%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU281+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:52:42 PM UTC 2026
% Result : Theorem 0.17s 0.58s
% Output : Refutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 128 ( 5 unt; 15 def)
% Number of atoms : 495 ( 152 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 549 ( 182 ~; 226 |; 116 &)
% ( 20 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 14 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 2 con; 0-3 aty)
% Number of variables : 216 ( 0 sgn 123 !; 93 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,cartesian_product2(X0,X1))
& ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& X5 = singleton(X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e16_22__wellord2__1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,cartesian_product2(X0,X1))
& ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& X5 = singleton(X4) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f16,axiom,
! [X0,X1] :
( ! [X2,X3,X4] :
( ( X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(X7,X0)
& X8 = singleton(X7) ) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,cartesian_product2(X0,X1))
& X4 = X3
& ? [X9,X10] :
( ordered_pair(X9,X10) = X3
& in(X9,X0)
& X10 = singleton(X9) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__2) ).
fof(f17,plain,
! [X0,X1] :
( ! [X2,X3,X4] :
( ( X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(X7,X0)
& X8 = singleton(X7) ) )
=> X3 = X4 )
=> ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( ordered_pair(X12,X13) = X10
& in(X12,X0)
& singleton(X12) = X13 ) ) ) ),
inference(rectify,[],[f16]) ).
fof(f19,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( in(X3,X2)
<~> ( in(X3,cartesian_product2(X0,X1))
& ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& X5 = singleton(X4) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f25,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( ordered_pair(X12,X13) = X10
& in(X12,X0)
& singleton(X12) = X13 ) ) )
| ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(X7,X0)
& X8 = singleton(X7) ) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f26,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( ordered_pair(X12,X13) = X10
& in(X12,X0)
& singleton(X12) = X13 ) ) )
| ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(X7,X0)
& X8 = singleton(X7) ) ) ),
inference(flattening,[],[f25]) ).
fof(f27,definition,
! [X4,X0] :
( ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(X7,X0)
& X8 = singleton(X7) )
| ~ sP0(X4,X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f28,definition,
! [X0] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& sP0(X4,X0) )
| ~ sP1(X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f29,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( ordered_pair(X12,X13) = X10
& in(X12,X0)
& singleton(X12) = X13 ) ) )
| sP1(X0) ),
inference(definition_folding,[],[f26,f28,f27]) ).
fof(f30,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( ~ in(X3,cartesian_product2(X0,X1))
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X4,X0)
| singleton(X4) != X5 )
| ~ in(X3,X2) )
& ( ( in(X3,cartesian_product2(X0,X1))
& ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& X5 = singleton(X4) ) )
| in(X3,X2) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f31,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( ~ in(X3,cartesian_product2(X0,X1))
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X4,X0)
| singleton(X4) != X5 )
| ~ in(X3,X2) )
& ( ( in(X3,cartesian_product2(X0,X1))
& ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& X5 = singleton(X4) ) )
| in(X3,X2) ) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( ~ in(X3,cartesian_product2(X0,X1))
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X4,X0)
| singleton(X4) != X5 )
| ~ in(X3,X2) )
& ( ( in(X3,cartesian_product2(X0,X1))
& ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X6,X0)
& singleton(X6) = X7 ) )
| in(X3,X2) ) ),
inference(rectify,[],[f31]) ).
fof(f33,plain,
! [X2] :
( ( ~ in(sK4(X2),cartesian_product2(sK2,sK3))
| ! [X4,X5] :
( ordered_pair(X4,X5) != sK4(X2)
| ~ in(X4,sK2)
| singleton(X4) != X5 )
| ~ in(sK4(X2),X2) )
& ( ( in(sK4(X2),cartesian_product2(sK2,sK3))
& sK4(X2) = ordered_pair(sK5(X2),sK6(X2))
& in(sK5(X2),sK2)
& sK6(X2) = singleton(sK5(X2)) )
| in(sK4(X2),X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X3,sK4(X2)),skolemize(X6,sK5(X2)),skolemize(X7,sK6(X2))],[f32]) ).
