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_int
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify int \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n107.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 07:53:24 CST 2018
31.08/31.25	% done 15369 iterations in 31.046s
31.08/31.25	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
31.08/31.25	% SZS output start Refutation
31.08/31.26	tff(fact_15_diff__bin__simps_I10_J, axiom,
31.08/31.26	  (![L1:int,K:int]:
31.08/31.26	     (minus_minus(int,bit1(K),bit1(L1)) = bit0(minus_minus(int,K,L1))))).
31.08/31.26	tff('0', plain,
31.08/31.26	    ![X17 : int, X18 : int]:
31.08/31.26	      minus_minus(int, bit1(X17), bit1(X18))
31.08/31.26	       = bit0(minus_minus(int, X17, X18)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_15_diff__bin__simps_I10_J])).
31.08/31.26	tff(fact_63_zle__diff1__eq, axiom,
31.08/31.26	  (![Z1:int,W1:int]:
31.08/31.26	     (ord_less_eq(int,W1,minus_minus(int,Z1,one_one(int))) <=>
31.08/31.26	      ord_less(int,W1,Z1)))).
31.08/31.26	tff('1', plain,
31.08/31.26	    ![X136 : int, X137 : int]:
31.08/31.26	      (ord_less_eq(int, X137, minus_minus(int, X136, one_one(int)))
31.08/31.26	       | ~ ord_less(int, X137, X136)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_63_zle__diff1__eq])).
31.08/31.26	tff(fact_90_number__of__is__id, axiom,
31.08/31.26	  (![K:int]: (number_number_of(int,K) = K))).
31.08/31.26	tff('2', plain, ![X196 : int]: number_number_of(int, X196) = X196,
31.08/31.26	    inference('cnf', [status(esa)], [fact_90_number__of__is__id])).
31.08/31.26	tff(fact_10_numeral__1__eq__1, axiom,
31.08/31.26	  (![A:$tType]:
31.08/31.26	     (number_ring(A) => (number_number_of(A,bit1(pls)) = one_one(A))))).
31.08/31.26	tff('3', plain,
31.08/31.26	    ![X13 : $tType]:
31.08/31.26	      (number_number_of(X13, bit1(pls)) = one_one(X13) | ~ number_ring(X13)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_10_numeral__1__eq__1])).
31.08/31.26	tff('4', plain, (bit1(pls) = one_one(int) | ~ number_ring(int)),
31.08/31.26	    inference('sup+', [status(thm)], ['2', '3'])).
31.08/31.26	tff(arity_Int_Oint___Int_Onumber__ring, axiom, (number_ring(int))).
31.08/31.26	tff('5', plain, number_ring(int),
31.08/31.26	    inference('cnf', [status(esa)], [arity_Int_Oint___Int_Onumber__ring])).
31.08/31.26	tff('6', plain, (bit1(pls) = one_one(int) | ~ $true),
31.08/31.26	    inference('demod', [status(thm)], ['4', '5'])).
31.08/31.26	tff('7', plain, bit1(pls) = one_one(int),
31.08/31.26	    inference('simplify', [status(thm)], ['6'])).
31.08/31.26	tff('8', plain,
31.08/31.26	    ![X136 : int, X137 : int]:
31.08/31.26	      (ord_less_eq(int, X137, minus_minus(int, X136, bit1(pls)))
31.08/31.26	       | ~ ord_less(int, X137, X136)),
31.08/31.26	    inference('demod', [status(thm)], ['1', '7'])).
31.08/31.26	tff('9', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      (ord_less_eq(int, X1, bit0(minus_minus(int, X0, pls)))
31.08/31.26	       | ~ ord_less(int, X1, bit1(X0))),
31.08/31.26	    inference('sup+', [status(thm)], ['0', '8'])).
31.08/31.26	tff(fact_46_add__number__of__left, axiom,
31.08/31.26	  (![A:$tType]:
31.08/31.26	     (number_ring(A) =>
31.08/31.26	      (![Z:A,W:int,V1:int]:
31.08/31.26	         (plus_plus(A,number_number_of(A,V1),
31.08/31.26	                    plus_plus(A,number_number_of(A,W),Z)) =
31.08/31.26	          plus_plus(A,number_number_of(A,plus_plus(int,V1,W)),Z)))))).
31.08/31.26	tff('10', plain,
31.08/31.26	    ![X93 : $tType, X94 : int, X95 : int, X96 : X93]:
31.08/31.26	      (plus_plus(X93, number_number_of(X93, X94), 
31.08/31.26	         plus_plus(X93, number_number_of(X93, X95), X96))
31.08/31.26	        = plus_plus(X93, number_number_of(X93, plus_plus(int, X94, X95)), 
31.08/31.26	            X96)
31.08/31.26	       | ~ number_ring(X93)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_46_add__number__of__left])).
31.08/31.26	tff('11', plain,
31.08/31.26	    ![X0 : int, X1 : int, X2 : int]:
31.08/31.26	      (plus_plus(int, X0, plus_plus(int, number_number_of(int, X2), X1))
31.08/31.26	        = plus_plus(int, number_number_of(int, plus_plus(int, X0, X2)), X1)
31.08/31.26	       | ~ number_ring(int)),
31.08/31.26	    inference('sup+', [status(thm)], ['2', '10'])).
31.08/31.26	tff('12', plain,
31.08/31.26	    ![X0 : int, X1 : int, X2 : int]:
31.08/31.26	      (plus_plus(int, X0, plus_plus(int, X2, X1))
31.08/31.26	        = plus_plus(int, plus_plus(int, X0, X2), X1)
31.08/31.26	       | ~ $true),
31.08/31.26	    inference('demod', [status(thm)], ['11', '2', '2', '5'])).
31.08/31.26	tff('13', plain,
31.08/31.26	    ![X0 : int, X1 : int, X2 : int]:
31.08/31.26	      plus_plus(int, X0, plus_plus(int, X2, X1))
31.08/31.26	       = plus_plus(int, plus_plus(int, X0, X2), X1),
31.08/31.26	    inference('simplify', [status(thm)], ['12'])).
31.08/31.26	tff(fact_97_number__of__Bit0, axiom,
31.08/31.26	  (![A:$tType]:
31.08/31.26	     (number_ring(A) =>
31.08/31.26	      (![W:int]:
31.08/31.26	         (number_number_of(A,bit0(W)) =
31.08/31.26	          plus_plus(A,plus_plus(A,zero_zero(A),number_number_of(A,W)),
31.08/31.26	                    number_number_of(A,W))))))).
