%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP655+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:40:37 PM UTC 2026
% Result : Theorem 160.72s 28.93s
% Output : CNFRefutation 160.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 6
% Syntax : Number of formulae : 113 ( 108 unt; 0 def)
% Number of atoms : 118 ( 117 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 244 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f05,axiom,
! [X3,X1,X2] : mult(X2,mult(X1,mult(X3,X1))) = mult(mult(mult(X2,X1),X3),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f01,axiom,
! [X1,X2] : mult(X2,ld(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f02,axiom,
! [X1,X2] : ld(X2,mult(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f04,axiom,
! [X1,X2] : rd(mult(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f03,axiom,
! [X1,X2] : mult(rd(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(goals,conjecture,
! [X4,X5] :
( mult(ld(X5,X5),X4) = X4
& mult(X4,ld(X5,X5)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c_0_6,plain,
! [X14,X15,X16] : mult(X16,mult(X15,mult(X14,X15))) = mult(mult(mult(X16,X15),X14),X15),
inference(variable_rename,[status(thm)],[f05]) ).
fof(c_0_7,plain,
! [X6,X7] : mult(X7,ld(X7,X6)) = X6,
inference(variable_rename,[status(thm)],[f01]) ).
fof(c_0_8,plain,
! [X8,X9] : ld(X9,mult(X9,X8)) = X8,
inference(variable_rename,[status(thm)],[f02]) ).
cnf(c_0_9,plain,
mult(X1,mult(X2,mult(X3,X2))) = mult(mult(mult(X1,X2),X3),X2),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
mult(X1,ld(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
mult(X1,mult(X2,mult(ld(mult(X1,X2),X3),X2))) = mult(X3,X2),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
mult(X1,mult(ld(mult(X2,X1),X3),X1)) = ld(X2,mult(X3,X1)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_14,plain,
! [X12,X13] : rd(mult(X13,X12),X12) = X13,
inference(variable_rename,[status(thm)],[f04]) ).
cnf(c_0_15,plain,
ld(X1,ld(X2,mult(X3,X1))) = mult(ld(mult(X2,X1),X3),X1),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_16,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,plain,
mult(ld(mult(X1,X2),X1),X2) = ld(X2,X2),
inference(spm,[status(thm)],[c_0_15,c_0_11]) ).
cnf(c_0_18,plain,
rd(ld(X1,X1),X1) = ld(mult(X2,X1),X2),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
ld(ld(X1,X2),ld(X1,X2)) = mult(ld(X2,X1),ld(X1,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_10]) ).
fof(c_0_20,plain,
! [X10,X11] : mult(rd(X11,X10),X10) = X11,
inference(variable_rename,[status(thm)],[f03]) ).
cnf(c_0_21,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_16,c_0_10]) ).
cnf(c_0_22,plain,
ld(mult(X1,ld(X2,X3)),X1) = ld(X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_16]) ).
cnf(c_0_23,plain,
rd(mult(X1,mult(X2,mult(X3,X2))),X2) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_16,c_0_9]) ).
cnf(c_0_24,plain,
mult(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
rd(X1,ld(X2,X3)) = mult(X1,ld(X3,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
rd(mult(X1,mult(X2,X3)),X2) = mult(mult(X1,X2),rd(X3,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
mult(X1,ld(mult(X2,X3),X2)) = rd(X1,X3),
inference(spm,[status(thm)],[c_0_25,c_0_11]) ).
cnf(c_0_28,plain,
mult(rd(X1,X2),mult(X2,X2)) = mult(mult(X1,ld(X2,X2)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_17]),c_0_25]),c_0_11]),c_0_27]),c_0_25]),c_0_11]) ).
cnf(c_0_29,plain,
ld(rd(X1,X2),mult(X3,X2)) = mult(X2,mult(ld(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_13,c_0_24]) ).
cnf(c_0_30,plain,
mult(X1,mult(ld(X1,X1),X1)) = mult(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_28]),c_0_29]),c_0_11]) ).
cnf(c_0_31,plain,
mult(X1,mult(ld(X1,X2),mult(X3,ld(X1,X2)))) = mult(mult(X2,X3),ld(X1,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_32,plain,
mult(ld(X1,X1),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_30]),c_0_11]) ).
