%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU222+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:47:50 PM UTC 2026
% Result : Theorem 8.68s 2.11s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 38
% Syntax : Number of formulae : 304 ( 31 unt; 29 def)
% Number of atoms : 1248 ( 184 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1684 ( 740 ~; 779 |; 103 &)
% ( 47 <=>; 13 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 30 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 349 ( 0 sgn 314 !; 35 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f7,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation(X2)
=> ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f8,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f9,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/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f10,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f11,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(f44,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f50,axiom,
! [X0,X1] :
( relation(X1)
=> relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_relat_1) ).
fof(f61,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) ) ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f62,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,[],[f9]) ).
fof(f63,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,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f83,plain,
? [X0,X1] :
( ? [X2] :
( ( X1 = relation_dom_restriction(X2,X0)
<~> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) ) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f84,plain,
? [X0,X1] :
( ? [X2] :
( ( X1 = relation_dom_restriction(X2,X0)
<~> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) ) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(flattening,[],[f83]) ).
fof(f89,plain,
! [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f90,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = relation_dom_restriction(X0,X1)
| ? [X3,X4] :
( ( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X0) )
& ( ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f61]) ).
fof(f91,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = relation_dom_restriction(X0,X1)
| ? [X3,X4] :
( ( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X0) )
& ( ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = relation_dom_restriction(X0,X1)
| ? [X3,X4] :
( ( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0) )
& ( ( in(X5,X1)
& in(ordered_pair(X5,X6),X0) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(rectify,[],[f91]) ).
fof(f93,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = relation_dom_restriction(X0,X1)
| ( ( ~ in(sK0(X0,X1,X2),X1)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2) )
& ( ( in(sK0(X0,X1,X2),X1)
& in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0) )
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0) )
& ( ( in(X5,X1)
& in(ordered_pair(X5,X6),X0) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X4,sK1(X0,X1,X2))],[f92]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK2(X0,X1,X2),X0)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X2) )
& ( ( in(sK2(X0,X1,X2),X0)
& in(sK2(X0,X1,X2),X1) )
| in(sK2(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f96]) ).
fof(f98,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( X2 = apply(X0,X1)
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) )
& ( ( ( X2 = apply(X0,X1)
| empty_set != X2 )
& ( X2 = empty_set
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f63]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f64]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK3(X0,X1),X3),X0)
| ~ in(sK3(X0,X1),X1) )
& ( in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0)
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK5(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f100]) ).
fof(f113,plain,
? [X0,X1] :
( ? [X2] :
( ( relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
| relation_dom_restriction(X2,X0) != X1 )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) )
| X1 = relation_dom_restriction(X2,X0) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(nnf_transformation,[],[f84]) ).
fof(f114,plain,
? [X0,X1] :
( ? [X2] :
( ( relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
| relation_dom_restriction(X2,X0) != X1 )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) )
| X1 = relation_dom_restriction(X2,X0) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
? [X0,X1] :
( ? [X2] :
( ( relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
| relation_dom_restriction(X2,X0) != X1 )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) ) )
| X1 = relation_dom_restriction(X2,X0) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(rectify,[],[f114]) ).
fof(f116,plain,
( ( relation_dom(sK18) != set_intersection2(relation_dom(sK19),sK17)
| ( apply(sK18,sK20) != apply(sK19,sK20)
& in(sK20,relation_dom(sK18)) )
| sK18 != relation_dom_restriction(sK19,sK17) )
& ( ( relation_dom(sK18) = set_intersection2(relation_dom(sK19),sK17)
& ! [X4] :
( apply(sK18,X4) = apply(sK19,X4)
| ~ in(X4,relation_dom(sK18)) ) )
| sK18 = relation_dom_restriction(sK19,sK17) )
& relation(sK19)
& function(sK19)
& relation(sK18)
& function(sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19,sK20]),skolemize(X0,sK17),skolemize(X1,sK18),skolemize(X2,sK19),skolemize(X3,sK20)],[f115]) ).
fof(f122,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f123,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f124,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X5,X6),X2)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f127,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0)
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f128,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| in(sK0(X0,X1,X2),X1)
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f129,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f130,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f97]) ).
fof(f131,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f97]) ).
fof(f132,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f97]) ).
fof(f138,plain,
! [X2,X0,X1] :
( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f139,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f140,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK5(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f141,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f144,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f192,plain,
function(sK18),
inference(cnf_transformation,[],[f116]) ).
fof(f193,plain,
relation(sK18),
inference(cnf_transformation,[],[f116]) ).
fof(f194,plain,
function(sK19),
inference(cnf_transformation,[],[f116]) ).
fof(f195,plain,
relation(sK19),
inference(cnf_transformation,[],[f116]) ).
fof(f196,plain,
! [X4] :
( apply(sK18,X4) = apply(sK19,X4)
| ~ in(X4,relation_dom(sK18))
| sK18 = relation_dom_restriction(sK19,sK17) ),
inference(cnf_transformation,[],[f116]) ).
fof(f197,plain,
( relation_dom(sK18) = set_intersection2(relation_dom(sK19),sK17)
| sK18 = relation_dom_restriction(sK19,sK17) ),
inference(cnf_transformation,[],[f116]) ).
fof(f198,plain,
( relation_dom(sK18) != set_intersection2(relation_dom(sK19),sK17)
| in(sK20,relation_dom(sK18))
| sK18 != relation_dom_restriction(sK19,sK17) ),
inference(cnf_transformation,[],[f116]) ).
fof(f199,plain,
( relation_dom(sK18) != set_intersection2(relation_dom(sK19),sK17)
| apply(sK18,sK20) != apply(sK19,sK20)
| sK18 != relation_dom_restriction(sK19,sK17) ),
inference(cnf_transformation,[],[f116]) ).
fof(f204,plain,
! [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f205,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X0)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f129,f144,f144]) ).
fof(f206,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| in(sK0(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f128,f144]) ).
fof(f207,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f127,f144,f144]) ).
fof(f210,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f124,f144,f144]) ).
fof(f211,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(definition_unfolding,[],[f139,f144]) ).
fof(f212,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| apply(X0,X1) != X2
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(definition_unfolding,[],[f138,f144]) ).
fof(f215,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f141,f144]) ).
fof(f216,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK5(X0,X5)),singleton(X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f140,f144]) ).
fof(f220,plain,
! [X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f210]) ).
fof(f221,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f132]) ).
fof(f222,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f131]) ).
fof(f223,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f130]) ).
fof(f224,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f212]) ).
fof(f227,plain,
! [X0,X6,X5] :
( in(X5,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f215]) ).
fof(f228,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK5(X0,X5)),singleton(X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f216]) ).
fof(f231,plain,
( relation_dom(sK18) = set_intersection2(sK17,relation_dom(sK19))
| sK18 = relation_dom_restriction(sK19,sK17) ),
inference(forward_demodulation,[],[f197,f123]) ).
fof(f232,plain,
( relation_dom(sK18) != set_intersection2(sK17,relation_dom(sK19))
| in(sK20,relation_dom(sK18))
| sK18 != relation_dom_restriction(sK19,sK17) ),
inference(forward_demodulation,[],[f198,f123]) ).
fof(f233,plain,
( relation_dom(sK18) != set_intersection2(sK17,relation_dom(sK19))
| apply(sK18,sK20) != apply(sK19,sK20)
| sK18 != relation_dom_restriction(sK19,sK17) ),
inference(forward_demodulation,[],[f199,f123]) ).
fof(f235,definition,
( spl22_1
<=> sK18 = relation_dom_restriction(sK19,sK17) ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
fof(f236,plain,
( sK18 = relation_dom_restriction(sK19,sK17)
| ~ spl22_1 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f237,plain,
( sK18 != relation_dom_restriction(sK19,sK17)
| spl22_1 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f239,definition,
( spl22_2
<=> in(sK20,relation_dom(sK18)) ),
introduced(definition,[new_symbols(definition,[spl22_2])],[avatar_definition]) ).
fof(f241,plain,
( in(sK20,relation_dom(sK18))
| ~ spl22_2 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f243,definition,
( spl22_3
<=> relation_dom(sK18) = set_intersection2(sK17,relation_dom(sK19)) ),
introduced(definition,[new_symbols(definition,[spl22_3])],[avatar_definition]) ).
