TSTP Solution File: GRP704+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP704+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:41:59 EDT 2023
% Result : Theorem 93.85s 75.33s
% Output : CNFRefutation 94.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 28
% Syntax : Number of formulae : 178 ( 161 unt; 14 typ; 0 def)
% Number of atoms : 169 ( 166 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 22 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 228 (; 228 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ rd > mult > ld > #nlpp > unit > op_f > op_e > op_d > op_c > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(ld,type,
ld: ( $i * $i ) > $i ).
tff(op_f,type,
op_f: $i ).
tff(rd,type,
rd: ( $i * $i ) > $i ).
tff(op_e,type,
op_e: $i ).
tff(op_c,type,
op_c: $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(unit,type,
unit: $i ).
tff(op_d,type,
op_d: $i ).
tff(mult,type,
mult: ( $i * $i ) > $i ).
tff(f_30,axiom,
! [B,A] : ( ld(A,mult(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
tff(f_28,axiom,
! [B,A] : ( mult(A,ld(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
tff(f_34,axiom,
! [B,A] : ( rd(mult(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
tff(f_48,axiom,
! [A] : ( op_d = ld(A,mult(op_c,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f11) ).
tff(f_36,axiom,
! [A] : ( mult(A,unit) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
tff(f_38,axiom,
! [A] : ( mult(unit,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
tff(f_52,axiom,
! [B,A] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f13) ).
tff(f_46,axiom,
! [B,A] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f10) ).
tff(f_32,axiom,
! [B,A] : ( mult(rd(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
tff(f_50,axiom,
! [B,A] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f12) ).
tff(f_40,axiom,
! [C,B,A] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
tff(f_44,axiom,
! [B,A] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).
tff(f_42,axiom,
! [B,A] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
tff(f_59,negated_conjecture,
~ ! [X4,X5] :
( ( mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5) )
& ( mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f) )
& ( mult(X4,mult(op_f,X5)) = mult(mult(X4,op_f),X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(c_4,plain,
! [A_4,B_3] : ( ld(A_4,mult(A_4,B_3)) = B_3 ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_898,plain,
! [A_59,B_60] : ( mult(A_59,ld(A_59,B_60)) = B_60 ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_8,plain,
! [A_8,B_7] : ( rd(mult(A_8,B_7),B_7) = A_8 ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_904,plain,
! [B_60,A_59] : ( rd(B_60,ld(A_59,B_60)) = A_59 ),
inference(superposition,[status(thm),theory(equality)],[c_898,c_8]) ).
tff(c_72,plain,
! [A_28,B_29] : ( ld(A_28,mult(A_28,B_29)) = B_29 ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_22,plain,
! [A_20] : ( ld(A_20,mult(op_c,A_20)) = op_d ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_79,plain,
op_d = op_c,
inference(superposition,[status(thm),theory(equality)],[c_72,c_22]) ).
tff(c_999,plain,
! [A_65] : ( ld(A_65,mult(op_c,A_65)) = op_c ),
inference(demodulation,[status(thm),theory(equality)],[c_79,c_22]) ).
tff(c_2,plain,
! [A_2,B_1] : ( mult(A_2,ld(A_2,B_1)) = B_1 ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_1007,plain,
! [A_65] : ( mult(op_c,A_65) = mult(A_65,op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_999,c_2]) ).
tff(c_10,plain,
! [A_9] : ( mult(A_9,unit) = A_9 ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_89,plain,
! [A_9] : ( ld(A_9,A_9) = unit ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_72]) ).
tff(c_12,plain,
! [A_10] : ( mult(unit,A_10) = A_10 ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_192521,plain,
! [A_759,B_760] : ( mult(A_759,mult(B_760,ld(mult(A_759,B_760),op_c))) = op_f ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_192559,plain,
! [B_760] : ( mult(B_760,ld(mult(unit,B_760),op_c)) = op_f ),
inference(superposition,[status(thm),theory(equality)],[c_192521,c_12]) ).
tff(c_192630,plain,
op_f = op_c,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12,c_192559]) ).
