%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP655+2 : 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 : n004.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 12:44:36 PM UTC 2026
% Result : Theorem 151.55s 22.68s
% Output : CNFRefutation 151.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 6
% Syntax : Number of formulae : 106 ( 102 unt; 0 def)
% Number of atoms : 110 ( 109 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 2 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 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 : 229 ( 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(f03,axiom,
! [X1,X2] : mult(rd(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
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(f01,axiom,
! [X1,X2] : mult(X2,ld(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(goals,conjecture,
! [X4,X5] :
( mult(rd(X5,X5),X4) = X4
& mult(X4,rd(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,
! [X10,X11] : mult(rd(X11,X10),X10) = X11,
inference(variable_rename,[status(thm)],[f03]) ).
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(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X12,X13] : rd(mult(X13,X12),X12) = X13,
inference(variable_rename,[status(thm)],[f04]) ).
cnf(c_0_12,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
mult(rd(X1,X2),mult(X2,mult(X3,X2))) = mult(mult(X1,X3),X2),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_14,plain,
! [X6,X7] : mult(X7,ld(X7,X6)) = X6,
inference(variable_rename,[status(thm)],[f01]) ).
cnf(c_0_15,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
ld(rd(X1,X2),mult(mult(X1,X3),X2)) = mult(X2,mult(X3,X2)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
mult(X1,ld(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
rd(mult(X1,mult(X2,mult(X3,X2))),X2) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_15,c_0_9]) ).
cnf(c_0_19,plain,
ld(rd(X1,X2),mult(X3,X2)) = mult(X2,mult(ld(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
rd(mult(X1,mult(X2,X3)),X2) = mult(mult(X1,X2),rd(X3,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_10]) ).
cnf(c_0_21,plain,
mult(X1,mult(ld(X2,rd(X2,X1)),X1)) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_22,plain,
mult(mult(X1,X2),ld(X3,rd(X3,X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_15]),c_0_15]) ).
cnf(c_0_23,plain,
mult(mult(rd(X1,mult(X2,X3)),X2),rd(X3,X2)) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_10]) ).
cnf(c_0_24,plain,
mult(ld(X1,rd(X1,X2)),X2) = ld(X2,X2),
inference(spm,[status(thm)],[c_0_12,c_0_21]) ).
cnf(c_0_25,plain,
rd(X1,ld(X2,rd(X2,X3))) = mult(X1,X3),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_26,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_27,plain,
rd(rd(X1,X2),rd(X3,X2)) = mult(rd(X1,mult(X2,X3)),X2),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
cnf(c_0_28,plain,
mult(mult(X1,rd(X2,X3)),rd(X3,rd(X2,X3))) = rd(mult(X1,X2),rd(X2,X3)),
inference(spm,[status(thm)],[c_0_20,c_0_10]) ).
cnf(c_0_29,plain,
rd(ld(X1,X1),X1) = ld(X2,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_24]) ).
cnf(c_0_30,plain,
mult(X1,ld(X2,rd(X2,X3))) = rd(X1,X3),
inference(spm,[status(thm)],[c_0_22,c_0_10]) ).
cnf(c_0_31,plain,
rd(X1,ld(X2,X3)) = mult(X1,ld(X3,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_33,plain,
mult(rd(X1,mult(X2,mult(X3,X2))),X2) = rd(rd(X1,X2),X3),
inference(spm,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_34,plain,
mult(mult(X1,ld(X2,X2)),X2) = mult(rd(X1,X2),mult(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_28,c_0_29]),c_0_30]),c_0_31]),c_0_32]),c_0_31]),c_0_32]) ).
cnf(c_0_35,plain,
rd(rd(rd(X1,X2),X3),X2) = rd(X1,mult(X2,mult(X3,X2))),
inference(spm,[status(thm)],[c_0_15,c_0_33]) ).
cnf(c_0_36,plain,
mult(rd(X1,X1),mult(X1,X1)) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_34,c_0_17]) ).