fof(f38,plain,
! [X0] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& sP0(X4,X0) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f28]) ).
fof(f39,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& X1 = X2
& ? [X4,X5] :
( ordered_pair(X4,X5) = X2
& in(X4,X0)
& singleton(X4) = X5 )
& X1 = X3
& sP0(X3,X0) )
| ~ sP1(X0) ),
inference(rectify,[],[f38]) ).
fof(f40,plain,
! [X0] :
( ( sK12(X0) != sK13(X0)
& sK11(X0) = sK12(X0)
& sK12(X0) = ordered_pair(sK14(X0),sK15(X0))
& in(sK14(X0),X0)
& sK15(X0) = singleton(sK14(X0))
& sK11(X0) = sK13(X0)
& sP0(sK13(X0),X0) )
| ~ sP1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14,sK15]),skolemize(X1,sK11(X0)),skolemize(X2,sK12(X0)),skolemize(X3,sK13(X0)),skolemize(X4,sK14(X0)),skolemize(X5,sK15(X0))],[f39]) ).
fof(f44,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( ( in(X10,X9)
| ! [X11] :
( ~ in(X11,cartesian_product2(X0,X1))
| X10 != X11
| ! [X12,X13] :
( ordered_pair(X12,X13) != X10
| ~ in(X12,X0)
| singleton(X12) != X13 ) ) )
& ( ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( ordered_pair(X12,X13) = X10
& in(X12,X0)
& singleton(X12) = X13 ) )
| ~ in(X10,X9) ) )
| sP1(X0) ),
inference(nnf_transformation,[],[f29]) ).
fof(f45,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,cartesian_product2(X0,X1))
| X3 != X4
| ! [X5,X6] :
( ordered_pair(X5,X6) != X3
| ~ in(X5,X0)
| singleton(X5) != X6 ) ) )
& ( ? [X7] :
( in(X7,cartesian_product2(X0,X1))
& X3 = X7
& ? [X8,X9] :
( ordered_pair(X8,X9) = X3
& in(X8,X0)
& singleton(X8) = X9 ) )
| ~ in(X3,X2) ) )
| sP1(X0) ),
inference(rectify,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK18(X0,X1))
| ! [X4] :
( ~ in(X4,cartesian_product2(X0,X1))
| X3 != X4
| ! [X5,X6] :
( ordered_pair(X5,X6) != X3
| ~ in(X5,X0)
| singleton(X5) != X6 ) ) )
& ( ( in(sK19(X0,X1,X3),cartesian_product2(X0,X1))
& sK19(X0,X1,X3) = X3
& ordered_pair(sK20(X0,X3),sK21(X0,X3)) = X3
& in(sK20(X0,X3),X0)
& sK21(X0,X3) = singleton(sK20(X0,X3)) )
| ~ in(X3,sK18(X0,X1)) ) )
| sP1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21]),skolemize(X2,sK18(X0,X1)),skolemize(X7,sK19(X0,X1,X3)),skolemize(X8,sK20(X0,X3)),skolemize(X9,sK21(X0,X3))],[f45]) ).
fof(f47,plain,
! [X2] :
( in(sK4(X2),X2)
| sK6(X2) = singleton(sK5(X2)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f48,plain,
! [X2] :
( in(sK5(X2),sK2)
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f49,plain,
! [X2] :
( in(sK4(X2),X2)
| sK4(X2) = ordered_pair(sK5(X2),sK6(X2)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f50,plain,
! [X2] :
( in(sK4(X2),cartesian_product2(sK2,sK3))
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f51,plain,
! [X2,X4,X5] :
( ~ in(sK4(X2),cartesian_product2(sK2,sK3))
| ordered_pair(X4,X5) != sK4(X2)
| ~ in(X4,sK2)
| singleton(X4) != X5
| ~ in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f70,plain,
! [X0] :
( ~ sP1(X0)
| sK11(X0) = sK13(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f74,plain,
! [X0] :
( ~ sP1(X0)
| sK11(X0) = sK12(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f75,plain,
! [X0] :
( sK12(X0) != sK13(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f79,plain,
! [X3,X0,X1] :
( sP1(X0)
| ~ in(X3,sK18(X0,X1))
| sK21(X0,X3) = singleton(sK20(X0,X3)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f80,plain,
! [X3,X0,X1] :
( sP1(X0)
| ~ in(X3,sK18(X0,X1))
| in(sK20(X0,X3),X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f81,plain,
! [X3,X0,X1] :
( sP1(X0)
| ~ in(X3,sK18(X0,X1))
| ordered_pair(sK20(X0,X3),sK21(X0,X3)) = X3 ),
inference(cnf_transformation,[],[f46]) ).
