%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU181+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 : 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 12:47:36 PM UTC 2026
% Result : Theorem 2.98s 1.33s
% Output : Refutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 118 ( 9 unt; 4 def)
% Number of atoms : 474 ( 83 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 638 ( 282 ~; 301 |; 31 &)
% ( 16 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-2 aty)
% Number of variables : 215 ( 0 sgn 194 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f8,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( X1 = relation_inverse(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
fof(f15,axiom,
! [X0] :
( relation(X0)
=> relation(relation_inverse(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f24,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f33,conjecture,
! [X0] :
( relation(X0)
=> ( relation_rng(X0) = relation_dom(relation_inverse(X0))
& relation_dom(X0) = relation_rng(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( relation_rng(X0) = relation_dom(relation_inverse(X0))
& relation_dom(X0) = relation_rng(relation_inverse(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_inverse(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f47,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f48,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f53,plain,
? [X0] :
( ( relation_rng(X0) != relation_dom(relation_inverse(X0))
| relation_dom(X0) != relation_rng(relation_inverse(X0)) )
& relation(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f65,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,[],[f44]) ).
fof(f66,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,[],[f65]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK1(X0,X1),X3),X0)
| ~ in(sK1(X0,X1),X1) )
& ( in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0)
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK3(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f66]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f45]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f68]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK4(X0,X1)),X0)
| ~ in(sK4(X0,X1),X1) )
& ( in(ordered_pair(sK5(X0,X1),sK4(X0,X1)),X0)
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK6(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X2,sK4(X0,X1)),skolemize(X4,sK5(X0,X1)),skolemize(X7,sK6(X0,X5))],[f69]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = relation_inverse(X0)
| ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X0) )
& ( in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f46]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = relation_inverse(X0)
| ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0) )
& ( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = relation_inverse(X0)
| ( ( ~ in(ordered_pair(sK8(X0,X1),sK7(X0,X1)),X0)
| ~ in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X1) )
& ( in(ordered_pair(sK8(X0,X1),sK7(X0,X1)),X0)
| in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0) )
& ( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X2,sK7(X0,X1)),skolemize(X3,sK8(X0,X1))],[f72]) ).
fof(f80,plain,
( ( relation_rng(sK15) != relation_dom(relation_inverse(sK15))
| relation_dom(sK15) != relation_rng(relation_inverse(sK15)) )
& relation(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X0,sK15)],[f53]) ).
fof(f90,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK3(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f91,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f92,plain,
! [X0,X1] :
( in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0)
| relation_dom(X0) = X1
| in(sK1(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f93,plain,
! [X3,X0,X1] :
( ~ in(sK1(X0,X1),X1)
| ~ in(ordered_pair(sK1(X0,X1),X3),X0)
| relation_dom(X0) = X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f94,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK6(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f95,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f96,plain,
! [X0,X1] :
( in(ordered_pair(sK5(X0,X1),sK4(X0,X1)),X0)
| relation_rng(X0) = X1
| in(sK4(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f97,plain,
! [X3,X0,X1] :
( ~ in(sK4(X0,X1),X1)
| ~ in(ordered_pair(X3,sK4(X0,X1)),X0)
| relation_rng(X0) = X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f99,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f100,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f103,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f110,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f122,plain,
relation(sK15),
inference(cnf_transformation,[],[f80]) ).
fof(f123,plain,
( relation_rng(sK15) != relation_dom(relation_inverse(sK15))
| relation_dom(sK15) != relation_rng(relation_inverse(sK15)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f133,plain,
! [X0,X6,X5] :
( in(X5,relation_dom(X0))
| ~ in(ordered_pair(X5,X6),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f91]) ).
fof(f134,plain,
! [X0,X5] :
( in(ordered_pair(X5,sK3(X0,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f90]) ).
fof(f135,plain,
! [X0,X6,X5] :
( in(X5,relation_rng(X0))
| ~ in(ordered_pair(X6,X5),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f95]) ).
fof(f136,plain,
! [X0,X5] :
( in(ordered_pair(sK6(X0,X5),X5),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f94]) ).
fof(f137,plain,
! [X0,X4,X5] :
( in(ordered_pair(X4,X5),relation_inverse(X0))
| ~ in(ordered_pair(X5,X4),X0)
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f100]) ).
fof(f138,plain,
! [X0,X4,X5] :
( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),relation_inverse(X0))
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f99]) ).
