%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU191+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 12:52:19 PM UTC 2026
% Result : Theorem 0.07s 0.37s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 111 ( 12 unt; 3 def)
% Number of atoms : 349 ( 34 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 440 ( 202 ~; 208 |; 9 &)
% ( 13 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 213 ( 0 sgn 207 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0,X1] :
( relation(X1)
=> ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( in(X2,X0)
& X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
fof(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f6,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/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f11,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f12,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f29,conjecture,
! [X0,X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(X0,X2)
& in(ordered_pair(X0,X1),X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_relat_1) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(X0,X2)
& in(ordered_pair(X0,X1),X3) ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f35,plain,
! [X0,X1] :
( ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( in(X2,X0)
& X2 = X3 ) ) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f36,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,[],[f6]) ).
fof(f37,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f38,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f37]) ).
fof(f47,plain,
? [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<~> ( in(X0,X2)
& in(ordered_pair(X0,X1),X3) ) )
& relation(X3) ),
inference(ennf_transformation,[],[f30]) ).
fof(f52,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( ~ relation(X1)
| X2 = X3
| ~ in(ordered_pair(X2,X3),X1)
| identity_relation(X0) != X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f57,plain,
! [X2,X3,X0,X1] :
( ~ relation(X1)
| in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1)
| identity_relation(X0) != X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f58,plain,
! [X2,X3,X0,X1] :
( ~ relation(X1)
| X2 != X3
| ~ in(X2,X0)
| in(ordered_pair(X2,X3),X1)
| identity_relation(X0) != X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f59,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK4(X0,X1,X3,X4),X4),X1)
| ~ in(ordered_pair(X3,X4),X2)
| relation_composition(X0,X1) != X2 ),
inference(cnf_transformation,[],[f36]) ).
fof(f64,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(X3,sK4(X0,X1,X3,X4)),X0)
| ~ in(ordered_pair(X3,X4),X2)
| relation_composition(X0,X1) != X2 ),
inference(cnf_transformation,[],[f36]) ).
fof(f65,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0)
| in(ordered_pair(X3,X4),X2)
| relation_composition(X0,X1) != X2 ),
inference(cnf_transformation,[],[f36]) ).
fof(f66,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f67,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f88,plain,
( ~ in(ordered_pair(sK11,sK12),sK14)
| ~ in(sK11,sK13)
| ~ in(ordered_pair(sK11,sK12),relation_composition(identity_relation(sK13),sK14)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f89,plain,
( in(ordered_pair(sK11,sK12),sK14)
| in(ordered_pair(sK11,sK12),relation_composition(identity_relation(sK13),sK14)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f90,plain,
( in(sK11,sK13)
| in(ordered_pair(sK11,sK12),relation_composition(identity_relation(sK13),sK14)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f91,plain,
relation(sK14),
inference(cnf_transformation,[],[f47]) ).
fof(f94,plain,
! [X2,X3,X0,X1] :
( ~ relation(X1)
| X2 != X3
| ~ in(X2,X0)
| in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X1)
| identity_relation(X0) != X1 ),
inference(definition_unfolding,[],[f58,f59]) ).
fof(f95,plain,
! [X2,X3,X0,X1] :
( ~ relation(X1)
| in(X2,X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X1)
| identity_relation(X0) != X1 ),
inference(definition_unfolding,[],[f57,f59]) ).
fof(f96,plain,
! [X2,X3,X0,X1] :
( ~ relation(X1)
| X2 = X3
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X1)
| identity_relation(X0) != X1 ),
inference(definition_unfolding,[],[f56,f59]) ).
fof(f100,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X1)
| ~ in(unordered_pair(unordered_pair(X3,X5),singleton(X3)),X0)
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X2)
| relation_composition(X0,X1) != X2 ),
inference(definition_unfolding,[],[f65,f59,f59,f59]) ).
fof(f101,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X3,sK4(X0,X1,X3,X4)),singleton(X3)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X2)
| relation_composition(X0,X1) != X2 ),
inference(definition_unfolding,[],[f64,f59,f59]) ).
fof(f102,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK4(X0,X1,X3,X4),X4),singleton(sK4(X0,X1,X3,X4))),X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X2)
| relation_composition(X0,X1) != X2 ),
inference(definition_unfolding,[],[f63,f59,f59]) ).
fof(f107,plain,
( in(sK11,sK13)
| in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),relation_composition(identity_relation(sK13),sK14)) ),
inference(definition_unfolding,[],[f90,f59]) ).