fof(f244,plain,
( relation_dom(sK18) = set_intersection2(sK17,relation_dom(sK19))
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f245,plain,
( relation_dom(sK18) != set_intersection2(sK17,relation_dom(sK19))
| spl22_3 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f246,plain,
( ~ spl22_1
| spl22_2
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f232,f243,f239,f235]) ).
fof(f247,plain,
( relation_dom(sK18) = set_intersection2(sK17,relation_dom(sK19))
| spl22_1 ),
inference(backward_subsumption_resolution,[],[f231,f237]) ).
fof(f261,plain,
( spl22_3
| spl22_1 ),
inference(avatar_split_clause,[],[f247,f235,f243]) ).
fof(f272,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK18))
| in(X0,sK17) )
| ~ spl22_3 ),
inference(superposition,[],[f222,f244]) ).
fof(f273,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK18))
| in(X0,relation_dom(sK19)) )
| ~ spl22_3 ),
inference(superposition,[],[f223,f244]) ).
fof(f279,definition,
( spl22_4
<=> relation(sK19) ),
introduced(definition,[new_symbols(definition,[spl22_4])],[avatar_definition]) ).
fof(f281,plain,
( relation(sK19)
| ~ spl22_4 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f282,plain,
spl22_4,
inference(avatar_split_clause,[],[f195,f279]) ).
fof(f284,definition,
( spl22_5
<=> relation(sK18) ),
introduced(definition,[new_symbols(definition,[spl22_5])],[avatar_definition]) ).
fof(f286,plain,
( relation(sK18)
| ~ spl22_5 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f287,plain,
spl22_5,
inference(avatar_split_clause,[],[f193,f284]) ).
fof(f289,definition,
( spl22_6
<=> function(sK19) ),
introduced(definition,[new_symbols(definition,[spl22_6])],[avatar_definition]) ).
fof(f291,plain,
( function(sK19)
| ~ spl22_6 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f292,plain,
spl22_6,
inference(avatar_split_clause,[],[f194,f289]) ).
fof(f316,plain,
( ! [X0] : relation_dom(relation_dom_restriction(sK19,X0)) = set_intersection2(relation_dom(sK19),X0)
| ~ spl22_4 ),
inference(resolution,[],[f281,f204]) ).
fof(f332,plain,
( ! [X0,X1] :
( in(X0,relation_dom(sK19))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK19) )
| ~ spl22_4 ),
inference(resolution,[],[f281,f227]) ).
fof(f335,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK19)
| in(X0,relation_dom(sK19)) )
| ~ spl22_4 ),
inference(forward_demodulation,[],[f332,f122]) ).
fof(f363,definition,
( spl22_7
<=> function(sK18) ),
introduced(definition,[new_symbols(definition,[spl22_7])],[avatar_definition]) ).
fof(f365,plain,
( function(sK18)
| ~ spl22_7 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f366,plain,
spl22_7,
inference(avatar_split_clause,[],[f192,f363]) ).
fof(f372,plain,
( ! [X0,X1] :
( apply(sK18,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK18)
| ~ in(X0,relation_dom(sK18))
| ~ relation(sK18) )
| ~ spl22_7 ),
inference(resolution,[],[f365,f211]) ).
fof(f373,plain,
( ! [X0,X1] :
( apply(sK18,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK18)
| ~ relation(sK18) )
| ~ spl22_7 ),
inference(forward_subsumption_resolution,[],[f372,f227]) ).
fof(f378,plain,
( ! [X0,X1] :
( apply(sK18,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK18) )
| ~ spl22_5
| ~ spl22_7 ),
inference(forward_subsumption_resolution,[],[f373,f286]) ).
fof(f380,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18)
| apply(sK18,X0) = X1 )
| ~ spl22_5
| ~ spl22_7 ),
inference(forward_demodulation,[],[f378,f122]) ).
fof(f382,definition,
( spl22_8
<=> ! [X0] :
( ~ in(X0,relation_dom(sK18))
| in(X0,sK17) ) ),
introduced(definition,[new_symbols(definition,[spl22_8])],[avatar_definition]) ).
fof(f383,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK18))
| in(X0,sK17) )
| ~ spl22_8 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f384,plain,
( spl22_8
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f272,f243,f382]) ).
fof(f440,definition,
( spl22_9
<=> ! [X0] :
( ~ in(X0,relation_dom(sK18))
| in(X0,relation_dom(sK19)) ) ),
introduced(definition,[new_symbols(definition,[spl22_9])],[avatar_definition]) ).
fof(f441,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK18))
| in(X0,relation_dom(sK19)) )
| ~ spl22_9 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f442,plain,
( spl22_9
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f273,f243,f440]) ).
fof(f514,plain,
( ! [X4] :
( apply(sK18,X4) = apply(sK19,X4)
| ~ in(X4,relation_dom(sK18)) )
| spl22_1 ),
inference(forward_subsumption_resolution,[],[f196,f237]) ).
fof(f543,definition,
( spl22_11
<=> ! [X4] :
( apply(sK18,X4) = apply(sK19,X4)
| ~ in(X4,relation_dom(sK18)) ) ),
introduced(definition,[new_symbols(definition,[spl22_11])],[avatar_definition]) ).
fof(f544,plain,
( ! [X4] :
( apply(sK18,X4) = apply(sK19,X4)
| ~ in(X4,relation_dom(sK18)) )
| ~ spl22_11 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f545,plain,
( spl22_11
| spl22_1 ),
inference(avatar_split_clause,[],[f514,f235,f543]) ).
fof(f564,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK18)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK19)
| ~ relation(sK18)
| ~ relation(sK19) )
| ~ spl22_1 ),
inference(superposition,[],[f220,f236]) ).
fof(f565,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK18)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK19)
| ~ relation(sK19) )
| ~ spl22_1
| ~ spl22_5 ),
inference(forward_subsumption_resolution,[],[f564,f286]) ).
fof(f577,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK18)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK19) )
| ~ spl22_1
| ~ spl22_4
| ~ spl22_5 ),
inference(forward_subsumption_resolution,[],[f565,f281]) ).
fof(f589,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK19) )
| ~ spl22_1
| ~ spl22_4
| ~ spl22_5 ),
inference(forward_demodulation,[],[f577,f122]) ).
fof(f599,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK19)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18) )
| ~ spl22_1
| ~ spl22_4
| ~ spl22_5 ),
inference(forward_demodulation,[],[f589,f122]) ).
fof(f613,definition,
( spl22_12
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18)
| apply(sK18,X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[spl22_12])],[avatar_definition]) ).
fof(f614,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18)
| apply(sK18,X0) = X1 )
| ~ spl22_12 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f615,plain,
( spl22_12
| ~ spl22_5
| ~ spl22_7 ),
inference(avatar_split_clause,[],[f380,f363,f284,f613]) ).
fof(f637,definition,
( spl22_14
<=> ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK19)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18) ) ),
introduced(definition,[new_symbols(definition,[spl22_14])],[avatar_definition]) ).
fof(f638,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK19) )
| ~ spl22_14 ),
inference(avatar_component_clause,[],[f637]) ).
fof(f639,plain,
( spl22_14
| ~ spl22_1
| ~ spl22_4
| ~ spl22_5 ),
inference(avatar_split_clause,[],[f599,f284,f279,f235,f637]) ).
fof(f640,plain,
( ! [X0,X1] :
( in(X0,sK17)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK18)
| ~ relation(sK18) )
| ~ spl22_8 ),
inference(resolution,[],[f383,f227]) ).
fof(f678,plain,
( ! [X0,X1] :
( in(X0,sK17)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK18) )
| ~ spl22_5
| ~ spl22_8 ),
inference(forward_subsumption_resolution,[],[f640,f286]) ).
fof(f687,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18)
| in(X0,sK17) )
| ~ spl22_5
| ~ spl22_8 ),
inference(forward_demodulation,[],[f678,f122]) ).
fof(f690,definition,
( spl22_15
<=> ! [X0] : relation_dom(relation_dom_restriction(sK19,X0)) = set_intersection2(relation_dom(sK19),X0) ),
introduced(definition,[new_symbols(definition,[spl22_15])],[avatar_definition]) ).
fof(f691,plain,
( ! [X0] : relation_dom(relation_dom_restriction(sK19,X0)) = set_intersection2(relation_dom(sK19),X0)
| ~ spl22_15 ),
inference(avatar_component_clause,[],[f690]) ).
