%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU216+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 12:52:25 PM UTC 2026
% Result : Theorem 0.16s 0.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 12
% Syntax : Number of formulae : 114 ( 15 unt; 5 def)
% Number of atoms : 352 ( 98 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 395 ( 157 ~; 198 |; 18 &)
% ( 14 <=>; 6 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn 117 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f5,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/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
fof(f7,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(f21,axiom,
! [X0] :
( relation(identity_relation(X0))
& function(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f37,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( X1 = identity_relation(X0)
<=> ( relation_dom(X1) = X0
& ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f38,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( X1 = identity_relation(X0)
<=> ( relation_dom(X1) = X0
& ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f40,axiom,
! [X0] :
( relation_dom(identity_relation(X0)) = X0
& relation_rng(identity_relation(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
fof(f43,axiom,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f49,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,[],[f5]) ).
fof(f61,plain,
? [X0,X1] :
( ( X1 = identity_relation(X0)
<~> ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) ) )
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f62,plain,
? [X0,X1] :
( ( X1 = identity_relation(X0)
<~> ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) ) )
& relation(X1)
& function(X1) ),
inference(flattening,[],[f61]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<=> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) )
| ~ relation(X2)
| ~ function(X2) ),
inference(ennf_transformation,[],[f43]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<=> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) )
| ~ relation(X2)
| ~ function(X2) ),
inference(flattening,[],[f66]) ).
fof(f71,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f72,plain,
! [X0,X1] :
( ~ relation(X1)
| sK0(X0,X1) != sK1(X0,X1)
| ~ in(sK0(X0,X1),X0)
| ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f49]) ).
fof(f73,plain,
! [X0,X1] :
( ~ relation(X1)
| sK0(X0,X1) = sK1(X0,X1)
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f49]) ).
fof(f74,plain,
! [X0,X1] :
( ~ relation(X1)
| in(sK0(X0,X1),X0)
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f49]) ).
fof(f77,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,[],[f49]) ).
fof(f82,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f90,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f112,plain,
! [X2] :
( ~ in(X2,sK9)
| apply(sK10,X2) = X2
| sK10 = identity_relation(sK9) ),
inference(cnf_transformation,[],[f62]) ).
fof(f113,plain,
( in(sK11,sK9)
| sK9 != relation_dom(sK10)
| sK10 != identity_relation(sK9) ),
inference(cnf_transformation,[],[f62]) ).
fof(f114,plain,
( sK11 != apply(sK10,sK11)
| sK9 != relation_dom(sK10)
| sK10 != identity_relation(sK9) ),
inference(cnf_transformation,[],[f62]) ).
fof(f115,plain,
( sK9 = relation_dom(sK10)
| sK10 = identity_relation(sK9) ),
inference(cnf_transformation,[],[f62]) ).
fof(f116,plain,
function(sK10),
inference(cnf_transformation,[],[f62]) ).
fof(f117,plain,
relation(sK10),
inference(cnf_transformation,[],[f62]) ).
fof(f120,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| apply(X2,X0) = X1
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f126,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,[],[f77,f82]) ).
fof(f129,plain,
! [X0,X1] :
( ~ relation(X1)
| in(sK0(X0,X1),X0)
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X1)
| identity_relation(X0) = X1 ),
inference(definition_unfolding,[],[f74,f82]) ).
fof(f130,plain,
! [X0,X1] :
( ~ relation(X1)
| sK0(X0,X1) = sK1(X0,X1)
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X1)
| identity_relation(X0) = X1 ),
inference(definition_unfolding,[],[f73,f82]) ).
fof(f131,plain,
! [X0,X1] :
( ~ relation(X1)
| sK0(X0,X1) != sK1(X0,X1)
| ~ in(sK0(X0,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X1)
| identity_relation(X0) = X1 ),
inference(definition_unfolding,[],[f72,f82]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(definition_unfolding,[],[f125,f82]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| in(X0,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(definition_unfolding,[],[f124,f82]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| apply(X2,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(definition_unfolding,[],[f123,f82]) ).
fof(f138,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,[],[f126]) ).
fof(f139,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,[],[f138]) ).
fof(f145,plain,
! [X2,X0] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X2))
| in(unordered_pair(unordered_pair(X0,apply(X2,X0)),singleton(X0)),X2) ),
inference(equality_resolution,[],[f135]) ).
fof(f147,definition,
( spl12_1
<=> sK10 = identity_relation(sK9) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f148,plain,
( sK10 != identity_relation(sK9)
| spl12_1 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f149,plain,
( sK10 = identity_relation(sK9)
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f151,definition,
( spl12_2
<=> ! [X2] :
( ~ in(X2,sK9)
| apply(sK10,X2) = X2 ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f152,plain,
( ! [X2] :
( ~ in(X2,sK9)
| apply(sK10,X2) = X2 )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f153,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f112,f151,f147]) ).