31.08/31.26	tff('14', plain,
31.08/31.26	    ![X206 : $tType, X207 : int]:
31.08/31.26	      (number_number_of(X206, bit0(X207))
31.08/31.26	        = plus_plus(X206, 
31.08/31.26	            plus_plus(X206, zero_zero(X206), number_number_of(X206, X207)), 
31.08/31.26	            number_number_of(X206, X207))
31.08/31.26	       | ~ number_ring(X206)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_97_number__of__Bit0])).
31.08/31.26	tff('15', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      (number_number_of(int, bit0(X0))
31.08/31.26	        = plus_plus(int, zero_zero(int), 
31.08/31.26	            plus_plus(int, number_number_of(int, X0), 
31.08/31.26	              number_number_of(int, X0)))
31.08/31.26	       | ~ number_ring(int)),
31.08/31.26	    inference('sup+', [status(thm)], ['13', '14'])).
31.08/31.26	tff(fact_83_Pls__def, axiom, (pls = zero_zero(int))).
31.08/31.26	tff('16', plain, pls = zero_zero(int),
31.08/31.26	    inference('cnf', [status(esa)], [fact_83_Pls__def])).
31.08/31.26	tff('17', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      (bit0(X0) = plus_plus(int, pls, plus_plus(int, X0, X0)) | ~ $true),
31.08/31.26	    inference('demod', [status(thm)], ['15', '2', '16', '2', '2', '5'])).
31.08/31.26	tff('18', plain,
31.08/31.26	    ![X0 : int]: bit0(X0) = plus_plus(int, pls, plus_plus(int, X0, X0)),
31.08/31.26	    inference('simplify', [status(thm)], ['17'])).
31.08/31.26	tff(fact_26_Bit0__Pls, axiom, (bit0(pls) = pls)).
31.08/31.26	tff('19', plain, bit0(pls) = pls,
31.08/31.26	    inference('cnf', [status(esa)], [fact_26_Bit0__Pls])).
31.08/31.26	tff(fact_57_add__Bit0__Bit1, axiom,
31.08/31.26	  (![L1:int,K:int]:
31.08/31.26	     (plus_plus(int,bit0(K),bit1(L1)) = bit1(plus_plus(int,K,L1))))).
31.08/31.26	tff('20', plain,
31.08/31.26	    ![X120 : int, X121 : int]:
31.08/31.26	      plus_plus(int, bit0(X120), bit1(X121))
31.08/31.26	       = bit1(plus_plus(int, X120, X121)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_57_add__Bit0__Bit1])).
31.08/31.26	tff('21', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      plus_plus(int, pls, bit1(X0)) = bit1(plus_plus(int, pls, X0)),
31.08/31.26	    inference('sup+', [status(thm)], ['19', '20'])).
31.08/31.26	tff(fact_19_double__eq__0__iff, axiom,
31.08/31.26	  (![A:$tType]:
31.08/31.26	     (linord219039673up_add(A) =>
31.08/31.26	      (![A1:A]: ((plus_plus(A,A1,A1) = zero_zero(A)) <=> (A1 = zero_zero(A))))))).
31.08/31.26	tff('22', plain,
31.08/31.26	    ![X29 : $tType, X30 : X29]:
31.08/31.26	      (X30 != zero_zero(X29)
31.08/31.26	       | plus_plus(X29, X30, X30) = zero_zero(X29)
31.08/31.26	       | ~ linord219039673up_add(X29)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_19_double__eq__0__iff])).
31.08/31.26	tff('23', plain,
31.08/31.26	    ![X29 : $tType]:
31.08/31.26	      (~ linord219039673up_add(X29)
31.08/31.26	       | plus_plus(X29, zero_zero(X29), zero_zero(X29)) = zero_zero(X29)),
31.08/31.26	    inference('simplify', [status(thm)], ['22'])).
31.08/31.26	tff('24', plain,
31.08/31.26	    (plus_plus(int, pls, zero_zero(int)) = zero_zero(int)
31.08/31.26	     | ~ linord219039673up_add(int)),
31.08/31.26	    inference('sup+', [status(thm)], ['16', '23'])).
31.08/31.26	tff(arity_Int_Oint___Groups_Olinordered__ab__group__add, axiom,
31.08/31.26	  (linord219039673up_add(int))).
31.08/31.26	tff('25', plain, linord219039673up_add(int),
31.08/31.26	    inference('cnf', [status(esa)],
31.08/31.26	              [arity_Int_Oint___Groups_Olinordered__ab__group__add])).
31.08/31.26	tff('26', plain, (plus_plus(int, pls, pls) = pls | ~ $true),
31.08/31.26	    inference('demod', [status(thm)], ['24', '16', '16', '25'])).
31.08/31.26	tff('27', plain, plus_plus(int, pls, pls) = pls,
31.08/31.26	    inference('simplify', [status(thm)], ['26'])).
31.08/31.26	tff(fact_56_add__Bit1__Bit0, axiom,
31.08/31.26	  (![L1:int,K:int]:
31.08/31.26	     (plus_plus(int,bit1(K),bit0(L1)) = bit1(plus_plus(int,K,L1))))).
31.08/31.26	tff('28', plain,
31.08/31.26	    ![X118 : int, X119 : int]:
31.08/31.26	      plus_plus(int, bit1(X118), bit0(X119))
31.08/31.26	       = bit1(plus_plus(int, X118, X119)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_56_add__Bit1__Bit0])).
31.08/31.26	tff('29', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      plus_plus(int, bit1(X0), pls) = bit1(plus_plus(int, X0, pls)),
31.08/31.26	    inference('sup+', [status(thm)], ['19', '28'])).
31.08/31.26	tff('30', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      plus_plus(int, bit1(X0), plus_plus(int, pls, X1))
31.08/31.26	       = plus_plus(int, bit1(plus_plus(int, X0, pls)), X1),
31.08/31.26	    inference('sup+', [status(thm)], ['29', '13'])).
31.08/31.26	tff('31', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      plus_plus(int, bit1(pls), plus_plus(int, pls, X0))
31.08/31.26	       = plus_plus(int, bit1(pls), X0),
31.08/31.26	    inference('sup+', [status(thm)], ['27', '30'])).