fof(f692,plain,
( spl22_15
| ~ spl22_4 ),
inference(avatar_split_clause,[],[f316,f279,f690]) ).
fof(f698,definition,
( spl22_17
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18)
| in(X0,sK17) ) ),
introduced(definition,[new_symbols(definition,[spl22_17])],[avatar_definition]) ).
fof(f699,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18)
| in(X0,sK17) )
| ~ spl22_17 ),
inference(avatar_component_clause,[],[f698]) ).
fof(f701,plain,
( ! [X0] :
( sK18 != X0
| in(unordered_pair(unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0)),singleton(sK0(sK19,sK17,X0))),sK19)
| in(unordered_pair(unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0)),singleton(sK0(sK19,sK17,X0))),X0)
| ~ relation(X0)
| ~ relation(sK19) )
| spl22_1 ),
inference(superposition,[],[f237,f207]) ).
fof(f703,plain,
( ! [X0] :
( sK18 != X0
| ~ in(sK0(sK19,sK17,X0),sK17)
| ~ in(unordered_pair(unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0)),singleton(sK0(sK19,sK17,X0))),sK19)
| ~ in(unordered_pair(unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0)),singleton(sK0(sK19,sK17,X0))),X0)
| ~ relation(X0)
| ~ relation(sK19) )
| spl22_1 ),
inference(superposition,[],[f237,f205]) ).
fof(f704,plain,
( ! [X0] :
( sK18 != X0
| ~ in(sK0(sK19,sK17,X0),sK17)
| ~ in(unordered_pair(unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0)),singleton(sK0(sK19,sK17,X0))),sK19)
| ~ in(unordered_pair(unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0)),singleton(sK0(sK19,sK17,X0))),X0)
| ~ relation(X0) )
| spl22_1
| ~ spl22_4 ),
inference(forward_subsumption_resolution,[],[f703,f281]) ).
fof(f706,plain,
( ! [X0] :
( sK18 != X0
| in(unordered_pair(unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0)),singleton(sK0(sK19,sK17,X0))),sK19)
| in(unordered_pair(unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0)),singleton(sK0(sK19,sK17,X0))),X0)
| ~ relation(X0) )
| spl22_1
| ~ spl22_4 ),
inference(forward_subsumption_resolution,[],[f701,f281]) ).
fof(f707,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK0(sK19,sK17,X0)),unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0))),sK19)
| sK18 != X0
| ~ in(sK0(sK19,sK17,X0),sK17)
| ~ in(unordered_pair(unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0)),singleton(sK0(sK19,sK17,X0))),X0)
| ~ relation(X0) )
| spl22_1
| ~ spl22_4 ),
inference(forward_demodulation,[],[f704,f122]) ).
fof(f709,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK0(sK19,sK17,X0)),unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0))),sK19)
| sK18 != X0
| in(unordered_pair(unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0)),singleton(sK0(sK19,sK17,X0))),X0)
| ~ relation(X0) )
| spl22_1
| ~ spl22_4 ),
inference(forward_demodulation,[],[f706,f122]) ).
fof(f710,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK0(sK19,sK17,X0)),unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0))),X0)
| ~ in(unordered_pair(singleton(sK0(sK19,sK17,X0)),unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0))),sK19)
| sK18 != X0
| ~ in(sK0(sK19,sK17,X0),sK17)
| ~ relation(X0) )
| spl22_1
| ~ spl22_4 ),
inference(forward_demodulation,[],[f707,f122]) ).
fof(f711,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK0(sK19,sK17,X0)),unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0))),X0)
| in(unordered_pair(singleton(sK0(sK19,sK17,X0)),unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0))),sK19)
| sK18 != X0
| ~ relation(X0) )
| spl22_1
| ~ spl22_4 ),
inference(forward_demodulation,[],[f709,f122]) ).
fof(f721,plain,
( ! [X0] :
( in(X0,relation_dom(sK18))
| ~ in(X0,sK17)
| ~ in(X0,relation_dom(sK19)) )
| ~ spl22_3 ),
inference(superposition,[],[f221,f244]) ).
fof(f733,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(X0,apply(sK18,X0)),singleton(X0)),sK19)
| ~ in(X0,relation_dom(sK19))
| ~ relation(sK19)
| ~ function(sK19)
| ~ in(X0,relation_dom(sK18)) )
| ~ spl22_11 ),
inference(superposition,[],[f224,f544]) ).
fof(f734,plain,
( ! [X0,X1] :
( apply(sK18,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK19)
| ~ in(X0,relation_dom(sK19))
| ~ relation(sK19)
| ~ function(sK19)
| ~ in(X0,relation_dom(sK18)) )
| ~ spl22_11 ),
inference(superposition,[],[f211,f544]) ).
fof(f735,plain,
( ! [X0,X1] :
( apply(sK18,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK19)
| ~ relation(sK19)
| ~ function(sK19)
| ~ in(X0,relation_dom(sK18)) )
| ~ spl22_11 ),
inference(forward_subsumption_resolution,[],[f734,f227]) ).
fof(f736,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(X0,apply(sK18,X0)),singleton(X0)),sK19)
| ~ relation(sK19)
| ~ function(sK19)
| ~ in(X0,relation_dom(sK18)) )
| ~ spl22_9
| ~ spl22_11 ),
inference(forward_subsumption_resolution,[],[f733,f441]) ).
fof(f742,plain,
( ! [X0,X1] :
( apply(sK18,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK19)
| ~ function(sK19)
| ~ in(X0,relation_dom(sK18)) )
| ~ spl22_4
| ~ spl22_11 ),
inference(forward_subsumption_resolution,[],[f735,f281]) ).
fof(f743,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(X0,apply(sK18,X0)),singleton(X0)),sK19)
| ~ function(sK19)
| ~ in(X0,relation_dom(sK18)) )
| ~ spl22_4
| ~ spl22_9
| ~ spl22_11 ),
inference(forward_subsumption_resolution,[],[f736,f281]) ).
fof(f749,plain,
( ! [X0,X1] :
( apply(sK18,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK19)
| ~ in(X0,relation_dom(sK18)) )
| ~ spl22_4
| ~ spl22_6
| ~ spl22_11 ),
inference(forward_subsumption_resolution,[],[f742,f291]) ).
fof(f750,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(X0,apply(sK18,X0)),singleton(X0)),sK19)
| ~ in(X0,relation_dom(sK18)) )
| ~ spl22_4
| ~ spl22_6
| ~ spl22_9
| ~ spl22_11 ),
inference(forward_subsumption_resolution,[],[f743,f291]) ).
fof(f756,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK19)
| apply(sK18,X0) = X1
| ~ in(X0,relation_dom(sK18)) )
| ~ spl22_4
| ~ spl22_6
| ~ spl22_11 ),
inference(forward_demodulation,[],[f749,f122]) ).
fof(f757,plain,
( ! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK18,X0))),sK19)
| ~ in(X0,relation_dom(sK18)) )
| ~ spl22_4
| ~ spl22_6
| ~ spl22_9
| ~ spl22_11 ),
inference(forward_demodulation,[],[f750,f122]) ).
fof(f759,plain,
( spl22_17
| ~ spl22_5
| ~ spl22_8 ),
inference(avatar_split_clause,[],[f687,f382,f284,f698]) ).
fof(f761,definition,
( spl22_18
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK19)
| apply(sK18,X0) = X1
| ~ in(X0,relation_dom(sK18)) ) ),
introduced(definition,[new_symbols(definition,[spl22_18])],[avatar_definition]) ).
fof(f762,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK19)
| apply(sK18,X0) = X1
| ~ in(X0,relation_dom(sK18)) )
| ~ spl22_18 ),
inference(avatar_component_clause,[],[f761]) ).
fof(f763,plain,
( spl22_18
| ~ spl22_4
| ~ spl22_6
| ~ spl22_11 ),
inference(avatar_split_clause,[],[f756,f543,f289,f279,f761]) ).
fof(f782,plain,
( ! [X0] : relation_dom(relation_dom_restriction(sK19,X0)) = set_intersection2(X0,relation_dom(sK19))
| ~ spl22_15 ),
inference(superposition,[],[f123,f691]) ).
fof(f795,definition,
( spl22_19
<=> ! [X0] :
( in(X0,relation_dom(sK18))
| ~ in(X0,sK17)
| ~ in(X0,relation_dom(sK19)) ) ),
introduced(definition,[new_symbols(definition,[spl22_19])],[avatar_definition]) ).