tff(c_26,plain,
! [A_24,B_23] : ( mult(A_24,mult(B_23,ld(mult(A_24,B_23),op_c))) = op_f ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_192914,plain,
! [A_766,B_767] : ( mult(A_766,mult(B_767,ld(mult(A_766,B_767),op_c))) = op_c ),
inference(demodulation,[status(thm),theory(equality)],[c_192630,c_26]) ).
tff(c_192412,plain,
! [A_757,B_758] : ( mult(mult(A_757,op_c),B_758) = mult(A_757,mult(op_c,B_758)) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_192452,plain,
! [A_757,B_758] : ( ld(mult(A_757,op_c),mult(A_757,mult(op_c,B_758))) = B_758 ),
inference(superposition,[status(thm),theory(equality)],[c_192412,c_4]) ).
tff(c_192923,plain,
! [B_767,A_757] : ( mult(B_767,ld(mult(op_c,B_767),op_c)) = ld(mult(A_757,op_c),mult(A_757,op_c)) ),
inference(superposition,[status(thm),theory(equality)],[c_192914,c_192452]) ).
tff(c_193058,plain,
! [B_768] : ( mult(B_768,ld(mult(op_c,B_768),op_c)) = unit ),
inference(demodulation,[status(thm),theory(equality)],[c_89,c_192923]) ).
tff(c_193422,plain,
! [B_772] : ( ld(mult(op_c,B_772),op_c) = ld(B_772,unit) ),
inference(superposition,[status(thm),theory(equality)],[c_193058,c_4]) ).
tff(c_193945,plain,
! [A_779] : ( ld(mult(A_779,op_c),op_c) = ld(A_779,unit) ),
inference(superposition,[status(thm),theory(equality)],[c_1007,c_193422]) ).
tff(c_192650,plain,
! [A_24,B_23] : ( mult(A_24,mult(B_23,ld(mult(A_24,B_23),op_c))) = op_c ),
inference(demodulation,[status(thm),theory(equality)],[c_192630,c_26]) ).
tff(c_194846,plain,
! [A_790] : ( mult(A_790,mult(op_c,ld(A_790,unit))) = op_c ),
inference(superposition,[status(thm),theory(equality)],[c_193945,c_192650]) ).
tff(c_194914,plain,
! [A_790] : ( mult(op_c,ld(A_790,unit)) = ld(A_790,op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_194846,c_4]) ).
tff(c_1136,plain,
! [B_69] : ( ld(ld(op_c,B_69),B_69) = op_c ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_999]) ).
tff(c_1144,plain,
! [B_69] : ( mult(ld(op_c,B_69),op_c) = B_69 ),
inference(superposition,[status(thm),theory(equality)],[c_1136,c_2]) ).
tff(c_936,plain,
! [A_61,B_62] : ( mult(rd(A_61,B_62),B_62) = A_61 ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_945,plain,
! [A_61,B_62] : ( ld(rd(A_61,B_62),A_61) = B_62 ),
inference(superposition,[status(thm),theory(equality)],[c_936,c_4]) ).
tff(c_193216,plain,
! [B_770] : ( mult(ld(op_c,B_770),ld(B_770,op_c)) = unit ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_193058]) ).
tff(c_194088,plain,
! [B_781] : ( mult(ld(op_c,rd(op_c,B_781)),B_781) = unit ),
inference(superposition,[status(thm),theory(equality)],[c_945,c_193216]) ).
tff(c_194105,plain,
! [B_758] : ( ld(mult(ld(op_c,rd(op_c,mult(op_c,B_758))),op_c),unit) = B_758 ),
inference(superposition,[status(thm),theory(equality)],[c_194088,c_192452]) ).
tff(c_194663,plain,
! [B_787] : ( ld(rd(op_c,mult(op_c,B_787)),unit) = B_787 ),
inference(demodulation,[status(thm),theory(equality)],[c_1144,c_194105]) ).
tff(c_194681,plain,
! [B_787] : ( rd(op_c,mult(op_c,B_787)) = rd(unit,B_787) ),
inference(superposition,[status(thm),theory(equality)],[c_194663,c_904]) ).
tff(c_1141,plain,
! [B_69] : ( rd(B_69,op_c) = ld(op_c,B_69) ),
inference(superposition,[status(thm),theory(equality)],[c_1136,c_904]) ).