cnf(c_0_37,plain,
rd(mult(X1,X2),mult(X2,mult(X3,X2))) = rd(rd(X1,X3),X2),
inference(spm,[status(thm)],[c_0_35,c_0_15]) ).
cnf(c_0_38,plain,
mult(X1,rd(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_36]),c_0_15]),c_0_10]) ).
cnf(c_0_39,plain,
rd(mult(X1,rd(X2,X2)),X2) = mult(rd(X1,mult(X2,X2)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_10]),c_0_27]) ).
cnf(c_0_40,plain,
mult(mult(X1,X2),rd(ld(X2,X3),X2)) = rd(mult(X1,X3),X2),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_41,plain,
mult(rd(mult(X1,X2),mult(X2,X3)),X2) = rd(X1,rd(X3,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_42,plain,
mult(rd(X1,mult(X1,X1)),X1) = rd(X1,X1),
inference(spm,[status(thm)],[c_0_39,c_0_38]) ).
cnf(c_0_43,plain,
mult(X1,rd(ld(X2,X3),X2)) = rd(mult(rd(X1,X2),X3),X2),
inference(spm,[status(thm)],[c_0_40,c_0_10]) ).
cnf(c_0_44,plain,
rd(X1,rd(rd(X2,X2),X2)) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_38]),c_0_15]) ).
cnf(c_0_45,plain,
rd(rd(X1,X1),X1) = rd(X1,mult(X1,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_42]) ).
cnf(c_0_46,plain,
mult(X1,ld(mult(X2,X3),X2)) = rd(X1,X3),
inference(spm,[status(thm)],[c_0_31,c_0_12]) ).
cnf(c_0_47,plain,
ld(X1,X1) = rd(X1,X1),
inference(spm,[status(thm)],[c_0_12,c_0_38]) ).
cnf(c_0_48,plain,
ld(X1,rd(mult(rd(X1,X2),X3),X2)) = rd(ld(X2,X3),X2),
inference(spm,[status(thm)],[c_0_12,c_0_43]) ).
cnf(c_0_49,plain,
rd(X1,rd(X2,mult(X2,X2))) = mult(X1,X2),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
rd(X1,rd(X2,X2)) = mult(X1,rd(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_38]),c_0_47]) ).
cnf(c_0_51,plain,
mult(mult(X1,rd(X2,X3)),X3) = mult(rd(X1,X3),mult(X3,X2)),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_52,plain,
rd(mult(X1,X1),mult(X1,X1)) = rd(X1,X1),
inference(spm,[status(thm)],[c_0_15,c_0_36]) ).
cnf(c_0_53,plain,
mult(X1,rd(rd(X2,X2),X2)) = rd(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_38]),c_0_10]) ).
cnf(c_0_54,plain,
rd(rd(X1,rd(X2,X3)),X3) = rd(mult(X1,X3),mult(X3,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_41]) ).
cnf(c_0_55,plain,
mult(ld(rd(X1,mult(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(spm,[status(thm)],[c_0_48,c_0_49]),c_0_49]),c_0_9]),c_0_12]),c_0_49]) ).
cnf(c_0_56,plain,
mult(rd(X1,X2),mult(X2,X2)) = mult(mult(X1,X2),rd(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_38]),c_0_10]),c_0_50]),c_0_51]) ).
cnf(c_0_57,plain,
mult(mult(X1,X1),rd(X1,X1)) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_38,c_0_52]) ).
cnf(c_0_58,plain,
mult(X1,rd(X2,mult(X2,X2))) = rd(X1,X2),
inference(rw,[status(thm)],[c_0_53,c_0_45]) ).
cnf(c_0_59,plain,
mult(rd(X1,X2),rd(X2,X2)) = rd(mult(X1,X2),mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_38]),c_0_10]),c_0_54]) ).
cnf(c_0_60,plain,
rd(rd(X1,mult(X1,X1)),X1) = rd(X1,mult(X1,mult(X1,X1))),
inference(spm,[status(thm)],[c_0_35,c_0_45]) ).
