TSTP Solution File: GRP703+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP703+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 : n020.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 10:41:58 EDT 2023
% Result : Theorem 134.87s 109.25s
% Output : CNFRefutation 134.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% 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 : 26 ( 21 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 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 : 230 (; 230 !; 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_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_36,axiom,
! [A] : ( mult(A,unit) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
tff(f_30,axiom,
! [B,A] : ( ld(A,mult(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
tff(f_48,axiom,
! [A] : ( op_d = ld(A,mult(op_c,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f11) ).
tff(f_32,axiom,
! [B,A] : ( mult(rd(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
tff(f_38,axiom,
! [A] : ( mult(unit,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
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_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_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_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_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_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_59,negated_conjecture,
~ ! [X2,X3] :
( ( mult(op_e,mult(X2,X3)) = mult(mult(op_e,X2),X3) )
& ( mult(X2,mult(X3,op_e)) = mult(mult(X2,X3),op_e) )
& ( mult(X2,mult(op_e,X3)) = mult(mult(X2,op_e),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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_1071,plain,
! [A_63,B_64] : ( mult(A_63,ld(A_63,B_64)) = B_64 ),
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_1077,plain,
! [B_64,A_63] : ( rd(B_64,ld(A_63,B_64)) = A_63 ),
inference(superposition,[status(thm),theory(equality)],[c_1071,c_8]) ).
tff(c_10,plain,
! [A_9] : ( mult(A_9,unit) = A_9 ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
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_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_1172,plain,
! [A_69] : ( ld(A_69,mult(op_c,A_69)) = op_c ),
inference(demodulation,[status(thm),theory(equality)],[c_79,c_22]) ).
tff(c_1309,plain,
! [B_73] : ( ld(ld(op_c,B_73),B_73) = op_c ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1172]) ).
tff(c_1314,plain,
! [B_73] : ( rd(B_73,op_c) = ld(op_c,B_73) ),
inference(superposition,[status(thm),theory(equality)],[c_1309,c_1077]) ).
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_89,plain,
! [A_9] : ( ld(A_9,A_9) = unit ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_72]) ).
tff(c_1180,plain,
! [A_69] : ( mult(op_c,A_69) = mult(A_69,op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_1172,c_2]) ).
tff(c_12,plain,
! [A_10] : ( mult(unit,A_10) = A_10 ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_157809,plain,
! [A_692,B_693] : ( mult(mult(rd(op_c,mult(A_692,B_693)),B_693),A_692) = op_e ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_157851,plain,
! [B_693] : ( mult(rd(op_c,mult(unit,B_693)),B_693) = op_e ),
inference(superposition,[status(thm),theory(equality)],[c_157809,c_10]) ).
tff(c_157919,plain,
op_e = op_c,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_12,c_157851]) ).
tff(c_157844,plain,
! [A_692,B_693] : ( mult(rd(op_c,mult(A_692,B_693)),B_693) = rd(op_e,A_692) ),
inference(superposition,[status(thm),theory(equality)],[c_157809,c_8]) ).
tff(c_158523,plain,
! [A_703,B_704] : ( mult(rd(op_c,mult(A_703,B_704)),B_704) = rd(op_c,A_703) ),
inference(demodulation,[status(thm),theory(equality)],[c_157919,c_157844]) ).
tff(c_158616,plain,
! [A_69] : ( mult(rd(op_c,mult(A_69,op_c)),A_69) = rd(op_c,op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_1180,c_158523]) ).
tff(c_158644,plain,
! [A_705] : ( mult(rd(op_c,mult(A_705,op_c)),A_705) = unit ),
inference(demodulation,[status(thm),theory(equality)],[c_89,c_1314,c_158616]) ).
tff(c_158747,plain,
! [A_6] : ( mult(rd(op_c,A_6),rd(A_6,op_c)) = unit ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_158644]) ).
tff(c_158822,plain,
! [A_706] : ( mult(rd(op_c,A_706),ld(op_c,A_706)) = unit ),
inference(demodulation,[status(thm),theory(equality)],[c_1314,c_158747]) ).
tff(c_158522,plain,
! [A_692,B_693] : ( mult(rd(op_c,mult(A_692,B_693)),B_693) = rd(op_c,A_692) ),
inference(demodulation,[status(thm),theory(equality)],[c_157919,c_157844]) ).