cnf(c_0_33,plain,
mult(ld(mult(X1,X2),rd(X3,X2)),X2) = ld(X2,ld(X1,X3)),
inference(spm,[status(thm)],[c_0_15,c_0_24]) ).
cnf(c_0_34,plain,
mult(mult(X1,X2),ld(X2,X1)) = mult(X2,mult(ld(X2,X1),X1)),
inference(spm,[status(thm)],[c_0_31,c_0_10]) ).
cnf(c_0_35,plain,
ld(ld(X1,X1),X1) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_32]) ).
cnf(c_0_36,plain,
rd(ld(X1,ld(X2,X3)),X1) = ld(mult(X2,X1),rd(X3,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_33]) ).
cnf(c_0_37,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_11,c_0_24]) ).
cnf(c_0_38,plain,
mult(ld(X1,X1),mult(X1,X1)) = mult(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_10]) ).
cnf(c_0_39,plain,
rd(X1,X1) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_16,c_0_32]) ).
cnf(c_0_40,plain,
ld(mult(rd(X1,X2),X3),rd(X1,X3)) = rd(ld(X3,X2),X3),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
ld(mult(X1,X1),mult(X1,X1)) = ld(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_38]),c_0_39]) ).
cnf(c_0_42,plain,
mult(ld(mult(rd(mult(X1,X2),X3),X2),X1),X2) = ld(X2,X3),
inference(spm,[status(thm)],[c_0_15,c_0_37]) ).
cnf(c_0_43,plain,
mult(ld(ld(mult(X1,X2),X1),X3),X2) = mult(X2,mult(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_27]),c_0_25]),c_0_11]),c_0_29]),c_0_37]),c_0_25]),c_0_11]) ).
cnf(c_0_44,plain,
mult(mult(ld(X1,X2),ld(X2,X1)),ld(X2,X1)) = ld(X2,X1),
inference(spm,[status(thm)],[c_0_32,c_0_19]) ).
cnf(c_0_45,plain,
ld(ld(X1,X2),mult(ld(X2,X1),ld(X1,X2))) = ld(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_32]),c_0_19]) ).
cnf(c_0_46,plain,
mult(mult(X1,ld(X2,X2)),X2) = mult(mult(X1,X2),ld(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_32]),c_0_25]),c_0_25]),c_0_10]) ).
cnf(c_0_47,plain,
ld(X1,mult(mult(X1,X1),X1)) = mult(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_41]),c_0_32]) ).
cnf(c_0_48,plain,
ld(mult(rd(mult(X1,X2),X3),X2),X1) = rd(ld(X2,X3),X2),
inference(spm,[status(thm)],[c_0_16,c_0_42]) ).
cnf(c_0_49,plain,
mult(ld(ld(X1,X2),X3),ld(X2,X1)) = mult(ld(X2,X1),mult(X3,ld(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_50,plain,
mult(rd(X1,X2),mult(X2,X2)) = mult(mult(X1,X2),ld(X2,X2)),
inference(rw,[status(thm)],[c_0_28,c_0_46]) ).
cnf(c_0_51,plain,
rd(ld(X1,X1),X1) = ld(X1,ld(X1,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_32]) ).
cnf(c_0_52,plain,
mult(X1,ld(X2,ld(X2,X2))) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_53,plain,
mult(mult(X1,X1),X1) = mult(X1,mult(X1,X1)),
inference(spm,[status(thm)],[c_0_10,c_0_47]) ).
cnf(c_0_54,plain,
mult(ld(mult(X1,X2),ld(X2,X2)),X2) = ld(X2,ld(X1,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_32]) ).
cnf(c_0_55,plain,
ld(mult(rd(X1,X2),ld(X3,X1)),X3) = mult(ld(X1,X3),mult(X2,ld(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_10]),c_0_25]),c_0_49]) ).
cnf(c_0_56,plain,
mult(mult(X1,ld(X2,X3)),ld(X3,X2)) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_22]) ).
cnf(c_0_57,plain,
mult(ld(X1,ld(X1,X1)),mult(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_32]),c_0_10]) ).
cnf(c_0_58,plain,
mult(ld(ld(X1,ld(X1,X1)),X2),X1) = mult(X1,mult(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_52]),c_0_25]),c_0_35]),c_0_29]),c_0_37]),c_0_25]),c_0_35]) ).
