%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP667+6 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n016.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 04:26:50 PM UTC 2026
% Result : Theorem 46.03s 26.83s
% Output : CNFRefutation 46.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 10
% Syntax : Number of formulae : 136 ( 133 unt; 0 def)
% Number of atoms : 145 ( 144 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 15 ( 6 ~; 6 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 13 con; 0-2 aty)
% Number of variables : 248 ( 0 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f07,axiom,
! [X3,X1,X2] : mult(mult(X2,X1),mult(mult(X3,X1),X3)) = mult(mult(X2,mult(mult(X1,X3),X1)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
fof(f08,axiom,
! [X1,X2] : mult(mult(X2,X1),X2) = mult(X2,mult(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
fof(f05,axiom,
! [X2] : mult(X2,unit) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f06,axiom,
! [X2] : mult(unit,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
fof(f04,axiom,
! [X1,X2] : rd(mult(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f03,axiom,
! [X1,X2] : mult(rd(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f09,axiom,
! [X2] : mult(f(X2),f(X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).
fof(f02,axiom,
! [X1,X2] : ld(X2,mult(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f01,axiom,
! [X1,X2] : mult(X2,ld(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(goals,conjecture,
( ! [X4,X5,X6] : mult(X6,mult(X4,mult(X6,X5))) = mult(mult(mult(X6,X4),X6),X5)
| ! [X7,X8,X9] : mult(X7,mult(X9,mult(X8,X9))) = mult(mult(mult(X7,X9),X8),X9)
| ! [X10,X11,X12] : mult(mult(X12,X10),mult(X11,X12)) = mult(mult(X12,mult(X10,X11)),X12)
| ! [X13,X14,X15] : mult(mult(X15,X13),mult(X14,X15)) = mult(X15,mult(mult(X13,X14),X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_10,plain,
! [X54,X55,X56] : mult(mult(X56,X55),mult(mult(X54,X55),X54)) = mult(mult(X56,mult(mult(X55,X54),X55)),X54),
inference(variable_rename,[status(thm)],[f07]) ).
fof(c_0_11,plain,
! [X57,X58] : mult(mult(X58,X57),X58) = mult(X58,mult(X57,X58)),
inference(variable_rename,[status(thm)],[f08]) ).
fof(c_0_12,plain,
! [X52] : mult(X52,unit) = X52,
inference(variable_rename,[status(thm)],[f05]) ).
cnf(c_0_13,plain,
mult(mult(X1,X2),mult(mult(X3,X2),X3)) = mult(mult(X1,mult(mult(X2,X3),X2)),X3),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X53] : mult(unit,X53) = X53,
inference(variable_rename,[status(thm)],[f06]) ).
fof(c_0_16,plain,
! [X50,X51] : rd(mult(X51,X50),X50) = X51,
inference(variable_rename,[status(thm)],[f04]) ).
cnf(c_0_17,plain,
mult(X1,unit) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
mult(mult(X1,mult(X2,mult(X3,X2))),X3) = mult(mult(X1,X2),mult(X3,mult(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).
cnf(c_0_19,plain,
mult(unit,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_17]),c_0_19]),c_0_19]) ).
fof(c_0_22,plain,
! [X48,X49] : mult(rd(X49,X48),X48) = X49,
inference(variable_rename,[status(thm)],[f03]) ).
cnf(c_0_23,plain,
rd(mult(X1,mult(X2,X2)),X2) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
mult(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,plain,
mult(rd(X1,mult(X2,X2)),X2) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_26,plain,
! [X59] : mult(f(X59),f(X59)) = X59,
inference(variable_rename,[status(thm)],[f09]) ).
fof(c_0_27,plain,
! [X46,X47] : ld(X47,mult(X47,X46)) = X46,
inference(variable_rename,[status(thm)],[f02]) ).
cnf(c_0_28,plain,
rd(mult(X1,mult(X2,X1)),X1) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_29,plain,
rd(rd(X1,X2),X2) = rd(X1,mult(X2,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_30,plain,
rd(X1,X1) = unit,
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_31,plain,
mult(f(X1),f(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
mult(X1,rd(X2,X1)) = rd(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_28,c_0_24]) ).
fof(c_0_34,plain,
! [X44,X45] : mult(X45,ld(X45,X44)) = X44,
inference(variable_rename,[status(thm)],[f01]) ).
cnf(c_0_35,plain,
rd(X1,mult(X1,X1)) = rd(unit,X1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,plain,
mult(f(X1),X1) = mult(X1,f(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_31]),c_0_31]) ).