fof(f108,plain,
( in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),sK14)
| in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),relation_composition(identity_relation(sK13),sK14)) ),
inference(definition_unfolding,[],[f89,f59,f59]) ).
fof(f109,plain,
( ~ in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),sK14)
| ~ in(sK11,sK13)
| ~ in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),relation_composition(identity_relation(sK13),sK14)) ),
inference(definition_unfolding,[],[f88,f59,f59]) ).
fof(f110,plain,
! [X3,X0,X1] :
( ~ relation(X1)
| ~ in(X3,X0)
| in(unordered_pair(unordered_pair(X3,X3),singleton(X3)),X1)
| identity_relation(X0) != X1 ),
inference(equality_resolution,[],[f94]) ).
fof(f111,plain,
! [X3,X0] :
( ~ relation(identity_relation(X0))
| ~ in(X3,X0)
| in(unordered_pair(unordered_pair(X3,X3),singleton(X3)),identity_relation(X0)) ),
inference(equality_resolution,[],[f110]) ).
fof(f112,plain,
! [X2,X3,X0] :
( ~ relation(identity_relation(X0))
| in(X2,X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),identity_relation(X0)) ),
inference(equality_resolution,[],[f95]) ).
fof(f113,plain,
! [X2,X3,X0] :
( ~ relation(identity_relation(X0))
| X2 = X3
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),identity_relation(X0)) ),
inference(equality_resolution,[],[f96]) ).
fof(f114,plain,
! [X3,X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X1)
| ~ in(unordered_pair(unordered_pair(X3,X5),singleton(X3)),X0)
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(equality_resolution,[],[f100]) ).
fof(f115,plain,
! [X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| in(unordered_pair(unordered_pair(X3,sK4(X0,X1,X3,X4)),singleton(X3)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(equality_resolution,[],[f101]) ).
fof(f116,plain,
! [X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| in(unordered_pair(unordered_pair(sK4(X0,X1,X3,X4),X4),singleton(sK4(X0,X1,X3,X4))),X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(equality_resolution,[],[f102]) ).
fof(f118,definition,
( spl15_1
<=> in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),relation_composition(identity_relation(sK13),sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f119,plain,
( in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),relation_composition(identity_relation(sK13),sK14))
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f120,plain,
( ~ in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),relation_composition(identity_relation(sK13),sK14))
| spl15_1 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f122,definition,
( spl15_2
<=> in(sK11,sK13) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f123,plain,
( in(sK11,sK13)
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f124,plain,
( ~ in(sK11,sK13)
| spl15_2 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f126,definition,
( spl15_3
<=> in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),sK14) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f127,plain,
( in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),sK14)
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f128,plain,
( ~ in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),sK14)
| spl15_3 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( ~ spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(avatar_split_clause,[],[f109,f126,f122,f118]) ).
fof(f130,plain,
( spl15_1
| spl15_3 ),
inference(avatar_split_clause,[],[f108,f126,f118]) ).
fof(f131,plain,
( spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f107,f122,f118]) ).
fof(f132,plain,
! [X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK4(X0,X1,X3,X4),X4),singleton(sK4(X0,X1,X3,X4))),X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f116,f66]) ).
fof(f133,plain,
! [X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X3,sK4(X0,X1,X3,X4)),singleton(X3)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f115,f66]) ).
fof(f134,plain,
! [X3,X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X1)
| ~ in(unordered_pair(unordered_pair(X3,X5),singleton(X3)),X0)
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f114,f66]) ).
fof(f135,plain,
! [X2,X3,X0] :
( X2 = X3
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f113,f67]) ).
fof(f136,plain,
! [X2,X3,X0] :
( in(X2,X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f112,f67]) ).
fof(f137,plain,
! [X3,X0] :
( ~ in(X3,X0)
| in(unordered_pair(unordered_pair(X3,X3),singleton(X3)),identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f111,f67]) ).
fof(f138,plain,
! [X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK4(X0,X1,X3,X4)),unordered_pair(sK4(X0,X1,X3,X4),X4)),X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(forward_demodulation,[],[f132,f52]) ).
fof(f139,plain,
! [X3,X0,X1,X4] :
( in(unordered_pair(singleton(X3),unordered_pair(X3,sK4(X0,X1,X3,X4))),X0)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(forward_demodulation,[],[f133,f52]) ).
fof(f140,plain,
! [X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X5),singleton(X3)),X0)
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(forward_demodulation,[],[f134,f52]) ).
fof(f141,plain,
! [X2,X3,X0] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),identity_relation(X0))
| X2 = X3 ),
inference(forward_demodulation,[],[f135,f52]) ).
