%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU222+1 : TPTP v9.3.1. Released v3.3.0.
% 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 8.65s 2.11s
% Output : Refutation 9.45s
% 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(f53,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(f54,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)],[f53]) ).
fof(f59,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(f70,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(f71,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(f72,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,[],[f71]) ).
fof(f73,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(f92,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,[],[f54]) ).
fof(f93,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,[],[f92]) ).
fof(f98,plain,
! [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f99,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,[],[f70]) ).
fof(f100,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,[],[f99]) ).
fof(f101,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,[],[f100]) ).
fof(f102,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))],[f101]) ).
fof(f103,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(f104,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,[],[f103]) ).
fof(f105,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,[],[f104]) ).
fof(f106,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))],[f105]) ).
fof(f107,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,[],[f72]) ).
fof(f108,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,[],[f73]) ).
fof(f109,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,[],[f108]) ).
fof(f110,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))],[f109]) ).
fof(f122,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,[],[f93]) ).
fof(f123,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,[],[f122]) ).
fof(f124,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,[],[f123]) ).
fof(f125,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)],[f124]) ).
fof(f131,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f132,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f133,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,[],[f102]) ).
fof(f136,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,[],[f102]) ).
fof(f137,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,[],[f102]) ).
fof(f138,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,[],[f102]) ).
fof(f139,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f106]) ).
fof(f140,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f106]) ).
fof(f141,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f106]) ).
fof(f147,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,[],[f107]) ).
fof(f148,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,[],[f107]) ).
fof(f149,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK5(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f150,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f153,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f201,plain,
function(sK18),
inference(cnf_transformation,[],[f125]) ).
fof(f202,plain,
relation(sK18),
inference(cnf_transformation,[],[f125]) ).
fof(f203,plain,
function(sK19),
inference(cnf_transformation,[],[f125]) ).
fof(f204,plain,
relation(sK19),
inference(cnf_transformation,[],[f125]) ).
fof(f205,plain,
! [X4] :
( apply(sK18,X4) = apply(sK19,X4)
| ~ in(X4,relation_dom(sK18))
| sK18 = relation_dom_restriction(sK19,sK17) ),
inference(cnf_transformation,[],[f125]) ).
fof(f206,plain,
( relation_dom(sK18) = set_intersection2(relation_dom(sK19),sK17)
| sK18 = relation_dom_restriction(sK19,sK17) ),
inference(cnf_transformation,[],[f125]) ).
fof(f207,plain,
( relation_dom(sK18) != set_intersection2(relation_dom(sK19),sK17)
| in(sK20,relation_dom(sK18))
| sK18 != relation_dom_restriction(sK19,sK17) ),
inference(cnf_transformation,[],[f125]) ).
fof(f208,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,[],[f125]) ).
fof(f213,plain,
! [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f214,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,[],[f138,f153,f153]) ).
fof(f215,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,[],[f137,f153]) ).
fof(f216,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,[],[f136,f153,f153]) ).
fof(f219,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,[],[f133,f153,f153]) ).
fof(f220,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,[],[f148,f153]) ).
fof(f221,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,[],[f147,f153]) ).
fof(f224,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,[],[f150,f153]) ).
fof(f225,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,[],[f149,f153]) ).
fof(f229,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,[],[f219]) ).
fof(f230,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f141]) ).
fof(f231,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f140]) ).
fof(f232,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f139]) ).
fof(f233,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,[],[f221]) ).
fof(f236,plain,
! [X0,X6,X5] :
( in(X5,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f224]) ).
fof(f237,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,[],[f225]) ).
fof(f240,plain,
( relation_dom(sK18) = set_intersection2(sK17,relation_dom(sK19))
| sK18 = relation_dom_restriction(sK19,sK17) ),
inference(forward_demodulation,[],[f206,f132]) ).
fof(f241,plain,
( relation_dom(sK18) != set_intersection2(sK17,relation_dom(sK19))
| in(sK20,relation_dom(sK18))
| sK18 != relation_dom_restriction(sK19,sK17) ),
inference(forward_demodulation,[],[f207,f132]) ).
