%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU182+2 : 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 : n007.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 12:47:37 PM UTC 2026
% Result : Theorem 6.28s 1.85s
% Output : Refutation 7.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 63 ( 12 unt; 0 def)
% Number of atoms : 256 ( 27 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 314 ( 121 ~; 131 |; 40 &)
% ( 10 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 2 con; 0-4 aty)
% Number of variables : 186 ( 164 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f16,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f18,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f24,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(f28,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f48,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f104,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f129,conjecture,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).
fof(f130,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f129]) ).
fof(f146,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f172,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f173,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f178,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f182,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f183,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f182]) ).
fof(f224,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f104]) ).
fof(f225,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f224]) ).
fof(f242,plain,
? [X0] :
( ? [X1] :
( ~ subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
& relation(X1) )
& relation(X0) ),
inference(ennf_transformation,[],[f130]) ).
fof(f302,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,[],[f172]) ).
fof(f303,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,[],[f302]) ).
fof(f304,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK16(X0,X1),X1)
& in(sK16(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X2,sK16(X0,X1))],[f303]) ).
fof(f309,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f173]) ).
fof(f310,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f309]) ).
fof(f311,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK18(X0,X1),X3),X0)
| ~ in(sK18(X0,X1),X1) )
& ( in(ordered_pair(sK18(X0,X1),sK19(X0,X1)),X0)
| in(sK18(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK20(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20]),skolemize(X2,sK18(X0,X1)),skolemize(X4,sK19(X0,X1)),skolemize(X7,sK20(X0,X5))],[f310]) ).
fof(f326,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) ) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f178]) ).
fof(f327,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X3,X6),X0)
& in(ordered_pair(X6,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ? [X10] :
( in(ordered_pair(X7,X10),X0)
& in(ordered_pair(X10,X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f326]) ).
fof(f328,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ( ( ! [X5] :
( ~ in(ordered_pair(sK30(X0,X1,X2),X5),X0)
| ~ in(ordered_pair(X5,sK31(X0,X1,X2)),X1) )
| ~ in(ordered_pair(sK30(X0,X1,X2),sK31(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK30(X0,X1,X2),sK32(X0,X1,X2)),X0)
& in(ordered_pair(sK32(X0,X1,X2),sK31(X0,X1,X2)),X1) )
| in(ordered_pair(sK30(X0,X1,X2),sK31(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ( in(ordered_pair(X7,sK33(X0,X1,X7,X8)),X0)
& in(ordered_pair(sK33(X0,X1,X7,X8),X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30,sK31,sK32,sK33]),skolemize(X3,sK30(X0,X1,X2)),skolemize(X4,sK31(X0,X1,X2)),skolemize(X6,sK32(X0,X1,X2)),skolemize(X10,sK33(X0,X1,X7,X8))],[f327]) ).
fof(f362,plain,
( ~ subset(relation_dom(relation_composition(sK45,sK46)),relation_dom(sK45))
& relation(sK46)
& relation(sK45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45,sK46]),skolemize(X0,sK45),skolemize(X1,sK46)],[f242]) ).
fof(f369,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f421,plain,
! [X0,X1] :
( in(sK16(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f304]) ).
fof(f422,plain,
! [X0,X1] :
( ~ in(sK16(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f304]) ).
fof(f429,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK20(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f311]) ).
fof(f451,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f460,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(X7,sK33(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f476,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f183]) ).
fof(f548,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f225]) ).
fof(f588,plain,
relation(sK45),
inference(cnf_transformation,[],[f362]) ).
fof(f589,plain,
relation(sK46),
inference(cnf_transformation,[],[f362]) ).
fof(f590,plain,
~ subset(relation_dom(relation_composition(sK45,sK46)),relation_dom(sK45)),
inference(cnf_transformation,[],[f362]) ).
fof(f608,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f146]) ).
fof(f626,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f451,f608]) ).
fof(f647,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK20(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f429,f626]) ).
fof(f662,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK33(X0,X1,X7,X8)),unordered_pair(X7,X7)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f460,f626,f626]) ).
fof(f686,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X0,relation_dom(X2)) ),
inference(definition_unfolding,[],[f548,f626]) ).
fof(f740,plain,
! [X0,X5] :
( ~ in(X5,relation_dom(X0))
| in(unordered_pair(unordered_pair(X5,sK20(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f647]) ).
fof(f752,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK33(X0,X1,X7,X8)),unordered_pair(X7,X7)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f662]) ).
fof(f765,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK33(X0,X1,X7,X8)),unordered_pair(X7,X7)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f752,f476]) ).
fof(f771,plain,
! [X0,X1,X8,X7] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X7,X7),unordered_pair(X7,sK33(X0,X1,X7,X8))),X0) ),
inference(forward_demodulation,[],[f765,f369]) ).