31.08/31.26	tff('32', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      plus_plus(int, bit1(pls), bit1(plus_plus(int, pls, X0)))
31.08/31.26	       = plus_plus(int, bit1(pls), bit1(X0)),
31.08/31.26	    inference('sup+', [status(thm)], ['21', '31'])).
31.08/31.26	tff(fact_4_add__special_I2_J, axiom,
31.08/31.26	  (![A:$tType]:
31.08/31.26	     (number_ring(A) =>
31.08/31.26	      (![W:int]:
31.08/31.26	         (plus_plus(A,one_one(A),number_number_of(A,W)) =
31.08/31.26	          number_number_of(A,plus_plus(int,bit1(pls),W))))))).
31.08/31.26	tff('33', plain,
31.08/31.26	    ![X0 : $tType, X1 : int]:
31.08/31.26	      (plus_plus(X0, one_one(X0), number_number_of(X0, X1))
31.08/31.26	        = number_number_of(X0, plus_plus(int, bit1(pls), X1))
31.08/31.26	       | ~ number_ring(X0)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_4_add__special_I2_J])).
31.08/31.26	tff('34', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      (plus_plus(int, one_one(int), X0)
31.08/31.26	        = number_number_of(int, plus_plus(int, bit1(pls), X0))
31.08/31.26	       | ~ number_ring(int)),
31.08/31.26	    inference('sup+', [status(thm)], ['2', '33'])).
31.08/31.26	tff('35', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      (plus_plus(int, one_one(int), X0) = plus_plus(int, bit1(pls), X0)
31.08/31.26	       | ~ $true),
31.08/31.26	    inference('demod', [status(thm)], ['34', '2', '5'])).
31.08/31.26	tff('36', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      plus_plus(int, one_one(int), X0) = plus_plus(int, bit1(pls), X0),
31.08/31.26	    inference('simplify', [status(thm)], ['35'])).
31.08/31.26	tff(fact_8_one__add__one__is__two, axiom,
31.08/31.26	  (![A:$tType]:
31.08/31.26	     (number_ring(A) =>
31.08/31.26	      (plus_plus(A,one_one(A),one_one(A)) =
31.08/31.26	       number_number_of(A,bit0(bit1(pls))))))).
31.08/31.26	tff('37', plain,
31.08/31.26	    ![X10 : $tType]:
31.08/31.26	      (plus_plus(X10, one_one(X10), one_one(X10))
31.08/31.26	        = number_number_of(X10, bit0(bit1(pls)))
31.08/31.26	       | ~ number_ring(X10)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_8_one__add__one__is__two])).
31.08/31.26	tff('38', plain,
31.08/31.26	    (plus_plus(int, bit1(pls), one_one(int))
31.08/31.26	      = number_number_of(int, bit0(bit1(pls)))
31.08/31.26	     | ~ number_ring(int)),
31.08/31.26	    inference('sup+', [status(thm)], ['36', '37'])).
31.08/31.26	tff(fact_5_add__special_I3_J, axiom,
31.08/31.26	  (![A:$tType]:
31.08/31.26	     (number_ring(A) =>
31.08/31.26	      (![V1:int]:
31.08/31.26	         (plus_plus(A,number_number_of(A,V1),one_one(A)) =
31.08/31.26	          number_number_of(A,plus_plus(int,V1,bit1(pls)))))))).
31.08/31.26	tff('39', plain,
31.08/31.26	    ![X2 : $tType, X3 : int]:
31.08/31.26	      (plus_plus(X2, number_number_of(X2, X3), one_one(X2))
31.08/31.26	        = number_number_of(X2, plus_plus(int, X3, bit1(pls)))
31.08/31.26	       | ~ number_ring(X2)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_5_add__special_I3_J])).
31.08/31.26	tff('40', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      (plus_plus(int, X0, one_one(int))
31.08/31.26	        = number_number_of(int, plus_plus(int, X0, bit1(pls)))
31.08/31.26	       | ~ number_ring(int)),
31.08/31.26	    inference('sup+', [status(thm)], ['2', '39'])).
31.08/31.26	tff('41', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      (plus_plus(int, X0, one_one(int)) = plus_plus(int, X0, bit1(pls))
31.08/31.26	       | ~ $true),
31.08/31.26	    inference('demod', [status(thm)], ['40', '2', '5'])).
31.08/31.26	tff('42', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      plus_plus(int, X0, one_one(int)) = plus_plus(int, X0, bit1(pls)),
31.08/31.26	    inference('simplify', [status(thm)], ['41'])).
31.08/31.26	tff('43', plain,
31.08/31.26	    (plus_plus(int, bit1(pls), bit1(pls)) = bit0(bit1(pls)) | ~ $true),
31.08/31.26	    inference('demod', [status(thm)], ['38', '42', '2', '5'])).
31.08/31.26	tff('44', plain, plus_plus(int, bit1(pls), bit1(pls)) = bit0(bit1(pls)),
31.08/31.26	    inference('simplify', [status(thm)], ['43'])).
31.08/31.26	tff('45', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      plus_plus(int, bit1(pls), plus_plus(int, bit1(pls), X0))
31.08/31.26	       = plus_plus(int, bit0(bit1(pls)), X0),
31.08/31.26	    inference('sup+', [status(thm)], ['44', '13'])).
31.08/31.26	tff('46', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      plus_plus(int, bit1(pls), bit1(plus_plus(int, pls, X0)))
31.08/31.26	       = plus_plus(int, bit0(bit1(pls)), bit0(X0)),
31.08/31.26	    inference('sup+', [status(thm)], ['28', '45'])).
31.08/31.26	tff(fact_35_add__Bit0__Bit0, axiom,
31.08/31.26	  (![L1:int,K:int]:
31.08/31.26	     (plus_plus(int,bit0(K),bit0(L1)) = bit0(plus_plus(int,K,L1))))).
31.08/31.26	tff('47', plain,
31.08/31.26	    ![X57 : int, X58 : int]:
31.08/31.26	      plus_plus(int, bit0(X57), bit0(X58)) = bit0(plus_plus(int, X57, X58)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_35_add__Bit0__Bit0])).
31.08/31.26	tff('48', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      plus_plus(int, bit1(pls), bit1(plus_plus(int, pls, X0)))
31.08/31.26	       = bit0(plus_plus(int, bit1(pls), X0)),
31.08/31.26	    inference('demod', [status(thm)], ['46', '47'])).