tff(c_158827,plain,
! [A_706] : ( mult(rd(op_c,unit),ld(op_c,A_706)) = rd(op_c,rd(op_c,A_706)) ),
inference(superposition,[status(thm),theory(equality)],[c_158822,c_158522]) ).
tff(c_158888,plain,
! [A_707] : ( rd(op_c,rd(op_c,A_707)) = A_707 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_104,c_158827]) ).
tff(c_158917,plain,
! [A_63] : ( rd(op_c,A_63) = ld(A_63,op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_1077,c_158888]) ).
tff(c_158877,plain,
! [A_706] : ( rd(op_c,rd(op_c,A_706)) = A_706 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_104,c_158827]) ).
tff(c_159062,plain,
! [A_706] : ( ld(ld(A_706,op_c),op_c) = A_706 ),
inference(demodulation,[status(thm),theory(equality)],[c_158917,c_158917,c_158877]) ).
tff(c_159674,plain,
! [A_716] : ( rd(op_c,mult(A_716,op_c)) = rd(unit,A_716) ),
inference(superposition,[status(thm),theory(equality)],[c_158644,c_8]) ).
tff(c_1109,plain,
! [A_65,B_66] : ( mult(rd(A_65,B_66),B_66) = A_65 ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
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_1118,plain,
! [A_65,B_66] : ( ld(rd(A_65,B_66),A_65) = B_66 ),
inference(superposition,[status(thm),theory(equality)],[c_1109,c_4]) ).
tff(c_160604,plain,
! [A_727] : ( ld(rd(unit,A_727),op_c) = mult(A_727,op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_159674,c_1118]) ).
tff(c_160645,plain,
! [A_63] : ( mult(ld(A_63,unit),op_c) = ld(A_63,op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_1077,c_160604]) ).
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_160265,plain,
! [A_723] : ( mult(A_723,ld(op_c,ld(A_723,op_c))) = unit ),
inference(superposition,[status(thm),theory(equality)],[c_1077,c_158822]) ).
tff(c_160350,plain,
! [A_19] : ( mult(A_19,mult(op_c,ld(op_c,ld(mult(A_19,op_c),op_c)))) = unit ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_160265]) ).
tff(c_161317,plain,
! [A_734] : ( mult(A_734,ld(mult(A_734,op_c),op_c)) = unit ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_160350]) ).
tff(c_161394,plain,
! [A_63] : ( mult(ld(A_63,unit),ld(ld(A_63,op_c),op_c)) = unit ),
inference(superposition,[status(thm),theory(equality)],[c_160645,c_161317]) ).
tff(c_161478,plain,
! [A_735] : ( mult(ld(A_735,unit),A_735) = unit ),
inference(demodulation,[status(thm),theory(equality)],[c_159062,c_161394]) ).
tff(c_161546,plain,
! [A_735] : ( ld(ld(A_735,unit),unit) = A_735 ),
inference(superposition,[status(thm),theory(equality)],[c_161478,c_4]) ).
tff(c_161469,plain,
! [A_63] : ( mult(ld(A_63,unit),A_63) = unit ),
inference(demodulation,[status(thm),theory(equality)],[c_159062,c_161394]) ).
tff(c_157942,plain,
! [A_694,B_695,C_696] : ( mult(mult(mult(A_694,B_695),B_695),C_696) = mult(A_694,mult(B_695,mult(B_695,C_696))) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_178243,plain,
! [A_843,B_844,C_845] : ( mult(rd(A_843,B_844),mult(B_844,mult(B_844,C_845))) = mult(mult(A_843,B_844),C_845) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_157942]) ).
tff(c_178528,plain,
! [A_843,A_63] : ( mult(rd(A_843,ld(A_63,unit)),mult(ld(A_63,unit),unit)) = mult(mult(A_843,ld(A_63,unit)),A_63) ),
inference(superposition,[status(thm),theory(equality)],[c_161469,c_178243]) ).
tff(c_178724,plain,
! [A_846,A_847] : ( mult(mult(A_846,ld(A_847,unit)),A_847) = A_846 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_10,c_178528]) ).