fof(f774,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK16(relation_dom(X0),X1),sK20(X0,sK16(relation_dom(X0),X1))),unordered_pair(sK16(relation_dom(X0),X1),sK16(relation_dom(X0),X1))),X0)
| ~ relation(X0)
| subset(relation_dom(X0),X1) ),
inference(resolution,[],[f740,f421]) ).
fof(f775,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK16(relation_dom(X0),X1),sK16(relation_dom(X0),X1)),unordered_pair(sK16(relation_dom(X0),X1),sK20(X0,sK16(relation_dom(X0),X1)))),X0)
| subset(relation_dom(X0),X1) ),
inference(forward_demodulation,[],[f774,f369]) ).
fof(f778,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| subset(relation_dom(relation_composition(X0,X1)),X2)
| ~ relation(X0)
| in(unordered_pair(unordered_pair(sK16(relation_dom(relation_composition(X0,X1)),X2),sK16(relation_dom(relation_composition(X0,X1)),X2)),unordered_pair(sK16(relation_dom(relation_composition(X0,X1)),X2),sK20(relation_composition(X0,X1),sK16(relation_dom(relation_composition(X0,X1)),X2)))),relation_composition(X0,X1)) ),
inference(resolution,[],[f775,f476]) ).
fof(f779,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK45)
| in(X0,relation_dom(sK45)) ),
inference(resolution,[],[f686,f588]) ).
fof(f785,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),sK45)
| in(X0,relation_dom(sK45)) ),
inference(superposition,[],[f779,f369]) ).
fof(f844,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(sK45,X2))
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK33(sK45,X2,X0,X1))),sK45) ),
inference(resolution,[],[f771,f588]) ).
fof(f848,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(sK45,sK46))
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK33(sK45,sK46,X0,X1))),sK45) ),
inference(resolution,[],[f844,f589]) ).
fof(f854,plain,
! [X0,X1] :
( ~ relation(X0)
| subset(relation_dom(relation_composition(X0,sK46)),X1)
| in(unordered_pair(unordered_pair(sK16(relation_dom(relation_composition(X0,sK46)),X1),sK16(relation_dom(relation_composition(X0,sK46)),X1)),unordered_pair(sK16(relation_dom(relation_composition(X0,sK46)),X1),sK20(relation_composition(X0,sK46),sK16(relation_dom(relation_composition(X0,sK46)),X1)))),relation_composition(X0,sK46)) ),
inference(resolution,[],[f778,f589]) ).
fof(f863,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK33(sK45,sK46,X0,X1))),sK45)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),relation_composition(sK45,sK46)) ),
inference(superposition,[],[f848,f369]) ).
fof(f883,plain,
! [X0] :
( in(unordered_pair(unordered_pair(sK16(relation_dom(relation_composition(sK45,sK46)),X0),sK16(relation_dom(relation_composition(sK45,sK46)),X0)),unordered_pair(sK16(relation_dom(relation_composition(sK45,sK46)),X0),sK20(relation_composition(sK45,sK46),sK16(relation_dom(relation_composition(sK45,sK46)),X0)))),relation_composition(sK45,sK46))
| subset(relation_dom(relation_composition(sK45,sK46)),X0) ),
inference(resolution,[],[f854,f588]) ).
fof(f1224,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),relation_composition(sK45,sK46))
| in(X0,relation_dom(sK45)) ),
inference(resolution,[],[f863,f785]) ).
fof(f1225,plain,
! [X0] :
( in(sK16(relation_dom(relation_composition(sK45,sK46)),X0),relation_dom(sK45))
| subset(relation_dom(relation_composition(sK45,sK46)),X0) ),
inference(resolution,[],[f1224,f883]) ).
fof(f1230,plain,
( subset(relation_dom(relation_composition(sK45,sK46)),relation_dom(sK45))
| subset(relation_dom(relation_composition(sK45,sK46)),relation_dom(sK45)) ),
inference(resolution,[],[f1225,f422]) ).
fof(f1232,plain,
subset(relation_dom(relation_composition(sK45,sK46)),relation_dom(sK45)),
inference(duplicate_literal_removal,[],[f1230]) ).
fof(f1234,plain,
$false,
inference(forward_subsumption_resolution,[],[f1232,f590]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU182+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % 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 03:53:25 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 6.28/1.85 % (2009553)Detected formulas, will run a generic FOF schedule.
% 6.28/1.85 % (2009559)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=1588258938:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.28/1.85 % (2009563)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1144402080:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.28/1.85 % (2009560)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=203374502:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.28/1.85 % (2009558)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=695521935:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.28/1.85 % (2009564)dis-21_1_sil=8000:lcm=predicate:random_seed=3946158977: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)
% 6.28/1.85 % (2009561)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3305529554:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.28/1.85 % (2009562)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2132792077:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.28/1.85 % (2009561)Instruction limit reached!
