%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET951+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:42:24 PM UTC 2026
% Result : Theorem 4.36s 1.53s
% Output : Refutation 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 90 ( 21 unt; 4 def)
% Number of atoms : 287 ( 86 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 335 ( 138 ~; 134 |; 54 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f15,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(f16,plain,
! [X0,X1,X2,X3] :
( ( X0 = X2
& X1 = X3 )
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f13]) ).
fof(f18,plain,
( in(sK0,set_intersection2(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))
& ! [X5,X6] :
( ordered_pair(X5,X6) != sK0
| ~ in(X5,set_intersection2(sK1,sK3))
| ~ in(X6,set_intersection2(sK2,sK4)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f15]) ).
fof(f19,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(f20,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,[],[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) ) ) )
& ( ! [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,[],[f20]) ).
fof(f22,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))],[f21]) ).
fof(f23,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(f24,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,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != sK6(X0,X1,X2) )
| ~ in(sK6(X0,X1,X2),X2) )
& ( ( in(sK7(X0,X1,X2),X0)
& in(sK8(X0,X1,X2),X1)
& sK6(X0,X1,X2) = ordered_pair(sK7(X0,X1,X2),sK8(X0,X1,X2)) )
| in(sK6(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ( in(sK9(X0,X1,X8),X0)
& in(sK10(X0,X1,X8),X1)
& ordered_pair(sK9(X0,X1,X8),sK10(X0,X1,X8)) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10]),skolemize(X3,sK6(X0,X1,X2)),skolemize(X6,sK7(X0,X1,X2)),skolemize(X7,sK8(X0,X1,X2)),skolemize(X11,sK9(X0,X1,X8)),skolemize(X12,sK10(X0,X1,X8))],[f24]) ).
fof(f28,plain,
! [X6,X5] :
( ordered_pair(X5,X6) != sK0
| ~ in(X5,set_intersection2(sK1,sK3))
| ~ in(X6,set_intersection2(sK2,sK4)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
in(sK0,set_intersection2(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f16]) ).
fof(f33,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f34,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK9(X0,X1,X8),sK10(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
! [X2,X0,X1,X8] :
( in(sK10(X0,X1,X8),X1)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
! [X2,X0,X1,X8] :
( in(sK9(X0,X1,X8),X0)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f49,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f54,plain,
! [X6,X5] :
( sK0 != unordered_pair(unordered_pair(X5,X6),singleton(X5))
| ~ in(X5,set_intersection2(sK1,sK3))
| ~ in(X6,set_intersection2(sK2,sK4)) ),
inference(definition_unfolding,[],[f28,f33]) ).
fof(f55,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,[],[f31,f33,f33]) ).
fof(f56,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,[],[f30,f33,f33]) ).
fof(f60,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK9(X0,X1,X8),sK10(X0,X1,X8)),singleton(sK9(X0,X1,X8))) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f40,f33]) ).
fof(f62,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f36]) ).
fof(f63,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f35]) ).
fof(f64,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f34]) ).
fof(f67,plain,
! [X0,X1,X8] :
( in(sK9(X0,X1,X8),X0)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f42]) ).
fof(f68,plain,
! [X0,X1,X8] :
( in(sK10(X0,X1,X8),X1)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f41]) ).
fof(f69,plain,
! [X0,X1,X8] :
( unordered_pair(unordered_pair(sK9(X0,X1,X8),sK10(X0,X1,X8)),singleton(sK9(X0,X1,X8))) = X8
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f60]) ).
fof(f70,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| unordered_pair(singleton(sK9(X0,X1,X8)),unordered_pair(sK9(X0,X1,X8),sK10(X0,X1,X8))) = X8 ),
inference(forward_demodulation,[],[f69,f49]) ).
fof(f74,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,[],[f56,f49]) ).
fof(f75,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,[],[f55,f49]) ).
fof(f76,plain,
! [X6,X5] :
( sK0 != unordered_pair(singleton(X5),unordered_pair(X5,X6))
| ~ in(X5,set_intersection2(sK1,sK3))
| ~ in(X6,set_intersection2(sK2,sK4)) ),
inference(forward_demodulation,[],[f54,f49]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( unordered_pair(singleton(X2),unordered_pair(X2,X3)) != unordered_pair(singleton(X0),unordered_pair(X0,X1))
| X1 = X3 ),
inference(forward_demodulation,[],[f74,f49]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( unordered_pair(singleton(X2),unordered_pair(X2,X3)) != unordered_pair(singleton(X0),unordered_pair(X0,X1))
| X0 = X2 ),
inference(forward_demodulation,[],[f75,f49]) ).
