%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU245+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 : n024.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 05:11:14 PM UTC 2026
% Result : Theorem 26.22s 17.48s
% Output : CNFRefutation 26.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 8 unt; 0 def)
% Number of atoms : 130 ( 27 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 154 ( 60 ~; 65 |; 18 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 87 ( 4 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(d6_wellord1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] : relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_wellord1) ).
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(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/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t16_wellord1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(c_0_5,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_6,plain,
! [X917,X918,X919,X920,X921,X922,X923,X924] :
( ( in(X920,X917)
| ~ in(X920,X919)
| X919 != set_difference(X917,X918) )
& ( ~ in(X920,X918)
| ~ in(X920,X919)
| X919 != set_difference(X917,X918) )
& ( ~ in(X921,X917)
| in(X921,X918)
| in(X921,X919)
| X919 != set_difference(X917,X918) )
& ( ~ in(esk56_3(X922,X923,X924),X924)
| ~ in(esk56_3(X922,X923,X924),X922)
| in(esk56_3(X922,X923,X924),X923)
| X924 = set_difference(X922,X923) )
& ( in(esk56_3(X922,X923,X924),X922)
| in(esk56_3(X922,X923,X924),X924)
| X924 = set_difference(X922,X923) )
& ( ~ in(esk56_3(X922,X923,X924),X923)
| in(esk56_3(X922,X923,X924),X924)
| X924 = set_difference(X922,X923) ) ),
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)],[c_0_5])])])])])]) ).
fof(c_0_7,plain,
! [X961,X962] :
( ~ relation(X961)
| relation_restriction(X961,X962) = set_intersection2(X961,cartesian_product2(X962,X962)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_wellord1])])]) ).
fof(c_0_8,lemma,
! [X1356,X1357] : set_difference(X1356,set_difference(X1356,X1357)) = set_intersection2(X1356,X1357),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_9,plain,
! [X874,X875,X876,X877,X878,X879,X880,X881] :
( ( in(X877,X874)
| ~ in(X877,X876)
| X876 != set_intersection2(X874,X875) )
& ( in(X877,X875)
| ~ in(X877,X876)
| X876 != set_intersection2(X874,X875) )
& ( ~ in(X878,X874)
| ~ in(X878,X875)
| in(X878,X876)
| X876 != set_intersection2(X874,X875) )
& ( ~ in(esk47_3(X879,X880,X881),X881)
| ~ in(esk47_3(X879,X880,X881),X879)
| ~ in(esk47_3(X879,X880,X881),X880)
| X881 = set_intersection2(X879,X880) )
& ( in(esk47_3(X879,X880,X881),X879)
| in(esk47_3(X879,X880,X881),X881)
| X881 = set_intersection2(X879,X880) )
& ( in(esk47_3(X879,X880,X881),X880)
| in(esk47_3(X879,X880,X881),X881)
| X881 = set_intersection2(X879,X880) ) ),
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])])])])])]) ).
cnf(c_0_10,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
inference(assume_negation,[status(cth)],[t16_wellord1]) ).
cnf(c_0_14,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( relation_restriction(X1,X2) = set_difference(X1,set_difference(X1,cartesian_product2(X2,X2)))
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_17,negated_conjecture,
( relation(esk106_0)
& ( ~ in(esk104_0,relation_restriction(esk106_0,esk105_0))
| ~ in(esk104_0,esk106_0)
| ~ in(esk104_0,cartesian_product2(esk105_0,esk105_0)) )
& ( in(esk104_0,esk106_0)
| in(esk104_0,relation_restriction(esk106_0,esk105_0)) )
& ( in(esk104_0,cartesian_product2(esk105_0,esk105_0))
| in(esk104_0,relation_restriction(esk106_0,esk105_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
cnf(c_0_18,plain,
( in(X1,X2)
| X3 != set_difference(X4,set_difference(X4,X2))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_19,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,plain,
( in(X1,X2)
| ~ relation(X2)
| ~ in(X1,relation_restriction(X2,X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( in(esk104_0,esk106_0)
| in(esk104_0,relation_restriction(esk106_0,esk105_0)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
relation(esk106_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( in(X1,X4)
| X4 != set_difference(X2,set_difference(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_25,negated_conjecture,
( ~ in(esk104_0,relation_restriction(esk106_0,esk105_0))
| ~ in(esk104_0,esk106_0)
| ~ in(esk104_0,cartesian_product2(esk105_0,esk105_0)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
in(esk104_0,esk106_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_27,plain,
( in(X1,cartesian_product2(X2,X2))
| ~ relation(X3)
| ~ in(X1,relation_restriction(X3,X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_28,negated_conjecture,
( in(esk104_0,cartesian_product2(esk105_0,esk105_0))
| in(esk104_0,relation_restriction(esk106_0,esk105_0)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,plain,
( in(X1,set_difference(X2,set_difference(X2,X3)))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( ~ in(esk104_0,cartesian_product2(esk105_0,esk105_0))
| ~ in(esk104_0,relation_restriction(esk106_0,esk105_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
cnf(c_0_31,negated_conjecture,
in(esk104_0,cartesian_product2(esk105_0,esk105_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_22])]) ).
cnf(c_0_32,plain,
( in(X1,relation_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X1,cartesian_product2(X3,X3))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_16]) ).
cnf(c_0_33,negated_conjecture,
~ in(esk104_0,relation_restriction(esk106_0,esk105_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_34,negated_conjecture,
( in(esk104_0,relation_restriction(X1,esk105_0))
| ~ relation(X1)
| ~ in(esk104_0,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_22]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU245+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 21:51:56 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.24 % start to proof: theBenchmark
% 26.22/17.48 % Version : CSE_E---1.7
% 26.22/17.48 % Problem : theBenchmark.p
% 26.22/17.48 % SZS status Theorem for theBenchmark.p
% 26.22/17.48 % SZS output start CNFRefutation
% See solution above
% 26.32/17.55 % Total time : 14.384s
%------------------------------------------------------------------------------