%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET978+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : 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 05:09:04 PM UTC 2026
% Result : Theorem 1.22s 1.68s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 3 unt; 0 def)
% Number of atoms : 31 ( 7 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 32 ( 15 ~; 9 |; 4 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 4 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t131_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( X1 != X2
=> ( disjoint(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X4))
& disjoint(cartesian_product2(X3,singleton(X1)),cartesian_product2(X4,singleton(X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_zfmisc_1) ).
fof(t127_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( ( disjoint(X1,X2)
| disjoint(X3,X4) )
=> disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).
fof(t17_zfmisc_1,axiom,
! [X1,X2] :
( X1 != X2
=> disjoint(singleton(X1),singleton(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_zfmisc_1) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( X1 != X2
=> ( disjoint(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X4))
& disjoint(cartesian_product2(X3,singleton(X1)),cartesian_product2(X4,singleton(X2))) ) ),
inference(assume_negation,[status(cth)],[t131_zfmisc_1]) ).
fof(c_0_4,negated_conjecture,
( esk3_0 != esk4_0
& ( ~ disjoint(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk6_0))
| ~ disjoint(cartesian_product2(esk5_0,singleton(esk3_0)),cartesian_product2(esk6_0,singleton(esk4_0))) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_5,plain,
! [X23,X24,X25,X26] :
( ( ~ disjoint(X23,X24)
| disjoint(cartesian_product2(X23,X25),cartesian_product2(X24,X26)) )
& ( ~ disjoint(X25,X26)
| disjoint(cartesian_product2(X23,X25),cartesian_product2(X24,X26)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t127_zfmisc_1])])]) ).
cnf(c_0_6,negated_conjecture,
( ~ disjoint(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk6_0))
| ~ disjoint(cartesian_product2(esk5_0,singleton(esk3_0)),cartesian_product2(esk6_0,singleton(esk4_0))) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4))
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( disjoint(cartesian_product2(X3,X1),cartesian_product2(X4,X2))
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_9,plain,
! [X31,X32] :
( X31 = X32
| disjoint(singleton(X31),singleton(X32)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t17_zfmisc_1])]) ).
cnf(c_0_10,negated_conjecture,
~ disjoint(singleton(esk3_0),singleton(esk4_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
cnf(c_0_11,plain,
( X1 = X2
| disjoint(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,negated_conjecture,
esk3_0 != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET978+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.10 % 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
% 0.12/0.30 % Computer : n028.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue May 5 02:41:31 EDT 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.31 % start to proof: theBenchmark
% 1.22/1.68 % Version : CSE_E---1.7
% 1.22/1.68 % Problem : theBenchmark.p
% 1.22/1.68 % SZS status Theorem for theBenchmark.p
% 1.22/1.68 % SZS output start CNFRefutation
% See solution above
% 1.22/1.68 % Total time : 1.368s
%------------------------------------------------------------------------------