%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP665+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 : n026.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 04:26:49 PM UTC 2026
% Result : Theorem 1.37s 1.76s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 25 unt; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 6 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f04,axiom,
! [X1,X2] : rd(mult(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f08,axiom,
! [X3,X1,X2] : mult(mult(X2,X1),X3) = mult(mult(X2,X3),ld(X3,mult(X1,X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
fof(goals,conjecture,
! [X4,X5] :
( mult(op_c,mult(X4,X5)) = mult(mult(op_c,X4),X5)
& mult(mult(X4,op_c),X5) = mult(X4,mult(op_c,X5))
& mult(mult(X4,X5),op_c) = mult(X4,mult(X5,op_c)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f09,axiom,
! [X2] : mult(op_c,X2) = mult(X2,op_c),
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(f07,axiom,
! [X3,X1,X2] : mult(X2,mult(X1,X3)) = mult(rd(mult(X2,X1),X2),mult(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
fof(f03,axiom,
! [X1,X2] : mult(rd(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(c_0_7,plain,
! [X31,X32] : rd(mult(X32,X31),X31) = X32,
inference(variable_rename,[status(thm)],[f04]) ).
fof(c_0_8,plain,
! [X38,X39,X40] : mult(mult(X40,X39),X38) = mult(mult(X40,X38),ld(X38,mult(X39,X38))),
inference(variable_rename,[status(thm)],[f08]) ).
fof(c_0_9,negated_conjecture,
~ ! [X4,X5] :
( mult(op_c,mult(X4,X5)) = mult(mult(op_c,X4),X5)
& mult(mult(X4,op_c),X5) = mult(X4,mult(op_c,X5))
& mult(mult(X4,X5),op_c) = mult(X4,mult(X5,op_c)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_10,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
mult(mult(X1,X2),X3) = mult(mult(X1,X3),ld(X3,mult(X2,X3))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X41] : mult(op_c,X41) = mult(X41,op_c),
inference(variable_rename,[status(thm)],[f09]) ).
fof(c_0_13,plain,
! [X27,X28] : ld(X28,mult(X28,X27)) = X27,
inference(variable_rename,[status(thm)],[f02]) ).
fof(c_0_14,negated_conjecture,
( mult(op_c,mult(esk1_0,esk2_0)) != mult(mult(op_c,esk1_0),esk2_0)
| mult(mult(esk1_0,op_c),esk2_0) != mult(esk1_0,mult(op_c,esk2_0))
| mult(mult(esk1_0,esk2_0),op_c) != mult(esk1_0,mult(esk2_0,op_c)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_15,plain,
! [X35,X36,X37] : mult(X37,mult(X36,X35)) = mult(rd(mult(X37,X36),X37),mult(X37,X35)),
inference(variable_rename,[status(thm)],[f07]) ).
fof(c_0_16,plain,
! [X29,X30] : mult(rd(X30,X29),X29) = X30,
inference(variable_rename,[status(thm)],[f03]) ).
cnf(c_0_17,plain,
rd(mult(mult(X1,X2),X3),ld(X3,mult(X2,X3))) = mult(X1,X3),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_18,plain,
mult(op_c,X1) = mult(X1,op_c),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( mult(op_c,mult(esk1_0,esk2_0)) != mult(mult(op_c,esk1_0),esk2_0)
| mult(mult(esk1_0,op_c),esk2_0) != mult(esk1_0,mult(op_c,esk2_0))
| mult(mult(esk1_0,esk2_0),op_c) != mult(esk1_0,mult(esk2_0,op_c)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
mult(X1,mult(X2,X3)) = mult(rd(mult(X1,X2),X1),mult(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
mult(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
rd(mult(op_c,mult(X1,X2)),X2) = mult(X1,op_c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( mult(mult(op_c,esk1_0),esk2_0) != mult(op_c,mult(esk1_0,esk2_0))
| mult(mult(op_c,esk1_0),esk2_0) != mult(esk1_0,mult(op_c,esk2_0))
| mult(esk1_0,mult(op_c,esk2_0)) != mult(op_c,mult(esk1_0,esk2_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_18]),c_0_18]),c_0_18]) ).
cnf(c_0_25,plain,
mult(X1,mult(op_c,X2)) = mult(op_c,mult(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_18]),c_0_10]) ).
cnf(c_0_26,plain,
mult(mult(X1,op_c),X2) = mult(op_c,mult(X1,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,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)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_25])]) ).
cnf(c_0_28,plain,
mult(mult(op_c,X1),X2) = mult(op_c,mult(X1,X2)),
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP665+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 19:00:53 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.37/1.76 % Version : CSE_E---1.7
% 1.37/1.76 % Problem : theBenchmark.p
% 1.37/1.76 % SZS status Theorem for theBenchmark.p
% 1.37/1.76 % SZS output start CNFRefutation
% See solution above
% 1.37/1.76 % Total time : 1.371s
%------------------------------------------------------------------------------