31.08/31.26	tff('49', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      plus_plus(int, bit1(pls), bit1(X0))
31.08/31.26	       = bit0(plus_plus(int, bit1(pls), X0)),
31.08/31.26	    inference('sup+', [status(thm)], ['32', '48'])).
31.08/31.26	tff(fact_38_right__distrib__number__of, axiom,
31.08/31.26	  (![B:$tType]:
31.08/31.26	     ((semiring(B) & number(B)) =>
31.08/31.26	      (![C:B,B1:B,V1:int]:
31.08/31.26	         (times_times(B,number_number_of(B,V1),plus_plus(B,B1,C)) =
31.08/31.26	          plus_plus(B,times_times(B,number_number_of(B,V1),B1),
31.08/31.26	                    times_times(B,number_number_of(B,V1),C))))))).
31.08/31.26	tff('50', plain,
31.08/31.26	    ![X65 : $tType, X66 : int, X67 : X65, X68 : X65]:
31.08/31.26	      (times_times(X65, number_number_of(X65, X66), plus_plus(X65, X67, X68))
31.08/31.26	        = plus_plus(X65, times_times(X65, number_number_of(X65, X66), X67), 
31.08/31.26	            times_times(X65, number_number_of(X65, X66), X68))
31.08/31.26	       | ~ number(X65)
31.08/31.26	       | ~ semiring(X65)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_38_right__distrib__number__of])).
31.08/31.26	tff(fact_37_left__distrib__number__of, axiom,
31.08/31.26	  (![B:$tType]:
31.08/31.26	     ((semiring(B) & number(B)) =>
31.08/31.26	      (![V1:int,B1:B,A2:B]:
31.08/31.26	         (times_times(B,plus_plus(B,A2,B1),number_number_of(B,V1)) =
31.08/31.26	          plus_plus(B,times_times(B,A2,number_number_of(B,V1)),
31.08/31.26	                    times_times(B,B1,number_number_of(B,V1)))))))).
31.08/31.26	tff('51', plain,
31.08/31.26	    ![X61 : $tType, X62 : X61, X63 : int, X64 : X61]:
31.08/31.26	      (times_times(X61, plus_plus(X61, X62, X64), number_number_of(X61, X63))
31.08/31.26	        = plus_plus(X61, times_times(X61, X62, number_number_of(X61, X63)), 
31.08/31.26	            times_times(X61, X64, number_number_of(X61, X63)))
31.08/31.26	       | ~ number(X61)
31.08/31.26	       | ~ semiring(X61)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_37_left__distrib__number__of])).
31.08/31.26	tff('52', plain,
31.08/31.26	    ![X0 : int, X1 : int, X2 : int]:
31.08/31.26	      (times_times(int, plus_plus(int, X2, X1), number_number_of(int, X0))
31.08/31.26	        = plus_plus(int, times_times(int, X2, X0), 
31.08/31.26	            times_times(int, X1, number_number_of(int, X0)))
31.08/31.26	       | ~ semiring(int)
31.08/31.26	       | ~ number(int)),
31.08/31.26	    inference('sup+', [status(thm)], ['2', '51'])).
31.08/31.26	tff(arity_Int_Oint___Rings_Osemiring, axiom, (semiring(int))).
31.08/31.26	tff('53', plain, semiring(int),
31.08/31.26	    inference('cnf', [status(esa)], [arity_Int_Oint___Rings_Osemiring])).
31.08/31.26	tff(arity_Int_Oint___Int_Onumber, axiom, (number(int))).
31.08/31.26	tff('54', plain, number(int),
31.08/31.26	    inference('cnf', [status(esa)], [arity_Int_Oint___Int_Onumber])).
31.08/31.26	tff('55', plain,
31.08/31.26	    ![X0 : int, X1 : int, X2 : int]:
31.08/31.26	      (times_times(int, plus_plus(int, X2, X1), X0)
31.08/31.26	        = plus_plus(int, times_times(int, X2, X0), times_times(int, X1, X0))
31.08/31.26	       | ~ $true
31.08/31.26	       | ~ $true),
31.08/31.26	    inference('demod', [status(thm)], ['52', '2', '2', '53', '54'])).
31.08/31.26	tff('56', plain,
31.08/31.26	    ![X0 : int, X1 : int, X2 : int]:
31.08/31.26	      times_times(int, plus_plus(int, X2, X1), X0)
31.08/31.26	       = plus_plus(int, times_times(int, X2, X0), times_times(int, X1, X0)),
31.08/31.26	    inference('simplify', [status(thm)], ['55'])).
31.08/31.26	tff('57', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      (times_times(int, 
31.08/31.26	         plus_plus(int, number_number_of(int, X1), number_number_of(int, X1)), 
31.08/31.26	         X0)
31.08/31.26	        = times_times(int, number_number_of(int, X1), plus_plus(int, X0, X0))
31.08/31.26	       | ~ semiring(int)
31.08/31.26	       | ~ number(int)),
31.08/31.26	    inference('sup+', [status(thm)], ['50', '56'])).
31.08/31.26	tff('58', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      (times_times(int, plus_plus(int, X1, X1), X0)
31.08/31.26	        = times_times(int, X1, plus_plus(int, X0, X0))
31.08/31.26	       | ~ $true
31.08/31.26	       | ~ $true),
31.08/31.26	    inference('demod', [status(thm)], ['57', '2', '2', '2', '53', '54'])).
31.08/31.26	tff('59', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      times_times(int, plus_plus(int, X1, X1), X0)
31.08/31.26	       = times_times(int, X1, plus_plus(int, X0, X0)),
31.08/31.26	    inference('simplify', [status(thm)], ['58'])).
31.08/31.26	tff('60', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      times_times(int, bit0(plus_plus(int, bit1(pls), pls)), X0)
31.08/31.26	       = times_times(int, bit1(pls), plus_plus(int, X0, X0)),
31.08/31.26	    inference('sup+', [status(thm)], ['49', '59'])).
31.08/31.26	tff(fact_34_mult__Bit0, axiom,
31.08/31.26	  (![L1:int,K:int]:
31.08/31.26	     (times_times(int,bit0(K),L1) = bit0(times_times(int,K,L1))))).
31.08/31.26	tff('61', plain,
31.08/31.26	    ![X55 : int, X56 : int]:
31.08/31.26	      times_times(int, bit0(X55), X56) = bit0(times_times(int, X55, X56)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_34_mult__Bit0])).
31.08/31.26	tff(fact_33_mult__Pls, axiom, (![W:int]: (times_times(int,pls,W) = pls))).