fof(f142,plain,
! [X2,X3,X0] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),identity_relation(X0))
| in(X2,X0) ),
inference(forward_demodulation,[],[f136,f52]) ).
fof(f143,plain,
! [X3,X0] :
( in(unordered_pair(singleton(X3),unordered_pair(X3,X3)),identity_relation(X0))
| ~ in(X3,X0) ),
inference(forward_demodulation,[],[f137,f52]) ).
fof(f144,plain,
! [X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK4(X0,X1,X3,X4)),unordered_pair(X4,sK4(X0,X1,X3,X4))),X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(forward_demodulation,[],[f138,f52]) ).
fof(f145,plain,
! [X3,X0,X1,X4] :
( in(unordered_pair(singleton(X3),unordered_pair(X3,sK4(X0,X1,X3,X4))),X0)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X4)),relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(forward_demodulation,[],[f139,f52]) ).
fof(f146,plain,
! [X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X5)),X0)
| ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),X1)
| ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(forward_demodulation,[],[f140,f52]) ).
fof(f147,plain,
! [X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK4(X0,X1,X3,X4)),unordered_pair(X4,sK4(X0,X1,X3,X4))),X1)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X4)),relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(forward_demodulation,[],[f144,f52]) ).
fof(f148,plain,
! [X3,X0,X1,X4,X5] :
( in(unordered_pair(singleton(X3),unordered_pair(X3,X4)),relation_composition(X0,X1))
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X5)),X0)
| ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),X1)
| ~ relation(X0)
| ~ relation(X1) ),
inference(forward_demodulation,[],[f146,f52]) ).
fof(f149,plain,
( ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),relation_composition(identity_relation(sK13),sK14))
| spl15_1 ),
inference(forward_demodulation,[],[f120,f52]) ).
fof(f150,plain,
( in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),sK14)
| ~ spl15_3 ),
inference(forward_demodulation,[],[f127,f52]) ).
fof(f236,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(identity_relation(X2),X3))
| ~ relation(identity_relation(X2))
| ~ relation(X3)
| in(X0,X2) ),
inference(resolution,[],[f145,f142]) ).
fof(f237,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(identity_relation(X2),X3))
| ~ relation(identity_relation(X2))
| ~ relation(X3)
| sK4(identity_relation(X2),X3,X0,X1) = X0 ),
inference(resolution,[],[f145,f141]) ).
fof(f242,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3)
| sK4(identity_relation(X2),X3,X0,X1) = X0 ),
inference(forward_subsumption_resolution,[],[f237,f67]) ).
fof(f243,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3)
| in(X0,X2) ),
inference(forward_subsumption_resolution,[],[f236,f67]) ).
fof(f261,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,X0)),identity_relation(sK13))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK12)),sK14)
| ~ relation(identity_relation(sK13))
| ~ relation(sK14) )
| spl15_1 ),
inference(resolution,[],[f148,f149]) ).
fof(f286,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,X0)),identity_relation(sK13))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK12)),sK14)
| ~ relation(sK14) )
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f261,f67]) ).
fof(f287,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,X0)),identity_relation(sK13))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK12)),sK14) )
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f286,f91]) ).
fof(f288,plain,
( ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),sK14)
| ~ in(sK11,sK13)
| spl15_1 ),
inference(resolution,[],[f287,f143]) ).
fof(f293,plain,
( ~ in(sK11,sK13)
| spl15_1
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f288,f150]) ).
fof(f294,plain,
( $false
| spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f293,f123]) ).
fof(f295,plain,
( spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(avatar_contradiction_clause,[],[f294]) ).
fof(f296,plain,
( in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),relation_composition(identity_relation(sK13),sK14))
| ~ spl15_1 ),
inference(forward_demodulation,[],[f119,f52]) ).
fof(f297,plain,
( ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),sK14)
| spl15_3 ),
inference(forward_demodulation,[],[f128,f52]) ).
fof(f654,plain,
( ~ relation(sK14)
| in(sK11,sK13)
| ~ spl15_1 ),
inference(resolution,[],[f243,f296]) ).
fof(f691,plain,
( ~ relation(sK14)
| sK11 = sK4(identity_relation(sK13),sK14,sK11,sK12)
| ~ spl15_1 ),
inference(resolution,[],[f242,f296]) ).
fof(f697,plain,
( sK11 = sK4(identity_relation(sK13),sK14,sK11,sK12)
| ~ spl15_1 ),
inference(forward_subsumption_resolution,[],[f691,f91]) ).