tff(c_179929,plain,
! [A_852,A_853] : ( mult(mult(A_852,A_853),ld(A_853,unit)) = A_852 ),
inference(superposition,[status(thm),theory(equality)],[c_161546,c_178724]) ).
tff(c_180705,plain,
! [A_856,A_857] : ( ld(mult(A_856,A_857),A_856) = ld(A_857,unit) ),
inference(superposition,[status(thm),theory(equality)],[c_179929,c_4]) ).
tff(c_181050,plain,
! [A_2,B_1] : ( ld(ld(A_2,B_1),unit) = ld(B_1,A_2) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_180705]) ).
tff(c_180018,plain,
! [A_852,A_853] : ( ld(mult(A_852,A_853),A_852) = ld(A_853,unit) ),
inference(superposition,[status(thm),theory(equality)],[c_179929,c_4]) ).
tff(c_158070,plain,
! [A_694,B_695] : ( mult(A_694,mult(B_695,mult(B_695,unit))) = mult(mult(A_694,B_695),B_695) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_157942]) ).
tff(c_158091,plain,
! [A_694,B_695] : ( mult(mult(A_694,B_695),B_695) = mult(A_694,mult(B_695,B_695)) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_158070]) ).
tff(c_161487,plain,
! [A_735] : ( mult(ld(A_735,unit),mult(A_735,A_735)) = mult(unit,A_735) ),
inference(superposition,[status(thm),theory(equality)],[c_161478,c_158091]) ).
tff(c_161593,plain,
! [A_735] : ( mult(ld(A_735,unit),mult(A_735,A_735)) = A_735 ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_161487]) ).
tff(c_158059,plain,
! [A_694,B_695,B_1] : ( mult(A_694,mult(B_695,mult(B_695,ld(mult(mult(A_694,B_695),B_695),B_1)))) = B_1 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_157942]) ).
tff(c_175037,plain,
! [A_825,B_826,B_827] : ( mult(A_825,mult(B_826,mult(B_826,ld(mult(A_825,mult(B_826,B_826)),B_827)))) = B_827 ),
inference(demodulation,[status(thm),theory(equality)],[c_158091,c_158059]) ).
tff(c_175282,plain,
! [A_735,B_827] : ( mult(ld(A_735,unit),mult(A_735,mult(A_735,ld(A_735,B_827)))) = B_827 ),
inference(superposition,[status(thm),theory(equality)],[c_161593,c_175037]) ).
tff(c_175545,plain,
! [A_828,B_829] : ( mult(ld(A_828,unit),mult(A_828,B_829)) = B_829 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_175282]) ).
tff(c_175855,plain,
! [A_2,B_1] : ( mult(ld(A_2,unit),B_1) = ld(A_2,B_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_175545]) ).
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_157879,plain,
! [A_15,B_14] : ( mult(mult(rd(op_c,mult(op_c,mult(A_15,B_14))),B_14),mult(op_c,A_15)) = op_e ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_157809]) ).
tff(c_182892,plain,
! [A_870,B_871] : ( mult(ld(mult(A_870,B_871),B_871),mult(op_c,A_870)) = op_c ),
inference(demodulation,[status(thm),theory(equality)],[c_175855,c_180018,c_158917,c_157919,c_157879]) ).
tff(c_157608,plain,
! [A_688,B_689] : ( mult(mult(A_688,op_c),B_689) = mult(A_688,mult(op_c,B_689)) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_157641,plain,
! [A_688,B_689] : ( ld(mult(A_688,op_c),mult(A_688,mult(op_c,B_689))) = B_689 ),
inference(superposition,[status(thm),theory(equality)],[c_157608,c_4]) ).
tff(c_182968,plain,
! [A_870,B_871] : ( ld(mult(ld(mult(A_870,B_871),B_871),op_c),op_c) = A_870 ),
inference(superposition,[status(thm),theory(equality)],[c_182892,c_157641]) ).
tff(c_183314,plain,
! [B_872,A_873] : ( ld(B_872,mult(A_873,B_872)) = A_873 ),
inference(demodulation,[status(thm),theory(equality)],[c_181050,c_180018,c_1180,c_182968]) ).
tff(c_183609,plain,
! [A_2,B_1] : ( ld(ld(A_2,B_1),B_1) = A_2 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_183314]) ).