31.08/31.26	tff('62', plain, ![X54 : int]: times_times(int, pls, X54) = pls,
31.08/31.26	    inference('cnf', [status(esa)], [fact_33_mult__Pls])).
31.08/31.26	tff(fact_9_mult__Bit1, axiom,
31.08/31.26	  (![L1:int,K:int]:
31.08/31.26	     (times_times(int,bit1(K),L1) =
31.08/31.26	      plus_plus(int,bit0(times_times(int,K,L1)),L1)))).
31.08/31.26	tff('63', plain,
31.08/31.26	    ![X11 : int, X12 : int]:
31.08/31.26	      times_times(int, bit1(X11), X12)
31.08/31.26	       = plus_plus(int, bit0(times_times(int, X11, X12)), X12),
31.08/31.26	    inference('cnf', [status(esa)], [fact_9_mult__Bit1])).
31.08/31.26	tff('64', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      times_times(int, bit1(pls), X0) = plus_plus(int, bit0(pls), X0),
31.08/31.26	    inference('sup+', [status(thm)], ['62', '63'])).
31.08/31.26	tff('65', plain,
31.08/31.26	    ![X0 : int]: times_times(int, bit1(pls), X0) = plus_plus(int, pls, X0),
31.08/31.26	    inference('demod', [status(thm)], ['64', '19'])).
31.08/31.26	tff('66', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      bit0(plus_plus(int, pls, X0))
31.08/31.26	       = plus_plus(int, pls, plus_plus(int, X0, X0)),
31.08/31.26	    inference('demod', [status(thm)], ['60', '29', '27', '61', '65', '65'])).
31.08/31.26	tff('67', plain, ![X0 : int]: bit0(plus_plus(int, pls, X0)) = bit0(X0),
31.08/31.26	    inference('sup+', [status(thm)], ['18', '66'])).
31.08/31.26	tff(fact_36_diff__bin__simps_I7_J, axiom,
31.08/31.26	  (![L1:int,K:int]:
31.08/31.26	     (minus_minus(int,bit0(K),bit0(L1)) = bit0(minus_minus(int,K,L1))))).
31.08/31.26	tff('68', plain,
31.08/31.26	    ![X59 : int, X60 : int]:
31.08/31.26	      minus_minus(int, bit0(X59), bit0(X60))
31.08/31.26	       = bit0(minus_minus(int, X59, X60)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_36_diff__bin__simps_I7_J])).
31.08/31.26	tff('69', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      minus_minus(int, bit0(X0), pls) = bit0(minus_minus(int, X0, pls)),
31.08/31.26	    inference('sup+', [status(thm)], ['19', '68'])).
31.08/31.26	tff('70', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      minus_minus(int, bit0(X0), pls)
31.08/31.26	       = bit0(minus_minus(int, plus_plus(int, pls, X0), pls)),
31.08/31.26	    inference('sup+', [status(thm)], ['67', '69'])).
31.08/31.26	tff(fact_40_left__diff__distrib__number__of, axiom,
31.08/31.26	  (![B:$tType]:
31.08/31.26	     ((ring(B) & number(B)) =>
31.08/31.26	      (![V1:int,B1:B,A2:B]:
31.08/31.26	         (times_times(B,minus_minus(B,A2,B1),number_number_of(B,V1)) =
31.08/31.26	          minus_minus(B,times_times(B,A2,number_number_of(B,V1)),
31.08/31.26	                      times_times(B,B1,number_number_of(B,V1)))))))).
31.08/31.26	tff('71', plain,
31.08/31.26	    ![X70 : $tType, X71 : X70, X72 : int, X73 : X70]:
31.08/31.26	      (times_times(X70, minus_minus(X70, X71, X73), 
31.08/31.26	         number_number_of(X70, X72))
31.08/31.26	        = minus_minus(X70, 
31.08/31.26	            times_times(X70, X71, number_number_of(X70, X72)), 
31.08/31.26	            times_times(X70, X73, number_number_of(X70, X72)))
31.08/31.26	       | ~ number(X70)
31.08/31.26	       | ~ ring(X70)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_40_left__diff__distrib__number__of])).
31.08/31.26	tff('72', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      (times_times(int, minus_minus(int, X1, pls), number_number_of(int, X0))
31.08/31.26	        = minus_minus(int, times_times(int, X1, number_number_of(int, X0)), 
31.08/31.26	            pls)
31.08/31.26	       | ~ ring(int)
31.08/31.26	       | ~ number(int)),
31.08/31.26	    inference('sup+', [status(thm)], ['62', '71'])).
31.08/31.26	tff(arity_Int_Oint___Rings_Oring, axiom, (ring(int))).
31.08/31.26	tff('73', plain, ring(int),
31.08/31.26	    inference('cnf', [status(esa)], [arity_Int_Oint___Rings_Oring])).
31.08/31.26	tff('74', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      (times_times(int, minus_minus(int, X1, pls), X0)
31.08/31.26	        = minus_minus(int, times_times(int, X1, X0), pls)
31.08/31.26	       | ~ $true
31.08/31.26	       | ~ $true),
31.08/31.26	    inference('demod', [status(thm)], ['72', '2', '2', '73', '54'])).
31.08/31.26	tff('75', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      times_times(int, minus_minus(int, X1, pls), X0)
31.08/31.26	       = minus_minus(int, times_times(int, X1, X0), pls),
31.08/31.26	    inference('simplify', [status(thm)], ['74'])).
31.08/31.26	tff('76', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      times_times(int, minus_minus(int, bit1(pls), pls), X0)
31.08/31.26	       = minus_minus(int, plus_plus(int, pls, X0), pls),
31.08/31.26	    inference('sup+', [status(thm)], ['65', '75'])).
31.08/31.26	tff(fact_14_diff__bin__simps_I9_J, axiom,
31.08/31.26	  (![L1:int,K:int]:
31.08/31.26	     (minus_minus(int,bit1(K),bit0(L1)) = bit1(minus_minus(int,K,L1))))).
31.08/31.26	tff('77', plain,
31.08/31.26	    ![X15 : int, X16 : int]:
31.08/31.26	      minus_minus(int, bit1(X15), bit0(X16))
31.08/31.26	       = bit1(minus_minus(int, X15, X16)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_14_diff__bin__simps_I9_J])).