fof(f796,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK19))
| ~ in(X0,sK17)
| in(X0,relation_dom(sK18)) )
| ~ spl22_19 ),
inference(avatar_component_clause,[],[f795]) ).
fof(f797,plain,
( spl22_19
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f721,f243,f795]) ).
fof(f949,definition,
( spl22_21
<=> ! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK18,X0))),sK19)
| ~ in(X0,relation_dom(sK18)) ) ),
introduced(definition,[new_symbols(definition,[spl22_21])],[avatar_definition]) ).
fof(f950,plain,
( ! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK18,X0))),sK19)
| ~ in(X0,relation_dom(sK18)) )
| ~ spl22_21 ),
inference(avatar_component_clause,[],[f949]) ).
fof(f951,plain,
( spl22_21
| ~ spl22_4
| ~ spl22_6
| ~ spl22_9
| ~ spl22_11 ),
inference(avatar_split_clause,[],[f757,f543,f440,f289,f279,f949]) ).
fof(f982,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK19)
| ~ in(X1,relation_dom(sK18))
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK18)
| ~ in(X1,relation_dom(sK18))
| ~ relation(sK18)
| ~ function(sK18) )
| ~ spl22_21 ),
inference(superposition,[],[f950,f211]) ).
fof(f983,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK19)
| ~ in(X1,relation_dom(sK18))
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK18)
| ~ relation(sK18)
| ~ function(sK18) )
| ~ spl22_21 ),
inference(duplicate_literal_removal,[],[f982]) ).
fof(f985,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK19)
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK18)
| ~ relation(sK18)
| ~ function(sK18) )
| ~ spl22_21 ),
inference(forward_subsumption_resolution,[],[f983,f227]) ).
fof(f987,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK19)
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK18)
| ~ function(sK18) )
| ~ spl22_5
| ~ spl22_21 ),
inference(forward_subsumption_resolution,[],[f985,f286]) ).
fof(f989,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK19)
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK18) )
| ~ spl22_5
| ~ spl22_7
| ~ spl22_21 ),
inference(forward_subsumption_resolution,[],[f987,f365]) ).
fof(f991,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK18)
| in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK19) )
| ~ spl22_5
| ~ spl22_7
| ~ spl22_21 ),
inference(forward_demodulation,[],[f989,f122]) ).
fof(f1083,definition,
( spl22_28
<=> ! [X0] :
( in(unordered_pair(singleton(sK0(sK19,sK17,X0)),unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0))),X0)
| in(unordered_pair(singleton(sK0(sK19,sK17,X0)),unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0))),sK19)
| sK18 != X0
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[spl22_28])],[avatar_definition]) ).
fof(f1084,plain,
( ! [X0] :
( sK18 != X0
| in(unordered_pair(singleton(sK0(sK19,sK17,X0)),unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0))),sK19)
| in(unordered_pair(singleton(sK0(sK19,sK17,X0)),unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0))),X0)
| ~ relation(X0) )
| ~ spl22_28 ),
inference(avatar_component_clause,[],[f1083]) ).
fof(f1085,plain,
( spl22_28
| spl22_1
| ~ spl22_4 ),
inference(avatar_split_clause,[],[f711,f279,f235,f1083]) ).
fof(f1086,plain,
( in(unordered_pair(singleton(sK0(sK19,sK17,sK18)),unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18))),sK19)
| in(unordered_pair(singleton(sK0(sK19,sK17,sK18)),unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18))),sK18)
| ~ relation(sK18)
| ~ spl22_28 ),
inference(equality_resolution,[],[f1084]) ).
fof(f1090,definition,
( spl22_29
<=> in(unordered_pair(singleton(sK0(sK19,sK17,sK18)),unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18))),sK19) ),
introduced(definition,[new_symbols(definition,[spl22_29])],[avatar_definition]) ).
fof(f1092,plain,
( in(unordered_pair(singleton(sK0(sK19,sK17,sK18)),unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18))),sK19)
| ~ spl22_29 ),
inference(avatar_component_clause,[],[f1090]) ).
fof(f1094,plain,
( in(unordered_pair(singleton(sK0(sK19,sK17,sK18)),unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18))),sK19)
| ~ relation(sK18)
| ~ spl22_5
| ~ spl22_7
| ~ spl22_21
| ~ spl22_28 ),
inference(forward_subsumption_resolution,[],[f1086,f991]) ).
fof(f1095,plain,
( in(unordered_pair(singleton(sK0(sK19,sK17,sK18)),unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18))),sK19)
| ~ spl22_5
| ~ spl22_7
| ~ spl22_21
| ~ spl22_28 ),
inference(forward_subsumption_resolution,[],[f1094,f286]) ).
fof(f1096,plain,
( spl22_29
| ~ spl22_5
| ~ spl22_7
| ~ spl22_21
| ~ spl22_28 ),
inference(avatar_split_clause,[],[f1095,f1083,f949,f363,f284,f1090]) ).
fof(f1098,plain,
( sK1(sK19,sK17,sK18) = apply(sK18,sK0(sK19,sK17,sK18))
| ~ in(sK0(sK19,sK17,sK18),relation_dom(sK18))
| ~ spl22_18
| ~ spl22_29 ),
inference(resolution,[],[f1092,f762]) ).
fof(f1117,plain,
( spl22_14
| ~ spl22_5
| ~ spl22_7
| ~ spl22_21 ),
inference(avatar_split_clause,[],[f991,f949,f363,f284,f637]) ).
fof(f1129,definition,
( spl22_30
<=> in(sK0(sK19,sK17,sK18),sK17) ),
introduced(definition,[new_symbols(definition,[spl22_30])],[avatar_definition]) ).
fof(f1130,plain,
( in(sK0(sK19,sK17,sK18),sK17)
| ~ spl22_30 ),
inference(avatar_component_clause,[],[f1129]) ).
fof(f1131,plain,
( ~ in(sK0(sK19,sK17,sK18),sK17)
| spl22_30 ),
inference(avatar_component_clause,[],[f1129]) ).
fof(f1133,definition,
( spl22_31
<=> in(unordered_pair(singleton(sK0(sK19,sK17,sK18)),unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18))),sK18) ),
introduced(definition,[new_symbols(definition,[spl22_31])],[avatar_definition]) ).
fof(f1134,plain,
( ~ in(unordered_pair(singleton(sK0(sK19,sK17,sK18)),unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18))),sK18)
| spl22_31 ),
inference(avatar_component_clause,[],[f1133]) ).
fof(f1135,plain,
( in(unordered_pair(singleton(sK0(sK19,sK17,sK18)),unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18))),sK18)
| ~ spl22_31 ),
inference(avatar_component_clause,[],[f1133]) ).
fof(f1137,plain,
( sK18 = relation_dom_restriction(sK19,sK17)
| in(unordered_pair(unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18)),singleton(sK0(sK19,sK17,sK18))),sK18)
| ~ relation(sK18)
| ~ relation(sK19)
| spl22_30 ),
inference(resolution,[],[f1131,f206]) ).
fof(f1143,plain,
( in(unordered_pair(unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18)),singleton(sK0(sK19,sK17,sK18))),sK18)
| ~ relation(sK18)
| ~ relation(sK19)
| spl22_1
| spl22_30 ),
inference(forward_subsumption_resolution,[],[f1137,f237]) ).
fof(f1145,plain,
( in(unordered_pair(unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18)),singleton(sK0(sK19,sK17,sK18))),sK18)
| ~ relation(sK19)
| spl22_1
| ~ spl22_5
| spl22_30 ),
inference(forward_subsumption_resolution,[],[f1143,f286]) ).
fof(f1146,plain,
( in(unordered_pair(unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18)),singleton(sK0(sK19,sK17,sK18))),sK18)
| spl22_1
| ~ spl22_4
| ~ spl22_5
| spl22_30 ),
inference(forward_subsumption_resolution,[],[f1145,f281]) ).
fof(f1147,plain,
( in(unordered_pair(singleton(sK0(sK19,sK17,sK18)),unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18))),sK18)
| spl22_1
| ~ spl22_4
| ~ spl22_5
| spl22_30 ),
inference(forward_demodulation,[],[f1146,f122]) ).
