%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET767+4 : TPTP v9.2.1. Released v2.2.0.
% 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 : n028.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 05:08:27 PM UTC 2026
% Result : Theorem 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 4 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 34 ( 12 ~; 11 |; 6 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 30 ( 2 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIII03,conjecture,
! [X4,X7,X1] :
( equivalence(X7,X4)
=> subset(equivalence_class(X1,X4,X7),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII03) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(equivalence_class,axiom,
! [X7,X4,X1,X3] :
( member(X3,equivalence_class(X1,X4,X7))
<=> ( member(X3,X4)
& apply(X7,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',equivalence_class) ).
fof(c_0_3,negated_conjecture,
~ ! [X4,X7,X1] :
( equivalence(X7,X4)
=> subset(equivalence_class(X1,X4,X7),X4) ),
inference(assume_negation,[status(cth)],[thIII03]) ).
fof(c_0_4,negated_conjecture,
( equivalence(esk16_0,esk15_0)
& ~ subset(equivalence_class(esk17_0,esk15_0,esk16_0),esk15_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_5,plain,
! [X68,X69,X70,X71,X72] :
( ( ~ subset(X68,X69)
| ~ member(X70,X68)
| member(X70,X69) )
& ( member(esk1_2(X71,X72),X71)
| subset(X71,X72) )
& ( ~ member(esk1_2(X71,X72),X72)
| subset(X71,X72) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subset])])])])])]) ).
fof(c_0_6,plain,
! [X129,X130,X131,X132] :
( ( member(X132,X130)
| ~ member(X132,equivalence_class(X131,X130,X129)) )
& ( apply(X129,X131,X132)
| ~ member(X132,equivalence_class(X131,X130,X129)) )
& ( ~ member(X132,X130)
| ~ apply(X129,X131,X132)
| member(X132,equivalence_class(X131,X130,X129)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_class])])]) ).
cnf(c_0_7,negated_conjecture,
~ subset(equivalence_class(esk17_0,esk15_0,esk16_0),esk15_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( member(X1,X2)
| ~ member(X1,equivalence_class(X3,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
member(esk1_2(equivalence_class(esk17_0,esk15_0,esk16_0),esk15_0),equivalence_class(esk17_0,esk15_0,esk16_0)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
member(esk1_2(equivalence_class(esk17_0,esk15_0,esk16_0),esk15_0),esk15_0),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_7]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET767+4 : TPTP v9.2.1. Released v2.2.0.
% 0.11/0.12 % 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
% 0.14/0.33 % Computer : n028.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 : Tue May 5 02:34:31 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.30/1.73 % Version : CSE_E---1.7
% 1.30/1.73 % Problem : theBenchmark.p
% 1.30/1.73 % SZS status Theorem for theBenchmark.p
% 1.30/1.73 % SZS output start CNFRefutation
% See solution above
% 1.30/1.73 % Total time : 1.370s
%------------------------------------------------------------------------------