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_157506,plain,
! [A_686,B_687] : ( mult(A_686,mult(B_687,ld(mult(A_686,B_687),op_c))) = op_f ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_157537,plain,
! [B_687] : ( mult(B_687,ld(mult(unit,B_687),op_c)) = op_f ),
inference(superposition,[status(thm),theory(equality)],[c_157506,c_12]) ).
tff(c_157589,plain,
op_f = op_c,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12,c_157537]) ).
tff(c_157530,plain,
! [B_687,A_686] : ( rd(op_f,mult(B_687,ld(mult(A_686,B_687),op_c))) = A_686 ),
inference(superposition,[status(thm),theory(equality)],[c_157506,c_8]) ).
tff(c_163128,plain,
! [B_750,A_751] : ( ld(mult(B_750,ld(mult(A_751,B_750),op_c)),op_c) = A_751 ),
inference(demodulation,[status(thm),theory(equality)],[c_158917,c_157589,c_157530]) ).
tff(c_163205,plain,
! [A_63] : ( ld(mult(op_c,ld(ld(A_63,op_c),op_c)),op_c) = ld(A_63,unit) ),
inference(superposition,[status(thm),theory(equality)],[c_160645,c_163128]) ).
tff(c_163294,plain,
! [A_63] : ( ld(mult(op_c,A_63),op_c) = ld(A_63,unit) ),
inference(demodulation,[status(thm),theory(equality)],[c_159062,c_163205]) ).
tff(c_157533,plain,
! [B_687,A_686] : ( mult(B_687,ld(mult(A_686,B_687),op_c)) = ld(A_686,op_f) ),
inference(superposition,[status(thm),theory(equality)],[c_157506,c_4]) ).
tff(c_164337,plain,
! [B_760,A_761] : ( mult(B_760,ld(mult(A_761,B_760),op_c)) = ld(A_761,op_c) ),
inference(demodulation,[status(thm),theory(equality)],[c_157589,c_157533]) ).
tff(c_164533,plain,
! [A_69] : ( mult(op_c,ld(mult(op_c,A_69),op_c)) = ld(A_69,op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_1180,c_164337]) ).
tff(c_164592,plain,
! [A_69] : ( mult(op_c,ld(A_69,unit)) = ld(A_69,op_c) ),
inference(demodulation,[status(thm),theory(equality)],[c_163294,c_164533]) ).
tff(c_180004,plain,
! [A_852,A_853] : ( mult(mult(A_852,A_853),mult(ld(A_853,unit),op_c)) = mult(A_852,op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_179929,c_18]) ).
tff(c_180275,plain,
! [A_852,A_853] : ( mult(mult(A_852,A_853),ld(A_853,op_c)) = mult(A_852,op_c) ),
inference(demodulation,[status(thm),theory(equality)],[c_164592,c_1180,c_180004]) ).
tff(c_175647,plain,
! [A_828,B_829] : ( ld(ld(A_828,unit),B_829) = mult(A_828,B_829) ),
inference(superposition,[status(thm),theory(equality)],[c_175545,c_4]) ).
tff(c_157902,plain,
! [B_1,A_2] : ( mult(mult(rd(op_c,B_1),ld(A_2,B_1)),A_2) = op_e ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_157809]) ).
tff(c_163781,plain,
! [B_756,A_757] : ( mult(mult(ld(B_756,op_c),ld(A_757,B_756)),A_757) = op_c ),
inference(demodulation,[status(thm),theory(equality)],[c_158917,c_157919,c_157902]) ).
tff(c_163127,plain,
! [B_687,A_686] : ( ld(mult(B_687,ld(mult(A_686,B_687),op_c)),op_c) = A_686 ),
inference(demodulation,[status(thm),theory(equality)],[c_158917,c_157589,c_157530]) ).
tff(c_163786,plain,
! [B_756,A_757] : ( mult(ld(B_756,op_c),ld(A_757,B_756)) = ld(mult(A_757,ld(op_c,op_c)),op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_163781,c_163127]) ).
tff(c_318486,plain,
! [B_1335,A_1336] : ( mult(ld(B_1335,op_c),ld(A_1336,B_1335)) = ld(A_1336,op_c) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_89,c_163786]) ).
tff(c_319174,plain,
! [B_829,A_828] : ( mult(ld(B_829,op_c),mult(A_828,B_829)) = ld(ld(A_828,unit),op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_175647,c_318486]) ).