fof(f82,plain,
! [X3,X0,X1] :
( sP1(X0)
| ~ in(X3,sK18(X0,X1))
| sK19(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f46]) ).
fof(f83,plain,
! [X3,X0,X1] :
( in(sK19(X0,X1,X3),cartesian_product2(X0,X1))
| ~ in(X3,sK18(X0,X1))
| sP1(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f84,plain,
! [X3,X0,X1,X6,X4,X5] :
( in(X3,sK18(X0,X1))
| ~ in(X4,cartesian_product2(X0,X1))
| X3 != X4
| ordered_pair(X5,X6) != X3
| ~ in(X5,X0)
| singleton(X5) != X6
| sP1(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f85,plain,
! [X2,X4] :
( sK4(X2) != ordered_pair(X4,singleton(X4))
| ~ in(sK4(X2),cartesian_product2(sK2,sK3))
| ~ in(X4,sK2)
| ~ in(sK4(X2),X2) ),
inference(equality_resolution,[],[f51]) ).
fof(f86,plain,
! [X0,X1,X6,X4,X5] :
( in(X4,sK18(X0,X1))
| ~ in(X4,cartesian_product2(X0,X1))
| ordered_pair(X5,X6) != X4
| ~ in(X5,X0)
| singleton(X5) != X6
| sP1(X0) ),
inference(equality_resolution,[],[f84]) ).
fof(f87,plain,
! [X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),sK18(X0,X1))
| ~ in(ordered_pair(X5,X6),cartesian_product2(X0,X1))
| ~ in(X5,X0)
| singleton(X5) != X6
| sP1(X0) ),
inference(equality_resolution,[],[f86]) ).
fof(f88,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,singleton(X5)),sK18(X0,X1))
| ~ in(ordered_pair(X5,singleton(X5)),cartesian_product2(X0,X1))
| ~ in(X5,X0)
| sP1(X0) ),
inference(equality_resolution,[],[f87]) ).
fof(f544,definition,
( spl22_1
<=> sK11(sK2) = sK12(sK2) ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
fof(f552,definition,
( spl22_3
<=> sK11(sK2) = sK13(sK2) ),
introduced(definition,[new_symbols(definition,[spl22_3])],[avatar_definition]) ).
fof(f554,plain,
( sK11(sK2) = sK13(sK2)
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f616,definition,
( spl22_6
<=> sK4(sK18(sK2,sK3)) = ordered_pair(sK5(sK18(sK2,sK3)),sK6(sK18(sK2,sK3))) ),
introduced(definition,[new_symbols(definition,[spl22_6])],[avatar_definition]) ).
fof(f618,plain,
( sK4(sK18(sK2,sK3)) = ordered_pair(sK5(sK18(sK2,sK3)),sK6(sK18(sK2,sK3)))
| ~ spl22_6 ),
inference(avatar_component_clause,[],[f616]) ).
fof(f620,definition,
( spl22_7
<=> sP1(sK2) ),
introduced(definition,[new_symbols(definition,[spl22_7])],[avatar_definition]) ).
fof(f621,plain,
( ~ sP1(sK2)
| spl22_7 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f622,plain,
( sP1(sK2)
| ~ spl22_7 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f624,definition,
( spl22_8
<=> in(sK4(sK18(sK2,sK3)),sK18(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl22_8])],[avatar_definition]) ).