% 6.28/1.85 % (2009561)------------------------------
% 6.28/1.85 % (2009561)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.85 % (2009561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.85 % (2009561)CaDiCaL version: 2.1.3
% 6.28/1.85 % (2009561)Termination reason: Instruction limit
% 6.28/1.85 % (2009561)Termination phase: Saturation
% 6.28/1.85 % (2009561)Time elapsed: 0.071 s
% 6.28/1.85 % (2009561)Peak memory usage: 90 MB
% 6.28/1.85 % (2009561)Instructions burned: 109 (million)
% 6.28/1.85 % (2009562)Instruction limit reached!
% 6.28/1.85 % (2009562)------------------------------
% 6.28/1.85 % (2009562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.85 % (2009562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.85 % (2009562)CaDiCaL version: 2.1.3
% 6.28/1.85 % (2009562)Termination reason: Instruction limit
% 6.28/1.85 % (2009562)Termination phase: Saturation
% 6.28/1.85 % (2009562)Time elapsed: 0.077 s
% 6.28/1.85 % (2009562)Peak memory usage: 89 MB
% 6.28/1.85 % (2009562)Instructions burned: 120 (million)
% 6.28/1.85 % (2009564)Instruction limit reached!
% 6.28/1.85 % (2009564)------------------------------
% 6.28/1.85 % (2009564)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.85 % (2009564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.85 % (2009564)CaDiCaL version: 2.1.3
% 6.28/1.85 % (2009564)Termination reason: Instruction limit
% 6.28/1.85 % (2009564)Termination phase: Saturation
% 6.28/1.85 % (2009564)Time elapsed: 0.079 s
% 6.28/1.85 % (2009564)Peak memory usage: 90 MB
% 6.28/1.85 % (2009564)Instructions burned: 130 (million)
% 6.28/1.85 % (2009563)Instruction limit reached!
% 6.28/1.85 % (2009563)------------------------------
% 6.28/1.85 % (2009563)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.85 % (2009563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.85 % (2009563)CaDiCaL version: 2.1.3
% 6.28/1.85 % (2009563)Termination reason: Instruction limit
% 6.28/1.85 % (2009563)Termination phase: Saturation
% 6.28/1.85 % (2009563)Time elapsed: 0.102 s
% 6.28/1.85 % (2009563)Peak memory usage: 90 MB
% 6.28/1.85 % (2009563)Instructions burned: 139 (million)
% 6.28/1.85 % (2009572)lrs+10_1_sil=8000:sp=occurrence:random_seed=1296723494:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.28/1.85 % (2009574)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3235734447:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.28/1.85 % (2009573)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2201046242:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.28/1.85 % (2009575)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=3409080855:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.28/1.85 % (2009573)Instruction limit reached!
% 6.28/1.85 % (2009573)------------------------------
% 6.28/1.85 % (2009573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.85 % (2009573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.85 % (2009573)CaDiCaL version: 2.1.3
% 6.28/1.85 % (2009573)Termination reason: Instruction limit
% 6.28/1.85 % (2009573)Termination phase: Saturation
% 6.28/1.85 % (2009573)Time elapsed: 0.080 s
% 6.28/1.85 % (2009573)Peak memory usage: 91 MB
% 6.28/1.85 % (2009573)Instructions burned: 159 (million)
% 6.28/1.85 % (2009572)Instruction limit reached!
% 6.28/1.85 % (2009572)------------------------------
% 6.28/1.85 % (2009572)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.85 % (2009572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.85 % (2009572)CaDiCaL version: 2.1.3
% 6.28/1.85 % (2009572)Termination reason: Instruction limit
% 6.28/1.85 % (2009572)Termination phase: Saturation
% 6.28/1.85 % (2009572)Time elapsed: 0.180 s
% 6.28/1.85 % (2009572)Peak memory usage: 92 MB
% 6.28/1.85 % (2009572)Instructions burned: 287 (million)
% 6.28/1.85 % (2009575)Instruction limit reached!
% 6.28/1.85 % (2009575)------------------------------
% 6.28/1.85 % (2009575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.85 % (2009575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.85 % (2009575)CaDiCaL version: 2.1.3
% 6.28/1.85 % (2009575)Termination reason: Instruction limit
% 6.28/1.85 % (2009575)Termination phase: Saturation
% 6.28/1.85 % (2009575)Time elapsed: 0.140 s
% 6.28/1.85 % (2009575)Peak memory usage: 94 MB
% 6.28/1.85 % (2009575)Instructions burned: 249 (million)
% 6.28/1.85 % (2009574)Instruction limit reached!