31.08/31.26	tff('78', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      minus_minus(int, bit1(X0), pls) = bit1(minus_minus(int, X0, pls)),
31.08/31.26	    inference('sup+', [status(thm)], ['19', '77'])).
31.08/31.26	tff('79', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      times_times(int, bit1(minus_minus(int, pls, pls)), X0)
31.08/31.26	       = minus_minus(int, plus_plus(int, pls, X0), pls),
31.08/31.26	    inference('demod', [status(thm)], ['76', '78'])).
31.08/31.26	tff('80', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      (times_times(int, minus_minus(int, pls, X1), number_number_of(int, X0))
31.08/31.26	        = minus_minus(int, pls, 
31.08/31.26	            times_times(int, X1, number_number_of(int, X0)))
31.08/31.26	       | ~ ring(int)
31.08/31.26	       | ~ number(int)),
31.08/31.26	    inference('sup+', [status(thm)], ['62', '71'])).
31.08/31.26	tff('81', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      (times_times(int, minus_minus(int, pls, X1), X0)
31.08/31.26	        = minus_minus(int, pls, times_times(int, X1, X0))
31.08/31.26	       | ~ $true
31.08/31.26	       | ~ $true),
31.08/31.26	    inference('demod', [status(thm)], ['80', '2', '2', '73', '54'])).
31.08/31.26	tff('82', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      times_times(int, minus_minus(int, pls, X1), X0)
31.08/31.26	       = minus_minus(int, pls, times_times(int, X1, X0)),
31.08/31.26	    inference('simplify', [status(thm)], ['81'])).
31.08/31.26	tff('83', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      times_times(int, minus_minus(int, pls, pls), X0)
31.08/31.26	       = minus_minus(int, pls, pls),
31.08/31.26	    inference('sup+', [status(thm)], ['62', '82'])).
31.08/31.26	tff('84', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      times_times(int, bit1(minus_minus(int, pls, pls)), X0)
31.08/31.26	       = plus_plus(int, bit0(minus_minus(int, pls, pls)), X0),
31.08/31.26	    inference('sup+', [status(thm)], ['83', '63'])).
31.08/31.26	tff(fact_13_diff__bin__simps_I3_J, axiom,
31.08/31.26	  (![L1:int]: (minus_minus(int,pls,bit0(L1)) = bit0(minus_minus(int,pls,L1))))).
31.08/31.26	tff('85', plain,
31.08/31.26	    ![X14 : int]:
31.08/31.26	      minus_minus(int, pls, bit0(X14)) = bit0(minus_minus(int, pls, X14)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_13_diff__bin__simps_I3_J])).
31.08/31.26	tff('86', plain,
31.08/31.26	    minus_minus(int, pls, pls) = bit0(minus_minus(int, pls, pls)),
31.08/31.26	    inference('sup+', [status(thm)], ['19', '85'])).
31.08/31.26	tff('87', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      times_times(int, bit1(minus_minus(int, pls, pls)), X0)
31.08/31.26	       = plus_plus(int, minus_minus(int, pls, pls), X0),
31.08/31.26	    inference('demod', [status(thm)], ['84', '86'])).
31.08/31.26	tff('88', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      minus_minus(int, plus_plus(int, pls, X0), pls)
31.08/31.26	       = plus_plus(int, minus_minus(int, pls, pls), X0),
31.08/31.26	    inference('sup+', [status(thm)], ['79', '87'])).
31.08/31.26	tff('89', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      bit0(minus_minus(int, X0, pls))
31.08/31.26	       = bit0(plus_plus(int, minus_minus(int, pls, pls), X0)),
31.08/31.26	    inference('demod', [status(thm)], ['70', '69', '88'])).
31.08/31.26	tff('90', plain,
31.08/31.26	    ![X0 : int, X1 : int, X2 : int]:
31.08/31.26	      (times_times(int, minus_minus(int, X2, X1), number_number_of(int, X0))
31.08/31.26	        = minus_minus(int, times_times(int, X2, X0), 
31.08/31.26	            times_times(int, X1, number_number_of(int, X0)))
31.08/31.26	       | ~ ring(int)
31.08/31.26	       | ~ number(int)),
31.08/31.26	    inference('sup+', [status(thm)], ['2', '71'])).
31.08/31.26	tff('91', plain,
31.08/31.26	    ![X0 : int, X1 : int, X2 : int]:
31.08/31.26	      (times_times(int, minus_minus(int, X2, X1), X0)
31.08/31.26	        = minus_minus(int, times_times(int, X2, X0), 
31.08/31.26	            times_times(int, X1, X0))
31.08/31.26	       | ~ $true
31.08/31.26	       | ~ $true),
31.08/31.26	    inference('demod', [status(thm)], ['90', '2', '2', '73', '54'])).
31.08/31.26	tff('92', plain,
31.08/31.26	    ![X0 : int, X1 : int, X2 : int]:
31.08/31.26	      times_times(int, minus_minus(int, X2, X1), X0)
31.08/31.26	       = minus_minus(int, times_times(int, X2, X0), times_times(int, X1, X0)),
31.08/31.26	    inference('simplify', [status(thm)], ['91'])).
31.08/31.26	tff(fact_39_number__of__Pls, axiom,
31.08/31.26	  (![A:$tType]: (number_ring(A) => (number_number_of(A,pls) = zero_zero(A))))).
31.08/31.26	tff('93', plain,
31.08/31.26	    ![X69 : $tType]:
31.08/31.26	      (number_number_of(X69, pls) = zero_zero(X69) | ~ number_ring(X69)),
31.08/31.26	    inference('cnf', [status(esa)], [fact_39_number__of__Pls])).
31.08/31.26	tff(fact_41_right__diff__distrib__number__of, axiom,
31.08/31.26	  (![B:$tType]:
31.08/31.26	     ((ring(B) & number(B)) =>
31.08/31.26	      (![C:B,B1:B,V1:int]:
31.08/31.26	         (times_times(B,number_number_of(B,V1),minus_minus(B,B1,C)) =
31.08/31.26	          minus_minus(B,times_times(B,number_number_of(B,V1),B1),
31.08/31.26	                      times_times(B,number_number_of(B,V1),C))))))).