fof(f625,plain,
( in(sK4(sK18(sK2,sK3)),sK18(sK2,sK3))
| ~ spl22_8 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f626,plain,
( ~ in(sK4(sK18(sK2,sK3)),sK18(sK2,sK3))
| spl22_8 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f628,definition,
( spl22_9
<=> sK6(sK18(sK2,sK3)) = singleton(sK5(sK18(sK2,sK3))) ),
introduced(definition,[new_symbols(definition,[spl22_9])],[avatar_definition]) ).
fof(f630,plain,
( sK6(sK18(sK2,sK3)) = singleton(sK5(sK18(sK2,sK3)))
| ~ spl22_9 ),
inference(avatar_component_clause,[],[f628]) ).
fof(f646,plain,
( sK4(sK18(sK2,sK3)) = ordered_pair(sK5(sK18(sK2,sK3)),sK6(sK18(sK2,sK3)))
| spl22_8 ),
inference(resolution,[],[f626,f49]) ).
fof(f647,plain,
( sK6(sK18(sK2,sK3)) = singleton(sK5(sK18(sK2,sK3)))
| spl22_8 ),
inference(resolution,[],[f626,f47]) ).
fof(f648,plain,
( spl22_9
| spl22_8 ),
inference(avatar_split_clause,[],[f647,f624,f628]) ).
fof(f649,plain,
( spl22_6
| spl22_8 ),
inference(avatar_split_clause,[],[f646,f624,f616]) ).
fof(f687,definition,
( spl22_12
<=> sK4(sK18(sK2,sK3)) = ordered_pair(sK20(sK2,sK4(sK18(sK2,sK3))),sK21(sK2,sK4(sK18(sK2,sK3)))) ),
introduced(definition,[new_symbols(definition,[spl22_12])],[avatar_definition]) ).
fof(f689,plain,
( sK4(sK18(sK2,sK3)) = ordered_pair(sK20(sK2,sK4(sK18(sK2,sK3))),sK21(sK2,sK4(sK18(sK2,sK3))))
| ~ spl22_12 ),
inference(avatar_component_clause,[],[f687]) ).
fof(f693,definition,
( spl22_13
<=> sK21(sK2,sK4(sK18(sK2,sK3))) = singleton(sK20(sK2,sK4(sK18(sK2,sK3)))) ),
introduced(definition,[new_symbols(definition,[spl22_13])],[avatar_definition]) ).
fof(f695,plain,
( sK21(sK2,sK4(sK18(sK2,sK3))) = singleton(sK20(sK2,sK4(sK18(sK2,sK3))))
| ~ spl22_13 ),
inference(avatar_component_clause,[],[f693]) ).
fof(f699,definition,
( spl22_14
<=> sK4(sK18(sK2,sK3)) = sK19(sK2,sK3,sK4(sK18(sK2,sK3))) ),
introduced(definition,[new_symbols(definition,[spl22_14])],[avatar_definition]) ).
fof(f701,plain,
( sK4(sK18(sK2,sK3)) = sK19(sK2,sK3,sK4(sK18(sK2,sK3)))
| ~ spl22_14 ),
inference(avatar_component_clause,[],[f699]) ).
fof(f743,plain,
( sK11(sK2) = sK13(sK2)
| ~ spl22_7 ),
inference(resolution,[],[f622,f70]) ).
fof(f744,plain,
( spl22_3
| ~ spl22_7 ),
inference(avatar_split_clause,[],[f743,f620,f552]) ).
fof(f748,plain,
( sK11(sK2) != sK12(sK2)
| ~ sP1(sK2)
| ~ spl22_3 ),
inference(superposition,[],[f75,f554]) ).
fof(f755,plain,
( ~ spl22_7
| ~ spl22_1
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f748,f552,f544,f620]) ).
