%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU213+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 : n013.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 12:52:24 PM UTC 2026
% Result : Theorem 0.16s 0.52s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 140 ( 19 unt; 5 def)
% Number of atoms : 518 ( 35 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 658 ( 280 ~; 313 |; 29 &)
% ( 21 <=>; 13 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 208 ( 0 sgn 198 !; 10 ?)
% 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] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) )
& ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f6,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(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(f8,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f15,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f20,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0)
& relation(X1)
& function(X1) )
=> ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f36,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f47,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f50,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,[],[f8]) ).
fof(f51,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f52,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f51]) ).
fof(f55,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f56,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f55]) ).
fof(f63,plain,
? [X0,X1] :
( ? [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<~> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f64,plain,
? [X0,X1] :
( ? [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<~> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(flattening,[],[f63]) ).
fof(f73,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f74,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0)
| apply(X0,X1) = X2 ),
inference(cnf_transformation,[],[f48]) ).
fof(f75,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ),
inference(cnf_transformation,[],[f48]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| relation_dom(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(f86,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK5(X0,X1,X3,X4),X4),X1)
| ~ in(ordered_pair(X3,X4),X2)
| relation_composition(X0,X1) != X2 ),
inference(cnf_transformation,[],[f50]) ).
fof(f87,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(X3,sK5(X0,X1,X3,X4)),X0)
| ~ in(ordered_pair(X3,X4),X2)
| relation_composition(X0,X1) != X2 ),
inference(cnf_transformation,[],[f50]) ).
fof(f88,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,[],[f50]) ).
fof(f89,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f95,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| function(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f118,plain,
( ~ in(apply(sK16,sK14),relation_dom(sK15))
| ~ in(sK14,relation_dom(sK16))
| ~ in(sK14,relation_dom(relation_composition(sK16,sK15))) ),
inference(cnf_transformation,[],[f64]) ).
fof(f119,plain,
( in(apply(sK16,sK14),relation_dom(sK15))
| in(sK14,relation_dom(relation_composition(sK16,sK15))) ),
inference(cnf_transformation,[],[f64]) ).
fof(f120,plain,
( in(sK14,relation_dom(sK16))
| in(sK14,relation_dom(relation_composition(sK16,sK15))) ),
inference(cnf_transformation,[],[f64]) ).
fof(f121,plain,
function(sK16),
inference(cnf_transformation,[],[f64]) ).
fof(f122,plain,
relation(sK16),
inference(cnf_transformation,[],[f64]) ).
fof(f123,plain,
function(sK15),
inference(cnf_transformation,[],[f64]) ).
fof(f124,plain,
relation(sK15),
inference(cnf_transformation,[],[f64]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| apply(X0,X1) != X2 ),
inference(definition_unfolding,[],[f75,f82]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| apply(X0,X1) = X2 ),
inference(definition_unfolding,[],[f74,f82]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
| in(X2,X1)
| relation_dom(X0) != X1 ),
inference(definition_unfolding,[],[f78,f82]) ).
fof(f135,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,[],[f88,f82,f82,f82]) ).
fof(f136,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X3,sK5(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,[],[f87,f82,f82]) ).
fof(f137,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK5(X0,X1,X3,X4),X4),singleton(sK5(X0,X1,X3,X4))),X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X2)
| relation_composition(X0,X1) != X2 ),
inference(definition_unfolding,[],[f86,f82,f82]) ).
fof(f144,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0) ),
inference(equality_resolution,[],[f129]) ).
fof(f146,plain,
! [X2,X3,X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
| in(X2,relation_dom(X0)) ),
inference(equality_resolution,[],[f134]) ).
fof(f147,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,[],[f135]) ).
fof(f148,plain,
! [X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| in(unordered_pair(unordered_pair(X3,sK5(X0,X1,X3,X4)),singleton(X3)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(equality_resolution,[],[f136]) ).
fof(f149,plain,
! [X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| in(unordered_pair(unordered_pair(sK5(X0,X1,X3,X4),X4),singleton(sK5(X0,X1,X3,X4))),X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(equality_resolution,[],[f137]) ).
