%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP702+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 : n008.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 04:27:06 PM UTC 2026
% Result : Theorem 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 18 unt; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 10 ~; 5 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( mult(op_d,mult(X4,X5)) = mult(mult(op_d,X4),X5)
& mult(X4,mult(X5,op_d)) = mult(mult(X4,X5),op_d)
& mult(X4,mult(op_d,X5)) = mult(mult(X4,op_d),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f11,axiom,
! [X2] : op_d = ld(X2,mult(op_c,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
fof(f02,axiom,
! [X1,X2] : ld(X2,mult(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
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(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(c_0_6,negated_conjecture,
~ ! [X4,X5] :
( mult(op_d,mult(X4,X5)) = mult(mult(op_d,X4),X5)
& mult(X4,mult(X5,op_d)) = mult(mult(X4,X5),op_d)
& mult(X4,mult(op_d,X5)) = mult(mult(X4,op_d),X5) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_7,plain,
! [X51] : op_d = ld(X51,mult(op_c,X51)),
inference(variable_rename,[status(thm)],[f11]) ).
fof(c_0_8,plain,
! [X34,X35] : ld(X35,mult(X35,X34)) = X34,
inference(variable_rename,[status(thm)],[f02]) ).
fof(c_0_9,negated_conjecture,
( mult(op_d,mult(esk1_0,esk2_0)) != mult(mult(op_d,esk1_0),esk2_0)
| mult(esk1_0,mult(esk2_0,op_d)) != mult(mult(esk1_0,esk2_0),op_d)
| mult(esk1_0,mult(op_d,esk2_0)) != mult(mult(esk1_0,op_d),esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_10,plain,
op_d = ld(X1,mult(op_c,X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X49,X50] : mult(X50,mult(op_c,X49)) = mult(mult(X50,op_c),X49),
inference(variable_rename,[status(thm)],[f10]) ).
cnf(c_0_13,negated_conjecture,
( mult(op_d,mult(esk1_0,esk2_0)) != mult(mult(op_d,esk1_0),esk2_0)
| mult(esk1_0,mult(esk2_0,op_d)) != mult(mult(esk1_0,esk2_0),op_d)
| mult(esk1_0,mult(op_d,esk2_0)) != mult(mult(esk1_0,op_d),esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
op_d = op_c,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
mult(X1,mult(op_c,X2)) = mult(mult(X1,op_c),X2),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X47,X48] : mult(X48,mult(X47,op_c)) = mult(mult(X48,X47),op_c),
inference(variable_rename,[status(thm)],[f09]) ).
cnf(c_0_17,negated_conjecture,
( mult(mult(op_c,esk1_0),esk2_0) != mult(op_c,mult(esk1_0,esk2_0))
| mult(mult(esk1_0,esk2_0),op_c) != mult(esk1_0,mult(esk2_0,op_c)) ),
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)],[c_0_13,c_0_14]),c_0_14]),c_0_14]),c_0_15]),c_0_14]),c_0_14]),c_0_14])]) ).
cnf(c_0_18,plain,
mult(X1,mult(X2,op_c)) = mult(mult(X1,X2),op_c),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X45,X46] : mult(op_c,mult(X46,X45)) = mult(mult(op_c,X46),X45),
inference(variable_rename,[status(thm)],[f08]) ).
cnf(c_0_20,negated_conjecture,
mult(mult(op_c,esk1_0),esk2_0) != mult(op_c,mult(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_21,plain,
mult(op_c,mult(X1,X2)) = mult(mult(op_c,X1),X2),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP702+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n008.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
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 19:03:13 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Theorem for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.368s
%------------------------------------------------------------------------------