fof(f762,plain,
( ! [X0,X1] :
( ~ in(X0,sK18(sK2,X1))
| ordered_pair(sK20(sK2,X0),sK21(sK2,X0)) = X0 )
| spl22_7 ),
inference(resolution,[],[f621,f81]) ).
fof(f763,plain,
( ! [X0,X1] :
( ~ in(X0,sK18(sK2,X1))
| sK21(sK2,X0) = singleton(sK20(sK2,X0)) )
| spl22_7 ),
inference(resolution,[],[f621,f79]) ).
fof(f764,plain,
( ! [X0,X1] :
( ~ in(X0,sK18(sK2,X1))
| sK19(sK2,X1,X0) = X0 )
| spl22_7 ),
inference(resolution,[],[f621,f82]) ).
fof(f765,plain,
( ! [X0,X1] :
( in(sK20(sK2,X0),sK2)
| ~ in(X0,sK18(sK2,X1)) )
| spl22_7 ),
inference(resolution,[],[f621,f80]) ).
fof(f875,plain,
( sK4(sK18(sK2,sK3)) = ordered_pair(sK5(sK18(sK2,sK3)),singleton(sK5(sK18(sK2,sK3))))
| ~ spl22_6
| ~ spl22_9 ),
inference(superposition,[],[f618,f630]) ).
fof(f918,plain,
( ! [X0,X1] :
( in(sK4(sK18(sK2,sK3)),sK18(X0,X1))
| ~ in(sK4(sK18(sK2,sK3)),cartesian_product2(X0,X1))
| ~ in(sK5(sK18(sK2,sK3)),X0)
| sP1(X0) )
| ~ spl22_6
| ~ spl22_9 ),
inference(superposition,[],[f88,f875]) ).
fof(f922,definition,
( spl22_24
<=> in(sK5(sK18(sK2,sK3)),sK2) ),
introduced(definition,[new_symbols(definition,[spl22_24])],[avatar_definition]) ).
fof(f924,plain,
( ~ in(sK5(sK18(sK2,sK3)),sK2)
| spl22_24 ),
inference(avatar_component_clause,[],[f922]) ).
fof(f926,definition,
( spl22_25
<=> ! [X0] :
( sK4(X0) != sK4(sK18(sK2,sK3))
| ~ in(sK4(X0),X0)
| ~ in(sK4(X0),cartesian_product2(sK2,sK3)) ) ),
introduced(definition,[new_symbols(definition,[spl22_25])],[avatar_definition]) ).
fof(f927,plain,
( ! [X0] :
( sK4(X0) != sK4(sK18(sK2,sK3))
| ~ in(sK4(X0),X0)
| ~ in(sK4(X0),cartesian_product2(sK2,sK3)) )
| ~ spl22_25 ),
inference(avatar_component_clause,[],[f926]) ).
fof(f929,plain,
( in(sK4(sK18(sK2,sK3)),sK18(sK2,sK3))
| spl22_24 ),
inference(resolution,[],[f924,f48]) ).
fof(f930,plain,
( spl22_8
| spl22_24 ),
inference(avatar_split_clause,[],[f929,f922,f624]) ).
fof(f947,plain,
( ~ in(sK4(sK18(sK2,sK3)),sK18(sK2,sK3))
| ~ in(sK4(sK18(sK2,sK3)),cartesian_product2(sK2,sK3))
| ~ spl22_25 ),
inference(equality_resolution,[],[f927]) ).
fof(f1115,definition,
( spl22_29
<=> in(sK4(sK18(sK2,sK3)),cartesian_product2(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl22_29])],[avatar_definition]) ).
fof(f1117,plain,
( ~ in(sK4(sK18(sK2,sK3)),cartesian_product2(sK2,sK3))
| spl22_29 ),
inference(avatar_component_clause,[],[f1115]) ).
fof(f1118,plain,
( ~ spl22_29
| ~ spl22_8
| ~ spl22_25 ),
inference(avatar_split_clause,[],[f947,f926,f624,f1115]) ).
