.06	    inference('cnf', [status(esa)], [fact_65_mult__Bit0])).
1.86/2.06	tff('29', plain,
1.86/2.06	    ![X109 : int, X110 : int]:
1.86/2.06	      times_times(int, plus_plus(int, X109, X109), X110)
1.86/2.06	       = plus_plus(int, times_times(int, X109, X110), 
1.86/2.06	           times_times(int, X109, X110)),
1.86/2.06	    inference('demod', [status(thm)], ['28', '1', '1'])).
1.86/2.06	tff('30', plain,
1.86/2.06	    ![X134 : int, X135 : int]:
1.86/2.06	      times_times(int, bit1(X134), X135)
1.86/2.06	       = plus_plus(int, times_times(int, plus_plus(int, X134, X134), X135), 
1.86/2.06	           X135),
1.86/2.06	    inference('demod', [status(thm)], ['27', '1', '29'])).
1.86/2.06	tff('31', plain,
1.86/2.06	    ![X0 : int]:
1.86/2.06	      times_times(int, bit1(pls), X0)
1.86/2.06	       = plus_plus(int, times_times(int, pls, X0), X0),
1.86/2.06	    inference('sup+', [status(thm)], ['10', '30'])).
1.86/2.06	tff(fact_64_mult__Pls, axiom, (![W:int]: (times_times(int,pls,W) = pls))).
1.86/2.06	tff('32', plain, ![X108 : int]: times_times(int, pls, X108) = pls,
1.86/2.06	    inference('cnf', [status(esa)], [fact_64_mult__Pls])).
1.86/2.06	tff(fact_40_add__Pls, axiom, (![K:int]: (plus_plus(int,pls,K) = K))).
1.86/2.06	tff('33', plain, ![X62 : int]: plus_plus(int, pls, X62) = X62,
1.86/2.06	    inference('cnf', [status(esa)], [fact_40_add__Pls])).
1.86/2.06	tff('34', plain, ![X0 : int]: times_times(int, bit1(pls), X0) = X0,
1.86/2.06	    inference('demod', [status(thm)], ['31', '32', '33'])).
1.86/2.06	tff('35', plain,
1.86/2.06	    ![X0 : int]: times_times(int, min, times_times(int, min, X0)) = X0,
1.86/2.06	    inference('demod', [status(thm)], ['26', '34'])).
1.86/2.06	tff(fact_87_int__distrib_I3_J, axiom,
1.86/2.06	  (![W:int,Z2:int,Z1:int]:
1.86/2.06	     (times_times(int,minus_minus(int,Z1,Z2),W) =
1.86/2.06	      minus_minus(int,times_times(int,Z1,W),times_times(int,Z2,W))))).
1.86/2.06	tff('36', plain,
1.86/2.06	    ![X177 : int, X178 : int, X179 : int]:
1.86/2.06	      times_times(int, minus_minus(int, X177, X179), X178)
1.86/2.06	       = minus_minus(int, times_times(int, X177, X178), 
1.86/2.06	           times_times(int, X179, X178)),
1.86/2.06	    inference('cnf', [status(esa)], [fact_87_int__distrib_I3_J])).
1.86/2.06	tff('37', plain,
1.86/2.06	    ![X0 : int, X1 : int]:
1.86/2.06	      times_times(int, minus_minus(int, pls, X1), X0)
1.86/2.06	       = minus_minus(int, pls, times_times(int, X1, X0)),
1.86/2.06	    inference('sup+', [status(thm)], ['32', '36'])).
1.86/2.06	tff('38', plain,
1.86/2.06	    ![X0 : int]:
1.86/2.06	      times_times(int, minus_minus(int, pls, min), times_times(int, min, X0))
1.86/2.06	       = minus_minus(int, pls, X0),
1.86/2.06	    inference('sup+', [status(thm)], ['35', '37'])).
1.86/2.06	tff('39', plain,
1.86/2.06	    ![X0 : int]:
1.86/2.06	      times_times(int, bit1(X0), pls)
1.86/2.06	       = times_times(int, plus_plus(int, X0, X0), pls),
1.86/2.06	    inference('sup+', [status(thm)], ['30', '10'])).