fof(f153,plain,
! [X0,X1] :
( function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0) ),
inference(consistent_polarity_flipping,[],[f144]) ).
fof(f154,plain,
! [X2,X0,X1] :
( function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| apply(X0,X1) = X2 ),
inference(consistent_polarity_flipping,[],[f130]) ).
fof(f156,plain,
! [X0,X1] :
( ~ function(relation_composition(X0,X1))
| ~ relation(X1)
| function(X0)
| ~ relation(X0)
| function(X1) ),
inference(consistent_polarity_flipping,[],[f95]) ).
fof(f158,plain,
~ function(sK15),
inference(consistent_polarity_flipping,[],[f123]) ).
fof(f159,plain,
~ function(sK16),
inference(consistent_polarity_flipping,[],[f121]) ).
fof(f161,definition,
( spl17_1
<=> in(sK14,relation_dom(relation_composition(sK16,sK15))) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
fof(f162,plain,
( in(sK14,relation_dom(relation_composition(sK16,sK15)))
| ~ spl17_1 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f163,plain,
( ~ in(sK14,relation_dom(relation_composition(sK16,sK15)))
| spl17_1 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f165,definition,
( spl17_2
<=> in(sK14,relation_dom(sK16)) ),
introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition]) ).
fof(f166,plain,
( in(sK14,relation_dom(sK16))
| ~ spl17_2 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f169,definition,
( spl17_3
<=> in(apply(sK16,sK14),relation_dom(sK15)) ),
introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition]) ).
fof(f170,plain,
( in(apply(sK16,sK14),relation_dom(sK15))
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,plain,
( ~ spl17_1
| ~ spl17_2
| ~ spl17_3 ),
inference(avatar_split_clause,[],[f118,f169,f165,f161]) ).
fof(f173,plain,
( spl17_1
| spl17_3 ),
inference(avatar_split_clause,[],[f119,f169,f161]) ).
fof(f174,plain,
( spl17_1
| spl17_2 ),
inference(avatar_split_clause,[],[f120,f165,f161]) ).
fof(f214,definition,
( spl17_5
<=> function(relation_composition(sK16,sK15)) ),
introduced(definition,[new_symbols(definition,[spl17_5])],[avatar_definition]) ).
fof(f215,plain,
( ~ function(relation_composition(sK16,sK15))
| spl17_5 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f216,plain,
( function(relation_composition(sK16,sK15))
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f218,definition,
( spl17_6
<=> relation(relation_composition(sK16,sK15)) ),
introduced(definition,[new_symbols(definition,[spl17_6])],[avatar_definition]) ).
fof(f219,plain,
( relation(relation_composition(sK16,sK15))
| ~ spl17_6 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f220,plain,
( ~ relation(relation_composition(sK16,sK15))
| spl17_6 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f224,plain,
( ~ relation(sK16)
| ~ relation(sK15)
| spl17_6 ),
inference(resolution,[],[f220,f89]) ).
fof(f225,plain,
( ~ relation(sK15)
| spl17_6 ),
inference(forward_subsumption_resolution,[],[f224,f122]) ).
fof(f226,plain,
( $false
| spl17_6 ),
inference(forward_subsumption_resolution,[],[f225,f124]) ).
fof(f227,plain,
spl17_6,
inference(avatar_contradiction_clause,[],[f226]) ).
fof(f228,plain,
! [X2,X3,X0] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)
| ~ relation(X0)
| in(X2,relation_dom(X0)) ),
inference(forward_demodulation,[],[f146,f73]) ).
fof(f230,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),X2)
| ~ relation(X2)
| in(X1,relation_dom(X2)) ),
inference(superposition,[],[f228,f73]) ).
fof(f243,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| function(X0)
| ~ relation(X0)
| in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X0,X1))),X0) ),
inference(forward_demodulation,[],[f153,f73]) ).