cnf(c_0_61,plain,
ld(rd(X1,mult(X1,X1)),X2) = rd(mult(X1,mult(X2,X1)),X1),
inference(spm,[status(thm)],[c_0_15,c_0_55]) ).
cnf(c_0_62,plain,
mult(mult(mult(X1,X2),X2),rd(X2,X2)) = mult(X1,mult(X2,X2)),
inference(spm,[status(thm)],[c_0_56,c_0_15]) ).
cnf(c_0_63,plain,
rd(rd(X1,X1),mult(X1,X1)) = rd(X1,mult(X1,mult(X1,X1))),
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_57,c_0_58]),c_0_49]),c_0_42]),c_0_59]),c_0_42]),c_0_60]) ).
cnf(c_0_64,plain,
rd(mult(X1,mult(mult(rd(X1,mult(X1,X1)),X2),X1)),X1) = X2,
inference(spm,[status(thm)],[c_0_12,c_0_61]) ).
cnf(c_0_65,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_51,c_0_62]),c_0_15]) ).
cnf(c_0_66,plain,
mult(X1,rd(X2,mult(X2,mult(X2,X2)))) = rd(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_57]),c_0_10]),c_0_63]) ).
cnf(c_0_67,plain,
mult(X1,mult(mult(rd(X1,mult(X1,X1)),X2),X1)) = mult(X2,X1),
inference(spm,[status(thm)],[c_0_10,c_0_64]) ).
cnf(c_0_68,plain,
rd(rd(X1,mult(X2,X2)),X2) = rd(rd(X1,X2),mult(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(spm,[status(thm)],[c_0_58,c_0_65]),c_0_58]),c_0_58]),c_0_60]),c_0_66]),c_0_58]),c_0_60]),c_0_66]) ).
cnf(c_0_69,plain,
rd(X1,rd(X2,mult(X2,mult(X2,X2)))) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_57]),c_0_15]),c_0_63]) ).
cnf(c_0_70,plain,
rd(rd(X1,X1),X1) = ld(X2,rd(X2,X1)),
inference(rw,[status(thm)],[c_0_29,c_0_47]) ).
cnf(c_0_71,plain,
mult(X1,mult(ld(X2,rd(X3,X1)),X1)) = ld(rd(X2,X1),X3),
inference(spm,[status(thm)],[c_0_19,c_0_10]) ).
cnf(c_0_72,plain,
mult(mult(X1,ld(X2,X3)),ld(X3,X2)) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_31]) ).
cnf(c_0_73,plain,
mult(rd(X1,mult(X1,X1)),rd(mult(X1,X2),X1)) = rd(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_67,c_0_58]),c_0_68]),c_0_63]),c_0_69]),c_0_10]),c_0_58]),c_0_58]) ).
cnf(c_0_74,plain,
mult(ld(X1,rd(X1,X2)),mult(X2,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_70]),c_0_10]),c_0_38]) ).
cnf(c_0_75,plain,
ld(mult(X1,X2),rd(mult(X1,X3),X2)) = rd(ld(X2,X3),X2),
inference(spm,[status(thm)],[c_0_48,c_0_15]) ).
cnf(c_0_76,plain,
ld(X1,ld(rd(X2,X1),X3)) = mult(ld(X2,rd(X3,X1)),X1),
inference(spm,[status(thm)],[c_0_12,c_0_71]) ).
cnf(c_0_77,plain,
mult(mult(X1,rd(X2,X2)),rd(X2,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_47]),c_0_47]) ).
cnf(c_0_78,plain,
mult(rd(X1,mult(X2,mult(X2,X1))),X2) = rd(X2,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_73]),c_0_27]) ).
cnf(c_0_79,plain,
mult(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_74]),c_0_24]),c_0_47]) ).
cnf(c_0_80,plain,
rd(ld(X1,rd(X2,X2)),X1) = ld(mult(X2,X1),rd(X2,X1)),
inference(spm,[status(thm)],[c_0_75,c_0_38]) ).
cnf(c_0_81,plain,
mult(ld(X1,rd(rd(X1,X2),X2)),X2) = ld(X2,mult(rd(X1,mult(X2,X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_47]),c_0_27]) ).