tff(c_193441,plain,
! [B_772] : ( mult(mult(op_c,B_772),ld(B_772,unit)) = op_c ),
inference(superposition,[status(thm),theory(equality)],[c_193422,c_2]) ).
tff(c_6,plain,
! [A_6,B_5] : ( mult(rd(A_6,B_5),B_5) = A_6 ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_192301,plain,
! [A_755,B_756] : ( mult(mult(rd(op_c,mult(A_755,B_756)),B_756),A_755) = op_e ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_192335,plain,
! [B_756] : ( mult(rd(op_c,mult(unit,B_756)),B_756) = op_e ),
inference(superposition,[status(thm),theory(equality)],[c_192301,c_10]) ).
tff(c_192396,plain,
op_e = op_c,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_12,c_192335]) ).
tff(c_192328,plain,
! [A_755,B_756] : ( mult(rd(op_c,mult(A_755,B_756)),B_756) = rd(op_e,A_755) ),
inference(superposition,[status(thm),theory(equality)],[c_192301,c_8]) ).
tff(c_196514,plain,
! [A_806,B_807] : ( mult(rd(op_c,mult(A_806,B_807)),B_807) = rd(op_c,A_806) ),
inference(demodulation,[status(thm),theory(equality)],[c_192396,c_192328]) ).
tff(c_196637,plain,
! [B_772] : ( mult(rd(op_c,op_c),ld(B_772,unit)) = rd(op_c,mult(op_c,B_772)) ),
inference(superposition,[status(thm),theory(equality)],[c_193441,c_196514]) ).
tff(c_196709,plain,
! [B_772] : ( rd(unit,B_772) = ld(B_772,unit) ),
inference(demodulation,[status(thm),theory(equality)],[c_194681,c_12,c_89,c_1141,c_196637]) ).
tff(c_194018,plain,
! [B_780] : ( rd(op_c,ld(B_780,unit)) = mult(op_c,B_780) ),
inference(superposition,[status(thm),theory(equality)],[c_193422,c_904]) ).
tff(c_194041,plain,
! [B_62] : ( mult(op_c,rd(unit,B_62)) = rd(op_c,B_62) ),
inference(superposition,[status(thm),theory(equality)],[c_945,c_194018]) ).
tff(c_196727,plain,
! [B_62] : ( mult(op_c,ld(B_62,unit)) = rd(op_c,B_62) ),
inference(demodulation,[status(thm),theory(equality)],[c_196709,c_194041]) ).
tff(c_196802,plain,
! [B_809] : ( rd(op_c,B_809) = ld(B_809,op_c) ),
inference(demodulation,[status(thm),theory(equality)],[c_194914,c_196727]) ).
tff(c_196858,plain,
! [A_59] : ( ld(ld(A_59,op_c),op_c) = A_59 ),
inference(superposition,[status(thm),theory(equality)],[c_904,c_196802]) ).
tff(c_192555,plain,
! [B_760,A_759] : ( mult(B_760,ld(mult(A_759,B_760),op_c)) = ld(A_759,op_f) ),
inference(superposition,[status(thm),theory(equality)],[c_192521,c_4]) ).
tff(c_206109,plain,
! [B_877,A_878] : ( mult(B_877,ld(mult(A_878,B_877),op_c)) = ld(A_878,op_c) ),
inference(demodulation,[status(thm),theory(equality)],[c_192630,c_192555]) ).
tff(c_206415,plain,
! [B_5,A_6] : ( mult(B_5,ld(A_6,op_c)) = ld(rd(A_6,B_5),op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_206109]) ).
tff(c_210712,plain,
! [B_905,A_906] : ( mult(B_905,ld(A_906,op_c)) = ld(rd(A_906,B_905),op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_206109]) ).
tff(c_196729,plain,
! [B_62] : ( rd(op_c,B_62) = ld(B_62,op_c) ),
inference(demodulation,[status(thm),theory(equality)],[c_194914,c_196727]) ).
tff(c_192331,plain,
! [A_755,B_756] : ( ld(mult(rd(op_c,mult(A_755,B_756)),B_756),op_e) = A_755 ),
inference(superposition,[status(thm),theory(equality)],[c_192301,c_4]) ).
