%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET951+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 12:45:04 PM UTC 2026
% Result : Theorem 0.41s 0.48s
% Output : Refutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 109 ( 25 unt; 8 def)
% Number of atoms : 323 ( 86 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 364 ( 150 ~; 147 |; 54 &)
% ( 12 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 193 ( 0 sgn 173 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = cartesian_product2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f11,conjecture,
! [X0,X1,X2,X3,X4] :
~ ( in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
& ! [X5,X6] :
~ ( X0 = ordered_pair(X5,X6)
& in(X5,set_intersection2(X1,X3))
& in(X6,set_intersection2(X2,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
~ ( in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
& ! [X5,X6] :
~ ( X0 = ordered_pair(X5,X6)
& in(X5,set_intersection2(X1,X3))
& in(X6,set_intersection2(X2,X4)) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [X0,X1,X2,X3] :
( ordered_pair(X0,X1) = ordered_pair(X2,X3)
=> ( X0 = X2
& X1 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f16,plain,
? [X0,X1,X2,X3,X4] :
( in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
& ! [X5,X6] :
( ordered_pair(X5,X6) != X0
| ~ in(X5,set_intersection2(X1,X3))
| ~ in(X6,set_intersection2(X2,X4)) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( ( X0 = X2
& X1 = X3 )
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f13]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ? [X3] :
( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 ) )
& ( ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) )
| ~ in(X3,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ? [X3] :
( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( in(X6,X0)
& in(X7,X1)
& ordered_pair(X6,X7) = X3 )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ? [X11,X12] :
( in(X11,X0)
& in(X12,X1)
& ordered_pair(X11,X12) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != sK0(X0,X1,X2) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),X0)
& in(sK2(X0,X1,X2),X1)
& sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2)) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ( in(sK3(X0,X1,X8),X0)
& in(sK4(X0,X1,X8),X1)
& ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X6,sK1(X0,X1,X2)),skolemize(X7,sK2(X0,X1,X2)),skolemize(X11,sK3(X0,X1,X8)),skolemize(X12,sK4(X0,X1,X8))],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( in(sK5(X0,X1,X2),X0)
& in(sK5(X0,X1,X2),X1) )
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f23]) ).
fof(f27,plain,
( in(sK8,set_intersection2(cartesian_product2(sK9,sK10),cartesian_product2(sK11,sK12)))
& ! [X5,X6] :
( ordered_pair(X5,X6) != sK8
| ~ in(X5,set_intersection2(sK9,sK11))
| ~ in(X6,set_intersection2(sK10,sK12)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X3,sK11),skolemize(X4,sK12)],[f16]) ).
fof(f29,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f31,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X2,X0,X1,X8] :
( in(sK4(X0,X1,X8),X1)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X2,X0,X1,X8] :
( in(sK3(X0,X1,X8),X0)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f24]) ).
fof(f40,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f50,plain,
! [X6,X5] :
( ordered_pair(X5,X6) != sK8
| ~ in(X5,set_intersection2(sK9,sK11))
| ~ in(X6,set_intersection2(sK10,sK12)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f51,plain,
in(sK8,set_intersection2(cartesian_product2(sK9,sK10),cartesian_product2(sK11,sK12))),
inference(cnf_transformation,[],[f27]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f57,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f31,f45]) ).
fof(f59,plain,
! [X6,X5] :
( sK8 != unordered_pair(unordered_pair(X5,X6),singleton(X5))
| ~ in(X5,set_intersection2(sK9,sK11))
| ~ in(X6,set_intersection2(sK10,sK12)) ),
inference(definition_unfolding,[],[f50,f45]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| unordered_pair(unordered_pair(X0,X1),singleton(X0)) != unordered_pair(unordered_pair(X2,X3),singleton(X2)) ),
inference(definition_unfolding,[],[f53,f45,f45]) ).
fof(f61,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| unordered_pair(unordered_pair(X0,X1),singleton(X0)) != unordered_pair(unordered_pair(X2,X3),singleton(X2)) ),
inference(definition_unfolding,[],[f52,f45,f45]) ).
fof(f64,plain,
! [X0,X1,X8] :
( in(sK3(X0,X1,X8),X0)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f33]) ).
fof(f65,plain,
! [X0,X1,X8] :
( in(sK4(X0,X1,X8),X1)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f32]) ).
fof(f66,plain,
! [X0,X1,X8] :
( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f57]) ).
fof(f67,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f41]) ).