fof(f1127,plain,
( sK4(sK18(sK2,sK3)) = ordered_pair(sK20(sK2,sK4(sK18(sK2,sK3))),sK21(sK2,sK4(sK18(sK2,sK3))))
| spl22_7
| ~ spl22_8 ),
inference(resolution,[],[f625,f762]) ).
fof(f1128,plain,
( sK21(sK2,sK4(sK18(sK2,sK3))) = singleton(sK20(sK2,sK4(sK18(sK2,sK3))))
| spl22_7
| ~ spl22_8 ),
inference(resolution,[],[f625,f763]) ).
fof(f1130,plain,
( sK4(sK18(sK2,sK3)) = sK19(sK2,sK3,sK4(sK18(sK2,sK3)))
| spl22_7
| ~ spl22_8 ),
inference(resolution,[],[f625,f764]) ).
fof(f1151,plain,
( spl22_14
| spl22_7
| ~ spl22_8 ),
inference(avatar_split_clause,[],[f1130,f624,f620,f699]) ).
fof(f1152,plain,
( spl22_13
| spl22_7
| ~ spl22_8 ),
inference(avatar_split_clause,[],[f1128,f624,f620,f693]) ).
fof(f1153,plain,
( spl22_12
| spl22_7
| ~ spl22_8 ),
inference(avatar_split_clause,[],[f1127,f624,f620,f687]) ).
fof(f1162,plain,
( in(sK4(sK18(sK2,sK3)),sK18(sK2,sK3))
| spl22_29 ),
inference(resolution,[],[f1117,f50]) ).
fof(f1175,plain,
( in(sK4(sK18(sK2,sK3)),cartesian_product2(sK2,sK3))
| ~ in(sK4(sK18(sK2,sK3)),sK18(sK2,sK3))
| sP1(sK2)
| ~ spl22_14 ),
inference(superposition,[],[f83,f701]) ).
fof(f1179,plain,
( spl22_7
| ~ spl22_8
| spl22_29
| ~ spl22_14 ),
inference(avatar_split_clause,[],[f1175,f699,f1115,f624,f620]) ).
fof(f1180,plain,
( spl22_8
| spl22_29 ),
inference(avatar_split_clause,[],[f1162,f1115,f624]) ).
fof(f1194,plain,
( sK4(sK18(sK2,sK3)) = ordered_pair(sK20(sK2,sK4(sK18(sK2,sK3))),singleton(sK20(sK2,sK4(sK18(sK2,sK3)))))
| ~ spl22_12
| ~ spl22_13 ),
inference(superposition,[],[f689,f695]) ).
fof(f1202,plain,
( ! [X0] :
( sK4(X0) != sK4(sK18(sK2,sK3))
| ~ in(sK4(X0),cartesian_product2(sK2,sK3))
| ~ in(sK20(sK2,sK4(sK18(sK2,sK3))),sK2)
| ~ in(sK4(X0),X0) )
| ~ spl22_12
| ~ spl22_13 ),
inference(superposition,[],[f85,f1194]) ).
fof(f1356,plain,
( ~ in(sK4(sK18(sK2,sK3)),cartesian_product2(sK2,sK3))
| ~ in(sK5(sK18(sK2,sK3)),sK2)
| sP1(sK2)
| ~ spl22_6
| spl22_8
| ~ spl22_9 ),
inference(resolution,[],[f918,f626]) ).
fof(f1397,plain,
( spl22_7
| ~ spl22_24
| ~ spl22_29
| ~ spl22_6
| spl22_8
| ~ spl22_9 ),
inference(avatar_split_clause,[],[f1356,f628,f624,f616,f1115,f922,f620]) ).
fof(f1399,definition,
( spl22_32
<=> in(sK20(sK2,sK4(sK18(sK2,sK3))),sK2) ),
introduced(definition,[new_symbols(definition,[spl22_32])],[avatar_definition]) ).
fof(f1401,plain,
( ~ in(sK20(sK2,sK4(sK18(sK2,sK3))),sK2)
| spl22_32 ),
inference(avatar_component_clause,[],[f1399]) ).