cnf(c_0_82,plain,
mult(ld(rd(X1,X1),X2),rd(X1,X1)) = mult(rd(X1,X1),mult(X2,rd(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_50]),c_0_50]),c_0_9]),c_0_12]),c_0_50]) ).
cnf(c_0_83,plain,
rd(X1,mult(rd(X2,X2),mult(rd(X2,X2),X1))) = rd(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]),c_0_50]),c_0_79]),c_0_79]) ).
cnf(c_0_84,plain,
ld(mult(mult(X1,X1),X2),rd(mult(X1,X1),X2)) = ld(mult(X1,X2),rd(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_57]),c_0_80]) ).
cnf(c_0_85,plain,
mult(mult(X1,mult(X2,rd(X3,X3))),rd(X3,X3)) = mult(mult(X1,rd(X3,X3)),mult(rd(X3,X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_50]),c_0_50]) ).
cnf(c_0_86,plain,
mult(rd(X1,X1),rd(X2,mult(rd(X1,X1),X2))) = rd(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(spm,[status(thm)],[c_0_77,c_0_81]),c_0_82]),c_0_77]),c_0_50]),c_0_50]),c_0_77]),c_0_47]) ).
cnf(c_0_87,plain,
mult(rd(X1,X1),mult(rd(X1,X1),X2)) = ld(rd(X1,X1),X2),
inference(spm,[status(thm)],[c_0_32,c_0_83]) ).
cnf(c_0_88,plain,
mult(mult(rd(X1,mult(rd(X2,X2),X3)),rd(X2,X2)),mult(X3,rd(X2,X2))) = mult(X1,rd(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_50]),c_0_50]) ).
cnf(c_0_89,plain,
rd(mult(X1,mult(rd(X2,X2),X1)),mult(X1,mult(rd(X2,X2),X1))) = rd(X1,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_77]),c_0_50]),c_0_9]),c_0_77]),c_0_47]),c_0_77]),c_0_50]),c_0_77]),c_0_47]) ).
cnf(c_0_90,plain,
rd(mult(X1,X2),mult(X2,X2)) = mult(rd(X1,mult(X2,X2)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_50]),c_0_59]) ).
cnf(c_0_91,plain,
ld(rd(X1,X1),rd(X2,X2)) = rd(X2,mult(rd(X1,X1),X2)),
inference(spm,[status(thm)],[c_0_12,c_0_86]) ).
fof(c_0_92,negated_conjecture,
~ ! [X4,X5] :
( mult(rd(X5,X5),X4) = X4
& mult(X4,rd(X5,X5)) = X4 ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_93,plain,
mult(mult(mult(X1,mult(X2,mult(X3,X2))),X4),X2) = mult(mult(mult(X1,X2),X3),mult(X2,mult(X4,X2))),
inference(spm,[status(thm)],[c_0_9,c_0_9]) ).
cnf(c_0_94,plain,
ld(rd(X1,X1),rd(X2,mult(rd(X1,X1),X2))) = mult(rd(X1,X1),rd(X2,X2)),
inference(spm,[status(thm)],[c_0_87,c_0_86]) ).
cnf(c_0_95,plain,
rd(X1,mult(rd(X2,X2),X1)) = mult(rd(X2,X2),rd(X1,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(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_88,c_0_89]),c_0_50]),c_0_59]),c_0_90]),c_0_42]),c_0_59]),c_0_90]),c_0_42]),c_0_77]),c_0_85]),c_0_59]),c_0_90]),c_0_42]),c_0_87]),c_0_91]) ).
fof(c_0_96,negated_conjecture,
( mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0
| mult(esk1_0,rd(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_92])])])]) ).
cnf(c_0_97,plain,
mult(mult(mult(X1,X2),X3),mult(X2,mult(rd(mult(X1,mult(X2,mult(X3,X2))),mult(X1,mult(X2,mult(X3,X2)))),X2))) = mult(mult(X1,mult(X2,mult(X3,X2))),X2),
inference(spm,[status(thm)],[c_0_93,c_0_38]) ).