fof(f244,plain,
( function(sK16)
| ~ relation(sK16)
| in(unordered_pair(singleton(sK14),unordered_pair(sK14,apply(sK16,sK14))),sK16)
| ~ spl17_2 ),
inference(resolution,[],[f243,f166]) ).
fof(f245,plain,
( function(sK15)
| ~ relation(sK15)
| in(unordered_pair(singleton(apply(sK16,sK14)),unordered_pair(apply(sK16,sK14),apply(sK15,apply(sK16,sK14)))),sK15)
| ~ spl17_3 ),
inference(resolution,[],[f243,f170]) ).
fof(f248,plain,
( ~ relation(sK15)
| in(unordered_pair(singleton(apply(sK16,sK14)),unordered_pair(apply(sK16,sK14),apply(sK15,apply(sK16,sK14)))),sK15)
| ~ spl17_3 ),
inference(forward_subsumption_resolution,[],[f245,f158]) ).
fof(f249,plain,
( ~ relation(sK16)
| in(unordered_pair(singleton(sK14),unordered_pair(sK14,apply(sK16,sK14))),sK16)
| ~ spl17_2 ),
inference(forward_subsumption_resolution,[],[f244,f159]) ).
fof(f250,plain,
( in(unordered_pair(singleton(apply(sK16,sK14)),unordered_pair(apply(sK16,sK14),apply(sK15,apply(sK16,sK14)))),sK15)
| ~ spl17_3 ),
inference(forward_subsumption_resolution,[],[f248,f124]) ).
fof(f251,plain,
( in(unordered_pair(singleton(sK14),unordered_pair(sK14,apply(sK16,sK14))),sK16)
| ~ spl17_2 ),
inference(forward_subsumption_resolution,[],[f249,f122]) ).
fof(f252,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) = X2 ),
inference(forward_demodulation,[],[f154,f73]) ).
fof(f253,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| function(X0)
| ~ relation(X0)
| apply(X0,X1) = X2 ),
inference(forward_subsumption_resolution,[],[f252,f228]) ).
fof(f280,plain,
! [X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X3,sK5(X0,X1,X3,X4)),singleton(X3)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f148,f89]) ).
fof(f281,plain,
! [X3,X0,X1,X4] :
( in(unordered_pair(singleton(X3),unordered_pair(X3,sK5(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,[],[f280,f73]) ).
fof(f282,plain,
! [X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X4)),relation_composition(X0,X1))
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK5(X0,X1,X3,X4))),X0)
| ~ relation(X0)
| ~ relation(X1) ),
inference(forward_demodulation,[],[f281,f73]) ).
fof(f287,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,[],[f147,f89]) ).
fof(f288,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,[],[f287,f73]) ).
fof(f289,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,[],[f288,f73]) ).
fof(f290,plain,
! [X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X5)),X0)
| in(unordered_pair(singleton(X3),unordered_pair(X3,X4)),relation_composition(X0,X1))
| ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),X1)
| ~ relation(X0)
| ~ relation(X1) ),
inference(forward_demodulation,[],[f289,f73]) ).
fof(f294,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK14),unordered_pair(sK14,X0)),relation_composition(sK16,X1))
| ~ in(unordered_pair(singleton(apply(sK16,sK14)),unordered_pair(apply(sK16,sK14),X0)),X1)
| ~ relation(sK16)
| ~ relation(X1) )
| ~ spl17_2 ),
inference(resolution,[],[f290,f251]) ).
fof(f299,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(apply(sK16,sK14)),unordered_pair(apply(sK16,sK14),X0)),X1)
| in(unordered_pair(singleton(sK14),unordered_pair(sK14,X0)),relation_composition(sK16,X1))
| ~ relation(X1) )
| ~ spl17_2 ),
inference(forward_subsumption_resolution,[],[f294,f122]) ).
fof(f302,plain,
! [X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK5(X0,X1,X3,X4),X4),singleton(sK5(X0,X1,X3,X4))),X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f149,f89]) ).
fof(f303,plain,
! [X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK5(X0,X1,X3,X4)),unordered_pair(sK5(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,[],[f302,f73]) ).