fof(f1402,plain,
( ~ spl22_32
| spl22_25
| ~ spl22_12
| ~ spl22_13 ),
inference(avatar_split_clause,[],[f1202,f693,f687,f926,f1399]) ).
fof(f1435,plain,
( ! [X0] : ~ in(sK4(sK18(sK2,sK3)),sK18(sK2,X0))
| spl22_7
| spl22_32 ),
inference(resolution,[],[f1401,f765]) ).
fof(f1440,plain,
( $false
| spl22_7
| ~ spl22_8
| spl22_32 ),
inference(resolution,[],[f1435,f625]) ).
fof(f1443,plain,
( sK4(sK18(sK2,sK3)) = ordered_pair(sK5(sK18(sK2,sK3)),sK6(sK18(sK2,sK3)))
| spl22_7
| spl22_32 ),
inference(resolution,[],[f1435,f49]) ).
fof(f1445,plain,
( spl22_7
| ~ spl22_8
| spl22_32 ),
inference(avatar_contradiction_clause,[],[f1440]) ).
fof(f1446,plain,
( spl22_6
| spl22_7
| spl22_32 ),
inference(avatar_split_clause,[],[f1443,f1399,f620,f616]) ).
fof(f1475,plain,
( sK11(sK2) = sK12(sK2)
| ~ spl22_7 ),
inference(resolution,[],[f622,f74]) ).
fof(f1477,plain,
( spl22_1
| ~ spl22_7 ),
inference(avatar_split_clause,[],[f1475,f620,f544]) ).
cnf(s13,plain,
( spl22_8
| spl22_9 ),
inference(sat_conversion,[],[f648]) ).
cnf(s14,plain,
( spl22_6
| spl22_8 ),
inference(sat_conversion,[],[f649]) ).
cnf(s27,plain,
( spl22_3
| ~ spl22_7 ),
inference(sat_conversion,[],[f744]) ).
cnf(s31,plain,
( ~ spl22_1
| ~ spl22_3
| ~ spl22_7 ),
inference(sat_conversion,[],[f755]) ).
cnf(s43,plain,
( spl22_8
| spl22_24 ),
inference(sat_conversion,[],[f930]) ).
cnf(s50,plain,
( ~ spl22_8
| ~ spl22_25
| ~ spl22_29 ),
inference(sat_conversion,[],[f1118]) ).
cnf(s51,plain,
( spl22_7
| ~ spl22_8
| spl22_14 ),
inference(sat_conversion,[],[f1151]) ).
cnf(s52,plain,
( spl22_7
| ~ spl22_8
| spl22_13 ),
inference(sat_conversion,[],[f1152]) ).
cnf(s53,plain,
( spl22_7
| ~ spl22_8
| spl22_12 ),
inference(sat_conversion,[],[f1153]) ).
cnf(s54,plain,
( spl22_7
| ~ spl22_8
| ~ spl22_14
| spl22_29 ),
inference(sat_conversion,[],[f1179]) ).
cnf(s55,plain,
( spl22_8
| spl22_29 ),
inference(sat_conversion,[],[f1180]) ).
cnf(s59,plain,
( ~ spl22_6
| spl22_7
| spl22_8
| ~ spl22_9
| ~ spl22_24
| ~ spl22_29 ),
inference(sat_conversion,[],[f1397]) ).
cnf(s60,plain,
( ~ spl22_12
| ~ spl22_13
| spl22_25
| ~ spl22_32 ),
inference(sat_conversion,[],[f1402]) ).
cnf(s61,plain,
( spl22_7
| ~ spl22_8
| spl22_32 ),
inference(sat_conversion,[],[f1445]) ).
cnf(s62,plain,
( spl22_6
| spl22_7
| spl22_32 ),
inference(sat_conversion,[],[f1446]) ).
cnf(s69,plain,
( spl22_1
| ~ spl22_7 ),
inference(sat_conversion,[],[f1477]) ).