1.86/2.06	tff(fact_84_int__distrib_I2_J, axiom,
1.86/2.06	  (![Z2:int,Z1:int,W:int]:
1.86/2.06	     (times_times(int,W,plus_plus(int,Z1,Z2)) =
1.86/2.06	      plus_plus(int,times_times(int,W,Z1),times_times(int,W,Z2))))).
1.86/2.06	tff('40', plain,
1.86/2.06	    ![X168 : int, X169 : int, X170 : int]:
1.86/2.06	      times_times(int, X168, plus_plus(int, X169, X170))
1.86/2.06	       = plus_plus(int, times_times(int, X168, X169), 
1.86/2.06	           times_times(int, X168, X170)),
1.86/2.06	    inference('cnf', [status(esa)], [fact_84_int__distrib_I2_J])).
1.86/2.06	tff('41', plain,
1.86/2.06	    ![X109 : int, X110 : int]:
1.86/2.06	      times_times(int, plus_plus(int, X109, X109), X110)
1.86/2.06	       = times_times(int, X109, plus_plus(int, X110, X110)),
1.86/2.06	    inference('demod', [status(thm)], ['29', '40'])).
1.86/2.06	tff('42', plain,
1.86/2.06	    ![X0 : int]:
1.86/2.06	      times_times(int, plus_plus(int, X0, X0), pls)
1.86/2.06	       = times_times(int, X0, pls),
1.86/2.06	    inference('sup+', [status(thm)], ['10', '41'])).
1.86/2.06	tff('43', plain,
1.86/2.06	    ![X0 : int]: times_times(int, bit1(X0), pls) = times_times(int, X0, pls),
1.86/2.06	    inference('demod', [status(thm)], ['39', '42'])).
1.86/2.06	tff(fact_85_int__distrib_I1_J, axiom,
1.86/2.06	  (![W:int,Z2:int,Z1:int]:
1.86/2.06	     (times_times(int,plus_plus(int,Z1,Z2),W) =
1.86/2.06	      plus_plus(int,times_times(int,Z1,W),times_times(int,Z2,W))))).
1.86/2.06	tff('44', plain,
1.86/2.06	    ![X171 : int, X172 : int, X173 : int]:
1.86/2.06	      times_times(int, plus_plus(int, X171, X173), X172)
1.86/2.06	       = plus_plus(int, times_times(int, X171, X172), 
1.86/2.06	           times_times(int, X173, X172)),
1.86/2.06	    inference('cnf', [status(esa)], [fact_85_int__distrib_I1_J])).
1.86/2.06	tff('45', plain,
1.86/2.06	    ![X0 : int, X1 : int]:
1.86/2.06	      times_times(int, plus_plus(int, bit1(X0), X1), pls)
1.86/2.06	       = plus_plus(int, times_times(int, X0, pls), times_times(int, X1, pls)),
1.86/2.06	    inference('sup+', [status(thm)], ['43', '44'])).
1.86/2.06	tff('46', plain,
1.86/2.06	    ![X0 : int, X1 : int]:
1.86/2.06	      times_times(int, plus_plus(int, bit1(X0), X1), pls)
1.86/2.06	       = times_times(int, plus_plus(int, X0, X1), pls),
1.86/2.06	    inference('demod', [status(thm)], ['45', '44'])).
1.86/2.06	tff(fact_86_int__distrib_I4_J, axiom,
1.86/2.06	  (![Z2:int,Z1:int,W:int]:
1.86/2.06	     (times_times(int,W,minus_minus(int,Z1,Z2)) =
1.86/2.06	      minus_minus(int,times_times(int,W,Z1),times_times(int,W,Z2))))).
1.86/2.06	tff('47', plain,
1.86/2.06	    ![X174 : int, X175 : int, X176 : int]:
1.86/2.06	      times_times(int, X174, minus_minus(int, X175, X176))
1.86/2.06	       = minus_minus(int, times_times(int, X174, X175), 
1.86/2.06	           times_times(int, X174, X176)),
1.86/2.06	    inference('cnf', [status(esa)], [fact_86_int__distrib_I4_J])).
1.86/2.06	tff('48', plain,
1.86/2.06	    ![X0 : int, X1 : int]:
1.86/2.06	      times_times(int, X1, minus_minus(int, X0, X0))
1.86/2.06	       = times_times(int, minus_minus(int, X1, X1), X0),
1.86/2.06	    inference('sup+', [status(thm)], ['36', '47'])).