cnf(c_0_98,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95]),c_0_12]) ).
cnf(c_0_99,plain,
rd(mult(X1,rd(X2,X2)),mult(X3,rd(X2,X2))) = mult(rd(X1,mult(rd(X2,X2),X3)),rd(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_50]),c_0_50]) ).
cnf(c_0_100,negated_conjecture,
( mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0
| mult(esk1_0,rd(esk2_0,esk2_0)) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_101,plain,
mult(X1,rd(X2,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(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_97,c_0_98]),c_0_79]),c_0_79]),c_0_99]),c_0_95]),c_0_98]),c_0_98]),c_0_79]),c_0_79]),c_0_9]),c_0_98]),c_0_79]),c_0_79]),c_0_77]) ).
cnf(c_0_102,plain,
ld(X1,mult(mult(X1,X2),rd(X1,X1))) = mult(rd(X1,X1),mult(X2,rd(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_38]),c_0_50]),c_0_50]),c_0_82]) ).
cnf(c_0_103,negated_conjecture,
mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101])]) ).
cnf(c_0_104,plain,
mult(rd(X1,X1),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_101]),c_0_12]),c_0_101]) ).
cnf(c_0_105,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP655+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.58 % Computer : n004.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Sun Sep 20 20:29:06 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.62 Running first-order theorem proving
% 0.14/0.63 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
% 151.55/22.68 % Version: 3.5.1
% 151.55/22.68 % Preprocessing class: FSSSSMSSSSSNFFN.
% 151.55/22.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 151.55/22.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 151.55/22.68 % Starting new_bool_3 with 300s (1) cores
% 151.55/22.68 % Starting new_bool_1 with 300s (1) cores
% 151.55/22.68 % Starting sh5l with 300s (1) cores
% 151.55/22.68 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1435453 completed with status 0
% 151.55/22.68 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 151.55/22.68 % Preprocessing class: FSSSSMSSSSSNFFN.
% 151.55/22.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 151.55/22.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 151.55/22.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 151.55/22.68 % No SInE strategy applied
% 151.55/22.68 % Search class: FUHPM-FFSF22-MFFFFFNN
% 151.55/22.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 151.55/22.68 % Starting SubtermCWHack with 136s (1) cores
% 151.55/22.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 151.55/22.68 % Starting H----_102_C18_F1_PI_AE_Q4_CS_SP_PS_S5PRR_S2S with 136s (1) cores
% 151.55/22.68 % Starting new_bool_3 with 136s (1) cores
% 151.55/22.68 % Starting new_bool_1 with 136s (1) cores
% 151.55/22.68 % new_bool_1 with pid 1435461 completed with status 0
% 151.55/22.68 % Result found by new_bool_1
% 151.55/22.68 % Preprocessing class: FSSSSMSSSSSNFFN.
% 151.55/22.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 151.55/22.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 151.55/22.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 151.55/22.68 % No SInE strategy applied
% 151.55/22.68 % Search class: FUHPM-FFSF22-MFFFFFNN
% 151.55/22.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 151.55/22.68 % Starting SubtermCWHack with 136s (1) cores
% 151.55/22.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 151.55/22.68 % Starting H----_102_C18_F1_PI_AE_Q4_CS_SP_PS_S5PRR_S2S with 136s (1) cores
% 151.55/22.68 % Starting new_bool_3 with 136s (1) cores
% 151.55/22.68 % Starting new_bool_1 with 136s (1) cores
% 151.55/22.68 % Preprocessing time : 0.001 s
% 151.55/22.68 % Presaturation interreduction done
% 151.55/22.68
% 151.55/22.68 % Proof found!