% 6.28/1.85 % (2009574)------------------------------
% 6.28/1.85 % (2009574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.85 % (2009574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.85 % (2009574)CaDiCaL version: 2.1.3
% 6.28/1.85 % (2009574)Termination reason: Instruction limit
% 6.28/1.85 % (2009574)Termination phase: Saturation
% 6.28/1.85 % (2009574)Time elapsed: 0.224 s
% 6.28/1.85 % (2009574)Peak memory usage: 92 MB
% 6.28/1.85 % (2009574)Instructions burned: 325 (million)
% 6.28/1.85 % (2009580)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3807106638:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.28/1.85 % (2009559)First to succeed.
% 6.28/1.85 % (2009559)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2009553"
% 6.28/1.85 % (2009582)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=729648762:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.28/1.85 % (2009581)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3228384531:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.28/1.85 % (2009583)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1063193278:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.28/1.85 % (2009583)Instruction limit reached!
% 6.28/1.85 % (2009583)------------------------------
% 6.28/1.85 % (2009583)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.85 % (2009583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.85 % (2009583)CaDiCaL version: 2.1.3
% 6.28/1.85 % (2009583)Termination reason: Instruction limit
% 6.28/1.85 % (2009583)Termination phase: Saturation
% 6.28/1.85 % (2009583)Time elapsed: 0.035 s
% 6.28/1.85 % (2009583)Peak memory usage: 89 MB
% 6.28/1.85 % (2009583)Instructions burned: 132 (million)
% 6.28/1.85 % (2009582)Instruction limit reached!
% 6.28/1.85 % (2009582)------------------------------
% 6.28/1.85 % (2009582)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.85 % (2009582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.85 % (2009582)CaDiCaL version: 2.1.3
% 6.28/1.85 % (2009582)Termination reason: Instruction limit
% 6.28/1.85 % (2009582)Termination phase: Saturation
% 6.28/1.85 % (2009582)Time elapsed: 0.067 s
% 6.28/1.85 % (2009582)Peak memory usage: 89 MB
% 6.28/1.85 % (2009582)Instructions burned: 114 (million)
% 6.28/1.85 % (2009580)Instruction limit reached!
% 6.28/1.85 % (2009580)------------------------------
% 6.28/1.85 % (2009580)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.85 % (2009580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.85 % (2009580)CaDiCaL version: 2.1.3
% 6.28/1.85 % (2009580)Termination reason: Instruction limit
% 6.28/1.85 % (2009580)Termination phase: Saturation
% 6.28/1.85 % (2009580)Time elapsed: 0.186 s
% 6.28/1.85 % (2009580)Peak memory usage: 90 MB
% 6.28/1.85 % (2009580)Instructions burned: 295 (million)
% 6.28/1.85 % (2009558)Also succeeded, but the first one will report.
% 6.28/1.85 % (2009588)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4212993425:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.28/1.85 % (2009588)Instruction limit reached!
% 6.28/1.85 % (2009588)------------------------------
% 6.28/1.85 % (2009588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.85 % (2009588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.85 % (2009588)CaDiCaL version: 2.1.3
% 6.28/1.85 % (2009588)Termination reason: Instruction limit
% 6.28/1.85 % (2009588)Termination phase: Saturation
% 6.28/1.85 % (2009588)Time elapsed: 0.038 s
% 6.28/1.85 % (2009588)Peak memory usage: 89 MB
% 6.28/1.85 % (2009588)Instructions burned: 118 (million)
% 6.28/1.85 % (2009589)lrs+10_1_sil=8000:sp=occurrence:random_seed=3988873656:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.28/1.85 % (2009559)Refutation found. Thanks to Tanya!
% 6.28/1.85 % SZS status Theorem for theBenchmark
% 6.28/1.85 % SZS output start Proof for theBenchmark
% See solution above
% 7.51/2.05 % (2009559)------------------------------
% 7.51/2.05 % (2009559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.51/2.05 % (2009559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.51/2.05 % (2009559)CaDiCaL version: 2.1.3
% 7.51/2.05 % (2009559)Termination reason: Refutation
% 7.51/2.05 % (2009559)Time elapsed: 0.573 s
% 7.51/2.05 % (2009559)Peak memory usage: 132 MB
% 7.51/2.05 % (2009559)Instructions burned: 1210 (million)
% 7.51/2.05 % (2009559)------------------------------
% 7.51/2.05 % (2009559)------------------------------
% 7.51/2.05 % (2009553)Success in time 0.981 s
% 7.51/2.05 % Vampire exiting
%------------------------------------------------------------------------------