cnf(s70,plain,
( spl22_6
| spl22_7 ),
inference(rat,[],[s50,s54,s60,s51,s52,s53,s14,s62]) ).
cnf(s71,plain,
( ~ spl22_8
| spl22_7 ),
inference(rat,[],[s50,s54,s60,s51,s52,s53,s61]) ).
cnf(s72,plain,
spl22_7,
inference(rat,[],[s59,s13,s43,s55,s71,s70]) ).
cnf(s73,plain,
spl22_1,
inference(rat,[],[s69,s72]) ).
cnf(s77,plain,
spl22_3,
inference(rat,[],[s27,s72]) ).
cnf(s78,plain,
$false,
inference(rat,[],[s31,s73,s72,s77]) ).
fof(f1478,plain,
$false,
inference(avatar_sat_refutation,[],[s78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU281+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n008.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Mon Sep 28 04:28:40 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.58 % (1872846)Will run a generic schedule for satisfiability detection.
% 0.17/0.58 % (1872855)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2327459490:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.58 % (1872852)% WARNING: option uhcvi not known.
% 0.17/0.58 % (1872851)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4103435283_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.58 % (1872853)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=110722743:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.58 % (1872852)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4253198319:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.58 % (1872854)dis+10_1_sil=32000:sp=arity:random_seed=2522513920:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.58 % (1872856)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1318262625:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.58 % (1872857)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=544506240:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.58 % TRYING [1]
% 0.17/0.58 % TRYING [2]
% 0.17/0.58 % TRYING [3]
% 0.17/0.58 % TRYING [4]
% 0.17/0.58 % (1872855)Instruction limit reached!
% 0.17/0.58 % (1872855)------------------------------
% 0.17/0.58 % (1872855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.58 % (1872855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.58 % (1872855)CaDiCaL version: 2.1.3
% 0.17/0.58 % (1872855)Termination reason: Instruction limit
% 0.17/0.58 % (1872855)Termination phase: Saturation
% 0.17/0.58 % (1872855)Time elapsed: 0.055 s
% 0.17/0.58 % (1872855)Peak memory usage: 12 MB
% 0.17/0.58 % (1872855)Instructions burned: 116 (million)
% 0.17/0.58 % (1872865)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2535785072:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.17/0.58 % TRYING [1]
% 0.17/0.58 % TRYING [2]
% 0.17/0.58 % TRYING [3]
% 0.17/0.58 % TRYING [4]
% 0.17/0.58 % (1872854)Instruction limit reached!
% 0.17/0.58 % (1872854)------------------------------
% 0.17/0.58 % (1872854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.58 % (1872854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.58 % (1872854)CaDiCaL version: 2.1.3
% 0.17/0.58 % (1872854)Termination reason: Instruction limit
% 0.17/0.58 % (1872854)Termination phase: Saturation
% 0.17/0.58 % (1872854)Time elapsed: 0.092 s
% 0.17/0.58 % (1872854)Peak memory usage: 12 MB
% 0.17/0.58 % (1872854)Instructions burned: 104 (million)
% 0.17/0.58 % (1872857) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1872846-1872857"...
% 0.17/0.58 % (1872857)...printing done.
% 0.17/0.58 % (1872857)Refutation found. Thanks to Tanya!
% 0.17/0.58 % SZS status Theorem for theBenchmark
% 0.17/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 0.50/0.58 % (1872857)------------------------------
% 0.50/0.58 % (1872857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.58 % (1872857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.58 % (1872857)CaDiCaL version: 2.1.3
% 0.50/0.58 % (1872857)Termination reason: Refutation
% 0.50/0.58 % (1872857)Time elapsed: 0.095 s
% 0.50/0.58 % (1872857)Peak memory usage: 13 MB
% 0.50/0.58 % (1872857)Instructions burned: 95 (million)
% 0.50/0.58 % (1872846)Success in time 0.136 s
% 0.50/0.58 % Vampire exiting
%------------------------------------------------------------------------------