fof(f68,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f40]) ).
fof(f69,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f39]) ).
fof(f72,plain,
! [X0,X1] :
( sK8 != unordered_pair(singleton(X0),unordered_pair(X0,X1))
| ~ in(X0,set_intersection2(sK9,sK11))
| ~ in(X1,set_intersection2(sK10,sK12)) ),
inference(superposition,[],[f59,f29]) ).
fof(f84,plain,
in(sK8,cartesian_product2(sK9,sK10)),
inference(resolution,[],[f68,f51]) ).
fof(f89,plain,
in(sK8,cartesian_product2(sK11,sK12)),
inference(resolution,[],[f69,f51]) ).
fof(f107,plain,
! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(X0,X1),singleton(X0)) != unordered_pair(singleton(X2),unordered_pair(X2,X3))
| X0 = X2 ),
inference(forward_demodulation,[],[f60,f29]) ).
fof(f108,plain,
! [X2,X3,X0,X1] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != unordered_pair(singleton(X2),unordered_pair(X2,X3))
| X0 = X2 ),
inference(forward_demodulation,[],[f107,f29]) ).
fof(f109,plain,
! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(X0,X1),singleton(X0)) != unordered_pair(singleton(X2),unordered_pair(X2,X3))
| X1 = X3 ),
inference(forward_demodulation,[],[f61,f29]) ).
fof(f110,plain,
! [X2,X3,X0,X1] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != unordered_pair(singleton(X2),unordered_pair(X2,X3))
| X1 = X3 ),
inference(forward_demodulation,[],[f109,f29]) ).
fof(f164,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| unordered_pair(singleton(sK3(X0,X1,X8)),unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8))) = X8 ),
inference(forward_demodulation,[],[f66,f29]) ).
fof(f178,plain,
sK8 = unordered_pair(singleton(sK3(sK9,sK10,sK8)),unordered_pair(sK3(sK9,sK10,sK8),sK4(sK9,sK10,sK8))),
inference(resolution,[],[f164,f84]) ).
fof(f179,plain,
sK8 = unordered_pair(singleton(sK3(sK11,sK12,sK8)),unordered_pair(sK3(sK11,sK12,sK8),sK4(sK11,sK12,sK8))),
inference(resolution,[],[f164,f89]) ).
fof(f182,plain,
! [X0,X1] :
( sK8 != unordered_pair(singleton(X0),unordered_pair(X0,X1))
| sK3(sK9,sK10,sK8) = X0 ),
inference(superposition,[],[f108,f178]) ).
fof(f184,plain,
! [X0,X1] :
( sK8 != unordered_pair(singleton(X0),unordered_pair(X0,X1))
| sK4(sK9,sK10,sK8) = X1 ),
inference(superposition,[],[f110,f178]) ).
fof(f261,definition,
( spl13_10
<=> in(sK4(sK9,sK10,sK8),sK10) ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
fof(f263,plain,
( ~ in(sK4(sK9,sK10,sK8),sK10)
| spl13_10 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f365,plain,
( sK8 != sK8
| ~ in(sK3(sK11,sK12,sK8),set_intersection2(sK9,sK11))
| ~ in(sK4(sK11,sK12,sK8),set_intersection2(sK10,sK12)) ),
inference(superposition,[],[f72,f179]) ).
fof(f375,plain,
( sK8 != sK8
| sK3(sK9,sK10,sK8) = sK3(sK11,sK12,sK8) ),
inference(superposition,[],[f182,f179]) ).
fof(f376,plain,
( sK8 != sK8
| sK4(sK9,sK10,sK8) = sK4(sK11,sK12,sK8) ),
inference(superposition,[],[f184,f179]) ).
fof(f399,plain,
sK4(sK9,sK10,sK8) = sK4(sK11,sK12,sK8),
inference(trivial_inequality_removal,[],[f376]) ).
fof(f400,plain,
sK3(sK9,sK10,sK8) = sK3(sK11,sK12,sK8),
inference(trivial_inequality_removal,[],[f375]) ).
fof(f401,plain,
( ~ in(sK3(sK11,sK12,sK8),set_intersection2(sK9,sK11))
| ~ in(sK4(sK11,sK12,sK8),set_intersection2(sK10,sK12)) ),
inference(trivial_inequality_removal,[],[f365]) ).
fof(f436,definition,
( spl13_17
<=> in(sK4(sK11,sK12,sK8),set_intersection2(sK10,sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_17])],[avatar_definition]) ).