fof(f699,plain,
( in(unordered_pair(singleton(sK11),unordered_pair(sK12,sK11)),sK14)
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),relation_composition(identity_relation(sK13),sK14))
| ~ relation(identity_relation(sK13))
| ~ relation(sK14)
| ~ spl15_1 ),
inference(superposition,[],[f147,f697]) ).
fof(f702,plain,
( in(unordered_pair(singleton(sK11),unordered_pair(sK12,sK11)),sK14)
| ~ relation(identity_relation(sK13))
| ~ relation(sK14)
| ~ spl15_1 ),
inference(forward_subsumption_resolution,[],[f699,f296]) ).
fof(f704,plain,
( in(unordered_pair(singleton(sK11),unordered_pair(sK12,sK11)),sK14)
| ~ relation(sK14)
| ~ spl15_1 ),
inference(forward_subsumption_resolution,[],[f702,f67]) ).
fof(f706,plain,
( in(unordered_pair(singleton(sK11),unordered_pair(sK12,sK11)),sK14)
| ~ spl15_1 ),
inference(forward_subsumption_resolution,[],[f704,f91]) ).
fof(f707,plain,
( in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),sK14)
| ~ spl15_1 ),
inference(forward_demodulation,[],[f706,f52]) ).
fof(f708,plain,
( $false
| ~ spl15_1
| spl15_3 ),
inference(forward_subsumption_resolution,[],[f707,f297]) ).
fof(f709,plain,
( ~ spl15_1
| spl15_3 ),
inference(avatar_contradiction_clause,[],[f708]) ).
fof(f711,plain,
( in(sK11,sK13)
| ~ spl15_1 ),
inference(forward_subsumption_resolution,[],[f654,f91]) ).
fof(f712,plain,
( $false
| ~ spl15_1
| spl15_2 ),
inference(forward_subsumption_resolution,[],[f711,f124]) ).
fof(f713,plain,
( ~ spl15_1
| spl15_2 ),
inference(avatar_contradiction_clause,[],[f712]) ).
cnf(s1,plain,
( ~ spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(sat_conversion,[],[f129]) ).
cnf(s2,plain,
( spl15_1
| spl15_3 ),
inference(sat_conversion,[],[f130]) ).
cnf(s3,plain,
( spl15_1
| spl15_2 ),
inference(sat_conversion,[],[f131]) ).
cnf(s4,plain,
( spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(sat_conversion,[],[f295]) ).
cnf(s5,plain,
( ~ spl15_1
| spl15_3 ),
inference(sat_conversion,[],[f709]) ).
cnf(s6,plain,
( ~ spl15_1
| spl15_2 ),
inference(sat_conversion,[],[f713]) ).
cnf(s7,plain,
spl15_1,
inference(rat,[],[s4,s2,s3]) ).
cnf(s8,plain,
spl15_2,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
spl15_3,
inference(rat,[],[s5,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s8,s9,s7]) ).
fof(f714,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU191+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Mon Sep 28 03:57:49 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.33 Running first-order model finding
% 0.07/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.37 % (3002735)Will run a generic schedule for satisfiability detection.
% 0.07/0.37 % (3002741)% WARNING: option uhcvi not known.
% 0.07/0.37 % (3002740)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2620756763_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.37 % (3002744)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3508607336:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.37 % (3002743)dis+10_1_sil=32000:sp=arity:random_seed=3624898478:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.37 % (3002741)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3524757199:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.37 % (3002742)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2182148528:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.37 % (3002745)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3152287522:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.37 % (3002746)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=499671695:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.37 % TRYING [1]
% 0.07/0.37 % TRYING [2]
% 0.07/0.37 % TRYING [3]
% 0.07/0.37 % (3002744) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3002735-3002744"...
% 0.07/0.37 % (3002741) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3002735-3002741"...
% 0.07/0.37 % (3002744)...printing done.
% 0.07/0.37 % (3002744)Refutation found. Thanks to Tanya!
% 0.07/0.37 % SZS status Theorem for theBenchmark
% 0.07/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.37 % (3002744)------------------------------
% 0.07/0.37 % (3002744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.37 % (3002744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.37 % (3002744)CaDiCaL version: 2.1.3
% 0.07/0.37 % (3002744)Termination reason: Refutation
% 0.07/0.37 % (3002744)Time elapsed: 0.012 s
% 0.07/0.37 % (3002744)Peak memory usage: 13 MB
% 0.07/0.37 % (3002744)Instructions burned: 34 (million)
% 0.07/0.37 % (3002735)Success in time 0.036 s
% 0.07/0.37 % Vampire exiting
%------------------------------------------------------------------------------