%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET696+4 : 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 : n016.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 05:08:20 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 9 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 78 ( 33 ~; 24 |; 13 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 4 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI28,conjecture,
! [X1,X4] :
( subset(X1,X4)
=> equal_set(intersection(difference(X4,X1),X1),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI28) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(difference,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',difference) ).
fof(intersection,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X4] :
( subset(X1,X4)
=> equal_set(intersection(difference(X4,X1),X1),empty_set) ),
inference(assume_negation,[status(cth)],[thI28]) ).
fof(c_0_7,negated_conjecture,
( subset(esk4_0,esk5_0)
& ~ equal_set(intersection(difference(esk5_0,esk4_0),esk4_0),empty_set) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X42,X43] :
( ( subset(X42,X43)
| ~ equal_set(X42,X43) )
& ( subset(X43,X42)
| ~ equal_set(X42,X43) )
& ( ~ subset(X42,X43)
| ~ subset(X43,X42)
| equal_set(X42,X43) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
cnf(c_0_9,negated_conjecture,
~ equal_set(intersection(difference(esk5_0,esk4_0),esk4_0),empty_set),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X36,X37,X38,X39,X40] :
( ( ~ subset(X36,X37)
| ~ member(X38,X36)
| member(X38,X37) )
& ( member(esk1_2(X39,X40),X39)
| subset(X39,X40) )
& ( ~ member(esk1_2(X39,X40),X40)
| subset(X39,X40) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subset])])])])])]) ).
fof(c_0_12,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
cnf(c_0_13,negated_conjecture,
( ~ subset(empty_set,intersection(difference(esk5_0,esk4_0),esk4_0))
| ~ subset(intersection(difference(esk5_0,esk4_0),esk4_0),empty_set) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X52] : ~ member(X52,empty_set),
inference(variable_rename,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[difference]) ).
fof(c_0_17,plain,
! [X46,X47,X48] :
( ( member(X46,X47)
| ~ member(X46,intersection(X47,X48)) )
& ( member(X46,X48)
| ~ member(X46,intersection(X47,X48)) )
& ( ~ member(X46,X47)
| ~ member(X46,X48)
| member(X46,intersection(X47,X48)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])]) ).
cnf(c_0_18,negated_conjecture,
( member(esk1_2(intersection(difference(esk5_0,esk4_0),esk4_0),empty_set),intersection(difference(esk5_0,esk4_0),esk4_0))
| ~ subset(empty_set,intersection(difference(esk5_0,esk4_0),esk4_0)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X53,X54,X55] :
( ( member(X53,X55)
| ~ member(X53,difference(X55,X54)) )
& ( ~ member(X53,X54)
| ~ member(X53,difference(X55,X54)) )
& ( ~ member(X53,X55)
| member(X53,X54)
| member(X53,difference(X55,X54)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
cnf(c_0_21,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
member(esk1_2(intersection(difference(esk5_0,esk4_0),esk4_0),empty_set),intersection(difference(esk5_0,esk4_0),esk4_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_14]),c_0_19]) ).
cnf(c_0_23,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
member(esk1_2(intersection(difference(esk5_0,esk4_0),esk4_0),empty_set),difference(esk5_0,esk4_0)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
member(esk1_2(intersection(difference(esk5_0,esk4_0),esk4_0),empty_set),esk4_0),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET696+4 : TPTP v9.2.1. Released v2.2.0.
% 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
% 0.15/0.33 % Computer : n016.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 02:32:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.370s
%------------------------------------------------------------------------------