fof(f438,plain,
( ~ in(sK4(sK11,sK12,sK8),set_intersection2(sK10,sK12))
| spl13_17 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f440,definition,
( spl13_18
<=> in(sK3(sK11,sK12,sK8),set_intersection2(sK9,sK11)) ),
introduced(definition,[new_symbols(definition,[spl13_18])],[avatar_definition]) ).
fof(f442,plain,
( ~ in(sK3(sK11,sK12,sK8),set_intersection2(sK9,sK11))
| spl13_18 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f443,plain,
( ~ spl13_17
| ~ spl13_18 ),
inference(avatar_split_clause,[],[f401,f440,f436]) ).
fof(f478,plain,
( ~ in(sK4(sK11,sK12,sK8),sK10)
| ~ in(sK4(sK11,sK12,sK8),sK12)
| spl13_17 ),
inference(resolution,[],[f438,f67]) ).
fof(f480,definition,
( spl13_26
<=> in(sK4(sK11,sK12,sK8),sK12) ),
introduced(definition,[new_symbols(definition,[spl13_26])],[avatar_definition]) ).
fof(f482,plain,
( ~ in(sK4(sK11,sK12,sK8),sK12)
| spl13_26 ),
inference(avatar_component_clause,[],[f480]) ).
fof(f484,definition,
( spl13_27
<=> in(sK4(sK11,sK12,sK8),sK10) ),
introduced(definition,[new_symbols(definition,[spl13_27])],[avatar_definition]) ).
fof(f486,plain,
( ~ in(sK4(sK11,sK12,sK8),sK10)
| spl13_27 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f487,plain,
( ~ spl13_26
| ~ spl13_27
| spl13_17 ),
inference(avatar_split_clause,[],[f478,f436,f484,f480]) ).
fof(f488,plain,
( ~ in(sK8,cartesian_product2(sK11,sK12))
| spl13_26 ),
inference(resolution,[],[f482,f65]) ).
fof(f489,plain,
( $false
| spl13_26 ),
inference(forward_subsumption_resolution,[],[f488,f89]) ).
fof(f490,plain,
spl13_26,
inference(avatar_contradiction_clause,[],[f489]) ).
fof(f493,plain,
( ~ in(sK4(sK9,sK10,sK8),sK10)
| spl13_27 ),
inference(superposition,[],[f486,f399]) ).
fof(f503,plain,
( ~ spl13_10
| spl13_27 ),
inference(avatar_split_clause,[],[f493,f484,f261]) ).
fof(f524,plain,
( ~ in(sK8,cartesian_product2(sK9,sK10))
| spl13_10 ),
inference(resolution,[],[f263,f65]) ).
fof(f525,plain,
( $false
| spl13_10 ),
inference(forward_subsumption_resolution,[],[f524,f84]) ).
fof(f526,plain,
spl13_10,
inference(avatar_contradiction_clause,[],[f525]) ).
fof(f639,definition,
( spl13_29
<=> in(sK3(sK9,sK10,sK8),sK9) ),
introduced(definition,[new_symbols(definition,[spl13_29])],[avatar_definition]) ).
fof(f641,plain,
( ~ in(sK3(sK9,sK10,sK8),sK9)
| spl13_29 ),
inference(avatar_component_clause,[],[f639]) ).
fof(f679,plain,
( ~ in(sK3(sK11,sK12,sK8),sK9)
| ~ in(sK3(sK11,sK12,sK8),sK11)
| spl13_18 ),
inference(resolution,[],[f442,f67]) ).
fof(f681,definition,
( spl13_30
<=> in(sK3(sK11,sK12,sK8),sK11) ),
introduced(definition,[new_symbols(definition,[spl13_30])],[avatar_definition]) ).
fof(f683,plain,
( ~ in(sK3(sK11,sK12,sK8),sK11)
| spl13_30 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f685,definition,
( spl13_31
<=> in(sK3(sK11,sK12,sK8),sK9) ),
introduced(definition,[new_symbols(definition,[spl13_31])],[avatar_definition]) ).
fof(f687,plain,
( ~ in(sK3(sK11,sK12,sK8),sK9)
| spl13_31 ),
inference(avatar_component_clause,[],[f685]) ).
fof(f688,plain,
( ~ spl13_30
| ~ spl13_31
| spl13_18 ),
inference(avatar_split_clause,[],[f679,f440,f685,f681]) ).