fof(f304,plain,
! [X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK5(X0,X1,X3,X4)),unordered_pair(X4,sK5(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,[],[f303,f73]) ).
fof(f305,plain,
! [X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X4)),relation_composition(X0,X1))
| in(unordered_pair(singleton(sK5(X0,X1,X3,X4)),unordered_pair(X4,sK5(X0,X1,X3,X4))),X1)
| ~ relation(X0)
| ~ relation(X1) ),
inference(forward_demodulation,[],[f304,f73]) ).
fof(f492,plain,
( in(unordered_pair(singleton(sK14),unordered_pair(sK14,apply(sK15,apply(sK16,sK14)))),relation_composition(sK16,sK15))
| ~ relation(sK15)
| ~ spl17_2
| ~ spl17_3 ),
inference(resolution,[],[f299,f250]) ).
fof(f495,plain,
( in(unordered_pair(singleton(sK14),unordered_pair(sK14,apply(sK15,apply(sK16,sK14)))),relation_composition(sK16,sK15))
| ~ spl17_2
| ~ spl17_3 ),
inference(forward_subsumption_resolution,[],[f492,f124]) ).
fof(f502,plain,
( ~ relation(relation_composition(sK16,sK15))
| in(sK14,relation_dom(relation_composition(sK16,sK15)))
| ~ spl17_2
| ~ spl17_3 ),
inference(resolution,[],[f495,f228]) ).
fof(f505,plain,
( in(sK14,relation_dom(relation_composition(sK16,sK15)))
| ~ spl17_2
| ~ spl17_3
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f502,f219]) ).
fof(f510,plain,
( $false
| spl17_1
| ~ spl17_2
| ~ spl17_3
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f505,f163]) ).
fof(f511,plain,
( spl17_1
| ~ spl17_2
| ~ spl17_3
| ~ spl17_6 ),
inference(avatar_contradiction_clause,[],[f510]) ).
fof(f520,plain,
( function(relation_composition(sK16,sK15))
| ~ relation(relation_composition(sK16,sK15))
| in(unordered_pair(singleton(sK14),unordered_pair(sK14,apply(relation_composition(sK16,sK15),sK14))),relation_composition(sK16,sK15))
| ~ spl17_1 ),
inference(resolution,[],[f162,f243]) ).
fof(f525,plain,
( function(relation_composition(sK16,sK15))
| in(unordered_pair(singleton(sK14),unordered_pair(sK14,apply(relation_composition(sK16,sK15),sK14))),relation_composition(sK16,sK15))
| ~ spl17_1
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f520,f219]) ).
fof(f642,plain,
( ~ relation(sK15)
| function(sK16)
| ~ relation(sK16)
| function(sK15)
| ~ spl17_5 ),
inference(resolution,[],[f216,f156]) ).
fof(f644,plain,
( function(sK16)
| ~ relation(sK16)
| function(sK15)
| ~ spl17_5 ),
inference(forward_subsumption_resolution,[],[f642,f124]) ).
fof(f645,plain,
( ~ relation(sK16)
| function(sK15)
| ~ spl17_5 ),
inference(forward_subsumption_resolution,[],[f644,f159]) ).
fof(f646,plain,
( function(sK15)
| ~ spl17_5 ),
inference(forward_subsumption_resolution,[],[f645,f122]) ).
fof(f647,plain,
( $false
| ~ spl17_5 ),
inference(forward_subsumption_resolution,[],[f646,f158]) ).
fof(f648,plain,
~ spl17_5,
inference(avatar_contradiction_clause,[],[f647]) ).
fof(f1245,plain,
( in(unordered_pair(singleton(sK14),unordered_pair(sK14,apply(relation_composition(sK16,sK15),sK14))),relation_composition(sK16,sK15))
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f525,f215]) ).
fof(f1249,plain,
( in(unordered_pair(singleton(sK5(sK16,sK15,sK14,apply(relation_composition(sK16,sK15),sK14))),unordered_pair(apply(relation_composition(sK16,sK15),sK14),sK5(sK16,sK15,sK14,apply(relation_composition(sK16,sK15),sK14)))),sK15)
| ~ relation(sK16)
| ~ relation(sK15)
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(resolution,[],[f1245,f305]) ).