tff(c_201206,plain,
! [A_755,B_756] : ( ld(mult(ld(mult(A_755,B_756),op_c),B_756),op_c) = A_755 ),
inference(demodulation,[status(thm),theory(equality)],[c_196729,c_192396,c_192331]) ).
tff(c_210806,plain,
! [A_906,B_905] : ( ld(mult(ld(ld(rd(A_906,B_905),op_c),op_c),ld(A_906,op_c)),op_c) = B_905 ),
inference(superposition,[status(thm),theory(equality)],[c_210712,c_201206]) ).
tff(c_211167,plain,
! [A_907,B_908] : ( rd(A_907,rd(A_907,B_908)) = B_908 ),
inference(demodulation,[status(thm),theory(equality)],[c_196858,c_206415,c_196858,c_210806]) ).
tff(c_211303,plain,
! [B_60,A_59] : ( rd(B_60,A_59) = ld(A_59,B_60) ),
inference(superposition,[status(thm),theory(equality)],[c_904,c_211167]) ).
tff(c_212390,plain,
! [B_916,A_917] : ( mult(ld(B_916,A_917),B_916) = A_917 ),
inference(demodulation,[status(thm),theory(equality)],[c_211303,c_6]) ).
tff(c_212679,plain,
! [B_3,A_4] : ( mult(B_3,A_4) = mult(A_4,B_3) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_212390]) ).
tff(c_192666,plain,
! [A_761,B_762,C_763] : ( mult(mult(mult(A_761,B_762),B_762),C_763) = mult(A_761,mult(B_762,mult(B_762,C_763))) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_192794,plain,
! [A_761,B_762] : ( mult(A_761,mult(B_762,mult(B_762,unit))) = mult(mult(A_761,B_762),B_762) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_192666]) ).
tff(c_192815,plain,
! [A_761,B_762] : ( mult(mult(A_761,B_762),B_762) = mult(A_761,mult(B_762,B_762)) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_192794]) ).
tff(c_14,plain,
! [A_13,B_12,C_11] : ( mult(mult(mult(A_13,B_12),B_12),C_11) = mult(A_13,mult(B_12,mult(B_12,C_11))) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_194481,plain,
! [A_13,B_12,C_11] : ( mult(mult(A_13,mult(B_12,B_12)),C_11) = mult(A_13,mult(B_12,mult(B_12,C_11))) ),
inference(demodulation,[status(thm),theory(equality)],[c_192815,c_14]) ).
tff(c_18,plain,
! [A_17,B_16] : ( mult(mult(A_17,B_16),op_c) = mult(A_17,mult(B_16,op_c)) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_1004,plain,
! [A_65] : ( rd(mult(op_c,A_65),op_c) = A_65 ),
inference(superposition,[status(thm),theory(equality)],[c_999,c_904]) ).
tff(c_16,plain,
! [A_15,B_14] : ( mult(mult(op_c,A_15),B_14) = mult(op_c,mult(A_15,B_14)) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_192215,plain,
! [A_753,B_754] : ( mult(mult(A_753,B_754),op_c) = mult(A_753,mult(B_754,op_c)) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_200657,plain,
! [A_844,B_845] : ( rd(mult(A_844,mult(B_845,op_c)),op_c) = mult(A_844,B_845) ),
inference(superposition,[status(thm),theory(equality)],[c_192215,c_8]) ).
tff(c_200778,plain,
! [A_15,B_845] : ( rd(mult(op_c,mult(A_15,mult(B_845,op_c))),op_c) = mult(mult(op_c,A_15),B_845) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_200657]) ).
tff(c_200828,plain,
! [A_15,B_845] : ( mult(op_c,mult(A_15,B_845)) = mult(A_15,mult(B_845,op_c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_1004,c_16,c_200778]) ).
tff(c_1283,plain,
! [A_73,B_74] : ( mult(mult(op_c,A_73),B_74) = mult(op_c,mult(A_73,B_74)) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_198839,plain,
! [B_829,B_830] : ( mult(op_c,mult(ld(op_c,B_829),B_830)) = mult(B_829,B_830) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1283]) ).
