%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP748+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 : n019.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 04:27:12 PM UTC 2026
% Result : Theorem 1.20s 1.97s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 47 unt; 0 def)
% Number of atoms : 71 ( 70 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 9 ~; 12 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 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 : 102 ( 0 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f07,axiom,
! [X3,X1,X2] : mult(mult(mult(X2,X1),X3),X1) = mult(X2,mult(mult(X1,X3),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
fof(f10,axiom,
! [X2] : mult(i(X2),X2) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
fof(f06,axiom,
! [X2] : mult(unit,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
fof(f01,axiom,
! [X1,X2] : mult(X2,ld(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f08,axiom,
! [X1,X2] : mult(mult(X2,X1),i(X1)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
fof(f03,axiom,
! [X1,X2] : mult(rd(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f09,axiom,
! [X2] : mult(X2,i(X2)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
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/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f11,axiom,
! [X1,X2] :
( mult(X2,X1) = mult(X1,X2)
| mult(i(X2),mult(X2,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
fof(f04,axiom,
! [X1,X2] : rd(mult(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f05,axiom,
! [X2] : mult(X2,unit) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f02,axiom,
! [X1,X2] : ld(X2,mult(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(c_0_12,plain,
! [X57,X58,X59] : mult(mult(mult(X59,X58),X57),X58) = mult(X59,mult(mult(X58,X57),X58)),
inference(variable_rename,[status(thm)],[f07]) ).
fof(c_0_13,plain,
! [X63] : mult(i(X63),X63) = unit,
inference(variable_rename,[status(thm)],[f10]) ).
fof(c_0_14,plain,
! [X56] : mult(unit,X56) = X56,
inference(variable_rename,[status(thm)],[f06]) ).
cnf(c_0_15,plain,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(mult(X2,X3),X2)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
mult(i(X1),X1) = unit,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
mult(unit,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,plain,
! [X47,X48] : mult(X48,ld(X48,X47)) = X47,
inference(variable_rename,[status(thm)],[f01]) ).
fof(c_0_19,plain,
! [X60,X61] : mult(mult(X61,X60),i(X60)) = X61,
inference(variable_rename,[status(thm)],[f08]) ).
fof(c_0_20,plain,
! [X51,X52] : mult(rd(X52,X51),X51) = X52,
inference(variable_rename,[status(thm)],[f03]) ).
fof(c_0_21,plain,
! [X62] : mult(X62,i(X62)) = unit,
inference(variable_rename,[status(thm)],[f09]) ).
cnf(c_0_22,plain,
mult(i(X1),mult(mult(X1,X2),X1)) = mult(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_23,plain,
mult(X1,ld(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
mult(mult(X1,X2),i(X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
mult(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
mult(X1,i(X1)) = unit,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
mult(i(X1),mult(X2,X1)) = mult(ld(X1,X2),X1),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
mult(X1,i(X2)) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
i(i(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_26]),c_0_17]) ).
fof(c_0_30,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]) ).
fof(c_0_31,plain,
! [X64,X65] :
( mult(X65,X64) = mult(X64,X65)
| mult(i(X65),mult(X65,X64)) = X64 ),
inference(variable_rename,[status(thm)],[f11]) ).
cnf(c_0_32,plain,
rd(ld(i(X1),X2),X1) = mult(X1,rd(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_28]) ).
fof(c_0_33,plain,
! [X53,X54] : rd(mult(X54,X53),X53) = X54,
inference(variable_rename,[status(thm)],[f04]) ).
fof(c_0_34,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_30])])]) ).
cnf(c_0_35,plain,
( mult(X1,X2) = mult(X2,X1)
| mult(i(X1),mult(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,plain,
mult(mult(X1,rd(X2,X1)),X1) = ld(i(X1),X2),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_37,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_38,plain,
! [X55] : mult(X55,unit) = X55,
inference(variable_rename,[status(thm)],[f05]) ).
cnf(c_0_39,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_34]) ).
cnf(c_0_40,plain,
( mult(i(X1),X2) = ld(X1,X2)
| mult(ld(X1,X2),X1) = X2 ),
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_41,plain,
ld(i(X1),mult(X2,X1)) = mult(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
mult(X1,unit) = X1,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,negated_conjecture,
mult(esk4_0,mult(mult(esk6_0,esk5_0),esk6_0)) != mult(esk4_0,mult(esk6_0,mult(esk5_0,esk6_0))),
inference(rw,[status(thm)],[c_0_39,c_0_15]) ).
cnf(c_0_44,plain,
( mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1))
| mult(X1,X2) = mult(X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_29]),c_0_28]),c_0_37]) ).
fof(c_0_45,plain,
! [X49,X50] : ld(X50,mult(X50,X49)) = X49,
inference(variable_rename,[status(thm)],[f02]) ).
cnf(c_0_46,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_42]),c_0_42]) ).
cnf(c_0_47,negated_conjecture,
mult(esk5_0,esk6_0) = mult(esk6_0,esk5_0),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,negated_conjecture,
mult(mult(esk6_0,esk5_0),esk6_0) = mult(esk5_0,mult(esk6_0,esk6_0)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
mult(esk4_0,mult(mult(esk6_0,esk5_0),esk6_0)) != mult(esk4_0,mult(esk6_0,mult(esk6_0,esk5_0))),
inference(rw,[status(thm)],[c_0_43,c_0_47]) ).
cnf(c_0_51,plain,
( ld(i(X1),X2) = mult(X1,X2)
| mult(X1,X2) = mult(X2,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_35]) ).
cnf(c_0_52,negated_conjecture,
ld(i(esk6_0),mult(esk6_0,esk5_0)) = mult(esk5_0,mult(esk6_0,esk6_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_47]),c_0_49]) ).
cnf(c_0_53,negated_conjecture,
mult(esk4_0,mult(esk5_0,mult(esk6_0,esk6_0))) != mult(esk4_0,mult(esk6_0,mult(esk6_0,esk5_0))),
inference(rw,[status(thm)],[c_0_50,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
mult(esk5_0,mult(esk6_0,esk6_0)) = mult(esk6_0,mult(esk6_0,esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_49])]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.21 % Problem : GRP748+1 : TPTP v9.2.1. Released v4.0.0.
% 0.02/0.21 % 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
% 0.12/0.49 % Computer : n019.cluster.edu
% 0.12/0.49 % Model : x86_64 x86_64
% 0.12/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.49 % Memory : 8042.1875MB
% 0.12/0.49 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.49 % CPULimit : 300
% 0.12/0.49 % WCLimit : 300
% 0.12/0.49 % DateTime : Mon May 4 19:03:59 EDT 2026
% 0.12/0.49 % CPUTime :
% 0.12/0.50 % start to proof: theBenchmark
% 1.20/1.97 % Version : CSE_E---1.7
% 1.20/1.97 % Problem : theBenchmark.p
% 1.20/1.97 % SZS status Theorem for theBenchmark.p
% 1.20/1.97 % SZS output start CNFRefutation
% See solution above
% 1.20/1.97 % Total time : 1.393s
%------------------------------------------------------------------------------