%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP747+1 : 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 : n005.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 1.89s 1.91s
% Output : CNFRefutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 62 ( 51 unt; 0 def)
% Number of atoms : 81 ( 80 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 29 ( 10 ~; 14 |; 5 &)
% ( 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 129 ( 0 sgn 28 !; 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/sandbox2/benchmark/theBenchmark.p',f07) ).
fof(f05,axiom,
! [X2] : mult(X2,unit) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f08,axiom,
! [X4,X5,X6] :
( ( mult(mult(X4,X5),X6) = mult(X4,mult(X6,X5))
& mult(mult(X4,X6),X5) = mult(X4,mult(X5,X6)) )
| ( mult(mult(X4,X5),X6) = mult(mult(X4,X6),X5)
& mult(X4,mult(X5,X6)) = mult(X4,mult(X6,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
fof(f06,axiom,
! [X2] : mult(unit,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
fof(f03,axiom,
! [X1,X2] : mult(rd(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f02,axiom,
! [X1,X2] : ld(X2,mult(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f04,axiom,
! [X1,X2] : rd(mult(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(goals,conjecture,
mult(mult(a,b),c) = mult(a,mult(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_8,plain,
! [X33,X34,X35] : mult(mult(mult(X35,X34),X33),X34) = mult(X35,mult(mult(X34,X33),X34)),
inference(variable_rename,[status(thm)],[f07]) ).
fof(c_0_9,plain,
! [X31] : mult(X31,unit) = X31,
inference(variable_rename,[status(thm)],[f05]) ).
fof(c_0_10,plain,
! [X36,X37,X38] :
( ( mult(mult(X36,X37),X38) = mult(mult(X36,X38),X37)
| mult(mult(X36,X37),X38) = mult(X36,mult(X38,X37)) )
& ( mult(X36,mult(X37,X38)) = mult(X36,mult(X38,X37))
| mult(mult(X36,X37),X38) = mult(X36,mult(X38,X37)) )
& ( mult(mult(X36,X37),X38) = mult(mult(X36,X38),X37)
| mult(mult(X36,X38),X37) = mult(X36,mult(X37,X38)) )
& ( mult(X36,mult(X37,X38)) = mult(X36,mult(X38,X37))
| mult(mult(X36,X38),X37) = mult(X36,mult(X37,X38)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[f08])]) ).
fof(c_0_11,plain,
! [X32] : mult(unit,X32) = X32,
inference(variable_rename,[status(thm)],[f06]) ).
cnf(c_0_12,plain,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(mult(X2,X3),X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
mult(X1,unit) = X1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X27,X28] : mult(rd(X28,X27),X27) = X28,
inference(variable_rename,[status(thm)],[f03]) ).
cnf(c_0_15,plain,
( mult(X1,mult(X2,X3)) = mult(X1,mult(X3,X2))
| mult(mult(X1,X3),X2) = mult(X1,mult(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
mult(unit,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X25,X26] : ld(X26,mult(X26,X25)) = X25,
inference(variable_rename,[status(thm)],[f02]) ).
cnf(c_0_18,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).
cnf(c_0_19,plain,
mult(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
mult(X1,X2) = mult(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_16]),c_0_16]),c_0_16])]) ).
cnf(c_0_21,plain,
( mult(mult(X1,X2),X3) = mult(mult(X1,X3),X2)
| mult(mult(X1,X3),X2) = mult(X1,mult(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
mult(rd(X1,X2),mult(X2,X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
mult(X1,rd(X2,X1)) = X2,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( mult(mult(X1,X2),X3) = mult(X1,mult(X3,X2))
| mult(mult(X1,X3),X2) != mult(X1,mult(X3,X2)) ),
inference(ef,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
ld(rd(X1,X2),mult(X1,X2)) = mult(X2,X2),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
ld(X1,X2) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_22,c_0_24]) ).
fof(c_0_28,plain,
! [X29,X30] : rd(mult(X30,X29),X29) = X30,
inference(variable_rename,[status(thm)],[f04]) ).
cnf(c_0_29,plain,
( mult(mult(X1,X2),X3) = mult(X1,mult(X3,X2))
| mult(X2,mult(X1,X3)) != mult(X1,mult(X3,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_30,plain,
rd(mult(X1,X2),rd(X1,X2)) = mult(X2,X2),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,plain,
mult(X1,mult(mult(X2,X1),X3)) = mult(X2,mult(X1,mult(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_20]),c_0_20]) ).
cnf(c_0_33,plain,
( mult(mult(X1,X2),X3) = mult(mult(X3,X2),X1)
| mult(mult(X3,X2),X1) != mult(X2,mult(X1,X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_20]) ).