31.08/31.26	tff('94', plain,
31.08/31.26	    ![X74 : $tType, X75 : int, X76 : X74, X77 : X74]:
31.08/31.26	      (times_times(X74, number_number_of(X74, X75), 
31.08/31.26	         minus_minus(X74, X76, X77))
31.08/31.26	        = minus_minus(X74, 
31.08/31.26	            times_times(X74, number_number_of(X74, X75), X76), 
31.08/31.26	            times_times(X74, number_number_of(X74, X75), X77))
31.08/31.26	       | ~ number(X74)
31.08/31.26	       | ~ ring(X74)),
31.08/31.26	    inference('cnf', [status(esa)],
31.08/31.26	              [fact_41_right__diff__distrib__number__of])).
31.08/31.26	tff('95', plain,
31.08/31.26	    ![X0 : $tType, X1 : X0, X2 : X0]:
31.08/31.26	      (times_times(X0, number_number_of(X0, pls), minus_minus(X0, X2, X1))
31.08/31.26	        = minus_minus(X0, times_times(X0, zero_zero(X0), X2), 
31.08/31.26	            times_times(X0, number_number_of(X0, pls), X1))
31.08/31.26	       | ~ number_ring(X0)
31.08/31.26	       | ~ ring(X0)
31.08/31.26	       | ~ number(X0)),
31.08/31.26	    inference('sup+', [status(thm)], ['93', '94'])).
31.08/31.26	tff('96', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      (times_times(int, number_number_of(int, pls), minus_minus(int, X0, X0))
31.08/31.26	        = times_times(int, 
31.08/31.26	            minus_minus(int, zero_zero(int), number_number_of(int, pls)), X0)
31.08/31.26	       | ~ number(int)
31.08/31.26	       | ~ ring(int)
31.08/31.26	       | ~ number_ring(int)),
31.08/31.26	    inference('sup+', [status(thm)], ['92', '95'])).
31.08/31.26	tff('97', plain,
31.08/31.26	    (pls = minus_minus(int, pls, pls) | ~ $true | ~ $true | ~ $true),
31.08/31.26	    inference('demod', [status(thm)],
31.08/31.26	              ['96', '2', '62', '16', '2', '83', '54', '73', '5'])).
31.08/31.26	tff('98', plain, pls = minus_minus(int, pls, pls),
31.08/31.26	    inference('simplify', [status(thm)], ['97'])).
31.08/31.26	tff('99', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      bit0(minus_minus(int, X0, pls)) = bit0(plus_plus(int, pls, X0)),
31.08/31.26	    inference('demod', [status(thm)], ['89', '98'])).
31.08/31.26	tff('100', plain, ![X0 : int]: bit0(minus_minus(int, X0, pls)) = bit0(X0),
31.08/31.26	    inference('demod', [status(thm)], ['99', '67'])).
31.08/31.26	tff('101', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      (ord_less_eq(int, X1, bit0(X0)) | ~ ord_less(int, X1, bit1(X0))),
31.08/31.26	    inference('demod', [status(thm)], ['9', '100'])).
31.08/31.26	tff(conj_0, conjecture,
31.08/31.26	  (ord_less_eq(int,s,
31.08/31.26	               minus_minus(int,
31.08/31.26	                           plus_plus(int,
31.08/31.26	                                     times_times(int,
31.08/31.26	                                                 number_number_of(int,
31.08/31.26	                                                                  bit0(
31.08/31.26	                                                                  bit0(
31.08/31.26	                                                                  bit1(pls)))),
31.08/31.26	                                                 m),
31.08/31.26	                                     one_one(int)),
31.08/31.26	                           one_one(int))))).
31.08/31.26	tff(zf_stmt_0, negated_conjecture,
31.08/31.26	  (~
31.08/31.26	    ord_less_eq(int,s,
31.08/31.26	                minus_minus(int,
31.08/31.26	                            plus_plus(int,
31.08/31.26	                                      times_times(int,
31.08/31.26	                                                  number_number_of(int,
31.08/31.26	                                                                   bit0(
31.08/31.26	                                                                   bit0(
31.08/31.26	                                                                   bit1(pls)))),
31.08/31.26	                                                  m),
31.08/31.26	                                      one_one(int)),
31.08/31.26	                            one_one(int))))).
31.08/31.26	tff('102', plain,
31.08/31.26	    ~ ord_less_eq(int, s, 
31.08/31.26	        minus_minus(int, 
31.08/31.26	          plus_plus(int, 
31.08/31.26	            times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), 
31.08/31.26	            one_one(int)), one_one(int))),
31.08/31.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
31.08/31.26	tff('103', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      plus_plus(int, bit0(X0), pls) = bit0(plus_plus(int, X0, pls)),
31.08/31.26	    inference('sup+', [status(thm)], ['19', '47'])).
31.08/31.26	tff('104', plain,
31.08/31.26	    ~ ord_less_eq(int, s, 
31.08/31.26	        minus_minus(int, 
31.08/31.26	          bit1(bit0(plus_plus(int, plus_plus(int, pls, m), pls))), 
31.08/31.26	          one_one(int))),
31.08/31.26	    inference('demod', [status(thm)],
31.08/31.26	              ['102', '2', '61', '61', '65', '42', '20', '103'])).
31.08/31.26	tff('105', plain,
31.08/31.26	    ~ ord_less_eq(int, s, 
31.08/31.26	        bit0(
31.08/31.26	          bit0(
31.08/31.26	            minus_minus(int, plus_plus(int, plus_plus(int, pls, m), pls), 
31.08/31.26	              pls)))),
31.08/31.26	    inference('demod', [status(thm)], ['104', '7', '0', '69'])).
31.08/31.26	tff('106', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      (times_times(int, plus_plus(int, pls, X1), number_number_of(int, X0))
31.08/31.26	        = plus_plus(int, pls, 
31.08/31.26	            times_times(int, X1, number_number_of(int, X0)))
31.08/31.26	       | ~ semiring(int)
31.08/31.26	       | ~ number(int)),
31.08/31.26	    inference('sup+', [status(thm)], ['62', '51'])).
31.08/31.26	tff('107', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      (times_times(int, plus_plus(int, pls, X1), X0)
31.08/31.26	        = plus_plus(int, pls, times_times(int, X1, X0))
31.08/31.26	       | ~ $true
31.08/31.26	       | ~ $true),
31.08/31.26	    inference('demod', [status(thm)], ['106', '2', '2', '53', '54'])).
31.08/31.26	tff('108', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      times_times(int, plus_plus(int, pls, X1), X0)
31.08/31.26	       = plus_plus(int, pls, times_times(int, X1, X0)),
31.08/31.26	    inference('simplify', [status(thm)], ['107'])).