fof(f90,plain,
in(sK0,cartesian_product2(sK1,sK2)),
inference(resolution,[],[f63,f29]) ).
fof(f95,plain,
in(sK0,cartesian_product2(sK3,sK4)),
inference(resolution,[],[f64,f29]) ).
fof(f168,plain,
sK0 = unordered_pair(singleton(sK9(sK1,sK2,sK0)),unordered_pair(sK9(sK1,sK2,sK0),sK10(sK1,sK2,sK0))),
inference(resolution,[],[f70,f90]) ).
fof(f169,plain,
sK0 = unordered_pair(singleton(sK9(sK3,sK4,sK0)),unordered_pair(sK9(sK3,sK4,sK0),sK10(sK3,sK4,sK0))),
inference(resolution,[],[f70,f95]) ).
fof(f183,plain,
( sK0 != sK0
| ~ in(sK9(sK1,sK2,sK0),set_intersection2(sK1,sK3))
| ~ in(sK10(sK1,sK2,sK0),set_intersection2(sK2,sK4)) ),
inference(superposition,[],[f76,f168]) ).
fof(f185,plain,
! [X0,X1] :
( sK0 != unordered_pair(singleton(X0),unordered_pair(X0,X1))
| sK10(sK1,sK2,sK0) = X1 ),
inference(superposition,[],[f77,f168]) ).
fof(f187,plain,
! [X0,X1] :
( sK0 != unordered_pair(singleton(X0),unordered_pair(X0,X1))
| sK9(sK1,sK2,sK0) = X0 ),
inference(superposition,[],[f78,f168]) ).
fof(f199,plain,
( ~ in(sK9(sK1,sK2,sK0),set_intersection2(sK1,sK3))
| ~ in(sK10(sK1,sK2,sK0),set_intersection2(sK2,sK4)) ),
inference(trivial_inequality_removal,[],[f183]) ).
fof(f210,definition,
( spl13_1
<=> in(sK10(sK1,sK2,sK0),set_intersection2(sK2,sK4)) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f212,plain,
( ~ in(sK10(sK1,sK2,sK0),set_intersection2(sK2,sK4))
| spl13_1 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f214,definition,
( spl13_2
<=> in(sK9(sK1,sK2,sK0),set_intersection2(sK1,sK3)) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f216,plain,
( ~ in(sK9(sK1,sK2,sK0),set_intersection2(sK1,sK3))
| spl13_2 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f217,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f199,f214,f210]) ).
fof(f260,plain,
( ~ in(sK10(sK1,sK2,sK0),sK2)
| ~ in(sK10(sK1,sK2,sK0),sK4)
| spl13_1 ),
inference(resolution,[],[f212,f62]) ).
fof(f262,definition,
( spl13_9
<=> in(sK10(sK1,sK2,sK0),sK4) ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
fof(f264,plain,
( ~ in(sK10(sK1,sK2,sK0),sK4)
| spl13_9 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f266,definition,
( spl13_10
<=> in(sK10(sK1,sK2,sK0),sK2) ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
fof(f268,plain,
( ~ in(sK10(sK1,sK2,sK0),sK2)
| spl13_10 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f269,plain,
( ~ spl13_9
| ~ spl13_10
| spl13_1 ),
inference(avatar_split_clause,[],[f260,f210,f266,f262]) ).
fof(f375,plain,
( sK0 != sK0
| sK10(sK1,sK2,sK0) = sK10(sK3,sK4,sK0) ),
inference(superposition,[],[f185,f169]) ).
fof(f376,plain,
( sK0 != sK0
| sK9(sK1,sK2,sK0) = sK9(sK3,sK4,sK0) ),
inference(superposition,[],[f187,f169]) ).
fof(f398,plain,
sK9(sK1,sK2,sK0) = sK9(sK3,sK4,sK0),
inference(trivial_inequality_removal,[],[f376]) ).
fof(f399,plain,
sK10(sK1,sK2,sK0) = sK10(sK3,sK4,sK0),
inference(trivial_inequality_removal,[],[f375]) ).
fof(f488,plain,
( in(sK9(sK1,sK2,sK0),sK3)
| ~ in(sK0,cartesian_product2(sK3,sK4)) ),
inference(superposition,[],[f67,f398]) ).