cnf(c_0_37,plain,
ld(X1,rd(mult(X1,X2),X1)) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
mult(X1,ld(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
rd(f(X1),X1) = rd(unit,f(X1)),
inference(spm,[status(thm)],[c_0_35,c_0_31]) ).
cnf(c_0_40,plain,
rd(mult(X1,f(X1)),X1) = f(X1),
inference(spm,[status(thm)],[c_0_20,c_0_36]) ).
cnf(c_0_41,plain,
mult(rd(X1,X2),mult(X2,X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
cnf(c_0_42,plain,
rd(ld(X1,X2),X1) = ld(X1,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
ld(X1,unit) = rd(unit,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_17]),c_0_30]) ).
cnf(c_0_44,plain,
mult(X1,mult(ld(X1,X2),X1)) = mult(X2,X1),
inference(spm,[status(thm)],[c_0_14,c_0_38]) ).
cnf(c_0_45,plain,
mult(mult(X1,mult(X2,X1)),X2) = mult(X1,mult(X2,mult(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_19]) ).
cnf(c_0_46,plain,
mult(X1,rd(unit,f(X1))) = f(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_39]),c_0_40]) ).
cnf(c_0_47,plain,
mult(rd(X1,f(X2)),X2) = mult(X1,f(X2)),
inference(spm,[status(thm)],[c_0_41,c_0_31]) ).
cnf(c_0_48,plain,
ld(X1,rd(unit,X1)) = rd(rd(unit,X1),X1),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_38]) ).
cnf(c_0_50,plain,
mult(ld(X1,X2),X1) = ld(X1,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_44]) ).
cnf(c_0_51,plain,
mult(rd(unit,f(X1)),mult(X1,f(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_24]),c_0_19]),c_0_47]),c_0_19]) ).
cnf(c_0_52,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_53,plain,
ld(rd(unit,X1),X1) = rd(X1,rd(unit,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_43]),c_0_43]) ).
cnf(c_0_54,plain,
ld(rd(X1,X2),mult(X1,X2)) = mult(X2,X2),
inference(spm,[status(thm)],[c_0_32,c_0_41]) ).
cnf(c_0_55,plain,
ld(ld(X1,X2),ld(X1,mult(X2,X1))) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_50]) ).
cnf(c_0_56,plain,
ld(rd(unit,f(X1)),X1) = mult(X1,f(X1)),
inference(spm,[status(thm)],[c_0_32,c_0_51]) ).
cnf(c_0_57,plain,
rd(X1,rd(unit,X1)) = mult(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_35]),c_0_53]) ).
cnf(c_0_58,plain,
mult(mult(X1,X2),mult(X1,mult(X2,X1))) = mult(X1,mult(X2,mult(X1,mult(X2,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_18]),c_0_45]) ).
cnf(c_0_59,plain,
rd(mult(X1,X2),f(X2)) = mult(X1,f(X2)),
inference(spm,[status(thm)],[c_0_23,c_0_31]) ).
cnf(c_0_60,plain,
mult(ld(X1,X2),ld(X1,X2)) = ld(X1,mult(X2,ld(X1,X2))),
inference(spm,[status(thm)],[c_0_54,c_0_49]) ).
cnf(c_0_61,plain,
ld(mult(X1,f(X1)),X1) = rd(unit,f(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_46]),c_0_53]),c_0_57]),c_0_31]) ).
cnf(c_0_62,plain,
mult(rd(unit,X1),rd(unit,X1)) = rd(unit,mult(X1,X1)),
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_49]),c_0_43]),c_0_29]),c_0_43]),c_0_43]) ).
cnf(c_0_63,plain,
mult(X1,mult(ld(X1,X2),mult(X2,X1))) = mult(X2,mult(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_50]),c_0_38]),c_0_38]),c_0_38]) ).
cnf(c_0_64,plain,
mult(mult(X1,f(X2)),X2) = mult(mult(X1,X2),f(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_59]),c_0_31]) ).
cnf(c_0_65,plain,
mult(mult(f(X1),X2),X1) = mult(f(X1),mult(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_28]),c_0_14]),c_0_21]),c_0_31]) ).
cnf(c_0_66,plain,
ld(mult(X1,f(X1)),f(X1)) = rd(unit,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_31]),c_0_46]) ).
cnf(c_0_67,plain,
mult(ld(X1,X2),mult(X2,X1)) = ld(X1,mult(X2,mult(X2,X1))),
inference(spm,[status(thm)],[c_0_32,c_0_63]) ).
cnf(c_0_68,plain,
mult(mult(X1,X1),rd(unit,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_35]),c_0_14]),c_0_20]) ).