tff(c_493601,plain,
! [B_1632,A_1633] : ( mult(ld(B_1632,op_c),mult(A_1633,B_1632)) = mult(A_1633,op_c) ),
inference(demodulation,[status(thm),theory(equality)],[c_175647,c_319174]) ).
tff(c_494497,plain,
! [A_853,A_852] : ( mult(ld(ld(A_853,op_c),op_c),mult(A_852,op_c)) = mult(mult(A_852,A_853),op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_180275,c_493601]) ).
tff(c_495206,plain,
! [A_853,A_852] : ( mult(A_853,mult(A_852,op_c)) = mult(A_852,mult(A_853,op_c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_183609,c_18,c_494497]) ).
tff(c_1177,plain,
! [A_69] : ( rd(mult(op_c,A_69),op_c) = A_69 ),
inference(superposition,[status(thm),theory(equality)],[c_1172,c_1077]) ).
tff(c_157700,plain,
! [A_690,B_691] : ( mult(mult(A_690,B_691),op_c) = mult(A_690,mult(B_691,op_c)) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_169174,plain,
! [A_795,B_796] : ( rd(mult(A_795,mult(B_796,op_c)),op_c) = mult(A_795,B_796) ),
inference(superposition,[status(thm),theory(equality)],[c_157700,c_8]) ).
tff(c_169323,plain,
! [A_15,B_796] : ( rd(mult(op_c,mult(A_15,mult(B_796,op_c))),op_c) = mult(mult(op_c,A_15),B_796) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_169174]) ).
tff(c_169381,plain,
! [A_15,B_796] : ( mult(op_c,mult(A_15,B_796)) = mult(A_15,mult(B_796,op_c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_1177,c_16,c_169323]) ).
tff(c_183411,plain,
! [B_872,A_873] : ( mult(B_872,A_873) = mult(A_873,B_872) ),
inference(superposition,[status(thm),theory(equality)],[c_183314,c_2]) ).
tff(c_107,plain,
! [A_10] : ( rd(A_10,A_10) = unit ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_95]) ).
tff(c_1694,plain,
! [A_82,B_83] : ( mult(A_82,mult(B_83,ld(mult(A_82,B_83),op_c))) = op_f ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_1725,plain,
! [B_83] : ( mult(B_83,ld(mult(unit,B_83),op_c)) = op_f ),
inference(superposition,[status(thm),theory(equality)],[c_1694,c_12]) ).
tff(c_1777,plain,
op_f = op_c,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12,c_1725]) ).
tff(c_1721,plain,
! [B_83,A_82] : ( mult(B_83,ld(mult(A_82,B_83),op_c)) = ld(A_82,op_f) ),
inference(superposition,[status(thm),theory(equality)],[c_1694,c_4]) ).
tff(c_2275,plain,
! [B_83,A_82] : ( mult(B_83,ld(mult(A_82,B_83),op_c)) = ld(A_82,op_c) ),
inference(demodulation,[status(thm),theory(equality)],[c_1777,c_1721]) ).
tff(c_1982,plain,
! [A_88,B_89] : ( mult(mult(rd(op_c,mult(A_88,B_89)),B_89),A_88) = op_e ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_2024,plain,
! [B_89] : ( mult(rd(op_c,mult(unit,B_89)),B_89) = op_e ),
inference(superposition,[status(thm),theory(equality)],[c_1982,c_10]) ).
tff(c_2089,plain,
op_e = op_c,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_12,c_2024]) ).
tff(c_2072,plain,
! [B_1,A_2] : ( mult(mult(rd(op_c,B_1),ld(A_2,B_1)),A_2) = op_e ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1982]) ).
tff(c_6621,plain,
! [B_143,A_144] : ( mult(mult(rd(op_c,B_143),ld(A_144,B_143)),A_144) = op_c ),
inference(demodulation,[status(thm),theory(equality)],[c_2089,c_2072]) ).
tff(c_6761,plain,
! [A_82] : ( mult(ld(A_82,op_c),mult(A_82,rd(op_c,op_c))) = op_c ),
inference(superposition,[status(thm),theory(equality)],[c_2275,c_6621]) ).