fof(f155,definition,
( spl12_3
<=> sK9 = relation_dom(sK10) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f156,plain,
( sK9 = relation_dom(sK10)
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f157,plain,
( sK9 != relation_dom(sK10)
| spl12_3 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f159,definition,
( spl12_4
<=> in(sK11,sK9) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f161,plain,
( in(sK11,sK9)
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f162,plain,
( ~ spl12_1
| ~ spl12_3
| spl12_4 ),
inference(avatar_split_clause,[],[f113,f159,f155,f147]) ).
fof(f164,definition,
( spl12_5
<=> sK11 = apply(sK10,sK11) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f167,plain,
( ~ spl12_1
| ~ spl12_3
| ~ spl12_5 ),
inference(avatar_split_clause,[],[f114,f164,f155,f147]) ).
fof(f168,plain,
( spl12_1
| spl12_3 ),
inference(avatar_split_clause,[],[f115,f155,f147]) ).
fof(f172,plain,
! [X3,X0] :
( ~ in(X3,X0)
| in(unordered_pair(unordered_pair(X3,X3),singleton(X3)),identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f139,f90]) ).
fof(f175,plain,
! [X3,X0] :
( in(unordered_pair(singleton(X3),unordered_pair(X3,X3)),identity_relation(X0))
| ~ in(X3,X0) ),
inference(forward_demodulation,[],[f172,f71]) ).
fof(f311,plain,
! [X0,X1] :
( ~ relation(sK10)
| in(X0,relation_dom(sK10))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK10) ),
inference(resolution,[],[f136,f116]) ).
fof(f312,plain,
! [X0,X1] :
( in(X0,relation_dom(sK10))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK10) ),
inference(forward_subsumption_resolution,[],[f311,f117]) ).
fof(f325,plain,
! [X0,X1] :
( ~ relation(sK10)
| apply(sK10,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK10) ),
inference(resolution,[],[f137,f116]) ).
fof(f326,plain,
! [X0,X1] :
( apply(sK10,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK10) ),
inference(forward_subsumption_resolution,[],[f325,f117]) ).
fof(f329,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK10)
| apply(sK10,X0) = X1 ),
inference(forward_demodulation,[],[f326,f71]) ).
fof(f335,plain,
! [X0] :
( ~ relation(sK10)
| ~ in(X0,relation_dom(sK10))
| in(unordered_pair(unordered_pair(X0,apply(sK10,X0)),singleton(X0)),sK10) ),
inference(resolution,[],[f145,f116]) ).
fof(f336,plain,
! [X0] :
( ~ in(X0,relation_dom(sK10))
| in(unordered_pair(unordered_pair(X0,apply(sK10,X0)),singleton(X0)),sK10) ),
inference(forward_subsumption_resolution,[],[f335,f117]) ).
fof(f357,plain,
! [X0] :
( in(sK0(X0,sK10),X0)
| in(unordered_pair(unordered_pair(sK0(X0,sK10),sK1(X0,sK10)),singleton(sK0(X0,sK10))),sK10)
| identity_relation(X0) = sK10 ),
inference(resolution,[],[f129,f117]) ).
fof(f358,plain,
! [X0] :
( in(unordered_pair(singleton(sK0(X0,sK10)),unordered_pair(sK0(X0,sK10),sK1(X0,sK10))),sK10)
| in(sK0(X0,sK10),X0)
| identity_relation(X0) = sK10 ),
inference(forward_demodulation,[],[f357,f71]) ).
fof(f385,plain,
! [X0] :
( sK0(X0,sK10) = sK1(X0,sK10)
| in(unordered_pair(unordered_pair(sK0(X0,sK10),sK1(X0,sK10)),singleton(sK0(X0,sK10))),sK10)
| identity_relation(X0) = sK10 ),
inference(resolution,[],[f130,f117]) ).
fof(f386,plain,
! [X0] :
( in(unordered_pair(singleton(sK0(X0,sK10)),unordered_pair(sK0(X0,sK10),sK1(X0,sK10))),sK10)
| sK0(X0,sK10) = sK1(X0,sK10)
| identity_relation(X0) = sK10 ),
inference(forward_demodulation,[],[f385,f71]) ).
fof(f416,plain,
! [X0] :
( sK0(X0,sK10) != sK1(X0,sK10)
| ~ in(sK0(X0,sK10),X0)
| ~ in(unordered_pair(unordered_pair(sK0(X0,sK10),sK1(X0,sK10)),singleton(sK0(X0,sK10))),sK10)
| identity_relation(X0) = sK10 ),
inference(resolution,[],[f131,f117]) ).