cnf(c_0_69,plain,
ld(rd(unit,X1),X1) = mult(X1,X1),
inference(rw,[status(thm)],[c_0_53,c_0_57]) ).
cnf(c_0_70,plain,
mult(f(X1),mult(X1,f(X1))) = mult(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_36]),c_0_36]),c_0_21]),c_0_31]) ).
cnf(c_0_71,plain,
ld(mult(X1,f(X2)),mult(X1,X2)) = f(X2),
inference(spm,[status(thm)],[c_0_52,c_0_59]) ).
cnf(c_0_72,plain,
rd(f(X1),rd(unit,X1)) = mult(X1,f(X1)),
inference(spm,[status(thm)],[c_0_49,c_0_66]) ).
cnf(c_0_73,plain,
mult(ld(X1,rd(X2,X1)),X2) = ld(X1,mult(rd(X2,X1),X2)),
inference(spm,[status(thm)],[c_0_67,c_0_24]) ).
cnf(c_0_74,plain,
mult(rd(unit,X1),mult(X1,mult(X1,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_45,c_0_68]),c_0_24]),c_0_19]),c_0_41]),c_0_19]),c_0_14]) ).
cnf(c_0_75,plain,
ld(rd(unit,X1),mult(X1,X1)) = rd(mult(X1,X1),rd(unit,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_69]),c_0_57]) ).
cnf(c_0_76,plain,
ld(rd(unit,X1),f(X1)) = mult(X1,f(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_66]),c_0_70]),c_0_71]) ).
cnf(c_0_77,plain,
rd(mult(X1,f(X1)),rd(unit,X1)) = rd(f(X1),rd(unit,mult(X1,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_72]),c_0_62]) ).
cnf(c_0_78,plain,
rd(rd(mult(X1,X2),X1),rd(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_33]) ).
cnf(c_0_79,plain,
rd(X1,mult(X1,f(X1))) = rd(unit,f(X1)),
inference(spm,[status(thm)],[c_0_20,c_0_51]) ).
cnf(c_0_80,plain,
rd(ld(X1,mult(rd(X2,X1),X2)),X2) = ld(X1,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_73]) ).
cnf(c_0_81,plain,
rd(mult(X1,X1),rd(unit,X1)) = mult(X1,mult(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_74]),c_0_75]) ).
cnf(c_0_82,plain,
rd(mult(X1,mult(X2,X1)),f(X1)) = mult(mult(X1,X2),f(X1)),
inference(spm,[status(thm)],[c_0_59,c_0_14]) ).
cnf(c_0_83,plain,
mult(mult(X1,X1),f(X1)) = mult(X1,mult(X1,f(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_64]),c_0_36]) ).
cnf(c_0_84,plain,
ld(rd(unit,X1),mult(X1,f(X1))) = rd(f(X1),rd(unit,mult(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_76]),c_0_72]),c_0_77]) ).
cnf(c_0_85,plain,
ld(X1,f(X1)) = rd(f(X1),X1),
inference(spm,[status(thm)],[c_0_37,c_0_40]) ).
cnf(c_0_86,plain,
ld(rd(X1,mult(X2,X2)),rd(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_32,c_0_25]) ).
cnf(c_0_87,plain,
rd(X1,rd(unit,f(X1))) = mult(X1,f(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_14]),c_0_36]),c_0_20]) ).
cnf(c_0_88,plain,
mult(mult(ld(X1,X2),X2),X1) = mult(ld(X1,X2),mult(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_38]),c_0_50]),c_0_38]) ).
cnf(c_0_89,plain,
rd(f(X1),rd(unit,mult(X1,X1))) = mult(X1,mult(X1,f(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(spm,[status(thm)],[c_0_80,c_0_72]),c_0_21]),c_0_31]),c_0_75]),c_0_81]),c_0_82]),c_0_83]),c_0_84]) ).
cnf(c_0_90,plain,
mult(mult(X1,X2),ld(X2,X1)) = mult(X2,mult(ld(X2,X1),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_50]),c_0_38]),c_0_38]) ).
cnf(c_0_91,plain,
ld(X1,f(X1)) = rd(unit,f(X1)),
inference(rw,[status(thm)],[c_0_85,c_0_39]) ).
cnf(c_0_92,plain,
ld(mult(X1,X1),mult(X1,f(X1))) = rd(unit,f(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_62]),c_0_31]),c_0_57]) ).
cnf(c_0_93,plain,
mult(mult(ld(X1,X2),X2),X1) = ld(X1,mult(X2,mult(X2,X1))),
inference(rw,[status(thm)],[c_0_88,c_0_67]) ).
