%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP683+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.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 May 5 04:26:53 PM UTC 2026
% Result : Theorem 1.59s 1.81s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 8
% Syntax : Number of formulae : 97 ( 90 unt; 0 def)
% Number of atoms : 104 ( 103 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 5 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 213 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f02,axiom,
! [X1] : rd(mult(X1,X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f04,axiom,
! [X2,X1] : mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f01,axiom,
! [X1] : ld(X1,mult(X1,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f03,axiom,
! [X2,X1] : mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f07,axiom,
! [X2,X1] : ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
fof(f06,axiom,
! [X3,X4,X2,X1] : rd(mult(mult(X1,X2),rd(X4,X3)),rd(X4,X3)) = mult(X1,rd(mult(X2,X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
fof(f05,axiom,
! [X3,X4,X2,X1] : ld(ld(X1,X2),mult(ld(X1,X2),mult(X4,X3))) = mult(ld(X1,mult(X1,X4)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(goals,conjecture,
! [X5,X6,X7] :
( mult(X5,ld(X6,mult(X6,X7))) = mult(X5,X7)
& mult(rd(mult(X5,X6),X6),X7) = mult(X5,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c_0_8,plain,
! [X28] : rd(mult(X28,X28),X28) = X28,
inference(variable_rename,[status(thm)],[f02]) ).
fof(c_0_9,plain,
! [X31,X32] : mult(rd(X32,X31),X31) = rd(mult(X32,X31),X31),
inference(variable_rename,[status(thm)],[f04]) ).
fof(c_0_10,plain,
! [X27] : ld(X27,mult(X27,X27)) = X27,
inference(variable_rename,[status(thm)],[f01]) ).
fof(c_0_11,plain,
! [X29,X30] : mult(X30,ld(X30,X29)) = ld(X30,mult(X30,X29)),
inference(variable_rename,[status(thm)],[f03]) ).
cnf(c_0_12,plain,
rd(mult(X1,X1),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X41,X42] : ld(X42,mult(X42,ld(X41,X41))) = rd(mult(rd(X42,X42),X41),X41),
inference(variable_rename,[status(thm)],[f07]) ).
cnf(c_0_15,plain,
ld(X1,mult(X1,X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X37,X38,X39,X40] : rd(mult(mult(X40,X39),rd(X38,X37)),rd(X38,X37)) = mult(X40,rd(mult(X39,X37),X37)),
inference(variable_rename,[status(thm)],[f06]) ).
cnf(c_0_18,plain,
mult(rd(X1,X1),X1) = X1,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
mult(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
mult(rd(rd(X1,X1),X1),X1) = rd(X1,X1),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_23,plain,
mult(rd(rd(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_13]),c_0_16]) ).
cnf(c_0_24,plain,
mult(X1,ld(X1,ld(X1,X1))) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_25,plain,
mult(rd(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,mult(rd(X2,X4),X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_13]),c_0_13]) ).
cnf(c_0_26,plain,
rd(X1,X1) = ld(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_27,plain,
mult(rd(mult(X1,X2),ld(X3,X3)),ld(X3,X3)) = mult(X1,mult(rd(X2,X3),X3)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,plain,
mult(rd(ld(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(rw,[status(thm)],[c_0_23,c_0_26]) ).
cnf(c_0_29,plain,
mult(mult(rd(X1,ld(X2,X2)),ld(X2,X2)),ld(X2,X2)) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_13]),c_0_28]),c_0_24]) ).
cnf(c_0_30,plain,
mult(rd(X1,ld(X1,X1)),ld(X1,X1)) = rd(X1,ld(X1,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_20]) ).
cnf(c_0_31,plain,
rd(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_30]),c_0_20]) ).
cnf(c_0_32,plain,
mult(X1,mult(rd(X2,ld(X3,X3)),ld(X3,X3))) = mult(rd(mult(X1,X2),X3),X3),
inference(spm,[status(thm)],[c_0_25,c_0_31]) ).
cnf(c_0_33,plain,
mult(ld(X1,X1),X1) = X1,
inference(rw,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_34,plain,
mult(mult(rd(X1,X2),X2),X2) = mult(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_31]),c_0_20]),c_0_13]) ).
fof(c_0_35,plain,
! [X33,X34,X35,X36] : ld(ld(X36,X35),mult(ld(X36,X35),mult(X34,X33))) = mult(ld(X36,mult(X36,X34)),X33),
inference(variable_rename,[status(thm)],[f05]) ).
cnf(c_0_36,plain,
mult(rd(mult(X1,ld(X2,X2)),X2),X2) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_26]),c_0_33]) ).
cnf(c_0_37,plain,
mult(mult(X1,ld(X1,ld(X2,X2))),X2) = mult(ld(X1,X1),X2),
inference(spm,[status(thm)],[c_0_34,c_0_28]) ).
cnf(c_0_38,plain,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,plain,
mult(X1,ld(ld(X2,X2),ld(X2,X2))) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_36]),c_0_28]),c_0_20]) ).
cnf(c_0_40,plain,
mult(ld(ld(X1,X1),ld(X1,X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_20]),c_0_33]) ).
