%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU216+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 12
% Syntax : Number of formulae : 116 ( 15 unt; 5 def)
% Number of atoms : 358 ( 99 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 402 ( 160 ~; 202 |; 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(f14,axiom,
! [X0] :
( relation(identity_relation(X0))
& function(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f33,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(f34,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)],[f33]) ).
fof(f39,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(f42,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(f50,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(f63,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,[],[f34]) ).
fof(f64,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,[],[f63]) ).
fof(f72,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,[],[f42]) ).
fof(f73,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,[],[f72]) ).
fof(f77,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f78,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,[],[f50]) ).
fof(f79,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,[],[f50]) ).
fof(f80,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,[],[f50]) ).
fof(f83,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,[],[f50]) ).
fof(f88,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f97,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f124,plain,
! [X2] :
( ~ in(X2,sK11)
| apply(sK12,X2) = X2
| sK12 = identity_relation(sK11) ),
inference(cnf_transformation,[],[f64]) ).
fof(f125,plain,
( in(sK13,sK11)
| sK11 != relation_dom(sK12)
| sK12 != identity_relation(sK11) ),
inference(cnf_transformation,[],[f64]) ).
fof(f126,plain,
( sK13 != apply(sK12,sK13)
| sK11 != relation_dom(sK12)
| sK12 != identity_relation(sK11) ),
inference(cnf_transformation,[],[f64]) ).
fof(f127,plain,
( sK11 = relation_dom(sK12)
| sK12 = identity_relation(sK11) ),
inference(cnf_transformation,[],[f64]) ).
fof(f128,plain,
function(sK12),
inference(cnf_transformation,[],[f64]) ).
fof(f129,plain,
relation(sK12),
inference(cnf_transformation,[],[f64]) ).
fof(f135,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f39]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| apply(X2,X0) = X1
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f140,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,[],[f73]) ).
fof(f141,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,[],[f83,f88]) ).
fof(f144,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,[],[f80,f88]) ).
fof(f145,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,[],[f79,f88]) ).
fof(f146,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,[],[f78,f88]) ).
fof(f150,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,[],[f140,f88]) ).
fof(f151,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,[],[f139,f88]) ).
fof(f152,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,[],[f138,f88]) ).
fof(f153,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,[],[f141]) ).
fof(f154,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,[],[f153]) ).
fof(f160,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,[],[f150]) ).
fof(f162,definition,
( spl14_1
<=> sK12 = identity_relation(sK11) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f163,plain,
( sK12 != identity_relation(sK11)
| spl14_1 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f164,plain,
( sK12 = identity_relation(sK11)
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f166,definition,
( spl14_2
<=> ! [X2] :
( ~ in(X2,sK11)
| apply(sK12,X2) = X2 ) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f167,plain,
( ! [X2] :
( ~ in(X2,sK11)
| apply(sK12,X2) = X2 )
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f168,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f124,f166,f162]) ).
fof(f170,definition,
( spl14_3
<=> sK11 = relation_dom(sK12) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f171,plain,
( sK11 = relation_dom(sK12)
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f172,plain,
( sK11 != relation_dom(sK12)
| spl14_3 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f174,definition,
( spl14_4
<=> in(sK13,sK11) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f176,plain,
( in(sK13,sK11)
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f177,plain,
( ~ spl14_1
| ~ spl14_3
| spl14_4 ),
inference(avatar_split_clause,[],[f125,f174,f170,f162]) ).
fof(f179,definition,
( spl14_5
<=> sK13 = apply(sK12,sK13) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
fof(f181,plain,
( sK13 != apply(sK12,sK13)
| spl14_5 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f182,plain,
( ~ spl14_1
| ~ spl14_3
| ~ spl14_5 ),
inference(avatar_split_clause,[],[f126,f179,f170,f162]) ).
fof(f183,plain,
( spl14_1
| spl14_3 ),
inference(avatar_split_clause,[],[f127,f170,f162]) ).
fof(f187,plain,
! [X3,X0] :
( ~ in(X3,X0)
| in(unordered_pair(unordered_pair(X3,X3),singleton(X3)),identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f154,f97]) ).
fof(f190,plain,
! [X3,X0] :
( in(unordered_pair(singleton(X3),unordered_pair(X3,X3)),identity_relation(X0))
| ~ in(X3,X0) ),
inference(forward_demodulation,[],[f187,f77]) ).
