%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP703+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 : n001.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 04:27:07 PM UTC 2026
% Result : Theorem 1.24s 1.72s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 23 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 7 ~; 4 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( mult(op_e,mult(X4,X5)) = mult(mult(op_e,X4),X5)
& mult(X4,mult(X5,op_e)) = mult(mult(X4,X5),op_e)
& mult(X4,mult(op_e,X5)) = mult(mult(X4,op_e),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f05,axiom,
! [X2] : mult(X2,unit) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f12,axiom,
! [X1,X2] : op_e = mult(mult(rd(op_c,mult(X2,X1)),X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f12) ).
fof(f06,axiom,
! [X2] : mult(unit,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
fof(f03,axiom,
! [X1,X2] : mult(rd(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f08,axiom,
! [X1,X2] : mult(op_c,mult(X2,X1)) = mult(mult(op_c,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
fof(f10,axiom,
! [X1,X2] : mult(X2,mult(op_c,X1)) = mult(mult(X2,op_c),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
fof(f09,axiom,
! [X1,X2] : mult(X2,mult(X1,op_c)) = mult(mult(X2,X1),op_c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
fof(c_0_8,negated_conjecture,
~ ! [X4,X5] :
( mult(op_e,mult(X4,X5)) = mult(mult(op_e,X4),X5)
& mult(X4,mult(X5,op_e)) = mult(mult(X4,X5),op_e)
& mult(X4,mult(op_e,X5)) = mult(mult(X4,op_e),X5) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_9,plain,
! [X40] : mult(X40,unit) = X40,
inference(variable_rename,[status(thm)],[f05]) ).
fof(c_0_10,plain,
! [X52,X53] : op_e = mult(mult(rd(op_c,mult(X53,X52)),X52),X53),
inference(variable_rename,[status(thm)],[f12]) ).
fof(c_0_11,plain,
! [X41] : mult(unit,X41) = X41,
inference(variable_rename,[status(thm)],[f06]) ).
fof(c_0_12,plain,
! [X36,X37] : mult(rd(X37,X36),X36) = X37,
inference(variable_rename,[status(thm)],[f03]) ).
fof(c_0_13,negated_conjecture,
( mult(op_e,mult(esk1_0,esk2_0)) != mult(mult(op_e,esk1_0),esk2_0)
| mult(esk1_0,mult(esk2_0,op_e)) != mult(mult(esk1_0,esk2_0),op_e)
| mult(esk1_0,mult(op_e,esk2_0)) != mult(mult(esk1_0,op_e),esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_14,plain,
mult(X1,unit) = X1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
op_e = mult(mult(rd(op_c,mult(X1,X2)),X2),X1),
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]) ).
cnf(c_0_17,plain,
mult(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,plain,
! [X45,X46] : mult(op_c,mult(X46,X45)) = mult(mult(op_c,X46),X45),
inference(variable_rename,[status(thm)],[f08]) ).
fof(c_0_19,plain,
! [X49,X50] : mult(X50,mult(op_c,X49)) = mult(mult(X50,op_c),X49),
inference(variable_rename,[status(thm)],[f10]) ).
fof(c_0_20,plain,
! [X47,X48] : mult(X48,mult(X47,op_c)) = mult(mult(X48,X47),op_c),
inference(variable_rename,[status(thm)],[f09]) ).
cnf(c_0_21,negated_conjecture,
( mult(op_e,mult(esk1_0,esk2_0)) != mult(mult(op_e,esk1_0),esk2_0)
| mult(esk1_0,mult(esk2_0,op_e)) != mult(mult(esk1_0,esk2_0),op_e)
| mult(esk1_0,mult(op_e,esk2_0)) != mult(mult(esk1_0,op_e),esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
op_e = op_c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]) ).
cnf(c_0_23,plain,
mult(op_c,mult(X1,X2)) = mult(mult(op_c,X1),X2),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
mult(X1,mult(op_c,X2)) = mult(mult(X1,op_c),X2),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
mult(X1,mult(X2,op_c)) = mult(mult(X1,X2),op_c),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[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)],[c_0_21,c_0_22]),c_0_23]),c_0_22]),c_0_22]),c_0_24]),c_0_22]),c_0_22]),c_0_25]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP703+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
% 0.14/0.33 % Computer : n001.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 19:03:33 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.24/1.72 % Version : CSE_E---1.7
% 1.24/1.72 % Problem : theBenchmark.p
% 1.24/1.72 % SZS status Theorem for theBenchmark.p
% 1.24/1.72 % SZS output start CNFRefutation
% See solution above
% 1.24/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------