fof(f417,plain,
! [X0] :
( ~ in(unordered_pair(singleton(sK0(X0,sK10)),unordered_pair(sK0(X0,sK10),sK1(X0,sK10))),sK10)
| sK0(X0,sK10) != sK1(X0,sK10)
| ~ in(sK0(X0,sK10),X0)
| identity_relation(X0) = sK10 ),
inference(forward_demodulation,[],[f416,f71]) ).
fof(f430,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK10)
| apply(sK10,X1) = X0 ),
inference(superposition,[],[f329,f71]) ).
fof(f459,plain,
! [X0] :
( sK1(X0,sK10) = apply(sK10,sK0(X0,sK10))
| identity_relation(X0) = sK10
| sK0(X0,sK10) = sK1(X0,sK10) ),
inference(resolution,[],[f386,f329]) ).
fof(f771,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK10)
| in(X0,relation_dom(sK10)) ),
inference(forward_demodulation,[],[f312,f71]) ).
fof(f772,plain,
! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK10,X0))),sK10)
| ~ in(X0,relation_dom(sK10)) ),
inference(forward_demodulation,[],[f336,f71]) ).
fof(f792,plain,
( sK9 = relation_dom(sK10)
| ~ spl12_1 ),
inference(superposition,[],[f120,f149]) ).
fof(f795,plain,
( ! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),sK10)
| ~ in(X0,sK9) )
| ~ spl12_1 ),
inference(superposition,[],[f175,f149]) ).
fof(f799,plain,
( $false
| ~ spl12_1
| spl12_3 ),
inference(forward_subsumption_resolution,[],[f792,f157]) ).
fof(f800,plain,
( ~ spl12_1
| spl12_3 ),
inference(avatar_contradiction_clause,[],[f799]) ).
fof(f804,plain,
( sK11 = apply(sK10,sK11)
| ~ spl12_2
| ~ spl12_4 ),
inference(resolution,[],[f161,f152]) ).
fof(f840,plain,
( ! [X0] :
( ~ in(X0,sK9)
| apply(sK10,X0) = X0 )
| ~ spl12_1 ),
inference(resolution,[],[f795,f430]) ).
fof(f843,plain,
( spl12_2
| ~ spl12_1 ),
inference(avatar_split_clause,[],[f840,f147,f151]) ).
fof(f844,plain,
( spl12_5
| ~ spl12_2
| ~ spl12_4 ),
inference(avatar_split_clause,[],[f804,f159,f151,f164]) ).
fof(f851,plain,
! [X0] :
( in(sK0(X0,sK10),relation_dom(sK10))
| in(sK0(X0,sK10),X0)
| identity_relation(X0) = sK10 ),
inference(resolution,[],[f771,f358]) ).
fof(f856,plain,
( ! [X0] :
( in(sK0(X0,sK10),sK9)
| in(sK0(X0,sK10),X0)
| identity_relation(X0) = sK10 )
| ~ spl12_3 ),
inference(forward_demodulation,[],[f851,f156]) ).
fof(f1215,plain,
( in(sK0(sK9,sK10),sK9)
| sK10 = identity_relation(sK9)
| ~ spl12_3 ),
inference(factoring,[],[f856]) ).
fof(f1216,plain,
( in(sK0(sK9,sK10),sK9)
| spl12_1
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f1215,f148]) ).
fof(f1217,plain,
( sK0(sK9,sK10) = apply(sK10,sK0(sK9,sK10))
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(resolution,[],[f1216,f152]) ).
fof(f1237,plain,
( in(unordered_pair(singleton(sK0(sK9,sK10)),unordered_pair(sK0(sK9,sK10),sK0(sK9,sK10))),sK10)
| ~ in(sK0(sK9,sK10),relation_dom(sK10))
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(superposition,[],[f772,f1217]) ).
fof(f1238,plain,
( ~ in(sK0(sK9,sK10),sK9)
| in(unordered_pair(singleton(sK0(sK9,sK10)),unordered_pair(sK0(sK9,sK10),sK0(sK9,sK10))),sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_demodulation,[],[f1237,f156]) ).
fof(f1240,plain,
( in(unordered_pair(singleton(sK0(sK9,sK10)),unordered_pair(sK0(sK9,sK10),sK0(sK9,sK10))),sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f1238,f1216]) ).
fof(f1255,plain,
( sK0(sK9,sK10) = sK1(sK9,sK10)
| sK10 = identity_relation(sK9)
| sK0(sK9,sK10) = sK1(sK9,sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(superposition,[],[f1217,f459]) ).