cnf(c_0_34,plain,
rd(mult(X1,mult(X2,X1)),X2) = mult(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_20]) ).
cnf(c_0_35,plain,
rd(mult(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_31,c_0_20]) ).
cnf(c_0_36,plain,
mult(mult(X1,mult(X1,X2)),X3) = mult(X1,mult(mult(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_20,c_0_32]) ).
cnf(c_0_37,plain,
( mult(X1,mult(X2,rd(X3,X1))) = mult(X3,X2)
| mult(rd(X3,X1),mult(X2,X1)) != mult(X3,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_24]),c_0_20]) ).
cnf(c_0_38,plain,
mult(mult(X1,X2),mult(X1,X2)) = mult(X1,mult(X2,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_34,c_0_32]),c_0_20]),c_0_35]),c_0_36]),c_0_20]) ).
cnf(c_0_39,plain,
( mult(X1,mult(X2,rd(X3,X1))) = mult(X3,X2)
| mult(rd(X3,X1),mult(X1,X2)) != mult(X3,X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_20]) ).
cnf(c_0_40,plain,
mult(X1,mult(X2,rd(X2,X1))) = mult(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_24]),c_0_20]),c_0_24]),c_0_20]) ).
cnf(c_0_41,plain,
( mult(X1,mult(X2,rd(X3,X1))) = mult(X3,X2)
| mult(mult(X1,X2),rd(X3,X1)) != mult(X3,X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_20]) ).
cnf(c_0_42,plain,
mult(X1,rd(X1,X2)) = rd(mult(X1,X1),X2),
inference(spm,[status(thm)],[c_0_35,c_0_40]) ).
cnf(c_0_43,plain,
mult(X1,mult(X2,rd(X3,X1))) = mult(X3,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_21]),c_0_24]),c_0_24])]) ).
cnf(c_0_44,plain,
rd(rd(mult(X1,X1),X2),X1) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_35,c_0_42]) ).
cnf(c_0_45,plain,
rd(X1,rd(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_46,plain,
mult(X1,rd(X2,X3)) = rd(mult(X2,X1),X3),
inference(spm,[status(thm)],[c_0_35,c_0_43]) ).
cnf(c_0_47,plain,
rd(X1,rd(mult(X1,X1),X2)) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,plain,
rd(mult(X1,X1),rd(X1,X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_45]) ).
cnf(c_0_49,plain,
rd(rd(mult(X1,X2),X3),X2) = rd(X1,X3),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
cnf(c_0_50,plain,
rd(rd(X1,X2),X1) = rd(X1,mult(X1,X2)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,plain,
mult(X1,mult(X1,X2)) = mult(X2,mult(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_35]),c_0_20]) ).
cnf(c_0_52,plain,
rd(X1,mult(X1,X2)) = rd(unit,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_16]),c_0_50]) ).
cnf(c_0_53,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_51]) ).
fof(c_0_54,negated_conjecture,
mult(mult(a,b),c) != mult(a,mult(b,c)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).
cnf(c_0_55,plain,
rd(X1,rd(unit,X2)) = mult(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_52]),c_0_53]),c_0_35]) ).
cnf(c_0_56,negated_conjecture,
mult(mult(a,b),c) != mult(a,mult(b,c)),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_57,plain,
( mult(mult(X1,X2),X3) = mult(X1,mult(X3,X2))
| mult(mult(X1,X2),X3) != mult(X2,mult(X1,X3)) ),
inference(spm,[status(thm)],[c_0_39,c_0_35]) ).
cnf(c_0_58,plain,
mult(mult(X1,X2),X3) = mult(X2,mult(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_55]),c_0_55]) ).
cnf(c_0_59,negated_conjecture,
mult(c,mult(a,b)) != mult(a,mult(b,c)),
inference(rw,[status(thm)],[c_0_56,c_0_20]) ).
cnf(c_0_60,plain,
mult(X1,mult(X2,X3)) = mult(X2,mult(X3,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58]),c_0_58])]) ).
cnf(c_0_61,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60]),c_0_20]),c_0_60]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP747+1 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % 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
% 0.15/0.34 % Computer : n005.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon May 4 19:03:45 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.89/1.91 % Version : CSE_E---1.7
% 1.89/1.91 % Problem : theBenchmark.p
% 1.89/1.91 % SZS status Theorem for theBenchmark.p
% 1.89/1.91 % SZS output start CNFRefutation
% See solution above
% 1.89/1.92 % Total time : 1.369s
%------------------------------------------------------------------------------