%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU166+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:47:32 PM UTC 2026
% Result : Theorem 3.87s 1.40s
% Output : Refutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 84 ( 10 unt; 4 def)
% Number of atoms : 266 ( 40 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 297 ( 115 ~; 138 |; 33 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 150 ( 0 sgn 133 !; 17 ?)
% 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(f3,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(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,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(f14,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
& subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
& subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ( ~ subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) )
& subset(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f18,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f20,plain,
( ( ~ subset(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))
| ~ subset(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)) )
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f17]) ).
fof(f21,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,[],[f3]) ).
fof(f22,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,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != sK3(X0,X1,X2) )
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(sK4(X0,X1,X2),X0)
& in(sK5(X0,X1,X2),X1)
& sK3(X0,X1,X2) = ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ( in(sK6(X0,X1,X8),X0)
& in(sK7(X0,X1,X8),X1)
& ordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7]),skolemize(X3,sK3(X0,X1,X2)),skolemize(X6,sK4(X0,X1,X2)),skolemize(X7,sK5(X0,X1,X2)),skolemize(X11,sK6(X0,X1,X8)),skolemize(X12,sK7(X0,X1,X8))],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f25,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK8(X0,X1),X1)
& in(sK8(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f25]) ).
fof(f29,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
( ~ subset(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))
| ~ subset(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f32,plain,
! [X2,X0,X1,X8] :
( in(sK7(X0,X1,X8),X1)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f33,plain,
! [X2,X0,X1,X8] :
( in(sK6(X0,X1,X8),X0)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f34,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
! [X0,X1] :
( in(sK8(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f42,plain,
! [X0,X1] :
( ~ in(sK8(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f44,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f51,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| ~ in(X9,X0)
| ~ in(X10,X1)
| unordered_pair(unordered_pair(X9,X10),singleton(X9)) != X8
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f34,f43]) ).
fof(f52,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)),singleton(sK6(X0,X1,X8))) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f31,f43]) ).
fof(f54,plain,
! [X2,X10,X0,X1,X9] :
( in(unordered_pair(unordered_pair(X9,X10),singleton(X9)),X2)
| ~ in(X9,X0)
| ~ in(X10,X1)
| cartesian_product2(X0,X1) != X2 ),
inference(equality_resolution,[],[f51]) ).
fof(f55,plain,
! [X10,X0,X1,X9] :
( in(unordered_pair(unordered_pair(X9,X10),singleton(X9)),cartesian_product2(X0,X1))
| ~ in(X9,X0)
| ~ in(X10,X1) ),
inference(equality_resolution,[],[f54]) ).
fof(f56,plain,
! [X0,X1,X8] :
( in(sK6(X0,X1,X8),X0)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f33]) ).
fof(f57,plain,
! [X0,X1,X8] :
( in(sK7(X0,X1,X8),X1)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f32]) ).
fof(f58,plain,
! [X0,X1,X8] :
( unordered_pair(unordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)),singleton(sK6(X0,X1,X8))) = X8
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f52]) ).
fof(f59,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| unordered_pair(singleton(sK6(X0,X1,X8)),unordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8))) = X8 ),
inference(forward_demodulation,[],[f58,f44]) ).
fof(f60,plain,
! [X10,X0,X1,X9] :
( in(unordered_pair(singleton(X9),unordered_pair(X9,X10)),cartesian_product2(X0,X1))
| ~ in(X9,X0)
| ~ in(X10,X1) ),
inference(forward_demodulation,[],[f55,f44]) ).
fof(f64,definition,
( spl11_1
<=> subset(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f66,plain,
( ~ subset(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))
| spl11_1 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl11_2
<=> subset(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f70,plain,
( ~ subset(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))
| spl11_2 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
( ~ spl11_1
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f30,f68,f64]) ).
fof(f85,plain,
! [X0] :
( ~ in(X0,sK0)
| in(X0,sK1) ),
inference(resolution,[],[f40,f29]) ).
fof(f89,plain,
! [X0,X1] :
( in(sK6(sK0,X1,X0),sK1)
| ~ in(X0,cartesian_product2(sK0,X1)) ),
inference(resolution,[],[f56,f85]) ).
