%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET914+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 : n018.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 05:08:57 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 97 ( 37 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 113 ( 44 ~; 45 |; 16 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 66 ( 4 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t55_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( disjoint(unordered_pair(X1,X2),X3)
& in(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_zfmisc_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( disjoint(unordered_pair(X1,X2),X3)
& in(X1,X3) ),
inference(assume_negation,[status(cth)],[t55_zfmisc_1]) ).
fof(c_0_7,plain,
! [X65,X66] :
( ~ disjoint(X65,X66)
| disjoint(X66,X65) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(c_0_8,negated_conjecture,
( disjoint(unordered_pair(esk6_0,esk7_0),esk8_0)
& in(esk6_0,esk8_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_10,plain,
! [X51,X52,X53,X54,X55,X56,X57,X58] :
( ( in(X54,X51)
| ~ in(X54,X53)
| X53 != set_intersection2(X51,X52) )
& ( in(X54,X52)
| ~ in(X54,X53)
| X53 != set_intersection2(X51,X52) )
& ( ~ in(X55,X51)
| ~ in(X55,X52)
| in(X55,X53)
| X53 != set_intersection2(X51,X52) )
& ( ~ in(esk3_3(X56,X57,X58),X58)
| ~ in(esk3_3(X56,X57,X58),X56)
| ~ in(esk3_3(X56,X57,X58),X57)
| X58 = set_intersection2(X56,X57) )
& ( in(esk3_3(X56,X57,X58),X56)
| in(esk3_3(X56,X57,X58),X58)
| X58 = set_intersection2(X56,X57) )
& ( in(esk3_3(X56,X57,X58),X57)
| in(esk3_3(X56,X57,X58),X58)
| X58 = set_intersection2(X56,X57) ) ),
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)],[d3_xboole_0])])])])])]) ).
fof(c_0_11,plain,
! [X60,X61] :
( ( ~ disjoint(X60,X61)
| set_intersection2(X60,X61) = empty_set )
& ( set_intersection2(X60,X61) != empty_set
| disjoint(X60,X61) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
cnf(c_0_12,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
disjoint(unordered_pair(esk6_0,esk7_0),esk8_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,plain,
! [X38,X39,X40] :
( ( X38 != empty_set
| ~ in(X39,X38) )
& ( in(esk1_1(X40),X40)
| X40 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])]) ).
cnf(c_0_15,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
disjoint(esk8_0,unordered_pair(esk6_0,esk7_0)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X42,X43,X44,X45,X46,X47,X48,X49] :
( ( ~ in(X45,X44)
| X45 = X42
| X45 = X43
| X44 != unordered_pair(X42,X43) )
& ( X46 != X42
| in(X46,X44)
| X44 != unordered_pair(X42,X43) )
& ( X46 != X43
| in(X46,X44)
| X44 != unordered_pair(X42,X43) )
& ( esk2_3(X47,X48,X49) != X47
| ~ in(esk2_3(X47,X48,X49),X49)
| X49 = unordered_pair(X47,X48) )
& ( esk2_3(X47,X48,X49) != X48
| ~ in(esk2_3(X47,X48,X49),X49)
| X49 = unordered_pair(X47,X48) )
& ( in(esk2_3(X47,X48,X49),X49)
| esk2_3(X47,X48,X49) = X47
| esk2_3(X47,X48,X49) = X48
| X49 = unordered_pair(X47,X48) ) ),
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)],[d2_tarski])])])])])]) ).
cnf(c_0_20,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
set_intersection2(esk8_0,unordered_pair(esk6_0,esk7_0)) = empty_set,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(X1,unordered_pair(esk6_0,esk7_0))
| ~ in(X1,esk8_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_25,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_23])]) ).
cnf(c_0_26,negated_conjecture,
in(esk6_0,esk8_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
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 : SET914+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
% 0.15/0.33 % Computer : n018.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 02:39:32 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 : 1.371s
%------------------------------------------------------------------------------