fof(f1250,plain,
( in(unordered_pair(singleton(sK14),unordered_pair(sK14,sK5(sK16,sK15,sK14,apply(relation_composition(sK16,sK15),sK14)))),sK16)
| ~ relation(sK16)
| ~ relation(sK15)
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(resolution,[],[f1245,f282]) ).
fof(f1257,plain,
( in(unordered_pair(singleton(sK14),unordered_pair(sK14,sK5(sK16,sK15,sK14,apply(relation_composition(sK16,sK15),sK14)))),sK16)
| ~ relation(sK15)
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f1250,f122]) ).
fof(f1258,plain,
( in(unordered_pair(singleton(sK5(sK16,sK15,sK14,apply(relation_composition(sK16,sK15),sK14))),unordered_pair(apply(relation_composition(sK16,sK15),sK14),sK5(sK16,sK15,sK14,apply(relation_composition(sK16,sK15),sK14)))),sK15)
| ~ relation(sK15)
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f1249,f122]) ).
fof(f1259,plain,
( in(unordered_pair(singleton(sK14),unordered_pair(sK14,sK5(sK16,sK15,sK14,apply(relation_composition(sK16,sK15),sK14)))),sK16)
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f1257,f124]) ).
fof(f1260,plain,
( in(unordered_pair(singleton(sK5(sK16,sK15,sK14,apply(relation_composition(sK16,sK15),sK14))),unordered_pair(apply(relation_composition(sK16,sK15),sK14),sK5(sK16,sK15,sK14,apply(relation_composition(sK16,sK15),sK14)))),sK15)
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f1258,f124]) ).
fof(f1332,plain,
( function(sK16)
| ~ relation(sK16)
| apply(sK16,sK14) = sK5(sK16,sK15,sK14,apply(relation_composition(sK16,sK15),sK14))
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(resolution,[],[f1259,f253]) ).
fof(f1333,plain,
( ~ relation(sK16)
| in(sK14,relation_dom(sK16))
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(resolution,[],[f1259,f228]) ).
fof(f1336,plain,
( ~ relation(sK16)
| apply(sK16,sK14) = sK5(sK16,sK15,sK14,apply(relation_composition(sK16,sK15),sK14))
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f1332,f159]) ).
fof(f1338,plain,
( apply(sK16,sK14) = sK5(sK16,sK15,sK14,apply(relation_composition(sK16,sK15),sK14))
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f1336,f122]) ).
fof(f1450,plain,
( ~ relation(sK15)
| in(sK5(sK16,sK15,sK14,apply(relation_composition(sK16,sK15),sK14)),relation_dom(sK15))
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(resolution,[],[f1260,f230]) ).
fof(f1453,plain,
( in(sK5(sK16,sK15,sK14,apply(relation_composition(sK16,sK15),sK14)),relation_dom(sK15))
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f1450,f124]) ).
fof(f1622,plain,
( in(apply(sK16,sK14),relation_dom(sK15))
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(superposition,[],[f1453,f1338]) ).
fof(f1632,plain,
( spl17_3
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(avatar_split_clause,[],[f1622,f218,f214,f161,f169]) ).
fof(f1654,plain,
( in(sK14,relation_dom(sK16))
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f1333,f122]) ).
fof(f1666,plain,
( spl17_2
| ~ spl17_1
| spl17_5
| ~ spl17_6 ),
inference(avatar_split_clause,[],[f1654,f218,f214,f161,f165]) ).
cnf(s1,plain,
( ~ spl17_1
| ~ spl17_2
| ~ spl17_3 ),
inference(sat_conversion,[],[f172]) ).
cnf(s2,plain,
( spl17_1
| spl17_3 ),
inference(sat_conversion,[],[f173]) ).
cnf(s3,plain,
( spl17_1
| spl17_2 ),
inference(sat_conversion,[],[f174]) ).