fof(f1148,plain,
( spl22_31
| spl22_1
| ~ spl22_4
| ~ spl22_5
| spl22_30 ),
inference(avatar_split_clause,[],[f1147,f1129,f284,f279,f235,f1133]) ).
fof(f1252,definition,
( spl22_37
<=> ! [X0] :
( ~ in(unordered_pair(singleton(sK0(sK19,sK17,X0)),unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0))),X0)
| ~ in(unordered_pair(singleton(sK0(sK19,sK17,X0)),unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0))),sK19)
| sK18 != X0
| ~ in(sK0(sK19,sK17,X0),sK17)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[spl22_37])],[avatar_definition]) ).
fof(f1253,plain,
( ! [X0] :
( sK18 != X0
| ~ in(unordered_pair(singleton(sK0(sK19,sK17,X0)),unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0))),sK19)
| ~ in(unordered_pair(singleton(sK0(sK19,sK17,X0)),unordered_pair(sK0(sK19,sK17,X0),sK1(sK19,sK17,X0))),X0)
| ~ in(sK0(sK19,sK17,X0),sK17)
| ~ relation(X0) )
| ~ spl22_37 ),
inference(avatar_component_clause,[],[f1252]) ).
fof(f1254,plain,
( spl22_37
| spl22_1
| ~ spl22_4 ),
inference(avatar_split_clause,[],[f710,f279,f235,f1252]) ).
fof(f1255,plain,
( ~ in(unordered_pair(singleton(sK0(sK19,sK17,sK18)),unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18))),sK19)
| ~ in(unordered_pair(singleton(sK0(sK19,sK17,sK18)),unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18))),sK18)
| ~ in(sK0(sK19,sK17,sK18),sK17)
| ~ relation(sK18)
| ~ spl22_37 ),
inference(equality_resolution,[],[f1253]) ).
fof(f1256,plain,
( ~ in(unordered_pair(singleton(sK0(sK19,sK17,sK18)),unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18))),sK18)
| ~ in(sK0(sK19,sK17,sK18),sK17)
| ~ relation(sK18)
| ~ spl22_14
| ~ spl22_37 ),
inference(forward_subsumption_resolution,[],[f1255,f638]) ).
fof(f1257,plain,
( ~ in(unordered_pair(singleton(sK0(sK19,sK17,sK18)),unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18))),sK18)
| ~ relation(sK18)
| ~ spl22_14
| ~ spl22_17
| ~ spl22_37 ),
inference(forward_subsumption_resolution,[],[f1256,f699]) ).
fof(f1259,definition,
( spl22_38
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK19)
| in(X0,relation_dom(sK19)) ) ),
introduced(definition,[new_symbols(definition,[spl22_38])],[avatar_definition]) ).
fof(f1260,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK19)
| in(X0,relation_dom(sK19)) )
| ~ spl22_38 ),
inference(avatar_component_clause,[],[f1259]) ).
fof(f1261,plain,
( spl22_38
| ~ spl22_4 ),
inference(avatar_split_clause,[],[f335,f279,f1259]) ).
fof(f1265,plain,
( in(sK0(sK19,sK17,sK18),relation_dom(sK19))
| ~ spl22_29
| ~ spl22_38 ),
inference(resolution,[],[f1260,f1092]) ).
fof(f1276,definition,
( spl22_39
<=> in(sK0(sK19,sK17,sK18),relation_dom(sK19)) ),
introduced(definition,[new_symbols(definition,[spl22_39])],[avatar_definition]) ).
fof(f1278,plain,
( in(sK0(sK19,sK17,sK18),relation_dom(sK19))
| ~ spl22_39 ),
inference(avatar_component_clause,[],[f1276]) ).
fof(f1279,plain,
( spl22_39
| ~ spl22_29
| ~ spl22_38 ),
inference(avatar_split_clause,[],[f1265,f1259,f1090,f1276]) ).
fof(f1280,plain,
( ~ in(sK0(sK19,sK17,sK18),sK17)
| in(sK0(sK19,sK17,sK18),relation_dom(sK18))
| ~ spl22_19
| ~ spl22_39 ),
inference(resolution,[],[f1278,f796]) ).
fof(f1303,plain,
( in(sK0(sK19,sK17,sK18),relation_dom(sK18))
| ~ spl22_19
| ~ spl22_30
| ~ spl22_39 ),
inference(forward_subsumption_resolution,[],[f1280,f1130]) ).
fof(f1310,plain,
( sK1(sK19,sK17,sK18) = apply(sK18,sK0(sK19,sK17,sK18))
| ~ spl22_18
| ~ spl22_19
| ~ spl22_29
| ~ spl22_30
| ~ spl22_39 ),
inference(backward_subsumption_resolution,[],[f1098,f1303]) ).
fof(f1342,definition,
( spl22_41
<=> sK1(sK19,sK17,sK18) = apply(sK18,sK0(sK19,sK17,sK18)) ),
introduced(definition,[new_symbols(definition,[spl22_41])],[avatar_definition]) ).
fof(f1344,plain,
( sK1(sK19,sK17,sK18) = apply(sK18,sK0(sK19,sK17,sK18))
| ~ spl22_41 ),
inference(avatar_component_clause,[],[f1342]) ).
fof(f1345,plain,
( spl22_41
| ~ spl22_18
| ~ spl22_19
| ~ spl22_29
| ~ spl22_30
| ~ spl22_39 ),
inference(avatar_split_clause,[],[f1310,f1276,f1129,f1090,f795,f761,f1342]) ).
fof(f1355,plain,
( in(unordered_pair(unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18)),singleton(sK0(sK19,sK17,sK18))),sK18)
| ~ in(sK0(sK19,sK17,sK18),relation_dom(sK18))
| ~ relation(sK18)
| ~ function(sK18)
| ~ spl22_41 ),
inference(superposition,[],[f224,f1344]) ).
fof(f1358,plain,
( in(unordered_pair(unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18)),singleton(sK0(sK19,sK17,sK18))),sK18)
| ~ relation(sK18)
| ~ function(sK18)
| ~ spl22_19
| ~ spl22_30
| ~ spl22_39
| ~ spl22_41 ),
inference(forward_subsumption_resolution,[],[f1355,f1303]) ).
fof(f1362,plain,
( in(unordered_pair(unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18)),singleton(sK0(sK19,sK17,sK18))),sK18)
| ~ function(sK18)
| ~ spl22_5
| ~ spl22_19
| ~ spl22_30
| ~ spl22_39
| ~ spl22_41 ),
inference(forward_subsumption_resolution,[],[f1358,f286]) ).
fof(f1367,plain,
( in(unordered_pair(unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18)),singleton(sK0(sK19,sK17,sK18))),sK18)
| ~ spl22_5
| ~ spl22_7
| ~ spl22_19
| ~ spl22_30
| ~ spl22_39
| ~ spl22_41 ),
inference(forward_subsumption_resolution,[],[f1362,f365]) ).
fof(f1370,plain,
( in(unordered_pair(singleton(sK0(sK19,sK17,sK18)),unordered_pair(sK0(sK19,sK17,sK18),sK1(sK19,sK17,sK18))),sK18)
| ~ spl22_5
| ~ spl22_7
| ~ spl22_19
| ~ spl22_30
| ~ spl22_39
| ~ spl22_41 ),
inference(forward_demodulation,[],[f1367,f122]) ).
fof(f1372,plain,
( $false
| ~ spl22_5
| ~ spl22_7
| ~ spl22_19
| ~ spl22_30
| spl22_31
| ~ spl22_39
| ~ spl22_41 ),
inference(forward_subsumption_resolution,[],[f1370,f1134]) ).
fof(f1373,plain,
( ~ spl22_5
| ~ spl22_7
| ~ spl22_19
| ~ spl22_30
| spl22_31
| ~ spl22_39
| ~ spl22_41 ),
inference(avatar_contradiction_clause,[],[f1372]) ).
fof(f1374,plain,
( ~ relation(sK18)
| ~ spl22_14
| ~ spl22_17
| ~ spl22_31
| ~ spl22_37 ),
inference(forward_subsumption_resolution,[],[f1257,f1135]) ).
fof(f1378,plain,
( $false
| ~ spl22_5
| ~ spl22_14
| ~ spl22_17
| ~ spl22_31
| ~ spl22_37 ),
inference(forward_subsumption_resolution,[],[f1374,f286]) ).