tff(c_242691,plain,
! [B_1079,B_1080] : ( mult(ld(op_c,B_1079),B_1080) = ld(op_c,mult(B_1079,B_1080)) ),
inference(superposition,[status(thm),theory(equality)],[c_198839,c_4]) ).
tff(c_244731,plain,
! [B_1088,B_1089] : ( rd(ld(op_c,mult(B_1088,B_1089)),B_1089) = ld(op_c,B_1088) ),
inference(superposition,[status(thm),theory(equality)],[c_242691,c_8]) ).
tff(c_244765,plain,
! [A_15,B_845] : ( rd(ld(op_c,mult(op_c,mult(A_15,B_845))),mult(B_845,op_c)) = ld(op_c,A_15) ),
inference(superposition,[status(thm),theory(equality)],[c_200828,c_244731]) ).
tff(c_412382,plain,
! [B_1523,A_1524] : ( ld(mult(B_1523,op_c),mult(A_1524,B_1523)) = ld(op_c,A_1524) ),
inference(demodulation,[status(thm),theory(equality)],[c_211303,c_4,c_244765]) ).
tff(c_192277,plain,
! [A_2,B_1] : ( mult(A_2,mult(ld(A_2,B_1),op_c)) = mult(B_1,op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_192215]) ).
tff(c_230044,plain,
! [A_1017,B_1018] : ( mult(A_1017,mult(op_c,ld(A_1017,B_1018))) = mult(B_1018,op_c) ),
inference(demodulation,[status(thm),theory(equality)],[c_1007,c_192277]) ).
tff(c_269188,plain,
! [A_1183,B_1184] : ( ld(mult(A_1183,op_c),mult(B_1184,op_c)) = ld(A_1183,B_1184) ),
inference(superposition,[status(thm),theory(equality)],[c_230044,c_192452]) ).
tff(c_269310,plain,
! [A_1183,B_1184] : ( mult(mult(A_1183,op_c),ld(A_1183,B_1184)) = mult(B_1184,op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_269188,c_2]) ).
tff(c_412530,plain,
! [B_1523,A_1524] : ( mult(mult(mult(B_1523,op_c),op_c),ld(op_c,A_1524)) = mult(mult(A_1524,B_1523),op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_412382,c_269310]) ).
tff(c_413340,plain,
! [B_1523,A_1524] : ( mult(B_1523,mult(op_c,A_1524)) = mult(A_1524,mult(B_1523,op_c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_194481,c_18,c_18,c_412530]) ).
tff(c_95,plain,
! [A_30,B_31] : ( rd(mult(A_30,B_31),B_31) = A_30 ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_104,plain,
! [A_9] : ( rd(A_9,unit) = A_9 ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_95]) ).
tff(c_1810,plain,
! [A_84,B_85] : ( mult(mult(rd(op_c,mult(A_84,B_85)),B_85),A_84) = op_e ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_1852,plain,
! [B_85] : ( mult(rd(op_c,mult(unit,B_85)),B_85) = op_e ),
inference(superposition,[status(thm),theory(equality)],[c_1810,c_10]) ).
tff(c_1914,plain,
op_e = op_c,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_12,c_1852]) ).
tff(c_24,plain,
! [A_22,B_21] : ( mult(mult(rd(op_c,mult(A_22,B_21)),B_21),A_22) = op_e ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_2190,plain,
! [A_91,B_92] : ( mult(mult(rd(op_c,mult(A_91,B_92)),B_92),A_91) = op_c ),
inference(demodulation,[status(thm),theory(equality)],[c_1914,c_24]) ).
tff(c_1084,plain,
! [A_68] : ( mult(op_c,A_68) = mult(A_68,op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_999,c_2]) ).
tff(c_1109,plain,
! [A_68] : ( ld(op_c,mult(A_68,op_c)) = A_68 ),
inference(superposition,[status(thm),theory(equality)],[c_1084,c_4]) ).
tff(c_2225,plain,
! [B_92] : ( mult(rd(op_c,mult(op_c,B_92)),B_92) = ld(op_c,op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_2190,c_1109]) ).