cnf(s5,plain,
spl17_6,
inference(sat_conversion,[],[f227]) ).
cnf(s6,plain,
( spl17_1
| ~ spl17_2
| ~ spl17_3
| ~ spl17_6 ),
inference(sat_conversion,[],[f511]) ).
cnf(s17,plain,
~ spl17_5,
inference(sat_conversion,[],[f648]) ).
cnf(s62,plain,
( ~ spl17_1
| spl17_3
| spl17_5
| ~ spl17_6 ),
inference(sat_conversion,[],[f1632]) ).
cnf(s72,plain,
( ~ spl17_1
| spl17_2
| spl17_5
| ~ spl17_6 ),
inference(sat_conversion,[],[f1666]) ).
cnf(s90,plain,
spl17_1,
inference(rat,[],[s6,s2,s3,s5]) ).
cnf(s91,plain,
spl17_2,
inference(rat,[],[s72,s5,s17,s90]) ).
cnf(s93,plain,
spl17_3,
inference(rat,[],[s62,s5,s17,s90]) ).
cnf(s94,plain,
$false,
inference(rat,[],[s1,s91,s93,s90]) ).
fof(f1667,plain,
$false,
inference(avatar_sat_refutation,[],[s94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU213+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n013.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 04:04:21 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.16/0.52 % (789984)Will run a generic schedule for satisfiability detection.
% 0.16/0.52 % (789993)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4013292281:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.52 % (789990)% WARNING: option uhcvi not known.
% 0.16/0.52 % (789989)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=712894521_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.52 % (789990)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1409167922:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.52 % (789991)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2458348356:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.52 % (789994)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1213762289:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.52 % (789992)dis+10_1_sil=32000:sp=arity:random_seed=3161299270:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.52 % (789995)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2376075833:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.52 % TRYING [1]
% 0.16/0.52 % TRYING [2]
% 0.16/0.52 % TRYING [3]
% 0.16/0.52 % (789993)Instruction limit reached!
% 0.16/0.52 % (789993)------------------------------
% 0.16/0.52 % (789993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (789993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (789993)CaDiCaL version: 2.1.3
% 0.16/0.52 % (789993)Termination reason: Instruction limit
% 0.16/0.52 % (789993)Termination phase: Saturation
% 0.16/0.52 % (789993)Time elapsed: 0.040 s
% 0.16/0.52 % (789993)Peak memory usage: 13 MB
% 0.16/0.52 % (789993)Instructions burned: 116 (million)
% 0.16/0.52 % (790003)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4046920208:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.16/0.52 % (789990) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-789984-789990"...
% 0.16/0.52 % TRYING [1]
% 0.16/0.52 % TRYING [2]
% 0.16/0.52 % (789990)...printing done.
% 0.16/0.52 % TRYING [3]
% 0.16/0.52 % (789992)Instruction limit reached!
% 0.16/0.52 % (789992)------------------------------
% 0.16/0.52 % (789992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (789992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (789992)CaDiCaL version: 2.1.3
% 0.16/0.52 % (789992)Termination reason: Instruction limit
% 0.16/0.52 % (789992)Termination phase: Saturation
% 0.16/0.52 % (789992)Time elapsed: 0.063 s
% 0.16/0.52 % (789992)Peak memory usage: 12 MB
% 0.16/0.52 % (789992)Instructions burned: 103 (million)
% 0.16/0.52 % (789990)Refutation found. Thanks to Tanya!
% 0.16/0.52 % SZS status Theorem for theBenchmark
% 0.16/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.52 % (789990)------------------------------
% 0.16/0.52 % (789990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (789990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (789990)CaDiCaL version: 2.1.3
% 0.16/0.52 % (789990)Termination reason: Refutation
% 0.16/0.52 % (789990)Time elapsed: 0.062 s
% 0.16/0.52 % (789990)Peak memory usage: 13 MB
% 0.16/0.52 % (789990)Instructions burned: 98 (million)
% 0.16/0.52 % (789984)Success in time 0.098 s
% 0.16/0.52 % Vampire exiting
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