fof(f242,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,[],[f208,f132]) ).
fof(f244,definition,
( spl22_1
<=> sK18 = relation_dom_restriction(sK19,sK17) ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
fof(f245,plain,
( sK18 = relation_dom_restriction(sK19,sK17)
| ~ spl22_1 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f246,plain,
( sK18 != relation_dom_restriction(sK19,sK17)
| spl22_1 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f248,definition,
( spl22_2
<=> in(sK20,relation_dom(sK18)) ),
introduced(definition,[new_symbols(definition,[spl22_2])],[avatar_definition]) ).
fof(f250,plain,
( in(sK20,relation_dom(sK18))
| ~ spl22_2 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f252,definition,
( spl22_3
<=> relation_dom(sK18) = set_intersection2(sK17,relation_dom(sK19)) ),
introduced(definition,[new_symbols(definition,[spl22_3])],[avatar_definition]) ).
fof(f253,plain,
( relation_dom(sK18) = set_intersection2(sK17,relation_dom(sK19))
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f254,plain,
( relation_dom(sK18) != set_intersection2(sK17,relation_dom(sK19))
| spl22_3 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f255,plain,
( ~ spl22_1
| spl22_2
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f241,f252,f248,f244]) ).
fof(f256,plain,
( relation_dom(sK18) = set_intersection2(sK17,relation_dom(sK19))
| spl22_1 ),
inference(backward_subsumption_resolution,[],[f240,f246]) ).
fof(f270,plain,
( spl22_3
| spl22_1 ),
inference(avatar_split_clause,[],[f256,f244,f252]) ).
fof(f281,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK18))
| in(X0,sK17) )
| ~ spl22_3 ),
inference(superposition,[],[f231,f253]) ).
fof(f282,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK18))
| in(X0,relation_dom(sK19)) )
| ~ spl22_3 ),
inference(superposition,[],[f232,f253]) ).
fof(f288,definition,
( spl22_4
<=> relation(sK19) ),
introduced(definition,[new_symbols(definition,[spl22_4])],[avatar_definition]) ).
fof(f290,plain,
( relation(sK19)
| ~ spl22_4 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f291,plain,
spl22_4,
inference(avatar_split_clause,[],[f204,f288]) ).
fof(f293,definition,
( spl22_5
<=> relation(sK18) ),
introduced(definition,[new_symbols(definition,[spl22_5])],[avatar_definition]) ).
fof(f295,plain,
( relation(sK18)
| ~ spl22_5 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f296,plain,
spl22_5,
inference(avatar_split_clause,[],[f202,f293]) ).
fof(f298,definition,
( spl22_6
<=> function(sK19) ),
introduced(definition,[new_symbols(definition,[spl22_6])],[avatar_definition]) ).
fof(f300,plain,
( function(sK19)
| ~ spl22_6 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f301,plain,
spl22_6,
inference(avatar_split_clause,[],[f203,f298]) ).
fof(f325,plain,
( ! [X0] : relation_dom(relation_dom_restriction(sK19,X0)) = set_intersection2(relation_dom(sK19),X0)
| ~ spl22_4 ),
inference(resolution,[],[f290,f213]) ).
fof(f341,plain,
( ! [X0,X1] :
( in(X0,relation_dom(sK19))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK19) )
| ~ spl22_4 ),
inference(resolution,[],[f290,f236]) ).
fof(f344,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK19)
| in(X0,relation_dom(sK19)) )
| ~ spl22_4 ),
inference(forward_demodulation,[],[f341,f131]) ).
fof(f372,definition,
( spl22_7
<=> function(sK18) ),
introduced(definition,[new_symbols(definition,[spl22_7])],[avatar_definition]) ).
fof(f374,plain,
( function(sK18)
| ~ spl22_7 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f375,plain,
spl22_7,
inference(avatar_split_clause,[],[f201,f372]) ).
fof(f381,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,[],[f374,f220]) ).