fof(f1379,plain,
( ~ spl22_5
| ~ spl22_14
| ~ spl22_17
| ~ spl22_31
| ~ spl22_37 ),
inference(avatar_contradiction_clause,[],[f1378]) ).
fof(f1387,plain,
( in(unordered_pair(unordered_pair(sK20,sK5(sK18,sK20)),singleton(sK20)),sK18)
| ~ relation(sK18)
| ~ spl22_2 ),
inference(resolution,[],[f241,f228]) ).
fof(f1410,plain,
( in(unordered_pair(unordered_pair(sK20,sK5(sK18,sK20)),singleton(sK20)),sK18)
| ~ spl22_2
| ~ spl22_5 ),
inference(forward_subsumption_resolution,[],[f1387,f286]) ).
fof(f1416,plain,
( in(unordered_pair(singleton(sK20),unordered_pair(sK20,sK5(sK18,sK20))),sK18)
| ~ spl22_2
| ~ spl22_5 ),
inference(forward_demodulation,[],[f1410,f122]) ).
fof(f1505,definition,
( spl22_42
<=> in(unordered_pair(singleton(sK20),unordered_pair(sK20,sK5(sK18,sK20))),sK18) ),
introduced(definition,[new_symbols(definition,[spl22_42])],[avatar_definition]) ).
fof(f1507,plain,
( in(unordered_pair(singleton(sK20),unordered_pair(sK20,sK5(sK18,sK20))),sK18)
| ~ spl22_42 ),
inference(avatar_component_clause,[],[f1505]) ).
fof(f1508,plain,
( spl22_42
| ~ spl22_2
| ~ spl22_5 ),
inference(avatar_split_clause,[],[f1416,f284,f239,f1505]) ).
fof(f1511,plain,
( in(unordered_pair(singleton(sK20),unordered_pair(sK20,sK5(sK18,sK20))),sK19)
| ~ spl22_14
| ~ spl22_42 ),
inference(resolution,[],[f1507,f638]) ).
fof(f1513,plain,
( apply(sK18,sK20) = sK5(sK18,sK20)
| ~ spl22_12
| ~ spl22_42 ),
inference(resolution,[],[f1507,f614]) ).
fof(f1525,plain,
( in(unordered_pair(singleton(sK20),unordered_pair(sK20,apply(sK18,sK20))),sK19)
| ~ spl22_12
| ~ spl22_14
| ~ spl22_42 ),
inference(forward_demodulation,[],[f1511,f1513]) ).
fof(f1571,definition,
( spl22_46
<=> apply(sK18,sK20) = apply(sK19,sK20) ),
introduced(definition,[new_symbols(definition,[spl22_46])],[avatar_definition]) ).
fof(f1572,plain,
( apply(sK18,sK20) = apply(sK19,sK20)
| ~ spl22_46 ),
inference(avatar_component_clause,[],[f1571]) ).
fof(f1573,plain,
( apply(sK18,sK20) != apply(sK19,sK20)
| spl22_46 ),
inference(avatar_component_clause,[],[f1571]) ).
fof(f1579,plain,
( ! [X0] :
( apply(sK18,sK20) != X0
| ~ in(unordered_pair(unordered_pair(sK20,X0),singleton(sK20)),sK19)
| ~ in(sK20,relation_dom(sK19))
| ~ relation(sK19)
| ~ function(sK19) )
| spl22_46 ),
inference(superposition,[],[f1573,f211]) ).
fof(f1581,plain,
( ! [X0] :
( apply(sK18,sK20) != X0
| ~ in(unordered_pair(unordered_pair(sK20,X0),singleton(sK20)),sK19)
| ~ relation(sK19)
| ~ function(sK19) )
| spl22_46 ),
inference(forward_subsumption_resolution,[],[f1579,f227]) ).
fof(f1584,plain,
( ! [X0] :
( apply(sK18,sK20) != X0
| ~ in(unordered_pair(unordered_pair(sK20,X0),singleton(sK20)),sK19)
| ~ function(sK19) )
| ~ spl22_4
| spl22_46 ),
inference(forward_subsumption_resolution,[],[f1581,f281]) ).
fof(f1585,plain,
( ! [X0] :
( apply(sK18,sK20) != X0
| ~ in(unordered_pair(unordered_pair(sK20,X0),singleton(sK20)),sK19) )
| ~ spl22_4
| ~ spl22_6
| spl22_46 ),
inference(forward_subsumption_resolution,[],[f1584,f291]) ).
fof(f1586,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK20),unordered_pair(sK20,X0)),sK19)
| apply(sK18,sK20) != X0 )
| ~ spl22_4
| ~ spl22_6
| spl22_46 ),
inference(forward_demodulation,[],[f1585,f122]) ).
fof(f1592,definition,
( spl22_47
<=> ! [X0] :
( ~ in(unordered_pair(singleton(sK20),unordered_pair(sK20,X0)),sK19)
| apply(sK18,sK20) != X0 ) ),
introduced(definition,[new_symbols(definition,[spl22_47])],[avatar_definition]) ).
fof(f1593,plain,
( ! [X0] :
( apply(sK18,sK20) != X0
| ~ in(unordered_pair(singleton(sK20),unordered_pair(sK20,X0)),sK19) )
| ~ spl22_47 ),
inference(avatar_component_clause,[],[f1592]) ).
fof(f1594,plain,
( spl22_47
| ~ spl22_4
| ~ spl22_6
| spl22_46 ),
inference(avatar_split_clause,[],[f1586,f1571,f289,f279,f1592]) ).
fof(f1632,definition,
( spl22_49
<=> in(unordered_pair(singleton(sK20),unordered_pair(sK20,apply(sK18,sK20))),sK19) ),
introduced(definition,[new_symbols(definition,[spl22_49])],[avatar_definition]) ).
fof(f1634,plain,
( in(unordered_pair(singleton(sK20),unordered_pair(sK20,apply(sK18,sK20))),sK19)
| ~ spl22_49 ),
inference(avatar_component_clause,[],[f1632]) ).
fof(f1635,plain,
( spl22_49
| ~ spl22_12
| ~ spl22_14
| ~ spl22_42 ),
inference(avatar_split_clause,[],[f1525,f1505,f637,f613,f1632]) ).
fof(f1764,plain,
( ~ in(unordered_pair(singleton(sK20),unordered_pair(sK20,apply(sK18,sK20))),sK19)
| ~ spl22_47 ),
inference(equality_resolution,[],[f1593]) ).
fof(f1765,plain,
( $false
| ~ spl22_47
| ~ spl22_49 ),
inference(forward_subsumption_resolution,[],[f1764,f1634]) ).
fof(f1766,plain,
( ~ spl22_47
| ~ spl22_49 ),
inference(avatar_contradiction_clause,[],[f1765]) ).
fof(f1771,plain,
( relation_dom(sK18) != relation_dom(relation_dom_restriction(sK19,sK17))
| spl22_3
| ~ spl22_15 ),
inference(forward_demodulation,[],[f245,f782]) ).
fof(f1772,plain,
( relation_dom(sK18) != set_intersection2(sK17,relation_dom(sK19))
| sK18 != relation_dom_restriction(sK19,sK17)
| ~ spl22_46 ),
inference(forward_subsumption_resolution,[],[f233,f1572]) ).
fof(f1773,plain,
( relation_dom(sK18) != relation_dom(sK18)
| ~ spl22_1
| spl22_3
| ~ spl22_15 ),
inference(forward_demodulation,[],[f1771,f236]) ).
fof(f1774,plain,
( $false
| ~ spl22_1
| spl22_3
| ~ spl22_15 ),
inference(trivial_inequality_removal,[],[f1773]) ).
fof(f1775,plain,
( ~ spl22_1
| spl22_3
| ~ spl22_15 ),
inference(avatar_contradiction_clause,[],[f1774]) ).
fof(f1776,plain,
( relation_dom(sK18) != set_intersection2(sK17,relation_dom(sK19))
| ~ spl22_1
| ~ spl22_46 ),
inference(forward_subsumption_resolution,[],[f1772,f236]) ).
fof(f1777,plain,
( relation_dom(sK18) != relation_dom(relation_dom_restriction(sK19,sK17))
| ~ spl22_1
| ~ spl22_15
| ~ spl22_46 ),
inference(forward_demodulation,[],[f1776,f782]) ).