cnf(c_0_59,plain,
mult(rd(X1,X2),mult(X2,mult(X3,X2))) = mult(mult(X1,X3),X2),
inference(spm,[status(thm)],[c_0_9,c_0_24]) ).
cnf(c_0_60,plain,
mult(ld(mult(X1,mult(X1,X1)),X1),X1) = ld(X1,ld(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_41]),c_0_53]) ).
cnf(c_0_61,plain,
rd(ld(X1,ld(X2,X1)),X1) = ld(mult(X2,X1),ld(X1,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_54]) ).
cnf(c_0_62,plain,
ld(mult(ld(X1,X1),ld(X2,X1)),X2) = mult(ld(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_39]),c_0_10]) ).
cnf(c_0_63,plain,
ld(mult(X1,ld(X2,X3)),mult(X4,ld(X3,X2))) = mult(ld(X3,X2),mult(ld(X1,X4),ld(X3,X2))),
inference(spm,[status(thm)],[c_0_13,c_0_56]) ).
cnf(c_0_64,plain,
ld(ld(X1,ld(X1,X1)),X1) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_11,c_0_57]) ).
cnf(c_0_65,plain,
ld(X1,ld(X1,X1)) = ld(mult(X2,X1),X2),
inference(rw,[status(thm)],[c_0_18,c_0_51]) ).
cnf(c_0_66,plain,
ld(ld(X1,ld(X1,X1)),X2) = rd(mult(X1,mult(X2,X1)),X1),
inference(spm,[status(thm)],[c_0_16,c_0_58]) ).
cnf(c_0_67,plain,
mult(mult(X1,rd(X2,X3)),X3) = mult(rd(X1,X3),mult(X3,X2)),
inference(spm,[status(thm)],[c_0_59,c_0_24]) ).
cnf(c_0_68,plain,
ld(mult(X1,X1),ld(X1,X1)) = ld(mult(X1,mult(X1,X1)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_60]),c_0_61]) ).
cnf(c_0_69,plain,
ld(mult(ld(mult(X1,X2),mult(X1,X2)),X2),X1) = mult(ld(mult(X1,X2),X1),X1),
inference(spm,[status(thm)],[c_0_62,c_0_11]) ).
cnf(c_0_70,plain,
mult(mult(ld(X1,X2),mult(ld(X3,X4),ld(X1,X2))),ld(X2,X1)) = ld(ld(X2,X1),ld(X3,X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_56]),c_0_63]) ).
cnf(c_0_71,plain,
ld(ld(mult(X1,X2),X1),X2) = mult(X2,X2),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,plain,
mult(ld(mult(X1,mult(X1,X1)),X1),mult(X1,X2)) = ld(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_66]),c_0_19]),c_0_35]),c_0_10]),c_0_32]),c_0_16]),c_0_52]),c_0_25]),c_0_35]),c_0_67]),c_0_61]),c_0_68]) ).
cnf(c_0_73,plain,
ld(mult(mult(X1,X2),X3),mult(X1,mult(X2,mult(X3,X2)))) = X2,
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_74,plain,
ld(ld(ld(X1,X1),ld(X2,X2)),X2) = mult(ld(X1,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_63]),c_0_70]),c_0_22]) ).
cnf(c_0_75,plain,
mult(X1,mult(ld(X2,rd(X3,X1)),X1)) = ld(rd(X2,X1),X3),
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_76,plain,
rd(ld(mult(X1,X2),X1),X2) = ld(X2,ld(mult(X1,X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_27]),c_0_37]),c_0_27]) ).
cnf(c_0_77,plain,
mult(mult(mult(X1,X2),X2),ld(X2,X2)) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_46]),c_0_32]) ).
cnf(c_0_78,plain,
mult(ld(mult(X1,mult(X1,X1)),X1),X2) = ld(X1,ld(X1,X2)),
inference(spm,[status(thm)],[c_0_72,c_0_10]) ).
cnf(c_0_79,plain,
ld(mult(X1,X2),X1) = ld(mult(X3,X2),X3),
inference(spm,[status(thm)],[c_0_18,c_0_18]) ).
cnf(c_0_80,plain,
ld(mult(mult(ld(mult(X1,mult(X2,X1)),mult(X1,mult(X2,X1))),X1),X2),mult(X1,mult(X2,X1))) = X1,
inference(spm,[status(thm)],[c_0_73,c_0_32]) ).