fof(f94,plain,
! [X0,X1] :
( in(sK7(X1,sK0,X0),sK1)
| ~ in(X0,cartesian_product2(X1,sK0)) ),
inference(resolution,[],[f57,f85]) ).
fof(f107,plain,
! [X2,X0,X1] :
( subset(cartesian_product2(X0,X1),X2)
| sK8(cartesian_product2(X0,X1),X2) = unordered_pair(singleton(sK6(X0,X1,sK8(cartesian_product2(X0,X1),X2))),unordered_pair(sK6(X0,X1,sK8(cartesian_product2(X0,X1),X2)),sK7(X0,X1,sK8(cartesian_product2(X0,X1),X2)))) ),
inference(resolution,[],[f59,f41]) ).
fof(f136,plain,
( sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)) = unordered_pair(singleton(sK6(sK2,sK0,sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))),unordered_pair(sK6(sK2,sK0,sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),sK7(sK2,sK0,sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)))))
| spl11_1 ),
inference(resolution,[],[f107,f66]) ).
fof(f140,plain,
( ! [X0,X1] :
( ~ in(sK7(sK2,sK0,sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),X1)
| ~ in(sK6(sK2,sK0,sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),X0)
| in(sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)),cartesian_product2(X0,X1)) )
| spl11_1 ),
inference(superposition,[],[f60,f136]) ).
fof(f210,definition,
( spl11_3
<=> in(sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)),cartesian_product2(sK2,sK0)) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
fof(f211,plain,
( in(sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)),cartesian_product2(sK2,sK0))
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f212,plain,
( ~ in(sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)),cartesian_product2(sK2,sK0))
| spl11_3 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f227,plain,
( subset(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))
| spl11_3 ),
inference(resolution,[],[f212,f41]) ).
fof(f228,plain,
( $false
| spl11_1
| spl11_3 ),
inference(forward_subsumption_resolution,[],[f227,f66]) ).
fof(f229,plain,
( spl11_1
| spl11_3 ),
inference(avatar_contradiction_clause,[],[f228]) ).
fof(f278,plain,
( ! [X0] :
( ~ in(sK6(sK2,sK0,sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),X0)
| in(sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)),cartesian_product2(X0,sK1))
| ~ in(sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)),cartesian_product2(sK2,sK0)) )
| spl11_1 ),
inference(resolution,[],[f140,f94]) ).
fof(f279,plain,
( ! [X0] :
( ~ in(sK6(sK2,sK0,sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))),X0)
| in(sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)),cartesian_product2(X0,sK1)) )
| spl11_1
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f278,f211]) ).
fof(f298,plain,
( in(sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)),cartesian_product2(sK2,sK1))
| ~ in(sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)),cartesian_product2(sK2,sK0))
| spl11_1
| ~ spl11_3 ),
inference(resolution,[],[f279,f56]) ).
fof(f299,plain,
( in(sK8(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1)),cartesian_product2(sK2,sK1))
| spl11_1
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f298,f211]) ).
fof(f302,plain,
( subset(cartesian_product2(sK2,sK0),cartesian_product2(sK2,sK1))
| spl11_1
| ~ spl11_3 ),
inference(resolution,[],[f299,f42]) ).
fof(f305,plain,
( $false
| spl11_1
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f302,f66]) ).
fof(f306,plain,
( spl11_1
| ~ spl11_3 ),
inference(avatar_contradiction_clause,[],[f305]) ).
fof(f308,plain,
( sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK6(sK0,sK2,sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))),unordered_pair(sK6(sK0,sK2,sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),sK7(sK0,sK2,sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)))))
| spl11_2 ),
inference(resolution,[],[f70,f107]) ).
fof(f417,plain,
( ! [X0,X1] :
( ~ in(sK7(sK0,sK2,sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),X1)
| ~ in(sK6(sK0,sK2,sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),X0)
| in(sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)),cartesian_product2(X0,X1)) )
| spl11_2 ),
inference(superposition,[],[f60,f308]) ).