cnf(c_0_41,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_16]),c_0_16]) ).
cnf(c_0_42,plain,
ld(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_39]),c_0_40]) ).
cnf(c_0_43,plain,
mult(mult(ld(X1,X1),ld(ld(X1,X1),X2)),X3) = mult(mult(X1,ld(X1,X2)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_41]) ).
cnf(c_0_44,plain,
mult(mult(mult(X1,ld(X1,X2)),X3),X4) = mult(mult(X1,ld(X1,mult(X2,X3))),X4),
inference(spm,[status(thm)],[c_0_43,c_0_41]) ).
cnf(c_0_45,plain,
mult(rd(mult(X1,X2),X3),X3) = mult(X1,mult(rd(X2,X3),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_42]),c_0_27]),c_0_32]) ).
cnf(c_0_46,plain,
mult(mult(X1,mult(X1,ld(X1,X2))),X3) = mult(mult(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_20]),c_0_16]) ).
cnf(c_0_47,plain,
mult(X1,mult(X1,ld(X1,ld(X2,X2)))) = mult(rd(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_20]),c_0_28]) ).
cnf(c_0_48,plain,
mult(mult(rd(X1,X2),X2),X3) = mult(mult(X1,ld(X2,X2)),X3),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_49,plain,
mult(mult(X1,ld(X2,X2)),X2) = mult(X1,X2),
inference(rw,[status(thm)],[c_0_34,c_0_48]) ).
cnf(c_0_50,plain,
mult(ld(X1,X1),mult(rd(X1,X2),X2)) = mult(rd(X1,X2),X2),
inference(spm,[status(thm)],[c_0_45,c_0_33]) ).
cnf(c_0_51,plain,
mult(X1,mult(rd(X2,rd(X3,X4)),rd(X3,X4))) = mult(X1,mult(rd(X2,X4),X4)),
inference(rw,[status(thm)],[c_0_25,c_0_45]) ).
cnf(c_0_52,plain,
mult(rd(X1,X2),X2) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_49]),c_0_13]),c_0_45]),c_0_28]),c_0_24]) ).
cnf(c_0_53,plain,
mult(rd(X1,rd(X2,X3)),rd(X2,X3)) = mult(rd(X1,X3),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_50]) ).
cnf(c_0_54,plain,
ld(ld(X1,X1),mult(rd(X1,X2),X2)) = mult(mult(X1,ld(X1,rd(X1,X2))),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_50]),c_0_41]) ).
cnf(c_0_55,plain,
mult(mult(ld(X1,X1),X2),X3) = mult(mult(X1,ld(X1,X2)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_37]),c_0_33]) ).
cnf(c_0_56,plain,
mult(ld(X1,X1),mult(X1,ld(X2,X2))) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_52]),c_0_52]) ).
cnf(c_0_57,plain,
mult(rd(rd(X1,X2),X2),X2) = rd(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_26]),c_0_33]) ).
cnf(c_0_58,plain,
ld(ld(X1,X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_31]),c_0_20]),c_0_20]),c_0_20]) ).
cnf(c_0_59,plain,
mult(mult(X1,ld(X1,ld(ld(X1,X1),X2))),X3) = mult(mult(X1,ld(X1,X2)),X3),
inference(rw,[status(thm)],[c_0_43,c_0_55]) ).
cnf(c_0_60,plain,
ld(ld(X1,X1),mult(X1,ld(X2,X2))) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_56]),c_0_41]),c_0_20]) ).
cnf(c_0_61,plain,
rd(mult(X1,X2),X2) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[c_0_13,c_0_52]) ).
cnf(c_0_62,plain,
mult(rd(X1,X2),ld(X2,X2)) = rd(X1,X2),
inference(rw,[status(thm)],[c_0_57,c_0_52]) ).
cnf(c_0_63,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_58]),c_0_55]),c_0_59]) ).
cnf(c_0_64,plain,
mult(mult(X1,ld(X1,rd(X1,X2))),X2) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_52]),c_0_60]) ).
cnf(c_0_65,plain,
rd(mult(X1,ld(X2,X2)),X2) = rd(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_52]),c_0_62]) ).
cnf(c_0_66,plain,
mult(mult(X1,X2),ld(X3,X3)) = mult(X1,mult(X2,ld(X3,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_52]),c_0_52]) ).
cnf(c_0_67,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(X1,ld(X1,mult(X3,X4))),
inference(rw,[status(thm)],[c_0_41,c_0_63]) ).
cnf(c_0_68,plain,
mult(X1,ld(X1,mult(mult(X1,X2),X3))) = mult(mult(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_16]),c_0_46]) ).
cnf(c_0_69,plain,
mult(X1,mult(ld(X1,rd(X1,X2)),ld(X2,X2))) = rd(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_64]),c_0_65]),c_0_66]) ).
cnf(c_0_70,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(X1,ld(X1,X3)),
inference(spm,[status(thm)],[c_0_67,c_0_20]) ).
cnf(c_0_71,plain,
mult(X1,ld(X1,mult(rd(X1,X2),X3))) = mult(rd(X1,X2),X3),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_72,plain,
mult(X1,ld(X1,ld(X1,X2))) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_70]) ).