fof(f140,definition,
( spl16_1
<=> relation_dom(sK15) = relation_rng(relation_inverse(sK15)) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f142,plain,
( relation_dom(sK15) != relation_rng(relation_inverse(sK15))
| spl16_1 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f144,definition,
( spl16_2
<=> relation_rng(sK15) = relation_dom(relation_inverse(sK15)) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f146,plain,
( relation_rng(sK15) != relation_dom(relation_inverse(sK15))
| spl16_2 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f147,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f123,f144,f140]) ).
fof(f171,plain,
! [X0,X4,X5] :
( in(ordered_pair(X4,X5),relation_inverse(X0))
| ~ in(ordered_pair(X5,X4),X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f137,f103]) ).
fof(f175,plain,
! [X0,X4,X5] :
( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),relation_inverse(X0))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f138,f103]) ).
fof(f190,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X3,sK1(X0,relation_rng(X1))),X1)
| relation_dom(X0) = relation_rng(X1)
| ~ relation(X0)
| ~ in(ordered_pair(sK1(X0,relation_rng(X1)),X2),X0)
| ~ relation(X1) ),
inference(resolution,[],[f93,f135]) ).
fof(f191,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(sK4(X1,relation_dom(X2)),X3),X2)
| relation_rng(X1) = relation_dom(X2)
| ~ relation(X1)
| ~ in(ordered_pair(X0,sK4(X1,relation_dom(X2))),X1)
| ~ relation(X2) ),
inference(resolution,[],[f97,f133]) ).
fof(f250,definition,
( spl16_10
<=> relation(relation_inverse(sK15)) ),
introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition]) ).
fof(f251,plain,
( relation(relation_inverse(sK15))
| ~ spl16_10 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f252,plain,
( ~ relation(relation_inverse(sK15))
| spl16_10 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f254,definition,
( spl16_11
<=> sK15 = relation_inverse(relation_inverse(sK15)) ),
introduced(definition,[new_symbols(definition,[spl16_11])],[avatar_definition]) ).
fof(f255,plain,
( sK15 != relation_inverse(relation_inverse(sK15))
| spl16_11 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f256,plain,
( sK15 = relation_inverse(relation_inverse(sK15))
| ~ spl16_11 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f276,plain,
( ~ relation(sK15)
| spl16_10 ),
inference(resolution,[],[f252,f103]) ).
fof(f277,plain,
( $false
| spl16_10 ),
inference(forward_subsumption_resolution,[],[f276,f122]) ).
fof(f278,plain,
spl16_10,
inference(avatar_contradiction_clause,[],[f277]) ).
fof(f481,plain,
! [X2,X3,X0,X1] :
( relation_dom(X0) = relation_rng(X1)
| ~ relation(X0)
| ~ in(ordered_pair(sK1(X0,relation_rng(X1)),X2),X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK1(X0,relation_rng(X1)),X3),relation_inverse(X1))
| ~ relation(X1) ),
inference(resolution,[],[f190,f175]) ).
fof(f482,plain,
! [X2,X3,X0,X1] :
( relation_dom(X0) = relation_rng(relation_inverse(X1))
| ~ relation(X0)
| ~ in(ordered_pair(sK1(X0,relation_rng(relation_inverse(X1))),X2),X0)
| ~ relation(relation_inverse(X1))
| ~ in(ordered_pair(sK1(X0,relation_rng(relation_inverse(X1))),X3),X1)
| ~ relation(X1) ),
inference(resolution,[],[f190,f171]) ).
fof(f487,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(sK1(X0,relation_rng(X1)),X3),relation_inverse(X1))
| ~ relation(X0)
| ~ in(ordered_pair(sK1(X0,relation_rng(X1)),X2),X0)
| ~ relation(X1)
| relation_dom(X0) = relation_rng(X1) ),
inference(duplicate_literal_removal,[],[f481]) ).
fof(f489,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(sK1(X0,relation_rng(relation_inverse(X1))),X3),X1)
| ~ relation(X0)
| ~ in(ordered_pair(sK1(X0,relation_rng(relation_inverse(X1))),X2),X0)
| relation_dom(X0) = relation_rng(relation_inverse(X1))
| ~ relation(X1) ),
inference(forward_subsumption_resolution,[],[f482,f103]) ).