1.86/2.06	tff(arity_Int_Oint___Groups_Ocomm__monoid__mult, axiom,
1.86/2.06	  (comm_monoid_mult(int))).
1.86/2.06	tff('49', plain, comm_monoid_mult(int),
1.86/2.06	    inference('cnf', [status(esa)],
1.86/2.06	              [arity_Int_Oint___Groups_Ocomm__monoid__mult])).
1.86/2.06	tff(fact_75_mult_Ocomm__neutral, axiom,
1.86/2.06	  (![A:$tType]:
1.86/2.06	     (comm_monoid_mult(A) => (![A1:A]: (times_times(A,A1,one_one(A)) = A1))))).
1.86/2.06	tff('50', plain,
1.86/2.06	    ![X143 : $tType, X144 : X143]:
1.86/2.06	      (times_times(X143, X144, one_one(X143)) = X144
1.86/2.06	       | ~ comm_monoid_mult(X143)),
1.86/2.06	    inference('cnf', [status(esa)], [fact_75_mult_Ocomm__neutral])).
1.86/2.06	tff('51', plain,
1.86/2.06	    ![X0 : int]: (~ $true | times_times(int, X0, one_one(int)) = X0),
1.86/2.06	    inference('sup-', [status(thm)], ['49', '50'])).
1.86/2.06	tff('52', plain,
1.86/2.06	    ![X0 : int]: (~ $true | times_times(int, X0, bit1(pls)) = X0),
1.86/2.06	    inference('demod', [status(thm)], ['51', '20'])).
1.86/2.06	tff('53', plain, ![X0 : int]: times_times(int, X0, bit1(pls)) = X0,
1.86/2.06	    inference('simplify', [status(thm)], ['52'])).
1.86/2.06	tff('54', plain,
1.86/2.06	    ![X0 : int, X1 : int]:
1.86/2.06	      times_times(int, X0, minus_minus(int, X1, bit1(pls)))
1.86/2.06	       = minus_minus(int, times_times(int, X0, X1), X0),
1.86/2.06	    inference('sup+', [status(thm)], ['53', '47'])).
1.86/2.06	tff(fact_42_diff__bin__simps_I1_J, axiom,
1.86/2.06	  (![K:int]: (minus_minus(int,K,pls) = K))).
1.86/2.06	tff('55', plain, ![X64 : int]: minus_minus(int, X64, pls) = X64,
1.86/2.06	    inference('cnf', [status(esa)], [fact_42_diff__bin__simps_I1_J])).
1.86/2.06	tff(fact_6_diff__bin__simps_I4_J, axiom,
1.86/2.06	  (![L:int]: (minus_minus(int,pls,bit1(L)) = bit1(minus_minus(int,min,L))))).
1.86/2.06	tff('56', plain,
1.86/2.06	    ![X8 : int]:
1.86/2.06	      minus_minus(int, pls, bit1(X8)) = bit1(minus_minus(int, min, X8)),
1.86/2.06	    inference('cnf', [status(esa)], [fact_6_diff__bin__simps_I4_J])).
1.86/2.06	tff('57', plain, minus_minus(int, pls, bit1(pls)) = bit1(min),
1.86/2.06	    inference('sup+', [status(thm)], ['55', '56'])).
1.86/2.06	tff(fact_26_Bit1__Min, axiom, (bit1(min) = min)).
1.86/2.06	tff('58', plain, bit1(min) = min,
1.86/2.06	    inference('cnf', [status(esa)], [fact_26_Bit1__Min])).
1.86/2.06	tff('59', plain, minus_minus(int, pls, bit1(pls)) = min,
1.86/2.06	    inference('demod', [status(thm)], ['57', '58'])).
1.86/2.06	tff('60', plain,
1.86/2.06	    ![X0 : int]: plus_plus(int, X0, min) = minus_minus(int, X0, bit1(pls)),
1.86/2.06	    inference('sup+', [status(thm)], ['59', '16'])).