fof(f373,plain,
! [X0,X1] :
( ~ relation(sK12)
| in(X0,relation_dom(sK12))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK12) ),
inference(resolution,[],[f151,f128]) ).
fof(f374,plain,
! [X0,X1] :
( in(X0,relation_dom(sK12))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK12) ),
inference(forward_subsumption_resolution,[],[f373,f129]) ).
fof(f387,plain,
! [X0,X1] :
( ~ relation(sK12)
| apply(sK12,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK12) ),
inference(resolution,[],[f152,f128]) ).
fof(f388,plain,
! [X0,X1] :
( apply(sK12,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK12) ),
inference(forward_subsumption_resolution,[],[f387,f129]) ).
fof(f391,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK12)
| apply(sK12,X0) = X1 ),
inference(forward_demodulation,[],[f388,f77]) ).
fof(f397,plain,
! [X0] :
( ~ relation(sK12)
| ~ in(X0,relation_dom(sK12))
| in(unordered_pair(unordered_pair(X0,apply(sK12,X0)),singleton(X0)),sK12) ),
inference(resolution,[],[f160,f128]) ).
fof(f398,plain,
! [X0] :
( ~ in(X0,relation_dom(sK12))
| in(unordered_pair(unordered_pair(X0,apply(sK12,X0)),singleton(X0)),sK12) ),
inference(forward_subsumption_resolution,[],[f397,f129]) ).
fof(f420,plain,
! [X0] :
( in(sK0(X0,sK12),X0)
| in(unordered_pair(unordered_pair(sK0(X0,sK12),sK1(X0,sK12)),singleton(sK0(X0,sK12))),sK12)
| identity_relation(X0) = sK12 ),
inference(resolution,[],[f144,f129]) ).
fof(f421,plain,
! [X0] :
( in(unordered_pair(singleton(sK0(X0,sK12)),unordered_pair(sK0(X0,sK12),sK1(X0,sK12))),sK12)
| in(sK0(X0,sK12),X0)
| identity_relation(X0) = sK12 ),
inference(forward_demodulation,[],[f420,f77]) ).
fof(f448,plain,
! [X0] :
( sK0(X0,sK12) = sK1(X0,sK12)
| in(unordered_pair(unordered_pair(sK0(X0,sK12),sK1(X0,sK12)),singleton(sK0(X0,sK12))),sK12)
| identity_relation(X0) = sK12 ),
inference(resolution,[],[f145,f129]) ).
fof(f449,plain,
! [X0] :
( in(unordered_pair(singleton(sK0(X0,sK12)),unordered_pair(sK0(X0,sK12),sK1(X0,sK12))),sK12)
| sK0(X0,sK12) = sK1(X0,sK12)
| identity_relation(X0) = sK12 ),
inference(forward_demodulation,[],[f448,f77]) ).
fof(f479,plain,
! [X0] :
( sK0(X0,sK12) != sK1(X0,sK12)
| ~ in(sK0(X0,sK12),X0)
| ~ in(unordered_pair(unordered_pair(sK0(X0,sK12),sK1(X0,sK12)),singleton(sK0(X0,sK12))),sK12)
| identity_relation(X0) = sK12 ),
inference(resolution,[],[f146,f129]) ).
fof(f480,plain,
! [X0] :
( ~ in(unordered_pair(singleton(sK0(X0,sK12)),unordered_pair(sK0(X0,sK12),sK1(X0,sK12))),sK12)
| sK0(X0,sK12) != sK1(X0,sK12)
| ~ in(sK0(X0,sK12),X0)
| identity_relation(X0) = sK12 ),
inference(forward_demodulation,[],[f479,f77]) ).
fof(f493,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK12)
| apply(sK12,X1) = X0 ),
inference(superposition,[],[f391,f77]) ).
fof(f524,plain,
! [X0] :
( sK1(X0,sK12) = apply(sK12,sK0(X0,sK12))
| identity_relation(X0) = sK12
| sK0(X0,sK12) = sK1(X0,sK12) ),
inference(resolution,[],[f449,f391]) ).
fof(f658,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK12)
| in(X0,relation_dom(sK12)) ),
inference(forward_demodulation,[],[f374,f77]) ).