fof(f514,plain,
! [X2,X3,X0,X1] :
( relation_rng(X0) = relation_dom(X1)
| ~ relation(X0)
| ~ in(ordered_pair(X2,sK4(X0,relation_dom(X1))),X0)
| ~ relation(X1)
| ~ in(ordered_pair(X3,sK4(X0,relation_dom(X1))),relation_inverse(X1))
| ~ relation(X1) ),
inference(resolution,[],[f191,f175]) ).
fof(f515,plain,
! [X2,X3,X0,X1] :
( relation_rng(X0) = relation_dom(relation_inverse(X1))
| ~ relation(X0)
| ~ in(ordered_pair(X2,sK4(X0,relation_dom(relation_inverse(X1)))),X0)
| ~ relation(relation_inverse(X1))
| ~ in(ordered_pair(X3,sK4(X0,relation_dom(relation_inverse(X1)))),X1)
| ~ relation(X1) ),
inference(resolution,[],[f191,f171]) ).
fof(f520,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X3,sK4(X0,relation_dom(X1))),relation_inverse(X1))
| ~ relation(X0)
| ~ in(ordered_pair(X2,sK4(X0,relation_dom(X1))),X0)
| ~ relation(X1)
| relation_rng(X0) = relation_dom(X1) ),
inference(duplicate_literal_removal,[],[f514]) ).
fof(f522,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X3,sK4(X0,relation_dom(relation_inverse(X1)))),X1)
| ~ relation(X0)
| ~ in(ordered_pair(X2,sK4(X0,relation_dom(relation_inverse(X1)))),X0)
| relation_rng(X0) = relation_dom(relation_inverse(X1))
| ~ relation(X1) ),
inference(forward_subsumption_resolution,[],[f515,f103]) ).
fof(f1565,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK1(relation_inverse(X0),relation_rng(X0)),X1),relation_inverse(X0))
| ~ relation(relation_inverse(X0))
| ~ relation(X0)
| relation_rng(X0) = relation_dom(relation_inverse(X0)) ),
inference(factoring,[],[f487]) ).
fof(f1574,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK1(relation_inverse(X0),relation_rng(X0)),X1),relation_inverse(X0))
| ~ relation(X0)
| relation_rng(X0) = relation_dom(relation_inverse(X0)) ),
inference(forward_subsumption_resolution,[],[f1565,f103]) ).
fof(f1586,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,sK4(relation_inverse(X1),relation_dom(X1))),relation_inverse(X1))
| ~ relation(relation_inverse(X1))
| ~ relation(X1)
| relation_dom(X1) = relation_rng(relation_inverse(X1)) ),
inference(factoring,[],[f520]) ).
fof(f1595,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,sK4(relation_inverse(X1),relation_dom(X1))),relation_inverse(X1))
| ~ relation(X1)
| relation_dom(X1) = relation_rng(relation_inverse(X1)) ),
inference(forward_subsumption_resolution,[],[f1586,f103]) ).
fof(f1650,plain,
( sK15 != sK15
| ~ relation(sK15)
| spl16_11 ),
inference(superposition,[],[f255,f110]) ).
fof(f1651,plain,
( ~ relation(sK15)
| spl16_11 ),
inference(trivial_inequality_removal,[],[f1650]) ).
fof(f1652,plain,
( $false
| spl16_11 ),
inference(forward_subsumption_resolution,[],[f1651,f122]) ).
fof(f1653,plain,
spl16_11,
inference(avatar_contradiction_clause,[],[f1652]) ).
fof(f1660,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK1(X0,relation_rng(relation_inverse(X0))),X1),X0)
| ~ relation(X0)
| relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ),
inference(factoring,[],[f489]) ).
fof(f1662,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK1(X0,relation_rng(relation_inverse(X0))),X1),X0)
| ~ relation(X0)
| relation_dom(X0) = relation_rng(relation_inverse(X0)) ),
inference(duplicate_literal_removal,[],[f1660]) ).
fof(f1699,plain,
( ! [X0,X1] :
( in(ordered_pair(X0,X1),sK15)
| ~ in(ordered_pair(X1,X0),relation_inverse(sK15))
| ~ relation(relation_inverse(sK15)) )
| ~ spl16_11 ),
inference(superposition,[],[f171,f256]) ).
fof(f1719,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(X1,X0),relation_inverse(sK15))
| in(ordered_pair(X0,X1),sK15) )
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f1699,f251]) ).