% 151.55/22.68 % SZS status Theorem
% 151.55/22.68 % SZS output start CNFRefutation
% See solution above
% 151.55/22.68 % Parsed axioms : 6
% 151.55/22.68 % Removed by relevancy pruning/SinE : 0
% 151.55/22.68 % Initial clauses : 6
% 151.55/22.68 % Removed in clause preprocessing : 0
% 151.55/22.68 % Initial clauses in saturation : 6
% 151.55/22.68 % Processed clauses : 7700
% 151.55/22.68 % ...of these trivial : 3325
% 151.55/22.68 % ...subsumed : 3194
% 151.55/22.68 % ...remaining for further processing : 1181
% 151.55/22.68 % Other redundant clauses eliminated : 0
% 151.55/22.68 % Clauses deleted for lack of memory : 0
% 151.55/22.68 % Backward-subsumed : 4
% 151.55/22.68 % Backward-rewritten : 280
% 151.55/22.68 % Generated clauses : 1001980
% 151.55/22.68 % ...of the previous two non-redundant : 894362
% 151.55/22.68 % ...aggressively subsumed : 0
% 151.55/22.68 % Contextual simplify-reflections : 0
% 151.55/22.68 % Paramodulations : 1001980
% 151.55/22.68 % Factorizations : 0
% 151.55/22.68 % NegExts : 0
% 151.55/22.68 % Equation resolutions : 0
% 151.55/22.68 % Disequality decompositions : 0
% 151.55/22.68 % Total rewrite steps : 2087628
% 151.55/22.68 % ...of those cached : 1881396
% 151.55/22.68 % Propositional unsat checks : 0
% 151.55/22.68 % Propositional check models : 0
% 151.55/22.68 % Propositional check unsatisfiable : 0
% 151.55/22.68 % Propositional clauses : 0
% 151.55/22.68 % Propositional clauses after purity: 0
% 151.55/22.68 % Propositional unsat core size : 0
% 151.55/22.68 % Propositional preprocessing time : 0.000
% 151.55/22.68 % Propositional encoding time : 0.000
% 151.55/22.68 % Propositional solver time : 0.000
% 151.55/22.68 % Success case prop preproc time : 0.000
% 151.55/22.68 % Success case prop encoding time : 0.000
% 151.55/22.68 % Success case prop solver time : 0.000
% 151.55/22.68 % Current number of processed clauses : 891
% 151.55/22.68 % Positive orientable unit clauses : 833
% 151.55/22.68 % Positive unorientable unit clauses: 58
% 151.55/22.68 % Negative unit clauses : 0
% 151.55/22.68 % Non-unit-clauses : 0
% 151.55/22.68 % Current number of unprocessed clauses: 885064
% 151.55/22.68 % ...number of literals in the above : 885064
% 151.55/22.68 % Current number of archived formulas : 0
% 151.55/22.68 % Current number of archived clauses : 290
% 151.55/22.68 % Clause-clause subsumption calls (NU) : 0
% 151.55/22.68 % Rec. Clause-clause subsumption calls : 0
% 151.55/22.68 % Non-unit clause-clause subsumptions : 0
% 151.55/22.68 % Unit Clause-clause subsumption calls : 1675
% 151.55/22.68 % Rewrite failures with RHS unbound : 5525
% 151.55/22.68 % BW rewrite match attempts : 14850
% 151.55/22.68 % BW rewrite match successes : 752
% 151.55/22.68 % Condensation attempts : 0
% 151.55/22.68 % Condensation successes : 0
% 151.55/22.68 % Termbank termtop insertions : 29957014
% 151.55/22.68 % Search garbage collected termcells : 25
% 151.55/22.68
% 151.55/22.68 % -------------------------------------------------
% 151.55/22.68 % User time : 20.884 s
% 151.55/22.68 % System time : 0.692 s
% 151.55/22.68 % Total time : 21.575 s
% 151.55/22.68 % Maximum resident set size: 3632 pages
% 151.55/22.68
% 151.55/22.68 % -------------------------------------------------
% 151.55/22.68 % User time : 104.211 s
% 151.55/22.68 % System time : 3.335 s
% 151.55/22.68 % Total time : 107.547 s
% 151.55/22.68 % Maximum resident set size: 4608 pages
% 151.55/22.68 % E exiting
%------------------------------------------------------------------------------