cnf(c_0_94,plain,
rd(mult(X1,f(X1)),rd(unit,X1)) = mult(X1,mult(X1,f(X1))),
inference(rw,[status(thm)],[c_0_77,c_0_89]) ).
cnf(c_0_95,plain,
mult(rd(unit,X1),mult(X1,f(X1))) = f(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_66]),c_0_70]),c_0_71]) ).
cnf(c_0_96,plain,
rd(mult(X1,mult(X1,f(X1))),f(X1)) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_20,c_0_83]) ).
cnf(c_0_97,plain,
mult(mult(X1,mult(X2,f(X2))),f(X2)) = mult(mult(X1,f(X2)),mult(X2,f(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_31]),c_0_36]),c_0_31]),c_0_36]) ).
cnf(c_0_98,plain,
mult(mult(X1,mult(X2,mult(X1,X2))),X2) = mult(mult(X1,mult(X2,X1)),mult(X2,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_45]) ).
cnf(c_0_99,plain,
mult(mult(X1,f(X1)),rd(unit,f(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_36]),c_0_24]),c_0_17]) ).
cnf(c_0_100,plain,
mult(mult(X1,X1),rd(unit,f(X1))) = mult(X1,f(X1)),
inference(spm,[status(thm)],[c_0_38,c_0_92]) ).
cnf(c_0_101,plain,
mult(mult(X1,X2),mult(X1,X1)) = mult(X1,mult(X2,mult(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_14]),c_0_14]),c_0_21]) ).
cnf(c_0_102,plain,
rd(rd(X1,mult(X2,X2)),X2) = rd(rd(X1,X2),mult(X2,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_29]) ).
cnf(c_0_103,plain,
mult(X1,mult(ld(X1,X2),X2)) = rd(mult(X2,mult(X2,X1)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_93]),c_0_38]) ).
cnf(c_0_104,plain,
mult(mult(rd(X1,mult(X2,mult(X3,X2))),X2),mult(X3,mult(X2,X3))) = mult(X1,X3),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_105,plain,
mult(rd(unit,X1),mult(X1,mult(X1,f(X1)))) = mult(X1,f(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_94]),c_0_95]),c_0_72]) ).
cnf(c_0_106,plain,
mult(mult(X1,f(X1)),mult(X1,f(X1))) = mult(X1,mult(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_96]),c_0_31]),c_0_14]),c_0_97]) ).
cnf(c_0_107,plain,
mult(mult(X1,mult(X1,f(X1))),rd(unit,X1)) = mult(X1,f(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(spm,[status(thm)],[c_0_98,c_0_99]),c_0_47]),c_0_19]),c_0_21]),c_0_31]),c_0_100]),c_0_51]),c_0_14]),c_0_36]),c_0_62]),c_0_31]) ).
cnf(c_0_108,plain,
mult(mult(X1,mult(X2,mult(X2,f(X2)))),f(X2)) = mult(mult(X1,X2),mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_36]),c_0_70]) ).
cnf(c_0_109,plain,
mult(rd(X1,mult(X2,mult(X2,mult(X2,X2)))),X2) = rd(rd(X1,X2),mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_25]),c_0_101]),c_0_102]) ).
cnf(c_0_110,plain,
mult(mult(X1,X2),ld(X2,X1)) = rd(mult(X1,mult(X1,X2)),X2),
inference(rw,[status(thm)],[c_0_90,c_0_103]) ).
cnf(c_0_111,plain,
mult(X1,rd(unit,X2)) = rd(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(spm,[status(thm)],[c_0_104,c_0_105]),c_0_21]),c_0_106]),c_0_107]),c_0_95]),c_0_108]),c_0_109]),c_0_24]) ).
cnf(c_0_112,plain,
ld(mult(X1,X2),rd(mult(X1,mult(X1,X2)),X2)) = ld(X2,X1),
inference(spm,[status(thm)],[c_0_32,c_0_110]) ).
cnf(c_0_113,plain,
rd(X1,rd(unit,X2)) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_49]),c_0_43]) ).
cnf(c_0_114,plain,
mult(mult(X1,rd(X1,X2)),X2) = mult(rd(X1,X2),mult(X2,X1)),
inference(spm,[status(thm)],[c_0_90,c_0_52]) ).
cnf(c_0_115,plain,
ld(rd(unit,X1),X2) = mult(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_111]),c_0_111]),c_0_114]),c_0_32]) ).
cnf(c_0_116,plain,
mult(rd(unit,X1),X2) = ld(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_113]),c_0_19]) ).