fof(f489,plain,
in(sK9(sK1,sK2,sK0),sK3),
inference(forward_subsumption_resolution,[],[f488,f95]) ).
fof(f495,plain,
( in(sK10(sK1,sK2,sK0),sK4)
| ~ in(sK0,cartesian_product2(sK3,sK4)) ),
inference(superposition,[],[f68,f399]) ).
fof(f496,plain,
( ~ in(sK0,cartesian_product2(sK3,sK4))
| spl13_9 ),
inference(forward_subsumption_resolution,[],[f495,f264]) ).
fof(f499,plain,
( $false
| spl13_9 ),
inference(forward_subsumption_resolution,[],[f496,f95]) ).
fof(f500,plain,
spl13_9,
inference(avatar_contradiction_clause,[],[f499]) ).
fof(f540,plain,
( ~ in(sK0,cartesian_product2(sK1,sK2))
| spl13_10 ),
inference(resolution,[],[f268,f68]) ).
fof(f541,plain,
( $false
| spl13_10 ),
inference(forward_subsumption_resolution,[],[f540,f90]) ).
fof(f542,plain,
spl13_10,
inference(avatar_contradiction_clause,[],[f541]) ).
fof(f636,plain,
( ~ in(sK9(sK1,sK2,sK0),sK1)
| ~ in(sK9(sK1,sK2,sK0),sK3)
| spl13_2 ),
inference(resolution,[],[f216,f62]) ).
fof(f637,plain,
( ~ in(sK9(sK1,sK2,sK0),sK1)
| spl13_2 ),
inference(forward_subsumption_resolution,[],[f636,f489]) ).
fof(f655,plain,
( ~ in(sK0,cartesian_product2(sK1,sK2))
| spl13_2 ),
inference(resolution,[],[f637,f67]) ).
fof(f656,plain,
( $false
| spl13_2 ),
inference(forward_subsumption_resolution,[],[f655,f90]) ).
fof(f657,plain,
spl13_2,
inference(avatar_contradiction_clause,[],[f656]) ).
cnf(s1,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f217]) ).
cnf(s4,plain,
( spl13_1
| ~ spl13_9
| ~ spl13_10 ),
inference(sat_conversion,[],[f269]) ).
cnf(s7,plain,
spl13_9,
inference(sat_conversion,[],[f500]) ).
cnf(s8,plain,
spl13_10,
inference(sat_conversion,[],[f542]) ).
cnf(s9,plain,
spl13_2,
inference(sat_conversion,[],[f657]) ).
cnf(s10,plain,
spl13_1,
inference(rat,[],[s4,s8,s7]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s9,s10]) ).
fof(f658,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET951+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:18:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.36/1.53 % (2963779)Detected formulas, will run a generic FOF schedule.
% 4.36/1.53 % (2963879)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4153806063:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.36/1.53 % (2963878)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3672504342:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.36/1.53 % (2963881)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1483794908:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.36/1.53 % (2963877)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=349452096:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.36/1.53 % (2963880)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1031855789:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.36/1.53 % (2963883)dis-21_1_sil=8000:lcm=predicate:random_seed=3051324933:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.36/1.53 % (2963882)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=830959865:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.36/1.53 % (2963880)Instruction limit reached!
% 4.36/1.53 % (2963880)------------------------------
% 4.36/1.53 % (2963880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.36/1.53 % (2963880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.36/1.53 % (2963880)CaDiCaL version: 2.1.3
% 4.36/1.53 % (2963880)Termination reason: Instruction limit
% 4.36/1.53 % (2963880)Termination phase: Saturation
% 4.36/1.53 % (2963880)Time elapsed: 0.066 s
% 4.36/1.53 % (2963880)Peak memory usage: 89 MB
% 4.36/1.53 % (2963880)Instructions burned: 111 (million)
% 4.36/1.53 % (2963881)Instruction limit reached!
% 4.36/1.53 % (2963881)------------------------------
% 4.36/1.53 % (2963881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.36/1.53 % (2963881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.36/1.53 % (2963881)CaDiCaL version: 2.1.3
% 4.36/1.53 % (2963881)Termination reason: Instruction limit
% 4.36/1.53 % (2963881)Termination phase: Saturation
% 4.36/1.53 % (2963881)Time elapsed: 0.073 s
% 4.36/1.53 % (2963881)Peak memory usage: 88 MB
% 4.36/1.53 % (2963881)Instructions burned: 120 (million)
% 4.36/1.53 % (2963883)Instruction limit reached!