fof(f382,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,[],[f381,f236]) ).
fof(f387,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,[],[f382,f295]) ).
fof(f389,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18)
| apply(sK18,X0) = X1 )
| ~ spl22_5
| ~ spl22_7 ),
inference(forward_demodulation,[],[f387,f131]) ).
fof(f391,definition,
( spl22_8
<=> ! [X0] :
( ~ in(X0,relation_dom(sK18))
| in(X0,sK17) ) ),
introduced(definition,[new_symbols(definition,[spl22_8])],[avatar_definition]) ).
fof(f392,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK18))
| in(X0,sK17) )
| ~ spl22_8 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f393,plain,
( spl22_8
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f281,f252,f391]) ).
fof(f449,definition,
( spl22_9
<=> ! [X0] :
( ~ in(X0,relation_dom(sK18))
| in(X0,relation_dom(sK19)) ) ),
introduced(definition,[new_symbols(definition,[spl22_9])],[avatar_definition]) ).
fof(f450,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK18))
| in(X0,relation_dom(sK19)) )
| ~ spl22_9 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f451,plain,
( spl22_9
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f282,f252,f449]) ).
fof(f523,plain,
( ! [X4] :
( apply(sK18,X4) = apply(sK19,X4)
| ~ in(X4,relation_dom(sK18)) )
| spl22_1 ),
inference(forward_subsumption_resolution,[],[f205,f246]) ).
fof(f552,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(f553,plain,
( ! [X4] :
( apply(sK18,X4) = apply(sK19,X4)
| ~ in(X4,relation_dom(sK18)) )
| ~ spl22_11 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f554,plain,
( spl22_11
| spl22_1 ),
inference(avatar_split_clause,[],[f523,f244,f552]) ).
fof(f573,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,[],[f229,f245]) ).
fof(f574,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,[],[f573,f295]) ).
fof(f586,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,[],[f574,f290]) ).
fof(f598,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,[],[f586,f131]) ).
fof(f608,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,[],[f598,f131]) ).
fof(f622,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(f623,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18)
| apply(sK18,X0) = X1 )
| ~ spl22_12 ),
inference(avatar_component_clause,[],[f622]) ).
fof(f624,plain,
( spl22_12
| ~ spl22_5
| ~ spl22_7 ),
inference(avatar_split_clause,[],[f389,f372,f293,f622]) ).
fof(f646,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(f647,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,[],[f646]) ).
fof(f648,plain,
( spl22_14
| ~ spl22_1
| ~ spl22_4
| ~ spl22_5 ),
inference(avatar_split_clause,[],[f608,f293,f288,f244,f646]) ).
fof(f649,plain,
( ! [X0,X1] :
( in(X0,sK17)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK18)
| ~ relation(sK18) )
| ~ spl22_8 ),
inference(resolution,[],[f392,f236]) ).
fof(f687,plain,
( ! [X0,X1] :
( in(X0,sK17)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK18) )
| ~ spl22_5
| ~ spl22_8 ),
inference(forward_subsumption_resolution,[],[f649,f295]) ).
fof(f696,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18)
| in(X0,sK17) )
| ~ spl22_5
| ~ spl22_8 ),
inference(forward_demodulation,[],[f687,f131]) ).
fof(f699,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(f700,plain,
( ! [X0] : relation_dom(relation_dom_restriction(sK19,X0)) = set_intersection2(relation_dom(sK19),X0)
| ~ spl22_15 ),
inference(avatar_component_clause,[],[f699]) ).
fof(f701,plain,
( spl22_15
| ~ spl22_4 ),
inference(avatar_split_clause,[],[f325,f288,f699]) ).
fof(f707,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(f708,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18)
| in(X0,sK17) )
| ~ spl22_17 ),
inference(avatar_component_clause,[],[f707]) ).
fof(f710,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,[],[f246,f216]) ).
fof(f712,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,[],[f246,f214]) ).
fof(f713,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,[],[f712,f290]) ).