tff(c_2346,plain,
! [B_93] : ( mult(rd(op_c,mult(op_c,B_93)),B_93) = unit ),
inference(demodulation,[status(thm),theory(equality)],[c_89,c_2225]) ).
tff(c_2630,plain,
! [B_97] : ( mult(rd(op_c,B_97),ld(op_c,B_97)) = unit ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_2346]) ).
tff(c_1934,plain,
! [A_22,B_21] : ( mult(mult(rd(op_c,mult(A_22,B_21)),B_21),A_22) = op_c ),
inference(demodulation,[status(thm),theory(equality)],[c_1914,c_24]) ).
tff(c_2635,plain,
! [B_97] : ( mult(mult(rd(op_c,unit),ld(op_c,B_97)),rd(op_c,B_97)) = op_c ),
inference(superposition,[status(thm),theory(equality)],[c_2630,c_1934]) ).
tff(c_2700,plain,
! [B_98] : ( mult(B_98,rd(op_c,B_98)) = op_c ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_104,c_2635]) ).
tff(c_2749,plain,
! [B_98] : ( rd(op_c,B_98) = ld(B_98,op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_2700,c_4]) ).
tff(c_2746,plain,
! [B_98] : ( rd(op_c,rd(op_c,B_98)) = B_98 ),
inference(superposition,[status(thm),theory(equality)],[c_2700,c_8]) ).
tff(c_2999,plain,
! [B_98] : ( ld(ld(B_98,op_c),op_c) = B_98 ),
inference(demodulation,[status(thm),theory(equality)],[c_2749,c_2749,c_2746]) ).
tff(c_1845,plain,
! [A_84,B_85] : ( mult(rd(op_c,mult(A_84,B_85)),B_85) = rd(op_e,A_84) ),
inference(superposition,[status(thm),theory(equality)],[c_1810,c_8]) ).
tff(c_4683,plain,
! [A_84,B_85] : ( mult(ld(mult(A_84,B_85),op_c),B_85) = ld(A_84,op_c) ),
inference(demodulation,[status(thm),theory(equality)],[c_2749,c_2749,c_1914,c_1845]) ).
tff(c_1521,plain,
! [A_78,B_79] : ( mult(A_78,mult(B_79,ld(mult(A_78,B_79),op_c))) = op_f ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_1552,plain,
! [B_79] : ( mult(B_79,ld(mult(unit,B_79),op_c)) = op_f ),
inference(superposition,[status(thm),theory(equality)],[c_1521,c_12]) ).
tff(c_1604,plain,
op_f = op_c,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12,c_1552]) ).
tff(c_1548,plain,
! [B_79,A_78] : ( mult(B_79,ld(mult(A_78,B_79),op_c)) = ld(A_78,op_f) ),
inference(superposition,[status(thm),theory(equality)],[c_1521,c_4]) ).
tff(c_10358,plain,
! [B_169,A_170] : ( mult(B_169,ld(mult(A_170,B_169),op_c)) = ld(A_170,op_c) ),
inference(demodulation,[status(thm),theory(equality)],[c_1604,c_1548]) ).
tff(c_10536,plain,
! [B_85,A_84] : ( mult(B_85,ld(ld(A_84,op_c),op_c)) = ld(ld(mult(A_84,B_85),op_c),op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_4683,c_10358]) ).
tff(c_10642,plain,
! [B_85,A_84] : ( mult(B_85,A_84) = mult(A_84,B_85) ),
inference(demodulation,[status(thm),theory(equality)],[c_2999,c_2999,c_10536]) ).
tff(c_1719,plain,
! [A_82,B_83] : ( mult(mult(A_82,B_83),op_c) = mult(A_82,mult(B_83,op_c)) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_7609,plain,
! [A_147,B_148] : ( rd(mult(A_147,mult(B_148,op_c)),op_c) = mult(A_147,B_148) ),
inference(superposition,[status(thm),theory(equality)],[c_1719,c_8]) ).
tff(c_7715,plain,
! [A_15,B_148] : ( rd(mult(op_c,mult(A_15,mult(B_148,op_c))),op_c) = mult(mult(op_c,A_15),B_148) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_7609]) ).
