%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU097+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 : n014.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 05:10:37 PM UTC 2026
% Result : Theorem 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 35 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 13 ~; 7 |; 5 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 1 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t28_finset_1,conjecture,
! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(symmetric_difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finset_1) ).
fof(d6_xboole_0,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = set_union2(set_difference(X1,X2),set_difference(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_xboole_0) ).
fof(fc9_finset_1,axiom,
! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(set_union2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_finset_1) ).
fof(fc12_finset_1,axiom,
! [X1,X2] :
( finite(X1)
=> finite(set_difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_finset_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(symmetric_difference(X1,X2)) ),
inference(assume_negation,[status(cth)],[t28_finset_1]) ).
fof(c_0_5,negated_conjecture,
( finite(esk27_0)
& finite(esk28_0)
& ~ finite(symmetric_difference(esk27_0,esk28_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_6,plain,
! [X119,X120] : symmetric_difference(X119,X120) = set_union2(set_difference(X119,X120),set_difference(X120,X119)),
inference(variable_rename,[status(thm)],[d6_xboole_0]) ).
cnf(c_0_7,negated_conjecture,
~ finite(symmetric_difference(esk27_0,esk28_0)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
symmetric_difference(X1,X2) = set_union2(set_difference(X1,X2),set_difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X134,X135] :
( ~ finite(X134)
| ~ finite(X135)
| finite(set_union2(X134,X135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc9_finset_1])]) ).
cnf(c_0_10,negated_conjecture,
~ finite(set_union2(set_difference(esk27_0,esk28_0),set_difference(esk28_0,esk27_0))),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( finite(set_union2(X1,X2))
| ~ finite(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X123,X124] :
( ~ finite(X123)
| finite(set_difference(X123,X124)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc12_finset_1])]) ).
cnf(c_0_13,negated_conjecture,
( ~ finite(set_difference(esk28_0,esk27_0))
| ~ finite(set_difference(esk27_0,esk28_0)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( finite(set_difference(X1,X2))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
finite(esk28_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
~ finite(set_difference(esk27_0,esk28_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_17,negated_conjecture,
finite(esk27_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_14]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU097+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n014.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 02:42:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Theorem for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.372s
%------------------------------------------------------------------------------