fof(f715,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,[],[f710,f290]) ).
fof(f716,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,[],[f713,f131]) ).
fof(f718,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,[],[f715,f131]) ).
fof(f719,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,[],[f716,f131]) ).
fof(f720,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,[],[f718,f131]) ).
fof(f730,plain,
( ! [X0] :
( in(X0,relation_dom(sK18))
| ~ in(X0,sK17)
| ~ in(X0,relation_dom(sK19)) )
| ~ spl22_3 ),
inference(superposition,[],[f230,f253]) ).
fof(f742,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,[],[f233,f553]) ).
fof(f743,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,[],[f220,f553]) ).
fof(f744,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,[],[f743,f236]) ).
fof(f745,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,[],[f742,f450]) ).
fof(f751,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,[],[f744,f290]) ).
fof(f752,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,[],[f745,f290]) ).
fof(f758,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,[],[f751,f300]) ).
fof(f759,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,[],[f752,f300]) ).
fof(f765,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,[],[f758,f131]) ).
fof(f766,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,[],[f759,f131]) ).
fof(f768,plain,
( spl22_17
| ~ spl22_5
| ~ spl22_8 ),
inference(avatar_split_clause,[],[f696,f391,f293,f707]) ).
fof(f770,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(f771,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,[],[f770]) ).
fof(f772,plain,
( spl22_18
| ~ spl22_4
| ~ spl22_6
| ~ spl22_11 ),
inference(avatar_split_clause,[],[f765,f552,f298,f288,f770]) ).
fof(f791,plain,
( ! [X0] : relation_dom(relation_dom_restriction(sK19,X0)) = set_intersection2(X0,relation_dom(sK19))
| ~ spl22_15 ),
inference(superposition,[],[f132,f700]) ).
fof(f804,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(f805,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK19))
| ~ in(X0,sK17)
| in(X0,relation_dom(sK18)) )
| ~ spl22_19 ),
inference(avatar_component_clause,[],[f804]) ).
fof(f806,plain,
( spl22_19
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f730,f252,f804]) ).
fof(f958,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(f959,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,[],[f958]) ).
fof(f960,plain,
( spl22_21
| ~ spl22_4
| ~ spl22_6
| ~ spl22_9
| ~ spl22_11 ),
inference(avatar_split_clause,[],[f766,f552,f449,f298,f288,f958]) ).
fof(f991,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,[],[f959,f220]) ).
fof(f992,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,[],[f991]) ).
fof(f994,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,[],[f992,f236]) ).
fof(f996,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,[],[f994,f295]) ).
fof(f998,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,[],[f996,f374]) ).
fof(f1000,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,[],[f998,f131]) ).
fof(f1092,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(f1093,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,[],[f1092]) ).
fof(f1094,plain,
( spl22_28
| spl22_1
| ~ spl22_4 ),
inference(avatar_split_clause,[],[f720,f288,f244,f1092]) ).
fof(f1095,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,[],[f1093]) ).
fof(f1099,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(f1101,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,[],[f1099]) ).
fof(f1103,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,[],[f1095,f1000]) ).
fof(f1104,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,[],[f1103,f295]) ).
fof(f1105,plain,
( spl22_29
| ~ spl22_5
| ~ spl22_7
| ~ spl22_21
| ~ spl22_28 ),
inference(avatar_split_clause,[],[f1104,f1092,f958,f372,f293,f1099]) ).
fof(f1107,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,[],[f1101,f771]) ).
fof(f1126,plain,
( spl22_14
| ~ spl22_5
| ~ spl22_7
| ~ spl22_21 ),
inference(avatar_split_clause,[],[f1000,f958,f372,f293,f646]) ).
fof(f1138,definition,
( spl22_30
<=> in(sK0(sK19,sK17,sK18),sK17) ),
introduced(definition,[new_symbols(definition,[spl22_30])],[avatar_definition]) ).
fof(f1139,plain,
( in(sK0(sK19,sK17,sK18),sK17)
| ~ spl22_30 ),
inference(avatar_component_clause,[],[f1138]) ).