fof(f1267,plain,
( sK0(sK9,sK10) = sK1(sK9,sK10)
| sK10 = identity_relation(sK9)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(duplicate_literal_removal,[],[f1255]) ).
fof(f1272,plain,
( sK0(sK9,sK10) = sK1(sK9,sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f1267,f148]) ).
fof(f1274,plain,
( ~ in(unordered_pair(singleton(sK0(sK9,sK10)),unordered_pair(sK0(sK9,sK10),sK0(sK9,sK10))),sK10)
| sK0(sK9,sK10) != sK0(sK9,sK10)
| ~ in(sK0(sK9,sK10),sK9)
| sK10 = identity_relation(sK9)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(superposition,[],[f417,f1272]) ).
fof(f1276,plain,
( ~ in(unordered_pair(singleton(sK0(sK9,sK10)),unordered_pair(sK0(sK9,sK10),sK0(sK9,sK10))),sK10)
| ~ in(sK0(sK9,sK10),sK9)
| sK10 = identity_relation(sK9)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(trivial_inequality_removal,[],[f1274]) ).
fof(f1277,plain,
( ~ in(sK0(sK9,sK10),sK9)
| sK10 = identity_relation(sK9)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f1276,f1240]) ).
fof(f1278,plain,
( sK10 = identity_relation(sK9)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f1277,f1216]) ).
fof(f1279,plain,
( $false
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f1278,f148]) ).
fof(f1280,plain,
( spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(avatar_contradiction_clause,[],[f1279]) ).
cnf(s1,plain,
( spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f153]) ).
cnf(s2,plain,
( ~ spl12_1
| ~ spl12_3
| spl12_4 ),
inference(sat_conversion,[],[f162]) ).
cnf(s3,plain,
( ~ spl12_1
| ~ spl12_3
| ~ spl12_5 ),
inference(sat_conversion,[],[f167]) ).
cnf(s4,plain,
( spl12_1
| spl12_3 ),
inference(sat_conversion,[],[f168]) ).
cnf(s20,plain,
( ~ spl12_1
| spl12_3 ),
inference(sat_conversion,[],[f800]) ).
cnf(s24,plain,
( ~ spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f843]) ).
cnf(s26,plain,
( ~ spl12_2
| ~ spl12_4
| spl12_5 ),
inference(sat_conversion,[],[f844]) ).
cnf(s32,plain,
( spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(sat_conversion,[],[f1280]) ).
cnf(s33,plain,
spl12_1,
inference(rat,[],[s32,s1,s4]) ).
cnf(s34,plain,
spl12_2,
inference(rat,[],[s24,s33]) ).
cnf(s35,plain,
spl12_3,
inference(rat,[],[s20,s33]) ).
cnf(s36,plain,
~ spl12_5,
inference(rat,[],[s3,s33,s35]) ).
cnf(s37,plain,
spl12_4,
inference(rat,[],[s2,s33,s35]) ).
cnf(s38,plain,
$false,
inference(rat,[],[s26,s34,s36,s37]) ).
fof(f1281,plain,
$false,
inference(avatar_sat_refutation,[],[s38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU216+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 % Computer : n010.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Mon Sep 28 04:06:02 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.50 % (1546286)Will run a generic schedule for satisfiability detection.
% 0.16/0.50 % (1546291)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1219077385_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.50 % TRYING [1]
% 0.16/0.50 % (1546292)% WARNING: option uhcvi not known.
% 0.16/0.50 % TRYING [2]
% 0.16/0.50 % TRYING [3]
% 0.16/0.50 % (1546292)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2263731345:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.50 % (1546295)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4043417012:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.50 % (1546293)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3995408394:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.50 % (1546296)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1719945546:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.50 % (1546294)dis+10_1_sil=32000:sp=arity:random_seed=871250961:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.50 % (1546297)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3301204232:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.50 % TRYING [4]
% 0.16/0.50 % (1546295) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1546286-1546295"...
% 0.16/0.50 % (1546295)...printing done.
% 0.16/0.50 % (1546295)Refutation found. Thanks to Tanya!
% 0.16/0.50 % SZS status Theorem for theBenchmark
% 0.16/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.50 % (1546295)------------------------------
% 0.16/0.50 % (1546295)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (1546295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (1546295)CaDiCaL version: 2.1.3
% 0.16/0.50 % (1546295)Termination reason: Refutation
% 0.16/0.50 % (1546295)Time elapsed: 0.034 s
% 0.16/0.50 % (1546295)Peak memory usage: 13 MB
% 0.16/0.50 % (1546295)Instructions burned: 49 (million)
% 0.16/0.50 % (1546286)Success in time 0.068 s
% 0.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------