31.08/31.26	tff('109', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      times_times(int, bit1(plus_plus(int, pls, X0)), X1)
31.08/31.26	       = plus_plus(int, pls, times_times(int, bit1(X0), X1)),
31.08/31.26	    inference('sup+', [status(thm)], ['21', '108'])).
31.08/31.26	tff('110', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      (times_times(int, plus_plus(int, X1, pls), number_number_of(int, X0))
31.08/31.26	        = plus_plus(int, times_times(int, X1, number_number_of(int, X0)), 
31.08/31.26	            pls)
31.08/31.26	       | ~ semiring(int)
31.08/31.26	       | ~ number(int)),
31.08/31.26	    inference('sup+', [status(thm)], ['62', '51'])).
31.08/31.26	tff('111', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      (times_times(int, plus_plus(int, X1, pls), X0)
31.08/31.26	        = plus_plus(int, times_times(int, X1, X0), pls)
31.08/31.26	       | ~ $true
31.08/31.26	       | ~ $true),
31.08/31.26	    inference('demod', [status(thm)], ['110', '2', '2', '53', '54'])).
31.08/31.26	tff('112', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      times_times(int, plus_plus(int, X1, pls), X0)
31.08/31.26	       = plus_plus(int, times_times(int, X1, X0), pls),
31.08/31.26	    inference('simplify', [status(thm)], ['111'])).
31.08/31.26	tff('113', plain,
31.08/31.26	    ![X0 : int, X1 : int]:
31.08/31.26	      times_times(int, bit1(plus_plus(int, X0, pls)), X1)
31.08/31.26	       = plus_plus(int, times_times(int, bit1(X0), X1), pls),
31.08/31.26	    inference('sup+', [status(thm)], ['29', '112'])).
31.08/31.26	tff('114', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      plus_plus(int, pls, times_times(int, bit1(pls), X0))
31.08/31.26	       = plus_plus(int, times_times(int, bit1(pls), X0), pls),
31.08/31.26	    inference('sup+', [status(thm)], ['109', '113'])).
31.08/31.26	tff('115', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      times_times(int, bit1(pls), X0)
31.08/31.26	       = plus_plus(int, pls, times_times(int, bit1(pls), X0)),
31.08/31.26	    inference('sup+', [status(thm)], ['27', '109'])).
31.08/31.26	tff('116', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      plus_plus(int, pls, X0) = plus_plus(int, pls, plus_plus(int, pls, X0)),
31.08/31.26	    inference('demod', [status(thm)], ['115', '65', '65'])).
31.08/31.26	tff('117', plain,
31.08/31.26	    ![X0 : int]:
31.08/31.26	      plus_plus(int, pls, X0) = plus_plus(int, plus_plus(int, pls, X0), pls),
31.08/31.26	    inference('demod', [status(thm)], ['114', '65', '116', '65'])).
31.08/31.26	tff('118', plain,
31.08/31.26	    ~ ord_less_eq(int, s, 
31.08/31.26	        bit0(bit0(minus_minus(int, plus_plus(int, pls, m), pls)))),
31.08/31.26	    inference('demod', [status(thm)], ['105', '117'])).
31.08/31.26	tff('119', plain,
31.08/31.26	    ~ ord_less_eq(int, s, 
31.08/31.26	        bit0(bit0(plus_plus(int, minus_minus(int, pls, pls), m)))),
31.08/31.26	    inference('demod', [status(thm)], ['118', '88'])).
31.08/31.26	tff('120', plain,
31.08/31.26	    ~ ord_less_eq(int, s, bit0(bit0(minus_minus(int, m, pls)))),
31.08/31.26	    inference('demod', [status(thm)], ['119', '89'])).
31.08/31.26	tff('121', plain, ~ ord_less_eq(int, s, bit0(bit0(m))),
31.08/31.26	    inference('demod', [status(thm)], ['120', '100'])).
31.08/31.26	tff('122', plain, (~ $true | ~ ord_less(int, s, bit1(bit0(m)))),
31.08/31.26	    inference('sup-', [status(thm)], ['101', '121'])).
31.08/31.26	tff(fact_0_s0p, axiom,
31.08/31.26	  (zcong(s1,s,
31.08/31.26	         plus_plus(int,
31.08/31.26	                   times_times(int,
31.08/31.26	                               number_number_of(int,bit0(bit0(bit1(pls)))),m),
31.08/31.26	                   one_one(int))) & 
31.08/31.26	   ord_less(int,s,
31.08/31.26	            plus_plus(int,
31.08/31.26	                      times_times(int,
31.08/31.26	                                  number_number_of(int,bit0(bit0(bit1(pls)))),
31.08/31.26	                                  m),
31.08/31.26	                      one_one(int))) & 
31.08/31.26	   ord_less_eq(int,zero_zero(int),s))).
31.08/31.26	tff('123', plain,
31.08/31.26	    ord_less(int, s, 
31.08/31.26	      plus_plus(int, 
31.08/31.26	        times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), 
31.08/31.26	        one_one(int))),
31.08/31.26	    inference('cnf', [status(esa)], [fact_0_s0p])).
31.08/31.26	tff('124', plain,
31.08/31.26	    ord_less(int, s, 
31.08/31.26	      plus_plus(int, times_times(int, bit0(bit0(bit1(pls))), m), 
31.08/31.26	        one_one(int))),
31.08/31.26	    inference('demod', [status(thm)], ['123', '2'])).
31.08/31.26	tff('125', plain,
31.08/31.26	    ord_less(int, s, bit1(bit0(plus_plus(int, plus_plus(int, pls, m), pls)))),
31.08/31.26	    inference('demod', [status(thm)],
31.08/31.26	              ['124', '61', '61', '65', '42', '20', '103'])).
31.08/31.26	tff('126', plain, ord_less(int, s, bit1(bit0(plus_plus(int, pls, m)))),
31.08/31.26	    inference('demod', [status(thm)], ['125', '117'])).
31.08/31.26	tff('127', plain, ord_less(int, s, bit1(bit0(m))),
31.08/31.26	    inference('demod', [status(thm)], ['126', '67'])).
31.08/31.26	tff('128', plain, (~ $true | ~ $true),
31.08/31.26	    inference('demod', [status(thm)], ['122', '127'])).
31.08/31.26	tff('129', plain, $false, inference('simplify', [status(thm)], ['128'])).
31.08/31.26	
31.08/31.26	% SZS output end Refutation
31.08/31.26	EOF