fof(f1036,definition,
( spl11_18
<=> in(sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)),cartesian_product2(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl11_18])],[avatar_definition]) ).
fof(f1037,plain,
( in(sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)),cartesian_product2(sK0,sK2))
| ~ spl11_18 ),
inference(avatar_component_clause,[],[f1036]) ).
fof(f1038,plain,
( ~ in(sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)),cartesian_product2(sK0,sK2))
| spl11_18 ),
inference(avatar_component_clause,[],[f1036]) ).
fof(f1083,plain,
( subset(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))
| spl11_18 ),
inference(resolution,[],[f1038,f41]) ).
fof(f1084,plain,
( $false
| spl11_2
| spl11_18 ),
inference(forward_subsumption_resolution,[],[f1083,f70]) ).
fof(f1085,plain,
( spl11_2
| spl11_18 ),
inference(avatar_contradiction_clause,[],[f1084]) ).
fof(f1170,plain,
( ! [X0] :
( ~ in(sK6(sK0,sK2,sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),X0)
| in(sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)),cartesian_product2(X0,sK2))
| ~ in(sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)),cartesian_product2(sK0,sK2)) )
| spl11_2 ),
inference(resolution,[],[f417,f57]) ).
fof(f1171,plain,
( ! [X0] :
( ~ in(sK6(sK0,sK2,sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))),X0)
| in(sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)),cartesian_product2(X0,sK2)) )
| spl11_2
| ~ spl11_18 ),
inference(forward_subsumption_resolution,[],[f1170,f1037]) ).
fof(f1224,plain,
( in(sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)),cartesian_product2(sK1,sK2))
| ~ in(sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)),cartesian_product2(sK0,sK2))
| spl11_2
| ~ spl11_18 ),
inference(resolution,[],[f1171,f89]) ).
fof(f1225,plain,
( in(sK8(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2)),cartesian_product2(sK1,sK2))
| spl11_2
| ~ spl11_18 ),
inference(forward_subsumption_resolution,[],[f1224,f1037]) ).
fof(f1254,plain,
( subset(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK2))
| spl11_2
| ~ spl11_18 ),
inference(resolution,[],[f1225,f42]) ).
fof(f1265,plain,
( $false
| spl11_2
| ~ spl11_18 ),
inference(forward_subsumption_resolution,[],[f1254,f70]) ).
fof(f1266,plain,
( spl11_2
| ~ spl11_18 ),
inference(avatar_contradiction_clause,[],[f1265]) ).
cnf(s1,plain,
( ~ spl11_1
| ~ spl11_2 ),
inference(sat_conversion,[],[f71]) ).
cnf(s4,plain,
( spl11_1
| spl11_3 ),
inference(sat_conversion,[],[f229]) ).
cnf(s5,plain,
( spl11_1
| ~ spl11_3 ),
inference(sat_conversion,[],[f306]) ).
cnf(s13,plain,
( spl11_2
| spl11_18 ),
inference(sat_conversion,[],[f1085]) ).
cnf(s14,plain,
( spl11_2
| ~ spl11_18 ),
inference(sat_conversion,[],[f1266]) ).
cnf(s15,plain,
spl11_1,
inference(rat,[],[s4,s5]) ).
cnf(s16,plain,
~ spl11_2,
inference(rat,[],[s1,s15]) ).
cnf(s17,plain,
~ spl11_18,
inference(rat,[],[s14,s16]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s13,s17,s16]) ).
fof(f1267,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU166+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 % Computer : n002.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Mon Sep 28 03:54:22 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.45 Running first-order theorem proving
% 0.12/0.45 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
% 3.87/1.40 % (4131262)Detected formulas, will run a generic FOF schedule.
% 3.87/1.40 % (4131271)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4157942844:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.87/1.40 % (4131271)Instruction limit reached!