cnf(c_0_73,plain,
mult(X1,ld(rd(X2,X3),rd(X2,X3))) = mult(X1,ld(X3,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_52]),c_0_52]) ).
cnf(c_0_74,plain,
mult(X1,ld(X1,ld(rd(X1,X2),X3))) = ld(rd(X1,X2),X3),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_75,plain,
mult(X1,ld(X1,ld(rd(X2,X3),rd(X2,X3)))) = mult(X1,ld(X1,ld(X3,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_73]),c_0_16]) ).
fof(c_0_76,negated_conjecture,
~ ! [X5,X6,X7] :
( mult(X5,ld(X6,mult(X6,X7))) = mult(X5,X7)
& mult(rd(mult(X5,X6),X6),X7) = mult(X5,X7) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_77,plain,
mult(ld(X1,X1),ld(X2,X2)) = mult(X1,ld(X1,ld(X2,X2))),
inference(rw,[status(thm)],[c_0_28,c_0_52]) ).
cnf(c_0_78,plain,
ld(rd(X1,X2),rd(X1,X2)) = mult(X1,ld(X1,ld(X2,X2))),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
fof(c_0_79,negated_conjecture,
( mult(esk1_0,ld(esk2_0,mult(esk2_0,esk3_0))) != mult(esk1_0,esk3_0)
| mult(rd(mult(esk1_0,esk2_0),esk2_0),esk3_0) != mult(esk1_0,esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])]) ).
cnf(c_0_80,plain,
mult(mult(X1,mult(rd(X2,X3),X3)),X3) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_34,c_0_45]) ).
cnf(c_0_81,plain,
mult(rd(X1,X2),mult(X2,ld(X3,X3))) = mult(X1,mult(X2,ld(X2,ld(X3,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_52]),c_0_66]),c_0_77]) ).
cnf(c_0_82,plain,
mult(X1,mult(X2,ld(X2,ld(X3,X3)))) = mult(X1,ld(X3,X3)),
inference(rw,[status(thm)],[c_0_73,c_0_78]) ).
cnf(c_0_83,negated_conjecture,
( mult(esk1_0,ld(esk2_0,mult(esk2_0,esk3_0))) != mult(esk1_0,esk3_0)
| mult(rd(mult(esk1_0,esk2_0),esk2_0),esk3_0) != mult(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_84,plain,
mult(mult(X1,mult(X2,ld(X3,X3))),X3) = mult(mult(X1,X2),X3),
inference(rw,[status(thm)],[c_0_80,c_0_52]) ).
cnf(c_0_85,plain,
mult(rd(X1,X2),mult(X2,ld(X3,X3))) = mult(X1,ld(X3,X3)),
inference(rw,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_86,negated_conjecture,
( mult(esk1_0,mult(esk2_0,ld(esk2_0,esk3_0))) != mult(esk1_0,esk3_0)
| mult(rd(mult(esk1_0,esk2_0),esk2_0),esk3_0) != mult(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[c_0_83,c_0_16]) ).
cnf(c_0_87,plain,
mult(mult(X1,ld(X2,X2)),X3) = mult(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_49]),c_0_52]) ).
cnf(c_0_88,plain,
mult(ld(X1,X1),X2) = mult(X1,ld(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_63]),c_0_33]) ).
cnf(c_0_89,negated_conjecture,
( mult(esk1_0,mult(esk2_0,ld(esk2_0,esk3_0))) != mult(esk1_0,esk3_0)
| mult(mult(rd(esk1_0,esk2_0),esk2_0),esk3_0) != mult(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[c_0_86,c_0_13]) ).
cnf(c_0_90,plain,
mult(X1,ld(X1,mult(X2,ld(X2,X3)))) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_63]),c_0_88]),c_0_88]) ).
cnf(c_0_91,negated_conjecture,
( mult(esk1_0,mult(esk2_0,ld(esk2_0,esk3_0))) != mult(esk1_0,esk3_0)
| mult(mult(esk1_0,ld(esk2_0,esk2_0)),esk3_0) != mult(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[c_0_89,c_0_48]) ).
cnf(c_0_92,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_20]),c_0_16]) ).
cnf(c_0_93,plain,
ld(X1,mult(X2,ld(X2,X3))) = ld(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_90]),c_0_16]),c_0_72]),c_0_72]) ).
cnf(c_0_94,negated_conjecture,
mult(esk1_0,mult(esk2_0,ld(esk2_0,esk3_0))) != mult(esk1_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_87])]) ).
cnf(c_0_95,plain,
mult(X1,mult(X2,ld(X2,X3))) = mult(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_92]) ).
cnf(c_0_96,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP683+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n029.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 19:02:14 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.59/1.81 % Version : CSE_E---1.7
% 1.59/1.81 % Problem : theBenchmark.p
% 1.59/1.81 % SZS status Theorem for theBenchmark.p
% 1.59/1.81 % SZS output start CNFRefutation
% See solution above
% 1.59/1.81 % Total time : 1.371s
%------------------------------------------------------------------------------