fof(f1727,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,sK4(X1,relation_dom(relation_inverse(X1)))),X1)
| ~ relation(X1)
| relation_rng(X1) = relation_dom(relation_inverse(X1))
| ~ relation(X1) ),
inference(factoring,[],[f522]) ).
fof(f1730,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,sK4(X1,relation_dom(relation_inverse(X1)))),X1)
| ~ relation(X1)
| relation_rng(X1) = relation_dom(relation_inverse(X1)) ),
inference(duplicate_literal_removal,[],[f1727]) ).
fof(f1771,plain,
( ! [X0] :
( in(ordered_pair(X0,sK6(relation_inverse(sK15),X0)),sK15)
| ~ in(X0,relation_rng(relation_inverse(sK15)))
| ~ relation(relation_inverse(sK15)) )
| ~ spl16_10
| ~ spl16_11 ),
inference(resolution,[],[f1719,f136]) ).
fof(f1773,plain,
( ! [X0] :
( in(ordered_pair(sK3(relation_inverse(sK15),X0),X0),sK15)
| ~ in(X0,relation_dom(relation_inverse(sK15)))
| ~ relation(relation_inverse(sK15)) )
| ~ spl16_10
| ~ spl16_11 ),
inference(resolution,[],[f1719,f134]) ).
fof(f1776,plain,
( ! [X0] :
( in(ordered_pair(sK3(relation_inverse(sK15),X0),X0),sK15)
| ~ in(X0,relation_dom(relation_inverse(sK15))) )
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f1773,f251]) ).
fof(f1778,plain,
( ! [X0] :
( in(ordered_pair(X0,sK6(relation_inverse(sK15),X0)),sK15)
| ~ in(X0,relation_rng(relation_inverse(sK15))) )
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f1771,f251]) ).
fof(f2751,plain,
( ~ relation(sK15)
| relation_dom(sK15) = relation_rng(relation_inverse(sK15))
| ~ in(sK1(sK15,relation_rng(relation_inverse(sK15))),relation_rng(relation_inverse(sK15)))
| ~ spl16_10
| ~ spl16_11 ),
inference(resolution,[],[f1662,f1778]) ).
fof(f2761,plain,
( relation_dom(sK15) = relation_rng(relation_inverse(sK15))
| ~ in(sK1(sK15,relation_rng(relation_inverse(sK15))),relation_rng(relation_inverse(sK15)))
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f2751,f122]) ).
fof(f2767,plain,
( ~ in(sK1(sK15,relation_rng(relation_inverse(sK15))),relation_rng(relation_inverse(sK15)))
| spl16_1
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f2761,f142]) ).
fof(f3003,plain,
( ~ relation(sK15)
| relation_rng(sK15) = relation_dom(relation_inverse(sK15))
| ~ in(sK4(sK15,relation_dom(relation_inverse(sK15))),relation_dom(relation_inverse(sK15)))
| ~ spl16_10
| ~ spl16_11 ),
inference(resolution,[],[f1730,f1776]) ).
fof(f3014,plain,
( relation_rng(sK15) = relation_dom(relation_inverse(sK15))
| ~ in(sK4(sK15,relation_dom(relation_inverse(sK15))),relation_dom(relation_inverse(sK15)))
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f3003,f122]) ).
fof(f3017,plain,
( ~ in(sK4(sK15,relation_dom(relation_inverse(sK15))),relation_dom(relation_inverse(sK15)))
| spl16_2
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f3014,f146]) ).
fof(f3154,plain,
( ! [X0] :
( ~ in(ordered_pair(sK1(sK15,relation_rng(relation_inverse(sK15))),X0),sK15)
| ~ relation(relation_inverse(sK15))
| relation_dom(sK15) = relation_rng(relation_inverse(sK15)) )
| ~ spl16_11 ),
inference(superposition,[],[f1574,f256]) ).
fof(f3189,plain,
( ! [X0] :
( ~ in(ordered_pair(X0,sK4(sK15,relation_dom(relation_inverse(sK15)))),sK15)
| ~ relation(relation_inverse(sK15))
| relation_rng(sK15) = relation_dom(relation_inverse(sK15)) )
| ~ spl16_11 ),
inference(superposition,[],[f1595,f256]) ).
fof(f3330,plain,
( ! [X0] :
( ~ in(ordered_pair(sK1(sK15,relation_rng(relation_inverse(sK15))),X0),sK15)
| relation_dom(sK15) = relation_rng(relation_inverse(sK15)) )
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f3154,f251]) ).