tff(c_45761,plain,
! [A_366,B_367] : ( mult(op_c,mult(A_366,B_367)) = mult(A_366,mult(B_367,op_c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_1004,c_7715]) ).
tff(c_1300,plain,
! [A_73,B_74] : ( ld(mult(op_c,A_73),mult(op_c,mult(A_73,B_74))) = B_74 ),
inference(superposition,[status(thm),theory(equality)],[c_1283,c_4]) ).
tff(c_60713,plain,
! [A_427,B_428] : ( ld(mult(op_c,A_427),mult(A_427,mult(B_428,op_c))) = B_428 ),
inference(superposition,[status(thm),theory(equality)],[c_45761,c_1300]) ).
tff(c_85681,plain,
! [A_510,B_511] : ( mult(mult(op_c,A_510),B_511) = mult(A_510,mult(B_511,op_c)) ),
inference(superposition,[status(thm),theory(equality)],[c_60713,c_2]) ).
tff(c_86543,plain,
! [B_85,A_510] : ( mult(B_85,mult(op_c,A_510)) = mult(A_510,mult(B_85,op_c)) ),
inference(superposition,[status(thm),theory(equality)],[c_10642,c_85681]) ).
tff(c_7762,plain,
! [A_15,B_148] : ( mult(op_c,mult(A_15,B_148)) = mult(A_15,mult(B_148,op_c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_1004,c_7715]) ).
tff(c_20,plain,
! [A_19,B_18] : ( mult(mult(A_19,op_c),B_18) = mult(A_19,mult(op_c,B_18)) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_292,plain,
! [A_42] : ( ld(A_42,mult(op_c,A_42)) = op_c ),
inference(demodulation,[status(thm),theory(equality)],[c_79,c_22]) ).
tff(c_300,plain,
! [A_42] : ( mult(op_c,A_42) = mult(A_42,op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_292,c_2]) ).
tff(c_529,plain,
! [A_49,B_50] : ( mult(A_49,mult(B_50,ld(mult(A_49,B_50),op_c))) = op_f ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_552,plain,
! [B_50] : ( mult(B_50,ld(mult(unit,B_50),op_c)) = op_f ),
inference(superposition,[status(thm),theory(equality)],[c_529,c_12]) ).
tff(c_586,plain,
op_f = op_c,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12,c_552]) ).
tff(c_28,plain,
( ( mult(mult(op_f,'#skF_5'),'#skF_6') != mult(op_f,mult('#skF_5','#skF_6')) )
| ( mult(mult('#skF_3','#skF_4'),op_f) != mult('#skF_3',mult('#skF_4',op_f)) )
| ( mult(mult('#skF_1',op_f),'#skF_2') != mult('#skF_1',mult(op_f,'#skF_2')) ) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_136,plain,
mult(mult('#skF_1',op_f),'#skF_2') != mult('#skF_1',mult(op_f,'#skF_2')),
inference(splitLeft,[status(thm)],[c_28]) ).
tff(c_593,plain,
mult(mult('#skF_1',op_c),'#skF_2') != mult('#skF_1',mult(op_c,'#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_586,c_586,c_136]) ).
tff(c_594,plain,
mult(mult('#skF_1',op_c),'#skF_2') != mult('#skF_1',mult('#skF_2',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_300,c_593]) ).
tff(c_838,plain,
mult('#skF_1',mult(op_c,'#skF_2')) != mult('#skF_1',mult('#skF_2',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_594]) ).
tff(c_841,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_300,c_838]) ).
tff(c_842,plain,
( ( mult(mult('#skF_3','#skF_4'),op_f) != mult('#skF_3',mult('#skF_4',op_f)) )
| ( mult(mult(op_f,'#skF_5'),'#skF_6') != mult(op_f,mult('#skF_5','#skF_6')) ) ),
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_1450,plain,
mult(mult(op_f,'#skF_5'),'#skF_6') != mult(op_f,mult('#skF_5','#skF_6')),
inference(splitLeft,[status(thm)],[c_842]) ).
tff(c_1620,plain,
mult(mult('#skF_5',op_c),'#skF_6') != mult(op_c,mult('#skF_5','#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_1604,c_1007,c_1604,c_1450]) ).