% 3.87/1.40 % (4131271)------------------------------
% 3.87/1.40 % (4131271)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.87/1.40 % (4131271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.87/1.40 % (4131271)CaDiCaL version: 2.1.3
% 3.87/1.40 % (4131271)Termination reason: Instruction limit
% 3.87/1.40 % (4131271)Termination phase: Saturation
% 3.87/1.40 % (4131271)Time elapsed: 0.034 s
% 3.87/1.40 % (4131271)Peak memory usage: 88 MB
% 3.87/1.40 % (4131271)Instructions burned: 119 (million)
% 3.87/1.40 % (4131270)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=295184617:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.87/1.40 % (4131267)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=1195000660:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.87/1.40 % (4131268)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=96930476:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.87/1.40 % (4131273)dis-21_1_sil=8000:lcm=predicate:random_seed=3960066106: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)
% 3.87/1.40 % (4131269)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=879767197:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.87/1.40 % (4131270)Refutation not found, incomplete strategy
% 3.87/1.40 % (4131270)------------------------------
% 3.87/1.40 % (4131270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.87/1.40 % (4131270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.87/1.40 % (4131270)CaDiCaL version: 2.1.3
% 3.87/1.40 % (4131270)Termination reason: Refutation not found, incomplete strategy
% 3.87/1.40 % (4131270)Time elapsed: 0.002 s
% 3.87/1.40 % (4131270)Peak memory usage: 88 MB
% 3.87/1.40 % (4131270)Instructions burned: 1 (million)
% 3.87/1.40 % (4131272)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=679466566:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.87/1.40 % (4131273)Instruction limit reached!
% 3.87/1.40 % (4131273)------------------------------
% 3.87/1.40 % (4131273)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.87/1.40 % (4131273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.87/1.40 % (4131273)CaDiCaL version: 2.1.3
% 3.87/1.40 % (4131273)Termination reason: Instruction limit
% 3.87/1.40 % (4131273)Termination phase: Saturation
% 3.87/1.40 % (4131273)Time elapsed: 0.076 s
% 3.87/1.40 % (4131273)Peak memory usage: 89 MB
% 3.87/1.40 % (4131273)Instructions burned: 129 (million)
% 3.87/1.40 % (4131272)Instruction limit reached!
% 3.87/1.40 % (4131272)------------------------------
% 3.87/1.40 % (4131272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.87/1.40 % (4131272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.87/1.40 % (4131272)CaDiCaL version: 2.1.3
% 3.87/1.40 % (4131272)Termination reason: Instruction limit
% 3.87/1.40 % (4131272)Termination phase: Saturation
% 3.87/1.40 % (4131272)Time elapsed: 0.091 s
% 3.87/1.40 % (4131272)Peak memory usage: 89 MB
% 3.87/1.40 % (4131272)Instructions burned: 140 (million)
% 3.87/1.40 % (4131275)lrs+10_1_sil=8000:sp=occurrence:random_seed=688901521:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.87/1.40 % (4131275)First to succeed.
% 3.87/1.40 % (4131275)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4131262"
% 3.87/1.40 % (4131282)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4111624873:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.87/1.40 % (4131282)Also succeeded, but the first one will report.
% 3.87/1.40 % (4131270)------------------------------
% 3.87/1.40 % (4131270)------------------------------
% 3.87/1.40 % (4131283)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2334604710:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.87/1.40 % (4131283)Also succeeded, but the first one will report.
% 3.87/1.40 % (4131275)Refutation found. Thanks to Tanya!
% 3.87/1.40 % SZS status Theorem for theBenchmark
% 3.87/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 4.19/1.60 % (4131275)------------------------------
% 4.19/1.60 % (4131275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.60 % (4131275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.60 % (4131275)CaDiCaL version: 2.1.3
% 4.19/1.60 % (4131275)Termination reason: Refutation
% 4.19/1.60 % (4131275)Time elapsed: 0.061 s
% 4.19/1.60 % (4131275)Peak memory usage: 92 MB
% 4.19/1.60 % (4131275)Instructions burned: 201 (million)
% 4.19/1.60 % (4131275)------------------------------
% 4.19/1.60 % (4131275)------------------------------
% 4.19/1.60 % (4131262)Success in time 0.513 s
% 4.19/1.60 % Vampire exiting
%------------------------------------------------------------------------------