fof(f3332,plain,
( ! [X0] :
( ~ in(ordered_pair(X0,sK4(sK15,relation_dom(relation_inverse(sK15)))),sK15)
| relation_rng(sK15) = relation_dom(relation_inverse(sK15)) )
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f3189,f251]) ).
fof(f3350,plain,
( ! [X0] : ~ in(ordered_pair(sK1(sK15,relation_rng(relation_inverse(sK15))),X0),sK15)
| spl16_1
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f3330,f142]) ).
fof(f3352,plain,
( ! [X0] : ~ in(ordered_pair(X0,sK4(sK15,relation_dom(relation_inverse(sK15)))),sK15)
| spl16_2
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f3332,f146]) ).
fof(f3389,plain,
( relation_dom(sK15) = relation_rng(relation_inverse(sK15))
| in(sK1(sK15,relation_rng(relation_inverse(sK15))),relation_rng(relation_inverse(sK15)))
| ~ relation(sK15)
| spl16_1
| ~ spl16_10
| ~ spl16_11 ),
inference(resolution,[],[f3350,f92]) ).
fof(f3394,plain,
( in(sK1(sK15,relation_rng(relation_inverse(sK15))),relation_rng(relation_inverse(sK15)))
| ~ relation(sK15)
| spl16_1
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f3389,f142]) ).
fof(f3395,plain,
( in(sK1(sK15,relation_rng(relation_inverse(sK15))),relation_rng(relation_inverse(sK15)))
| spl16_1
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f3394,f122]) ).
fof(f3429,plain,
( relation_rng(sK15) = relation_dom(relation_inverse(sK15))
| in(sK4(sK15,relation_dom(relation_inverse(sK15))),relation_dom(relation_inverse(sK15)))
| ~ relation(sK15)
| spl16_2
| ~ spl16_10
| ~ spl16_11 ),
inference(resolution,[],[f3352,f96]) ).
fof(f3434,plain,
( in(sK4(sK15,relation_dom(relation_inverse(sK15))),relation_dom(relation_inverse(sK15)))
| ~ relation(sK15)
| spl16_2
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f3429,f146]) ).
fof(f3435,plain,
( in(sK4(sK15,relation_dom(relation_inverse(sK15))),relation_dom(relation_inverse(sK15)))
| spl16_2
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f3434,f122]) ).
fof(f3502,plain,
( $false
| spl16_1
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f2767,f3395]) ).
fof(f3503,plain,
( spl16_1
| ~ spl16_10
| ~ spl16_11 ),
inference(avatar_contradiction_clause,[],[f3502]) ).
fof(f3735,plain,
( $false
| spl16_2
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f3017,f3435]) ).
fof(f3736,plain,
( spl16_2
| ~ spl16_10
| ~ spl16_11 ),
inference(avatar_contradiction_clause,[],[f3735]) ).
cnf(s1,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(sat_conversion,[],[f147]) ).
cnf(s10,plain,
spl16_10,
inference(sat_conversion,[],[f278]) ).
cnf(s153,plain,
spl16_11,
inference(sat_conversion,[],[f1653]) ).
cnf(s294,plain,
( spl16_1
| ~ spl16_10
| ~ spl16_11 ),
inference(sat_conversion,[],[f3503]) ).
cnf(s310,plain,
( spl16_2
| ~ spl16_10
| ~ spl16_11 ),
inference(sat_conversion,[],[f3736]) ).
cnf(s329,plain,
spl16_2,
inference(rat,[],[s310,s153,s10]) ).
cnf(s330,plain,
spl16_1,
inference(rat,[],[s294,s153,s10]) ).
cnf(s332,plain,
$false,
inference(rat,[],[s1,s329,s330]) ).
fof(f3737,plain,
$false,
inference(avatar_sat_refutation,[],[s332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU181+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n007.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:52:56 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 2.98/1.33 % (2008752)Detected formulas, will run a generic FOF schedule.
