%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET985+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : 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 05:09:05 PM UTC 2026
% Result : Theorem 1.25s 1.72s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 58 ( 24 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 50 ( 15 ~; 23 |; 6 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 33 ( 3 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t139_zfmisc_1,conjecture,
! [X1] :
( ~ empty(X1)
=> ! [X2,X3,X4] :
( ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| subset(cartesian_product2(X2,X1),cartesian_product2(X4,X3)) )
=> subset(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
fof(t138_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
=> ( cartesian_product2(X1,X2) = empty_set
| ( subset(X1,X3)
& subset(X2,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
fof(t113_zfmisc_1,axiom,
! [X1,X2] :
( cartesian_product2(X1,X2) = empty_set
<=> ( X1 = empty_set
| X2 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(t2_xboole_1,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ~ empty(X1)
=> ! [X2,X3,X4] :
( ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| subset(cartesian_product2(X2,X1),cartesian_product2(X4,X3)) )
=> subset(X2,X4) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t139_zfmisc_1])]) ).
fof(c_0_6,plain,
! [X25,X26,X27,X28] :
( ( subset(X25,X27)
| cartesian_product2(X25,X26) = empty_set
| ~ subset(cartesian_product2(X25,X26),cartesian_product2(X27,X28)) )
& ( subset(X26,X28)
| cartesian_product2(X25,X26) = empty_set
| ~ subset(cartesian_product2(X25,X26),cartesian_product2(X27,X28)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t138_zfmisc_1])])]) ).
fof(c_0_7,negated_conjecture,
( ~ empty(esk3_0)
& ( subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
| subset(cartesian_product2(esk4_0,esk3_0),cartesian_product2(esk6_0,esk5_0)) )
& ~ subset(esk4_0,esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_8,plain,
( subset(X1,X2)
| cartesian_product2(X1,X3) = empty_set
| ~ subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
| subset(cartesian_product2(esk4_0,esk3_0),cartesian_product2(esk6_0,esk5_0)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
~ subset(esk4_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X23,X24] :
( ( cartesian_product2(X23,X24) != empty_set
| X23 = empty_set
| X24 = empty_set )
& ( X23 != empty_set
| cartesian_product2(X23,X24) = empty_set )
& ( X24 != empty_set
| cartesian_product2(X23,X24) = empty_set ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t113_zfmisc_1])])]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| cartesian_product2(X3,X1) = empty_set
| ~ subset(cartesian_product2(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
( cartesian_product2(esk4_0,esk3_0) = empty_set
| subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_14,plain,
( X1 = empty_set
| X2 = empty_set
| cartesian_product2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( cartesian_product2(esk4_0,esk3_0) = empty_set
| cartesian_product2(esk3_0,esk4_0) = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_10]) ).
fof(c_0_16,plain,
! [X33] : subset(empty_set,X33),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_17,negated_conjecture,
( esk4_0 = empty_set
| esk3_0 = empty_set ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_14]) ).
cnf(c_0_18,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
~ empty(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,negated_conjecture,
esk3_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_17]),c_0_18])]) ).
cnf(c_0_21,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET985+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n008.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 : Tue May 5 02:41:14 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.25/1.72 % Version : CSE_E---1.7
% 1.25/1.72 % Problem : theBenchmark.p
% 1.25/1.72 % SZS status Theorem for theBenchmark.p
% 1.25/1.72 % SZS output start CNFRefutation
% See solution above
% 1.25/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------