tff(c_6850,plain,
! [A_145] : ( mult(ld(A_145,op_c),A_145) = op_c ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_107,c_6761]) ).
tff(c_6937,plain,
! [A_145] : ( ld(ld(A_145,op_c),op_c) = A_145 ),
inference(superposition,[status(thm),theory(equality)],[c_6850,c_4]) ).
tff(c_7019,plain,
! [B_146] : ( mult(B_146,rd(op_c,B_146)) = op_c ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_6621]) ).
tff(c_7102,plain,
! [B_146] : ( rd(op_c,B_146) = ld(B_146,op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_7019,c_4]) ).
tff(c_2017,plain,
! [A_88,B_89] : ( mult(rd(op_c,mult(A_88,B_89)),B_89) = rd(op_e,A_88) ),
inference(superposition,[status(thm),theory(equality)],[c_1982,c_8]) ).
tff(c_11046,plain,
! [A_177,B_178] : ( mult(ld(mult(A_177,B_178),op_c),B_178) = ld(A_177,op_c) ),
inference(demodulation,[status(thm),theory(equality)],[c_7102,c_7102,c_2089,c_2017]) ).
tff(c_11123,plain,
! [B_178,A_177] : ( mult(B_178,ld(ld(A_177,op_c),op_c)) = ld(ld(mult(A_177,B_178),op_c),op_c) ),
inference(superposition,[status(thm),theory(equality)],[c_11046,c_2275]) ).
tff(c_11300,plain,
! [B_178,A_177] : ( mult(B_178,A_177) = mult(A_177,B_178) ),
inference(demodulation,[status(thm),theory(equality)],[c_6937,c_6937,c_11123]) ).
tff(c_11346,plain,
! [B_179,A_180] : ( mult(B_179,A_180) = mult(A_180,B_179) ),
inference(demodulation,[status(thm),theory(equality)],[c_6937,c_6937,c_11123]) ).
tff(c_11906,plain,
! [B_18,A_19] : ( mult(B_18,mult(A_19,op_c)) = mult(A_19,mult(op_c,B_18)) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_11346]) ).
tff(c_1887,plain,
! [A_86,B_87] : ( mult(mult(A_86,B_87),op_c) = mult(A_86,mult(B_87,op_c)) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_1913,plain,
! [A_86,B_87] : ( mult(op_c,mult(A_86,B_87)) = mult(A_86,mult(B_87,op_c)) ),
inference(superposition,[status(thm),theory(equality)],[c_1887,c_1180]) ).
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_724,plain,
! [A_54,B_55] : ( mult(mult(rd(op_c,mult(A_54,B_55)),B_55),A_54) = op_e ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_754,plain,
! [B_55] : ( mult(rd(op_c,mult(unit,B_55)),B_55) = op_e ),
inference(superposition,[status(thm),theory(equality)],[c_724,c_10]) ).
tff(c_803,plain,
op_e = op_c,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_12,c_754]) ).
tff(c_28,plain,
( ( mult(mult(op_e,'#skF_5'),'#skF_6') != mult(op_e,mult('#skF_5','#skF_6')) )
| ( mult(mult('#skF_3','#skF_4'),op_e) != mult('#skF_3',mult('#skF_4',op_e)) )
| ( mult(mult('#skF_1',op_e),'#skF_2') != mult('#skF_1',mult(op_e,'#skF_2')) ) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_136,plain,
mult(mult('#skF_1',op_e),'#skF_2') != mult('#skF_1',mult(op_e,'#skF_2')),
inference(splitLeft,[status(thm)],[c_28]) ).
tff(c_812,plain,
mult(mult('#skF_1',op_c),'#skF_2') != mult('#skF_1',mult(op_c,'#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_803,c_803,c_136]) ).
tff(c_813,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_812]) ).
tff(c_1011,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_813]) ).
tff(c_1014,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_300,c_1011]) ).
tff(c_1015,plain,
( ( mult(mult('#skF_3','#skF_4'),op_e) != mult('#skF_3',mult('#skF_4',op_e)) )
| ( mult(mult(op_e,'#skF_5'),'#skF_6') != mult(op_e,mult('#skF_5','#skF_6')) ) ),
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_1623,plain,
mult(mult(op_e,'#skF_5'),'#skF_6') != mult(op_e,mult('#skF_5','#skF_6')),
inference(splitLeft,[status(thm)],[c_1015]) ).
