%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET643+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n011.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 05:08:13 PM UTC 2026
% Result : Theorem 1.24s 1.71s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 7 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 36 ( 14 ~; 11 |; 2 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 1 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( subset(X1,cross_product(X2,X3))
=> ilf_type(X1,relation_type(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p19,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(p10,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> subset(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
fof(prove_relset_1_5,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ilf_type(cross_product(X1,X2),relation_type(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_5) ).
fof(c_0_4,plain,
! [X54,X55,X56] :
( ~ ilf_type(X54,set_type)
| ~ ilf_type(X55,set_type)
| ~ ilf_type(X56,set_type)
| ~ subset(X54,cross_product(X55,X56))
| ilf_type(X54,relation_type(X55,X56)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
fof(c_0_5,plain,
! [X107] : ilf_type(X107,set_type),
inference(variable_rename,[status(thm)],[p19]) ).
fof(c_0_6,plain,
! [X83] :
( ~ ilf_type(X83,set_type)
| subset(X83,X83) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ilf_type(cross_product(X1,X2),relation_type(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_5]) ).
cnf(c_0_8,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ subset(X1,cross_product(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( subset(X1,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
( ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,set_type)
& ~ ilf_type(cross_product(esk12_0,esk13_0),relation_type(esk12_0,esk13_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ subset(X1,cross_product(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_9]),c_0_9])]) ).
cnf(c_0_13,plain,
subset(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_9])]) ).
cnf(c_0_14,negated_conjecture,
~ ilf_type(cross_product(esk12_0,esk13_0),relation_type(esk12_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
ilf_type(cross_product(X1,X2),relation_type(X1,X2)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET643+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n011.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
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:32:17 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.24/1.71 % Version : CSE_E---1.7
% 1.24/1.71 % Problem : theBenchmark.p
% 1.24/1.71 % SZS status Theorem for theBenchmark.p
% 1.24/1.71 % SZS output start CNFRefutation
% See solution above
% 1.24/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------