% 2.98/1.33 % (2008760)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3706888511:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.98/1.33 % (2008760)Refutation not found, incomplete strategy
% 2.98/1.33 % (2008760)------------------------------
% 2.98/1.33 % (2008760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.33 % (2008760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.33 % (2008760)CaDiCaL version: 2.1.3
% 2.98/1.33 % (2008760)Termination reason: Refutation not found, incomplete strategy
% 2.98/1.33 % (2008760)Time elapsed: 0.001 s
% 2.98/1.33 % (2008760)Peak memory usage: 88 MB
% 2.98/1.33 % (2008760)Instructions burned: 1 (million)
% 2.98/1.33 % (2008763)dis-21_1_sil=8000:lcm=predicate:random_seed=2330555171: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)
% 2.98/1.33 % (2008761)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2144676400:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.98/1.33 % (2008762)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=912665770:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.98/1.33 % (2008759)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=4005342818:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.98/1.33 % (2008757)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=2355677461:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.98/1.33 % (2008758)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=2279754962:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.98/1.33 % (2008761)Instruction limit reached!
% 2.98/1.33 % (2008761)------------------------------
% 2.98/1.33 % (2008761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.33 % (2008761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.33 % (2008761)CaDiCaL version: 2.1.3
% 2.98/1.33 % (2008761)Termination reason: Instruction limit
% 2.98/1.33 % (2008761)Termination phase: Saturation
% 2.98/1.33 % (2008761)Time elapsed: 0.065 s
% 2.98/1.33 % (2008761)Peak memory usage: 88 MB
% 2.98/1.33 % (2008761)Instructions burned: 121 (million)
% 2.98/1.33 % (2008763)Instruction limit reached!
% 2.98/1.33 % (2008763)------------------------------
% 2.98/1.33 % (2008763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.33 % (2008763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.33 % (2008763)CaDiCaL version: 2.1.3
% 2.98/1.33 % (2008763)Termination reason: Instruction limit
% 2.98/1.33 % (2008763)Termination phase: Saturation
% 2.98/1.33 % (2008763)Time elapsed: 0.077 s
% 2.98/1.33 % (2008763)Peak memory usage: 89 MB
% 2.98/1.33 % (2008763)Instructions burned: 129 (million)
% 2.98/1.33 % (2008762)First to succeed.
% 2.98/1.33 % (2008762)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2008752"
% 2.98/1.33 % (2008760)------------------------------
% 2.98/1.33 % (2008760)------------------------------
% 2.98/1.33 % (2008771)lrs+10_1_sil=8000:sp=occurrence:random_seed=188021949:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.98/1.33 % (2008772)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3157967995:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.98/1.33 % (2008772)Refutation not found, incomplete strategy
% 2.98/1.33 % (2008772)------------------------------
% 2.98/1.33 % (2008772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.33 % (2008772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.33 % (2008772)CaDiCaL version: 2.1.3
% 2.98/1.33 % (2008772)Termination reason: Refutation not found, incomplete strategy
% 2.98/1.33 % (2008772)Time elapsed: 0.003 s
% 2.98/1.33 % (2008772)Peak memory usage: 89 MB
% 2.98/1.33 % (2008772)Instructions burned: 2 (million)
% 2.98/1.33 % (2008773)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3830336483:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.98/1.33 % (2008773)Instruction limit reached!
% 2.98/1.33 % (2008773)------------------------------
% 2.98/1.33 % (2008773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.33 % (2008773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.33 % (2008773)CaDiCaL version: 2.1.3
% 2.98/1.33 % (2008773)Termination reason: Instruction limit
% 2.98/1.33 % (2008773)Termination phase: Saturation
% 2.98/1.33 % (2008773)Time elapsed: 0.109 s
% 2.98/1.33 % (2008773)Peak memory usage: 92 MB
% 2.98/1.33 % (2008773)Instructions burned: 325 (million)
% 2.98/1.33 % (2008762)Refutation found. Thanks to Tanya!
% 2.98/1.33 % SZS status Theorem for theBenchmark
% 2.98/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.97/1.43 % (2008762)------------------------------
% 3.97/1.43 % (2008762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.43 % (2008762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.43 % (2008762)CaDiCaL version: 2.1.3
% 3.97/1.43 % (2008762)Termination reason: Refutation
% 3.97/1.43 % (2008762)Time elapsed: 0.087 s
% 3.97/1.43 % (2008762)Peak memory usage: 91 MB
% 3.97/1.43 % (2008762)Instructions burned: 130 (million)
% 3.97/1.43 % (2008762)------------------------------
% 3.97/1.43 % (2008762)------------------------------
% 3.97/1.43 % (2008752)Success in time 0.488 s
% 3.97/1.43 % Vampire exiting
%------------------------------------------------------------------------------