cnf(c_0_81,plain,
mult(mult(X1,ld(X2,X3)),mult(ld(X3,X2),mult(X4,ld(X3,X2)))) = mult(mult(X1,X4),ld(X3,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_56]) ).
cnf(c_0_82,plain,
mult(mult(X1,mult(X2,ld(X3,X4))),ld(X4,X3)) = mult(mult(X1,ld(X3,X4)),mult(ld(X4,X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_56]),c_0_25]) ).
cnf(c_0_83,plain,
mult(ld(ld(X1,X1),ld(X2,X2)),mult(ld(X1,X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_10,c_0_74]) ).
cnf(c_0_84,plain,
mult(ld(ld(X1,X1),ld(mult(X2,X1),X2)),X1) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_17,c_0_17]) ).
cnf(c_0_85,plain,
mult(ld(mult(X1,X2),X1),mult(X2,X2)) = X2,
inference(spm,[status(thm)],[c_0_57,c_0_65]) ).
cnf(c_0_86,plain,
ld(ld(X1,ld(mult(X2,X1),X2)),X3) = mult(X1,mult(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_43]),c_0_24]),c_0_76]) ).
cnf(c_0_87,plain,
mult(mult(X1,mult(ld(X1,X2),X2)),ld(X2,X1)) = mult(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_34]),c_0_25]) ).
cnf(c_0_88,plain,
ld(mult(X1,X2),mult(X2,mult(ld(X2,X1),X1))) = ld(X2,X1),
inference(spm,[status(thm)],[c_0_11,c_0_34]) ).
cnf(c_0_89,plain,
ld(ld(X1,X2),ld(X2,X1)) = mult(ld(X2,X1),ld(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_56]),c_0_11]) ).
cnf(c_0_90,plain,
mult(mult(X1,mult(X1,X1)),X1) = mult(X1,mult(X1,mult(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_53]),c_0_11]),c_0_11]) ).
cnf(c_0_91,plain,
mult(mult(X1,mult(X2,X2)),X2) = mult(mult(X1,X2),mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_77]),c_0_32]) ).
cnf(c_0_92,plain,
mult(ld(mult(X1,mult(X2,X2)),X1),X3) = ld(X2,ld(X2,X3)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
fof(c_0_93,negated_conjecture,
~ ! [X4,X5] :
( mult(ld(X5,X5),X4) = X4
& mult(X4,ld(X5,X5)) = X4 ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_94,plain,
ld(X1,mult(mult(X1,X1),ld(X2,X2))) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_63]),c_0_41]),c_0_82]),c_0_70]),c_0_83]) ).
cnf(c_0_95,plain,
mult(mult(ld(X1,X2),ld(X1,X2)),mult(ld(X2,X1),X3)) = ld(ld(X2,X1),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_43]),c_0_22]),c_0_82]) ).
cnf(c_0_96,plain,
mult(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_46]),c_0_15]),c_0_56]),c_0_46]),c_0_17]) ).
cnf(c_0_97,plain,
mult(ld(X1,X2),mult(ld(X2,X1),ld(X2,X1))) = ld(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_56]),c_0_11]) ).
cnf(c_0_98,plain,
ld(mult(ld(X1,X2),ld(X1,X2)),X3) = mult(ld(X2,X1),mult(ld(X2,X1),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]),c_0_89]) ).
cnf(c_0_99,plain,
mult(mult(X1,X1),mult(X1,X1)) = mult(X1,mult(X1,mult(X1,X1))),
inference(rw,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_100,plain,
mult(ld(X1,ld(mult(X2,X1),X2)),X3) = ld(X1,ld(X1,X3)),
inference(spm,[status(thm)],[c_0_92,c_0_85]) ).
fof(c_0_101,negated_conjecture,
( mult(ld(esk2_0,esk2_0),esk1_0) != esk1_0
| mult(esk1_0,ld(esk2_0,esk2_0)) != esk1_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_93])])])]) ).
cnf(c_0_102,plain,
ld(ld(X1,X1),ld(mult(X2,X1),X2)) = ld(X1,ld(X1,X1)),
inference(spm,[status(thm)],[c_0_65,c_0_17]) ).
cnf(c_0_103,plain,
mult(ld(X1,X1),ld(X2,X2)) = ld(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]),c_0_19]),c_0_96]),c_0_11]),c_0_96]) ).