fof(f1778,plain,
( relation_dom(sK18) != relation_dom(sK18)
| ~ spl22_1
| ~ spl22_15
| ~ spl22_46 ),
inference(forward_demodulation,[],[f1777,f236]) ).
fof(f1779,plain,
( $false
| ~ spl22_1
| ~ spl22_15
| ~ spl22_46 ),
inference(trivial_inequality_removal,[],[f1778]) ).
fof(f1780,plain,
( ~ spl22_1
| ~ spl22_15
| ~ spl22_46 ),
inference(avatar_contradiction_clause,[],[f1779]) ).
cnf(s1,plain,
( ~ spl22_1
| spl22_2
| ~ spl22_3 ),
inference(sat_conversion,[],[f246]) ).
cnf(s2,plain,
( spl22_1
| spl22_3 ),
inference(sat_conversion,[],[f261]) ).
cnf(s3,plain,
spl22_4,
inference(sat_conversion,[],[f282]) ).
cnf(s4,plain,
spl22_5,
inference(sat_conversion,[],[f287]) ).
cnf(s5,plain,
spl22_6,
inference(sat_conversion,[],[f292]) ).
cnf(s6,plain,
spl22_7,
inference(sat_conversion,[],[f366]) ).
cnf(s7,plain,
( ~ spl22_3
| spl22_8 ),
inference(sat_conversion,[],[f384]) ).
cnf(s8,plain,
( ~ spl22_3
| spl22_9 ),
inference(sat_conversion,[],[f442]) ).
cnf(s10,plain,
( spl22_1
| spl22_11 ),
inference(sat_conversion,[],[f545]) ).
cnf(s11,plain,
( ~ spl22_5
| ~ spl22_7
| spl22_12 ),
inference(sat_conversion,[],[f615]) ).
cnf(s13,plain,
( ~ spl22_1
| ~ spl22_4
| ~ spl22_5
| spl22_14 ),
inference(sat_conversion,[],[f639]) ).
cnf(s14,plain,
( ~ spl22_4
| spl22_15 ),
inference(sat_conversion,[],[f692]) ).
cnf(s17,plain,
( ~ spl22_5
| ~ spl22_8
| spl22_17 ),
inference(sat_conversion,[],[f759]) ).
cnf(s18,plain,
( ~ spl22_4
| ~ spl22_6
| ~ spl22_11
| spl22_18 ),
inference(sat_conversion,[],[f763]) ).
cnf(s19,plain,
( ~ spl22_3
| spl22_19 ),
inference(sat_conversion,[],[f797]) ).
cnf(s21,plain,
( ~ spl22_4
| ~ spl22_6
| ~ spl22_9
| ~ spl22_11
| spl22_21 ),
inference(sat_conversion,[],[f951]) ).
cnf(s28,plain,
( spl22_1
| ~ spl22_4
| spl22_28 ),
inference(sat_conversion,[],[f1085]) ).
cnf(s30,plain,
( ~ spl22_5
| ~ spl22_7
| ~ spl22_21
| ~ spl22_28
| spl22_29 ),
inference(sat_conversion,[],[f1096]) ).
cnf(s31,plain,
( ~ spl22_5
| ~ spl22_7
| spl22_14
| ~ spl22_21 ),
inference(sat_conversion,[],[f1117]) ).
cnf(s33,plain,
( spl22_1
| ~ spl22_4
| ~ spl22_5
| spl22_30
| spl22_31 ),
inference(sat_conversion,[],[f1148]) ).
cnf(s40,plain,
( spl22_1
| ~ spl22_4
| spl22_37 ),
inference(sat_conversion,[],[f1254]) ).
cnf(s41,plain,
( ~ spl22_4
| spl22_38 ),
inference(sat_conversion,[],[f1261]) ).
cnf(s42,plain,
( ~ spl22_29
| ~ spl22_38
| spl22_39 ),
inference(sat_conversion,[],[f1279]) ).
cnf(s44,plain,
( ~ spl22_18
| ~ spl22_19
| ~ spl22_29
| ~ spl22_30
| ~ spl22_39
| spl22_41 ),
inference(sat_conversion,[],[f1345]) ).
cnf(s46,plain,
( ~ spl22_5
| ~ spl22_7
| ~ spl22_19
| ~ spl22_30
| spl22_31
| ~ spl22_39
| ~ spl22_41 ),
inference(sat_conversion,[],[f1373]) ).
cnf(s47,plain,
( ~ spl22_5
| ~ spl22_14
| ~ spl22_17
| ~ spl22_31
| ~ spl22_37 ),
inference(sat_conversion,[],[f1379]) ).
cnf(s49,plain,
( ~ spl22_2
| ~ spl22_5
| spl22_42 ),
inference(sat_conversion,[],[f1508]) ).
cnf(s55,plain,
( ~ spl22_4
| ~ spl22_6
| spl22_46
| spl22_47 ),
inference(sat_conversion,[],[f1594]) ).
cnf(s57,plain,
( ~ spl22_12
| ~ spl22_14
| ~ spl22_42
| spl22_49 ),
inference(sat_conversion,[],[f1635]) ).
cnf(s60,plain,
( ~ spl22_47
| ~ spl22_49 ),
inference(sat_conversion,[],[f1766]) ).
cnf(s61,plain,
( ~ spl22_1
| spl22_3
| ~ spl22_15 ),
inference(sat_conversion,[],[f1775]) ).
cnf(s62,plain,
( ~ spl22_1
| ~ spl22_15
| ~ spl22_46 ),
inference(sat_conversion,[],[f1780]) ).
cnf(s68,plain,
spl22_12,
inference(rat,[],[s11,s6,s4]) ).
cnf(s71,plain,
spl22_38,
inference(rat,[],[s41,s3]) ).
cnf(s75,plain,
spl22_15,
inference(rat,[],[s14,s3]) ).
cnf(s78,plain,
spl22_1,
inference(rat,[],[s44,s46,s33,s47,s42,s31,s30,s17,s21,s7,s8,s19,s18,s2,s10,s28,s40,s6,s4,s3,s71,s5]) ).
cnf(s79,plain,
~ spl22_46,
inference(rat,[],[s62,s75,s78]) ).
cnf(s80,plain,
spl22_3,
inference(rat,[],[s61,s75,s78]) ).
cnf(s82,plain,
spl22_14,
inference(rat,[],[s13,s3,s4,s78]) ).
cnf(s84,plain,
spl22_47,
inference(rat,[],[s55,s3,s5,s79]) ).
cnf(s88,plain,
spl22_2,
inference(rat,[],[s1,s78,s80]) ).
cnf(s89,plain,
~ spl22_49,
inference(rat,[],[s60,s84]) ).
cnf(s94,plain,
spl22_42,
inference(rat,[],[s49,s4,s88]) ).
cnf(s97,plain,
$false,
inference(rat,[],[s57,s82,s68,s89,s94]) ).
fof(f1781,plain,
$false,
inference(avatar_sat_refutation,[],[s97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU222+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n016.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 04:13:33 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.68/2.11 % (3249146)Detected formulas, will run a generic FOF schedule.
% 8.68/2.11 % (3249155)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1062836798:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.68/2.11 % (3249155)Instruction limit reached!
% 8.68/2.11 % (3249155)------------------------------
% 8.68/2.11 % (3249155)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.11 % (3249155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.11 % (3249155)CaDiCaL version: 2.1.3
% 8.68/2.11 % (3249155)Termination reason: Instruction limit
% 8.68/2.11 % (3249155)Termination phase: Saturation
% 8.68/2.11 % (3249155)Time elapsed: 0.039 s
% 8.68/2.11 % (3249155)Peak memory usage: 88 MB
% 8.68/2.11 % (3249155)Instructions burned: 122 (million)
% 8.68/2.11 % (3249151)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3766779810:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.68/2.11 % (3249153)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2956124389:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.68/2.11 % (3249154)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1224219120:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.68/2.11 % (3249152)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3233319003:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.68/2.11 % (3249154)Refutation not found, incomplete strategy
% 8.68/2.11 % (3249154)------------------------------
% 8.68/2.11 % (3249154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.11 % (3249154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.11 % (3249154)CaDiCaL version: 2.1.3
% 8.68/2.11 % (3249154)Termination reason: Refutation not found, incomplete strategy
% 8.68/2.11 % (3249154)Time elapsed: 0.008 s
% 8.68/2.11 % (3249154)Peak memory usage: 88 MB
% 8.68/2.11 % (3249154)Instructions burned: 11 (million)
% 8.68/2.11 % (3249157)dis-21_1_sil=8000:lcm=predicate:random_seed=1679600335:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 8.68/2.11 % (3249156)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=964319013:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.68/2.11 % (3249157)Instruction limit reached!