fof(f659,plain,
! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK12,X0))),sK12)
| ~ in(X0,relation_dom(sK12)) ),
inference(forward_demodulation,[],[f398,f77]) ).
fof(f663,plain,
( sK11 = relation_dom(sK12)
| ~ spl14_1 ),
inference(superposition,[],[f135,f164]) ).
fof(f666,plain,
( ! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),sK12)
| ~ in(X0,sK11) )
| ~ spl14_1 ),
inference(superposition,[],[f190,f164]) ).
fof(f670,plain,
( $false
| ~ spl14_1
| spl14_3 ),
inference(forward_subsumption_resolution,[],[f663,f172]) ).
fof(f671,plain,
( ~ spl14_1
| spl14_3 ),
inference(avatar_contradiction_clause,[],[f670]) ).
fof(f767,plain,
( ! [X0] :
( ~ in(X0,sK11)
| apply(sK12,X0) = X0 )
| ~ spl14_1 ),
inference(resolution,[],[f666,f493]) ).
fof(f780,plain,
( spl14_2
| ~ spl14_1 ),
inference(avatar_split_clause,[],[f767,f162,f166]) ).
fof(f789,plain,
( sK13 = apply(sK12,sK13)
| ~ spl14_2
| ~ spl14_4 ),
inference(resolution,[],[f167,f176]) ).
fof(f790,plain,
( $false
| ~ spl14_2
| ~ spl14_4
| spl14_5 ),
inference(forward_subsumption_resolution,[],[f789,f181]) ).
fof(f791,plain,
( ~ spl14_2
| ~ spl14_4
| spl14_5 ),
inference(avatar_contradiction_clause,[],[f790]) ).
fof(f796,plain,
! [X0] :
( in(sK0(X0,sK12),relation_dom(sK12))
| in(sK0(X0,sK12),X0)
| identity_relation(X0) = sK12 ),
inference(resolution,[],[f658,f421]) ).
fof(f801,plain,
( ! [X0] :
( in(sK0(X0,sK12),sK11)
| in(sK0(X0,sK12),X0)
| identity_relation(X0) = sK12 )
| ~ spl14_3 ),
inference(forward_demodulation,[],[f796,f171]) ).
fof(f1516,plain,
( in(sK0(sK11,sK12),sK11)
| sK12 = identity_relation(sK11)
| ~ spl14_3 ),
inference(factoring,[],[f801]) ).
fof(f1517,plain,
( in(sK0(sK11,sK12),sK11)
| spl14_1
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f1516,f163]) ).
fof(f1518,plain,
( sK0(sK11,sK12) = apply(sK12,sK0(sK11,sK12))
| spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(resolution,[],[f1517,f167]) ).
fof(f1695,plain,
( sK0(sK11,sK12) = sK1(sK11,sK12)
| sK12 = identity_relation(sK11)
| sK0(sK11,sK12) = sK1(sK11,sK12)
| spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(superposition,[],[f524,f1518]) ).
fof(f1698,plain,
( in(unordered_pair(singleton(sK0(sK11,sK12)),unordered_pair(sK0(sK11,sK12),sK0(sK11,sK12))),sK12)
| ~ in(sK0(sK11,sK12),relation_dom(sK12))
| spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(superposition,[],[f659,f1518]) ).
fof(f1699,plain,
( sK0(sK11,sK12) = sK1(sK11,sK12)
| sK12 = identity_relation(sK11)
| spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(duplicate_literal_removal,[],[f1695]) ).
fof(f1701,plain,
( ~ in(sK0(sK11,sK12),sK11)
| in(unordered_pair(singleton(sK0(sK11,sK12)),unordered_pair(sK0(sK11,sK12),sK0(sK11,sK12))),sK12)
| spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(forward_demodulation,[],[f1698,f171]) ).
fof(f1703,plain,
( sK0(sK11,sK12) = sK1(sK11,sK12)
| spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f1699,f163]) ).
fof(f1705,plain,
( in(unordered_pair(singleton(sK0(sK11,sK12)),unordered_pair(sK0(sK11,sK12),sK0(sK11,sK12))),sK12)
| spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f1701,f1517]) ).