% 4.36/1.53 % (2963883)------------------------------
% 4.36/1.53 % (2963883)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.36/1.53 % (2963883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.36/1.53 % (2963883)CaDiCaL version: 2.1.3
% 4.36/1.53 % (2963883)Termination reason: Instruction limit
% 4.36/1.53 % (2963883)Termination phase: Saturation
% 4.36/1.53 % (2963883)Time elapsed: 0.075 s
% 4.36/1.53 % (2963883)Peak memory usage: 89 MB
% 4.36/1.53 % (2963883)Instructions burned: 130 (million)
% 4.36/1.53 % (2963882)Instruction limit reached!
% 4.36/1.53 % (2963882)------------------------------
% 4.36/1.53 % (2963882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.36/1.53 % (2963882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.36/1.53 % (2963882)CaDiCaL version: 2.1.3
% 4.36/1.53 % (2963882)Termination reason: Instruction limit
% 4.36/1.53 % (2963882)Termination phase: Saturation
% 4.36/1.53 % (2963882)Time elapsed: 0.092 s
% 4.36/1.53 % (2963882)Peak memory usage: 89 MB
% 4.36/1.53 % (2963882)Instructions burned: 140 (million)
% 4.36/1.53 % (2963918)lrs+10_1_sil=8000:sp=occurrence:random_seed=474788364:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.36/1.53 % (2963919)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3747117301:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.36/1.53 % (2963926)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1232213010:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.36/1.53 % (2963918)First to succeed.
% 4.36/1.53 % (2963918)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2963779"
% 4.36/1.53 % (2963945)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3768765181:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 4.36/1.53 % (2963919)Instruction limit reached!
% 4.36/1.53 % (2963919)------------------------------
% 4.36/1.53 % (2963919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.36/1.53 % (2963919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.36/1.53 % (2963919)CaDiCaL version: 2.1.3
% 4.36/1.53 % (2963919)Termination reason: Instruction limit
% 4.36/1.53 % (2963919)Termination phase: Saturation
% 4.36/1.53 % (2963919)Time elapsed: 0.082 s
% 4.36/1.53 % (2963919)Peak memory usage: 90 MB
% 4.36/1.53 % (2963919)Instructions burned: 159 (million)
% 4.36/1.53 % (2963945)Instruction limit reached!
% 4.36/1.53 % (2963945)------------------------------
% 4.36/1.53 % (2963945)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.36/1.53 % (2963945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.36/1.53 % (2963945)CaDiCaL version: 2.1.3
% 4.36/1.53 % (2963945)Termination reason: Instruction limit
% 4.36/1.53 % (2963945)Termination phase: Saturation
% 4.36/1.53 % (2963945)Time elapsed: 0.130 s
% 4.36/1.53 % (2963945)Peak memory usage: 91 MB
% 4.36/1.53 % (2963945)Instructions burned: 248 (million)
% 4.36/1.53 % (2964017)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2170843346:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.36/1.53 % (2963926)Instruction limit reached!
% 4.36/1.53 % (2963926)------------------------------
% 4.36/1.53 % (2963926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.36/1.53 % (2963926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.36/1.53 % (2963926)CaDiCaL version: 2.1.3
% 4.36/1.53 % (2963926)Termination reason: Instruction limit
% 4.36/1.53 % (2963926)Termination phase: Saturation
% 4.36/1.53 % (2963926)Time elapsed: 0.209 s
% 4.36/1.53 % (2963926)Peak memory usage: 91 MB
% 4.36/1.53 % (2963926)Instructions burned: 326 (million)
% 4.36/1.53 % (2963918)Refutation found. Thanks to Tanya!
% 4.36/1.53 % SZS status Theorem for theBenchmark
% 4.36/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 5.36/1.72 % (2963918)------------------------------
% 5.36/1.72 % (2963918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.72 % (2963918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.72 % (2963918)CaDiCaL version: 2.1.3
% 5.36/1.72 % (2963918)Termination reason: Refutation
% 5.36/1.72 % (2963918)Time elapsed: 0.024 s
% 5.36/1.72 % (2963918)Peak memory usage: 90 MB
% 5.36/1.72 % (2963918)Instructions burned: 35 (million)
% 5.36/1.72 % (2963918)------------------------------
% 5.36/1.72 % (2963918)------------------------------
% 5.36/1.72 % (2963779)Success in time 0.669 s
% 5.36/1.72 % Vampire exiting
%------------------------------------------------------------------------------