cnf(c_0_117,plain,
ld(X1,rd(X1,X2)) = rd(unit,X2),
inference(spm,[status(thm)],[c_0_32,c_0_111]) ).
cnf(c_0_118,plain,
ld(rd(X1,X2),rd(mult(X1,X2),rd(X1,X2))) = rd(mult(X2,X2),rd(X1,X2)),
inference(spm,[status(thm)],[c_0_37,c_0_41]) ).
cnf(c_0_119,plain,
rd(ld(X1,X2),X2) = rd(unit,X1),
inference(spm,[status(thm)],[c_0_20,c_0_116]) ).
cnf(c_0_120,plain,
ld(mult(X1,X2),X1) = rd(unit,X2),
inference(spm,[status(thm)],[c_0_117,c_0_20]) ).
cnf(c_0_121,plain,
mult(mult(X1,mult(X2,X3)),ld(X3,X2)) = mult(mult(X1,X3),mult(ld(X3,X2),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_50]),c_0_38]),c_0_38]) ).
cnf(c_0_122,plain,
mult(ld(X1,X2),X2) = ld(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_116]),c_0_116]) ).
cnf(c_0_123,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(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(spm,[status(thm)],[c_0_118,c_0_119]),c_0_113]),c_0_88]),c_0_67]),c_0_115]),c_0_38]),c_0_113]) ).
cnf(c_0_124,plain,
rd(rd(unit,X1),X2) = rd(unit,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_125,plain,
mult(mult(X1,mult(X2,X3)),ld(X3,X2)) = mult(mult(X1,X3),ld(X3,mult(X2,X2))),
inference(rw,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_126,plain,
mult(f(X1),mult(f(X1),X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_123,c_0_31]) ).
cnf(c_0_127,plain,
ld(mult(f(X1),X2),X1) = ld(X2,f(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_124]),c_0_116]),c_0_116]) ).
fof(c_0_128,negated_conjecture,
~ ( ! [X4,X5,X6] : mult(X6,mult(X4,mult(X6,X5))) = mult(mult(mult(X6,X4),X6),X5)
| ! [X7,X8,X9] : mult(X7,mult(X9,mult(X8,X9))) = mult(mult(mult(X7,X9),X8),X9)
| ! [X10,X11,X12] : mult(mult(X12,X10),mult(X11,X12)) = mult(mult(X12,mult(X10,X11)),X12)
| ! [X13,X14,X15] : mult(mult(X15,X13),mult(X14,X15)) = mult(X15,mult(mult(X13,X14),X15)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_129,plain,
mult(mult(X1,X2),ld(X2,X3)) = rd(mult(X1,mult(X3,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_125,c_0_126]),c_0_120]),c_0_111]),c_0_31]),c_0_127]),c_0_125]),c_0_31]) ).
fof(c_0_130,negated_conjecture,
( mult(esk3_0,mult(esk1_0,mult(esk3_0,esk2_0))) != mult(mult(mult(esk3_0,esk1_0),esk3_0),esk2_0)
& mult(esk4_0,mult(esk6_0,mult(esk5_0,esk6_0))) != mult(mult(mult(esk4_0,esk6_0),esk5_0),esk6_0)
& mult(mult(esk9_0,esk7_0),mult(esk8_0,esk9_0)) != mult(mult(esk9_0,mult(esk7_0,esk8_0)),esk9_0)
& mult(mult(esk12_0,esk10_0),mult(esk11_0,esk12_0)) != mult(esk12_0,mult(mult(esk10_0,esk11_0),esk12_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_128])])]) ).
cnf(c_0_131,plain,
rd(mult(mult(X1,X2),mult(X3,mult(X2,X3))),X3) = mult(X1,mult(X2,mult(X3,X2))),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_132,plain,
rd(mult(X1,mult(X2,mult(X3,X2))),X2) = mult(mult(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_32]),c_0_14]) ).
cnf(c_0_133,negated_conjecture,
mult(esk4_0,mult(esk6_0,mult(esk5_0,esk6_0))) != mult(mult(mult(esk4_0,esk6_0),esk5_0),esk6_0),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_134,plain,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(X2,mult(X3,X2))),
inference(rw,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_135,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_134])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP667+6 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n016.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 19:01:36 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 46.03/26.83 % Version : CSE_E---1.7
% 46.03/26.83 % Problem : theBenchmark.p
% 46.03/26.83 % SZS status Theorem for theBenchmark.p
% 46.03/26.83 % SZS output start CNFRefutation
% See solution above
% 46.13/27.01 % Total time : 20.406s
%------------------------------------------------------------------------------