tff(c_2111,plain,
mult(mult(op_c,'#skF_5'),'#skF_6') != mult(op_c,mult('#skF_5','#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_2089,c_2089,c_1623]) ).
tff(c_2114,plain,
mult(op_c,mult('#skF_5','#skF_6')) != mult('#skF_5',mult('#skF_6',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_1180,c_20,c_1180,c_2111]) ).
tff(c_11345,plain,
mult(op_c,mult('#skF_6','#skF_5')) != mult('#skF_5',mult('#skF_6',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_11300,c_2114]) ).
tff(c_49842,plain,
mult('#skF_5',mult('#skF_6',op_c)) != mult('#skF_6',mult('#skF_5',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_1913,c_11345]) ).
tff(c_157431,plain,
mult('#skF_6',mult(op_c,'#skF_5')) != mult('#skF_6',mult('#skF_5',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_11906,c_49842]) ).
tff(c_157434,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11300,c_157431]) ).
tff(c_157435,plain,
mult(mult('#skF_3','#skF_4'),op_e) != mult('#skF_3',mult('#skF_4',op_e)),
inference(splitRight,[status(thm)],[c_1015]) ).
tff(c_157930,plain,
mult(mult('#skF_3','#skF_4'),op_c) != mult('#skF_3',mult('#skF_4',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_157919,c_157919,c_157435]) ).
tff(c_157933,plain,
mult(op_c,mult('#skF_3','#skF_4')) != mult('#skF_3',mult('#skF_4',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_1180,c_157930]) ).
tff(c_184329,plain,
mult(op_c,mult('#skF_4','#skF_3')) != mult('#skF_3',mult('#skF_4',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_183411,c_157933]) ).
tff(c_201805,plain,
mult('#skF_3',mult('#skF_4',op_c)) != mult('#skF_4',mult('#skF_3',op_c)),
inference(demodulation,[status(thm),theory(equality)],[c_169381,c_184329]) ).
tff(c_539797,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_495206,c_201805]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP703+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
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 22:13:22 EDT 2023
% 0.15/0.36 % CPUTime :
% 134.87/109.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 134.87/109.28
% 134.87/109.28 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 134.87/109.33
% 134.87/109.33 Inference rules
% 134.87/109.33 ----------------------
% 134.87/109.33 #Ref : 0
% 134.87/109.33 #Sup : 128206
% 134.87/109.33 #Fact : 0
% 134.87/109.33 #Define : 0
% 134.87/109.33 #Split : 2
% 134.87/109.33 #Chain : 0
% 134.87/109.33 #Close : 0
% 134.87/109.33
% 134.87/109.33 Ordering : KBO
% 134.87/109.33
% 134.87/109.33 Simplification rules
% 134.87/109.33 ----------------------
% 134.87/109.33 #Subsume : 7884
% 134.87/109.33 #Demod : 267919
% 134.87/109.33 #Tautology : 52578
% 134.87/109.33 #SimpNegUnit : 0
% 134.87/109.33 #BackRed : 249
% 134.87/109.33
% 134.87/109.33 #Partial instantiations: 0
% 134.87/109.33 #Strategies tried : 1
% 134.87/109.33
% 134.87/109.33 Timing (in seconds)
% 134.87/109.33 ----------------------
% 134.87/109.33 Preprocessing : 0.49
% 134.87/109.33 Parsing : 0.27
% 134.87/109.33 CNF conversion : 0.03
% 134.87/109.33 Main loop : 107.71
% 134.87/109.33 Inferencing : 7.13
% 134.87/109.33 Reduction : 77.43
% 134.87/109.33 Demodulation : 74.38
% 134.87/109.33 BG Simplification : 0.97
% 134.87/109.33 Subsumption : 15.96
% 134.87/109.33 Abstraction : 1.97
% 134.87/109.33 MUC search : 0.00
% 134.87/109.33 Cooper : 0.00
% 134.87/109.33 Total : 108.29
% 134.87/109.33 Index Insertion : 0.00
% 134.87/109.33 Index Deletion : 0.00
% 134.87/109.33 Index Matching : 0.00
% 134.87/109.33 BG Taut test : 0.00
%------------------------------------------------------------------------------