cnf(c_0_104,plain,
ld(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(mult(ld(X2,X1),ld(X2,X1)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_97]),c_0_89]) ).
cnf(c_0_105,plain,
ld(X1,ld(X1,ld(X1,ld(X1,X2)))) = ld(mult(X1,mult(X1,mult(X1,X1))),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_71]),c_0_99]),c_0_100]),c_0_100]) ).
cnf(c_0_106,negated_conjecture,
( mult(ld(esk2_0,esk2_0),esk1_0) != esk1_0
| mult(esk1_0,ld(esk2_0,esk2_0)) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_107,plain,
ld(X1,X1) = ld(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_19]),c_0_103]),c_0_104]),c_0_103]),c_0_103]),c_0_19]),c_0_103]),c_0_19]),c_0_103]) ).
cnf(c_0_108,plain,
ld(ld(X1,ld(X1,ld(X1,X2))),X1) = ld(X2,mult(X1,mult(X1,mult(X1,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_105]),c_0_22]) ).
cnf(c_0_109,negated_conjecture,
( mult(ld(X1,X1),esk1_0) != esk1_0
| mult(esk1_0,ld(X1,X1)) != esk1_0 ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_110,plain,
mult(X1,ld(mult(X1,mult(X1,mult(X1,X1))),X2)) = ld(X1,ld(X1,ld(X1,X2))),
inference(spm,[status(thm)],[c_0_10,c_0_105]) ).
cnf(c_0_111,plain,
ld(mult(X1,X2),mult(X1,mult(X1,mult(X1,X1)))) = ld(ld(X1,ld(X1,X2)),X1),
inference(spm,[status(thm)],[c_0_108,c_0_11]) ).
cnf(c_0_112,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_11]),c_0_11]),c_0_11]),c_0_111]),c_0_11]),c_0_11]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP655+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.40 % Computer : n026.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.13/5.40 % CPULimit : 300
% 0.13/5.40 % WCLimit : 300
% 0.13/5.40 % DateTime : Sun Sep 20 20:32:28 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.47 Running first-order theorem proving
% 0.13/5.47 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 160.72/28.93 % Version: 3.5.1
% 160.72/28.93 % Preprocessing class: FSSSSMSSSSSNFFN.
% 160.72/28.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 160.72/28.93 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 160.72/28.93 % Starting new_bool_3 with 300s (1) cores
% 160.72/28.93 % Starting new_bool_1 with 300s (1) cores
% 160.72/28.93 % Starting sh5l with 300s (1) cores
% 160.72/28.93 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 547440 completed with status 0
% 160.72/28.93 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 160.72/28.93 % Preprocessing class: FSSSSMSSSSSNFFN.
% 160.72/28.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 160.72/28.93 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 160.72/28.93 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 160.72/28.93 % No SInE strategy applied
% 160.72/28.93 % Search class: FUHPM-FFSF22-MFFFFFNN
% 160.72/28.93 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 160.72/28.93 % Starting SubtermCWHack with 136s (1) cores
% 160.72/28.93 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 160.72/28.93 % Starting H----_102_C18_F1_PI_AE_Q4_CS_SP_PS_S5PRR_S2S with 136s (1) cores
% 160.72/28.93 % Starting new_bool_3 with 136s (1) cores
% 160.72/28.93 % Starting new_bool_1 with 136s (1) cores
% 160.72/28.93 % new_bool_1 with pid 547449 completed with status 0
% 160.72/28.93 % Result found by new_bool_1
% 160.72/28.93 % Preprocessing class: FSSSSMSSSSSNFFN.
% 160.72/28.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 160.72/28.93 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 160.72/28.93 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 160.72/28.93 % No SInE strategy applied
% 160.72/28.93 % Search class: FUHPM-FFSF22-MFFFFFNN
% 160.72/28.93 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 160.72/28.93 % Starting SubtermCWHack with 136s (1) cores
% 160.72/28.93 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 160.72/28.93 % Starting H----_102_C18_F1_PI_AE_Q4_CS_SP_PS_S5PRR_S2S with 136s (1) cores
% 160.72/28.93 % Starting new_bool_3 with 136s (1) cores
% 160.72/28.93 % Starting new_bool_1 with 136s (1) cores
% 160.72/28.93 % Preprocessing time : 0.001 s
% 160.72/28.93 % Presaturation interreduction done
% 160.72/28.93
% 160.72/28.93 % Proof found!