tff(c_1626,plain,
mult(op_c,mult('#skF_5','#skF_6')) != mult('#skF_5',mult(op_c,'#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_1620]) ).
tff(c_1627,plain,
mult(op_c,mult('#skF_5','#skF_6')) != mult('#skF_5',mult('#skF_6',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_1007,c_1626]) ).
tff(c_10655,plain,
mult(op_c,mult('#skF_6','#skF_5')) != mult('#skF_5',mult('#skF_6',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_10642,c_1627]) ).
tff(c_177001,plain,
mult('#skF_5',mult('#skF_6',op_c)) != mult('#skF_6',mult('#skF_5',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_7762,c_10655]) ).
tff(c_192128,plain,
mult('#skF_6',mult(op_c,'#skF_5')) != mult('#skF_6',mult('#skF_5',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_86543,c_177001]) ).
tff(c_192132,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10642,c_192128]) ).
tff(c_192133,plain,
mult(mult('#skF_3','#skF_4'),op_f) != mult('#skF_3',mult('#skF_4',op_f)),
inference(splitRight,[status(thm)],[c_842]) ).
tff(c_192651,plain,
mult(mult('#skF_3','#skF_4'),op_c) != mult('#skF_3',mult('#skF_4',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_192630,c_192630,c_192133]) ).
tff(c_192655,plain,
mult(op_c,mult('#skF_3','#skF_4')) != mult('#skF_3',mult('#skF_4',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_1007,c_192651]) ).
tff(c_213818,plain,
mult(op_c,mult('#skF_4','#skF_3')) != mult('#skF_3',mult('#skF_4',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_212679,c_192655]) ).
tff(c_241558,plain,
mult('#skF_3',mult('#skF_4',op_c)) != mult('#skF_4',mult('#skF_3',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_200828,c_213818]) ).
tff(c_426763,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_212679,c_413340,c_241558]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP704+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 22:57:11 EDT 2023
% 0.14/0.35 % CPUTime :
% 93.85/75.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 93.85/75.35
% 93.85/75.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 94.06/75.40
% 94.06/75.40 Inference rules
% 94.06/75.40 ----------------------
% 94.06/75.40 #Ref : 0
% 94.06/75.40 #Sup : 101629
% 94.06/75.40 #Fact : 0
% 94.06/75.40 #Define : 0
% 94.06/75.40 #Split : 2
% 94.06/75.40 #Chain : 0
% 94.06/75.40 #Close : 0
% 94.06/75.40
% 94.06/75.40 Ordering : KBO
% 94.06/75.40
% 94.06/75.40 Simplification rules
% 94.06/75.40 ----------------------
% 94.06/75.40 #Subsume : 5888
% 94.06/75.40 #Demod : 205747
% 94.06/75.40 #Tautology : 42741
% 94.06/75.40 #SimpNegUnit : 0
% 94.06/75.40 #BackRed : 223
% 94.06/75.40
% 94.06/75.40 #Partial instantiations: 0
% 94.06/75.40 #Strategies tried : 1
% 94.06/75.40
% 94.06/75.40 Timing (in seconds)
% 94.06/75.40 ----------------------
% 94.06/75.40 Preprocessing : 0.47
% 94.06/75.40 Parsing : 0.26
% 94.06/75.40 CNF conversion : 0.03
% 94.06/75.40 Main loop : 73.81
% 94.06/75.40 Inferencing : 5.67
% 94.06/75.40 Reduction : 52.10
% 94.06/75.40 Demodulation : 49.99
% 94.06/75.40 BG Simplification : 0.73
% 94.06/75.40 Subsumption : 10.73
% 94.06/75.41 Abstraction : 1.53
% 94.06/75.41 MUC search : 0.00
% 94.06/75.41 Cooper : 0.00
% 94.06/75.41 Total : 74.37
% 94.06/75.41 Index Insertion : 0.00
% 94.06/75.41 Index Deletion : 0.00
% 94.06/75.41 Index Matching : 0.00
% 94.06/75.41 BG Taut test : 0.00
%------------------------------------------------------------------------------