%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU295+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n031.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 05:11:23 PM UTC 2026
% Result : Theorem 2.13s 1.97s
% Output : CNFRefutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 13 unt; 0 def)
% Number of atoms : 27 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 7 ~; 3 |; 1 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc10_finset_1,axiom,
! [X1,X2] :
( finite(X2)
=> finite(set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(t15_finset_1,conjecture,
! [X1,X2] :
( finite(X1)
=> finite(set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finset_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(c_0_4,plain,
! [X1506,X1507] :
( ~ finite(X1507)
| finite(set_intersection2(X1506,X1507)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc10_finset_1])]) ).
fof(c_0_5,lemma,
! [X2166,X2167] : set_difference(X2166,set_difference(X2166,X2167)) = set_intersection2(X2166,X2167),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( finite(X1)
=> finite(set_intersection2(X1,X2)) ),
inference(assume_negation,[status(cth)],[t15_finset_1]) ).
cnf(c_0_7,plain,
( finite(set_intersection2(X2,X1))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_9,negated_conjecture,
( finite(esk233_0)
& ~ finite(set_intersection2(esk233_0,esk234_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X1055,X1056] : set_intersection2(X1055,X1056) = set_intersection2(X1056,X1055),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_11,plain,
( finite(set_difference(X2,set_difference(X2,X1)))
| ~ finite(X1) ),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,negated_conjecture,
finite(esk233_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
~ finite(set_intersection2(esk233_0,esk234_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
finite(set_difference(X1,set_difference(X1,esk233_0))),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_8]),c_0_8]) ).
cnf(c_0_17,negated_conjecture,
~ finite(set_difference(esk233_0,set_difference(esk233_0,esk234_0))),
inference(rw,[status(thm)],[c_0_14,c_0_8]) ).
cnf(c_0_18,negated_conjecture,
finite(set_difference(esk233_0,set_difference(esk233_0,X1))),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU295+2 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.15/0.33 % Computer : n031.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:56:54 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.13/1.97 % Version : CSE_E---1.7
% 2.13/1.97 % Problem : theBenchmark.p
% 2.13/1.97 % SZS status Theorem for theBenchmark.p
% 2.13/1.97 % SZS output start CNFRefutation
% See solution above
% 2.13/1.97 % Total time : 1.477s
%------------------------------------------------------------------------------