% 160.72/28.93 % SZS status Theorem
% 160.72/28.93 % SZS output start CNFRefutation
% See solution above
% 160.72/28.93 % Parsed axioms : 6
% 160.72/28.93 % Removed by relevancy pruning/SinE : 0
% 160.72/28.93 % Initial clauses : 6
% 160.72/28.93 % Removed in clause preprocessing : 0
% 160.72/28.93 % Initial clauses in saturation : 6
% 160.72/28.93 % Processed clauses : 5135
% 160.72/28.93 % ...of these trivial : 2015
% 160.72/28.93 % ...subsumed : 2318
% 160.72/28.93 % ...remaining for further processing : 802
% 160.72/28.93 % Other redundant clauses eliminated : 0
% 160.72/28.93 % Clauses deleted for lack of memory : 0
% 160.72/28.93 % Backward-subsumed : 4
% 160.72/28.93 % Backward-rewritten : 154
% 160.72/28.93 % Generated clauses : 512415
% 160.72/28.93 % ...of the previous two non-redundant : 449927
% 160.72/28.93 % ...aggressively subsumed : 0
% 160.72/28.93 % Contextual simplify-reflections : 0
% 160.72/28.93 % Paramodulations : 512415
% 160.72/28.93 % Factorizations : 0
% 160.72/28.93 % NegExts : 0
% 160.72/28.93 % Equation resolutions : 0
% 160.72/28.93 % Disequality decompositions : 0
% 160.72/28.93 % Total rewrite steps : 1136765
% 160.72/28.93 % ...of those cached : 1044647
% 160.72/28.93 % Propositional unsat checks : 0
% 160.72/28.93 % Propositional check models : 0
% 160.72/28.93 % Propositional check unsatisfiable : 0
% 160.72/28.93 % Propositional clauses : 0
% 160.72/28.93 % Propositional clauses after purity: 0
% 160.72/28.93 % Propositional unsat core size : 0
% 160.72/28.93 % Propositional preprocessing time : 0.000
% 160.72/28.93 % Propositional encoding time : 0.000
% 160.72/28.93 % Propositional solver time : 0.000
% 160.72/28.93 % Success case prop preproc time : 0.000
% 160.72/28.93 % Success case prop encoding time : 0.000
% 160.72/28.93 % Success case prop solver time : 0.000
% 160.72/28.93 % Current number of processed clauses : 638
% 160.72/28.93 % Positive orientable unit clauses : 599
% 160.72/28.93 % Positive unorientable unit clauses: 38
% 160.72/28.93 % Negative unit clauses : 0
% 160.72/28.93 % Non-unit-clauses : 1
% 160.72/28.93 % Current number of unprocessed clauses: 443833
% 160.72/28.93 % ...number of literals in the above : 443834
% 160.72/28.93 % Current number of archived formulas : 0
% 160.72/28.93 % Current number of archived clauses : 164
% 160.72/28.93 % Clause-clause subsumption calls (NU) : 1
% 160.72/28.93 % Rec. Clause-clause subsumption calls : 1
% 160.72/28.93 % Non-unit clause-clause subsumptions : 1
% 160.72/28.93 % Unit Clause-clause subsumption calls : 1152
% 160.72/28.93 % Rewrite failures with RHS unbound : 3018
% 160.72/28.93 % BW rewrite match attempts : 8302
% 160.72/28.93 % BW rewrite match successes : 472
% 160.72/28.93 % Condensation attempts : 0
% 160.72/28.93 % Condensation successes : 0
% 160.72/28.93 % Termbank termtop insertions : 18498856
% 160.72/28.93 % Search garbage collected termcells : 25
% 160.72/28.93
% 160.72/28.93 % -------------------------------------------------
% 160.72/28.93 % User time : 22.376 s
% 160.72/28.93 % System time : 0.634 s
% 160.72/28.93 % Total time : 23.010 s
% 160.72/28.93 % Maximum resident set size: 3632 pages
% 160.72/28.93
% 160.72/28.93 % -------------------------------------------------
% 160.72/28.93 % User time : 110.888 s
% 160.72/28.93 % System time : 3.298 s
% 160.72/28.93 % Total time : 114.186 s
% 160.72/28.93 % Maximum resident set size: 4608 pages
% 160.72/28.93 % E exiting
%------------------------------------------------------------------------------