1.86/2.06	tff('61', plain,
1.86/2.06	    ![X0 : int, X1 : int]:
1.86/2.06	      times_times(int, X0, plus_plus(int, X1, min))
1.86/2.06	       = minus_minus(int, times_times(int, X0, X1), X0),
1.86/2.06	    inference('demod', [status(thm)], ['54', '60'])).
1.86/2.06	tff('62', plain,
1.86/2.06	    ![X0 : int]:
1.86/2.06	      times_times(int, X0, plus_plus(int, bit1(pls), min))
1.86/2.06	       = minus_minus(int, X0, X0),
1.86/2.06	    inference('sup+', [status(thm)], ['53', '61'])).
1.86/2.06	tff('63', plain,
1.86/2.06	    ![X0 : int, X1 : int]:
1.86/2.06	      times_times(int, X1, 
1.86/2.06	        times_times(int, X0, plus_plus(int, bit1(pls), min)))
1.86/2.06	       = times_times(int, X1, 
1.86/2.06	           times_times(int, plus_plus(int, bit1(pls), min), X0)),
1.86/2.06	    inference('demod', [status(thm)], ['48', '62', '62', '25'])).
1.86/2.06	tff('64', plain,
1.86/2.06	    ![X0 : int]:
1.86/2.06	      times_times(int, X0, 
1.86/2.06	        times_times(int, pls, plus_plus(int, bit1(pls), min)))
1.86/2.06	       = times_times(int, X0, 
1.86/2.06	           times_times(int, plus_plus(int, pls, min), pls)),
1.86/2.06	    inference('sup+', [status(thm)], ['46', '63'])).
1.86/2.06	tff('65', plain,
1.86/2.06	    ![X0 : int]:
1.86/2.06	      times_times(int, X0, pls)
1.86/2.06	       = times_times(int, X0, times_times(int, min, pls)),
1.86/2.06	    inference('demod', [status(thm)], ['64', '32', '33'])).
1.86/2.06	tff('66', plain,
1.86/2.06	    times_times(int, bit1(pls), pls) = times_times(int, min, pls),
1.86/2.06	    inference('sup+', [status(thm)], ['34', '65'])).
1.86/2.06	tff('67', plain, pls = times_times(int, min, pls),
1.86/2.06	    inference('demod', [status(thm)], ['66', '34'])).
1.86/2.06	tff('68', plain,
1.86/2.06	    times_times(int, min, plus_plus(int, pls, min))
1.86/2.06	     = minus_minus(int, pls, min),
1.86/2.06	    inference('sup+', [status(thm)], ['67', '61'])).
1.86/2.06	tff('69', plain, times_times(int, min, min) = minus_minus(int, pls, min),
1.86/2.06	    inference('demod', [status(thm)], ['68', '33'])).
1.86/2.06	tff('70', plain, bit1(pls) = minus_minus(int, pls, min),
1.86/2.06	    inference('demod', [status(thm)], ['69', '21'])).
1.86/2.06	tff('71', plain,
1.86/2.06	    ![X0 : int]: plus_plus(int, X0, bit1(pls)) = minus_minus(int, X0, min),
1.86/2.06	    inference('sup+', [status(thm)], ['70', '16'])).
1.86/2.06	tff('72', plain,
1.86/2.06	    ![X0 : int]: times_times(int, min, X0) = minus_minus(int, pls, X0),
1.86/2.06	    inference('demod', [status(thm)], ['38', '71', '33', '34'])).
1.86/2.06	tff('73', plain,
1.86/2.06	    ![X0 : int, X1 : int]:
1.86/2.06	      plus_plus(int, X0, times_times(int, min, X1))
1.86/2.06	       = minus_minus(int, X0, X1),
1.86/2.06	    inference('demod', [status(thm)], ['16', '72'])).
1.86/2.06	tff('74', plain,
1.86/2.06	    plus_plus(int, times_times(int, s, s), bit1(pls))
1.86/2.06	     != plus_plus(int, times_times(int, s, s), bit1(pls)),
1.86/2.06	    inference('demod', [status(thm)],
1.86/2.06	              ['0', '1', '9', '7', '73', '21', '1', '9', '20'])).
1.86/2.06	tff('75', plain, $false, inference('simplify', [status(thm)], ['74'])).
1.86/2.06	
1.86/2.06	% SZS output end Refutation
1.86/2.06	EOF