fof(f1714,plain,
( ~ in(unordered_pair(singleton(sK0(sK11,sK12)),unordered_pair(sK0(sK11,sK12),sK0(sK11,sK12))),sK12)
| sK0(sK11,sK12) != sK0(sK11,sK12)
| ~ in(sK0(sK11,sK12),sK11)
| sK12 = identity_relation(sK11)
| spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(superposition,[],[f480,f1703]) ).
fof(f1716,plain,
( ~ in(unordered_pair(singleton(sK0(sK11,sK12)),unordered_pair(sK0(sK11,sK12),sK0(sK11,sK12))),sK12)
| ~ in(sK0(sK11,sK12),sK11)
| sK12 = identity_relation(sK11)
| spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(trivial_inequality_removal,[],[f1714]) ).
fof(f1717,plain,
( ~ in(sK0(sK11,sK12),sK11)
| sK12 = identity_relation(sK11)
| spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f1716,f1705]) ).
fof(f1718,plain,
( sK12 = identity_relation(sK11)
| spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f1717,f1517]) ).
fof(f1719,plain,
( $false
| spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f1718,f163]) ).
fof(f1720,plain,
( spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(avatar_contradiction_clause,[],[f1719]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f168]) ).
cnf(s2,plain,
( ~ spl14_1
| ~ spl14_3
| spl14_4 ),
inference(sat_conversion,[],[f177]) ).
cnf(s3,plain,
( ~ spl14_1
| ~ spl14_3
| ~ spl14_5 ),
inference(sat_conversion,[],[f182]) ).
cnf(s4,plain,
( spl14_1
| spl14_3 ),
inference(sat_conversion,[],[f183]) ).
cnf(s23,plain,
( ~ spl14_1
| spl14_3 ),
inference(sat_conversion,[],[f671]) ).
cnf(s41,plain,
( ~ spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f780]) ).
cnf(s45,plain,
( ~ spl14_2
| ~ spl14_4
| spl14_5 ),
inference(sat_conversion,[],[f791]) ).
cnf(s71,plain,
( spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(sat_conversion,[],[f1720]) ).
cnf(s72,plain,
spl14_1,
inference(rat,[],[s71,s1,s4]) ).
cnf(s73,plain,
spl14_2,
inference(rat,[],[s41,s72]) ).
cnf(s74,plain,
spl14_3,
inference(rat,[],[s23,s72]) ).
cnf(s75,plain,
~ spl14_5,
inference(rat,[],[s3,s72,s74]) ).
cnf(s76,plain,
spl14_4,
inference(rat,[],[s2,s72,s74]) ).
cnf(s77,plain,
$false,
inference(rat,[],[s45,s73,s75,s76]) ).
fof(f1721,plain,
$false,
inference(avatar_sat_refutation,[],[s77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU216+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 04:11:47 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.17/0.49 % (8669)Will run a generic schedule for satisfiability detection.
% 0.17/0.49 % (8678)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2880152425:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.49 % (8675)% WARNING: option uhcvi not known.
% 0.17/0.49 % (8677)dis+10_1_sil=32000:sp=arity:random_seed=3434276679:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.49 % (8674)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=963726808_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.49 % (8675)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2989931364:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.49 % (8676)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=505158416:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.49 % (8679)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4141575426:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.49 % (8680)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3368859981:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.49 % TRYING [1]
% 0.17/0.49 % TRYING [2]
% 0.17/0.49 % TRYING [3]
% 0.17/0.49 % TRYING [4]
% 0.17/0.49 % (8678) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-8669-8678"...
% 0.17/0.49 % (8678)...printing done.
% 0.17/0.49 % (8678)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Theorem for theBenchmark
% 0.17/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.49 % (8678)------------------------------
% 0.17/0.49 % (8678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (8678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (8678)CaDiCaL version: 2.1.3
% 0.17/0.49 % (8678)Termination reason: Refutation
% 0.17/0.49 % (8678)Time elapsed: 0.025 s
% 0.17/0.49 % (8678)Peak memory usage: 13 MB
% 0.17/0.49 % (8678)Instructions burned: 66 (million)
% 0.17/0.49 % (8669)Success in time 0.065 s
% 0.17/0.49 % Vampire exiting
%------------------------------------------------------------------------------