fof(f706,plain,
( ~ in(sK8,cartesian_product2(sK11,sK12))
| spl13_30 ),
inference(resolution,[],[f683,f64]) ).
fof(f707,plain,
( $false
| spl13_30 ),
inference(forward_subsumption_resolution,[],[f706,f89]) ).
fof(f708,plain,
spl13_30,
inference(avatar_contradiction_clause,[],[f707]) ).
fof(f803,plain,
( ~ in(sK3(sK9,sK10,sK8),sK9)
| spl13_31 ),
inference(superposition,[],[f687,f400]) ).
fof(f809,plain,
( ~ spl13_29
| spl13_31 ),
inference(avatar_split_clause,[],[f803,f685,f639]) ).
fof(f830,plain,
( ~ in(sK8,cartesian_product2(sK9,sK10))
| spl13_29 ),
inference(resolution,[],[f641,f64]) ).
fof(f831,plain,
( $false
| spl13_29 ),
inference(forward_subsumption_resolution,[],[f830,f84]) ).
fof(f832,plain,
spl13_29,
inference(avatar_contradiction_clause,[],[f831]) ).
cnf(s9,plain,
( ~ spl13_17
| ~ spl13_18 ),
inference(sat_conversion,[],[f443]) ).
cnf(s16,plain,
( spl13_17
| ~ spl13_26
| ~ spl13_27 ),
inference(sat_conversion,[],[f487]) ).
cnf(s17,plain,
spl13_26,
inference(sat_conversion,[],[f490]) ).
cnf(s19,plain,
( ~ spl13_10
| spl13_27 ),
inference(sat_conversion,[],[f503]) ).
cnf(s23,plain,
spl13_10,
inference(sat_conversion,[],[f526]) ).
cnf(s27,plain,
( spl13_18
| ~ spl13_30
| ~ spl13_31 ),
inference(sat_conversion,[],[f688]) ).
cnf(s28,plain,
spl13_30,
inference(sat_conversion,[],[f708]) ).
cnf(s29,plain,
( ~ spl13_29
| spl13_31 ),
inference(sat_conversion,[],[f809]) ).
cnf(s34,plain,
spl13_29,
inference(sat_conversion,[],[f832]) ).
cnf(s35,plain,
spl13_31,
inference(rat,[],[s29,s34]) ).
cnf(s36,plain,
spl13_18,
inference(rat,[],[s27,s35,s28]) ).
cnf(s38,plain,
spl13_27,
inference(rat,[],[s19,s23]) ).
cnf(s39,plain,
spl13_17,
inference(rat,[],[s16,s38,s17]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s9,s36,s39]) ).
fof(f833,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET951+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:16:00 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.41/0.48 % (2982836)Will run a generic schedule for satisfiability detection.
% 0.41/0.48 % (2982842)% WARNING: option uhcvi not known.
% 0.41/0.48 % (2982842)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1450531525:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.41/0.48 % (2982844)dis+10_1_sil=32000:sp=arity:random_seed=658364365:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.41/0.48 % (2982845)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3738206156:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.41/0.48 % (2982841)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3646132137_2999 on theBenchmark for (2999ds/0Mi)
% 0.41/0.48 % (2982843)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1378327955:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.41/0.48 % (2982846)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=352353420:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.41/0.48 % TRYING [1]
% 0.41/0.48 % TRYING [2]
% 0.41/0.48 % (2982847)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4242896866:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.41/0.48 % TRYING [3]
% 0.41/0.48 % (2982844) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2982836-2982844"...
% 0.41/0.48 % (2982844)...printing done.
% 0.41/0.48 % (2982844)Refutation found. Thanks to Tanya!
% 0.41/0.48 % SZS status Theorem for theBenchmark
% 0.41/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.41/0.48 % (2982844)------------------------------
% 0.41/0.48 % (2982844)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.48 % (2982844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.48 % (2982844)CaDiCaL version: 2.1.3
% 0.41/0.48 % (2982844)Termination reason: Refutation
% 0.41/0.48 % (2982844)Time elapsed: 0.030 s
% 0.41/0.48 % (2982844)Peak memory usage: 12 MB
% 0.41/0.48 % (2982844)Instructions burned: 45 (million)
% 0.41/0.48 % (2982836)Success in time 0.064 s
% 0.41/0.48 % Vampire exiting
%------------------------------------------------------------------------------