% 8.68/2.11 % (3249157)------------------------------
% 8.68/2.11 % (3249157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.11 % (3249157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.11 % (3249157)CaDiCaL version: 2.1.3
% 8.68/2.11 % (3249157)Termination reason: Instruction limit
% 8.68/2.11 % (3249157)Termination phase: Saturation
% 8.68/2.11 % (3249157)Time elapsed: 0.080 s
% 8.68/2.11 % (3249157)Peak memory usage: 90 MB
% 8.68/2.11 % (3249157)Instructions burned: 130 (million)
% 8.68/2.11 % (3249156)Instruction limit reached!
% 8.68/2.11 % (3249156)------------------------------
% 8.68/2.11 % (3249156)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.11 % (3249156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.11 % (3249156)CaDiCaL version: 2.1.3
% 8.68/2.11 % (3249156)Termination reason: Instruction limit
% 8.68/2.11 % (3249156)Termination phase: Saturation
% 8.68/2.11 % (3249156)Time elapsed: 0.094 s
% 8.68/2.11 % (3249156)Peak memory usage: 90 MB
% 8.68/2.11 % (3249156)Instructions burned: 139 (million)
% 8.68/2.11 % (3249163)lrs+10_1_sil=8000:sp=occurrence:random_seed=910588337:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 8.68/2.11 % (3249163)Instruction limit reached!
% 8.68/2.11 % (3249163)------------------------------
% 8.68/2.11 % (3249163)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.11 % (3249163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.11 % (3249163)CaDiCaL version: 2.1.3
% 8.68/2.11 % (3249163)Termination reason: Instruction limit
% 8.68/2.11 % (3249163)Termination phase: Saturation
% 8.68/2.11 % (3249163)Time elapsed: 0.096 s
% 8.68/2.11 % (3249163)Peak memory usage: 91 MB
% 8.68/2.11 % (3249163)Instructions burned: 288 (million)
% 8.68/2.11 % (3249154)------------------------------
% 8.68/2.11 % (3249154)------------------------------
% 8.68/2.11 % (3249166)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4225124994:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.68/2.11 % (3249167)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1492417259:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.68/2.11 % (3249169)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1042748039:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 8.68/2.11 % (3249166)Instruction limit reached!
% 8.68/2.11 % (3249166)------------------------------
% 8.68/2.11 % (3249166)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.11 % (3249166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.11 % (3249166)CaDiCaL version: 2.1.3
% 8.68/2.11 % (3249166)Termination reason: Instruction limit
% 8.68/2.11 % (3249166)Termination phase: Saturation
% 8.68/2.11 % (3249166)Time elapsed: 0.087 s
% 8.68/2.11 % (3249166)Peak memory usage: 90 MB
% 8.68/2.11 % (3249166)Instructions burned: 158 (million)
% 8.68/2.11 % (3249169)Instruction limit reached!
% 8.68/2.11 % (3249169)------------------------------
% 8.68/2.11 % (3249169)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.11 % (3249169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.11 % (3249169)CaDiCaL version: 2.1.3
% 8.68/2.11 % (3249169)Termination reason: Instruction limit
% 8.68/2.11 % (3249169)Termination phase: Saturation
% 8.68/2.11 % (3249169)Time elapsed: 0.078 s
% 8.68/2.11 % (3249169)Peak memory usage: 95 MB
% 8.68/2.11 % (3249169)Instructions burned: 249 (million)
% 8.68/2.11 % (3249171)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2274743016:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 8.68/2.11 % (3249167)Instruction limit reached!
% 8.68/2.11 % (3249167)------------------------------
% 8.68/2.11 % (3249167)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.11 % (3249167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.11 % (3249167)CaDiCaL version: 2.1.3
% 8.68/2.11 % (3249167)Termination reason: Instruction limit
% 8.68/2.11 % (3249167)Termination phase: Saturation
% 8.68/2.11 % (3249167)Time elapsed: 0.221 s
% 8.68/2.11 % (3249167)Peak memory usage: 92 MB
% 8.68/2.11 % (3249167)Instructions burned: 326 (million)
% 8.68/2.11 % (3249174)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=54582998:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 8.68/2.11 % (3249176)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3144192417:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 8.68/2.11 % (3249176)Instruction limit reached!
% 8.68/2.11 % (3249176)------------------------------
% 8.68/2.11 % (3249176)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.11 % (3249176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.11 % (3249176)CaDiCaL version: 2.1.3
% 8.68/2.11 % (3249176)Termination reason: Instruction limit
% 8.68/2.11 % (3249176)Termination phase: Saturation
% 8.68/2.11 % (3249176)Time elapsed: 0.043 s
% 8.68/2.11 % (3249176)Peak memory usage: 90 MB
% 8.68/2.11 % (3249176)Instructions burned: 115 (million)
% 8.68/2.11 % (3249171)Instruction limit reached!
% 8.68/2.11 % (3249171)------------------------------
% 8.68/2.11 % (3249171)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.11 % (3249171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.11 % (3249171)CaDiCaL version: 2.1.3
% 8.68/2.11 % (3249171)Termination reason: Instruction limit
% 8.68/2.11 % (3249171)Termination phase: Saturation
% 8.68/2.11 % (3249171)Time elapsed: 0.186 s
% 8.68/2.11 % (3249171)Peak memory usage: 90 MB
% 8.68/2.11 % (3249171)Instructions burned: 295 (million)
% 8.68/2.11 % (3249178)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3571789709:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 8.68/2.11 % (3249180)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=188268977:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 8.68/2.11 % (3249178)Instruction limit reached!
% 8.68/2.11 % (3249178)------------------------------
% 8.68/2.11 % (3249178)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.11 % (3249178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.11 % (3249178)CaDiCaL version: 2.1.3
% 8.68/2.11 % (3249178)Termination reason: Instruction limit
% 8.68/2.11 % (3249178)Termination phase: Saturation
% 8.68/2.11 % (3249178)Time elapsed: 0.067 s
% 8.68/2.11 % (3249178)Peak memory usage: 89 MB
% 8.68/2.11 % (3249178)Instructions burned: 127 (million)
% 8.68/2.11 % (3249180)Instruction limit reached!
% 8.68/2.11 % (3249180)------------------------------
% 8.68/2.11 % (3249180)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.11 % (3249180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.11 % (3249180)CaDiCaL version: 2.1.3
% 8.68/2.11 % (3249180)Termination reason: Instruction limit
% 8.68/2.11 % (3249180)Termination phase: Saturation
% 8.68/2.11 % (3249180)Time elapsed: 0.039 s
% 8.68/2.11 % (3249180)Peak memory usage: 89 MB
% 8.68/2.11 % (3249180)Instructions burned: 114 (million)
% 8.68/2.11 % (3249181)lrs+10_1_sil=8000:sp=occurrence:random_seed=1386466586:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 8.68/2.11 % (3249153)First to succeed.
% 8.68/2.11 % (3249153)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3249146"
% 8.68/2.11 % (3249185)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2573018553:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 8.68/2.11 % (3249184)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1931603049:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 8.68/2.11 % (3249153)Refutation found. Thanks to Tanya!
% 8.68/2.11 % SZS status Theorem for theBenchmark
% 8.68/2.11 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/2.31 % (3249153)------------------------------
% 0.15/2.31 % (3249153)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/2.31 % (3249153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/2.31 % (3249153)CaDiCaL version: 2.1.3
% 0.15/2.31 % (3249153)Termination reason: Refutation
% 0.15/2.31 % (3249153)Time elapsed: 0.811 s
% 0.15/2.31 % (3249153)Peak memory usage: 130 MB
% 0.15/2.31 % (3249153)Instructions burned: 1199 (million)
% 0.15/2.31 % (3249153)------------------------------
% 0.15/2.31 % (3249153)------------------------------
% 0.15/2.31 % (3249146)Success in time 1.249 s
% 0.15/2.31 % Vampire exiting
%------------------------------------------------------------------------------