fof(f1140,plain,
( ~ in(sK0(sK19,sK17,sK18),sK17)
| spl22_30 ),
inference(avatar_component_clause,[],[f1138]) ).
fof(f1142,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(f1143,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,[],[f1142]) ).
fof(f1144,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,[],[f1142]) ).
fof(f1146,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,[],[f1140,f215]) ).
fof(f1152,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,[],[f1146,f246]) ).
fof(f1154,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,[],[f1152,f295]) ).
fof(f1155,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,[],[f1154,f290]) ).
fof(f1156,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,[],[f1155,f131]) ).
fof(f1157,plain,
( spl22_31
| spl22_1
| ~ spl22_4
| ~ spl22_5
| spl22_30 ),
inference(avatar_split_clause,[],[f1156,f1138,f293,f288,f244,f1142]) ).
fof(f1261,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(f1262,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,[],[f1261]) ).
fof(f1263,plain,
( spl22_37
| spl22_1
| ~ spl22_4 ),
inference(avatar_split_clause,[],[f719,f288,f244,f1261]) ).
fof(f1264,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,[],[f1262]) ).
fof(f1265,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,[],[f1264,f647]) ).
fof(f1266,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,[],[f1265,f708]) ).
fof(f1268,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(f1269,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK19)
| in(X0,relation_dom(sK19)) )
| ~ spl22_38 ),
inference(avatar_component_clause,[],[f1268]) ).
fof(f1270,plain,
( spl22_38
| ~ spl22_4 ),
inference(avatar_split_clause,[],[f344,f288,f1268]) ).
fof(f1274,plain,
( in(sK0(sK19,sK17,sK18),relation_dom(sK19))
| ~ spl22_29
| ~ spl22_38 ),
inference(resolution,[],[f1269,f1101]) ).
fof(f1285,definition,
( spl22_39
<=> in(sK0(sK19,sK17,sK18),relation_dom(sK19)) ),
introduced(definition,[new_symbols(definition,[spl22_39])],[avatar_definition]) ).
fof(f1287,plain,
( in(sK0(sK19,sK17,sK18),relation_dom(sK19))
| ~ spl22_39 ),
inference(avatar_component_clause,[],[f1285]) ).
fof(f1288,plain,
( spl22_39
| ~ spl22_29
| ~ spl22_38 ),
inference(avatar_split_clause,[],[f1274,f1268,f1099,f1285]) ).
fof(f1289,plain,
( ~ in(sK0(sK19,sK17,sK18),sK17)
| in(sK0(sK19,sK17,sK18),relation_dom(sK18))
| ~ spl22_19
| ~ spl22_39 ),
inference(resolution,[],[f1287,f805]) ).
fof(f1312,plain,
( in(sK0(sK19,sK17,sK18),relation_dom(sK18))
| ~ spl22_19
| ~ spl22_30
| ~ spl22_39 ),
inference(forward_subsumption_resolution,[],[f1289,f1139]) ).
fof(f1319,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,[],[f1107,f1312]) ).
fof(f1351,definition,
( spl22_41
<=> sK1(sK19,sK17,sK18) = apply(sK18,sK0(sK19,sK17,sK18)) ),
introduced(definition,[new_symbols(definition,[spl22_41])],[avatar_definition]) ).
fof(f1353,plain,
( sK1(sK19,sK17,sK18) = apply(sK18,sK0(sK19,sK17,sK18))
| ~ spl22_41 ),
inference(avatar_component_clause,[],[f1351]) ).
fof(f1354,plain,
( spl22_41
| ~ spl22_18
| ~ spl22_19
| ~ spl22_29
| ~ spl22_30
| ~ spl22_39 ),
inference(avatar_split_clause,[],[f1319,f1285,f1138,f1099,f804,f770,f1351]) ).
fof(f1364,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,[],[f233,f1353]) ).
fof(f1367,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,[],[f1364,f1312]) ).
fof(f1371,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,[],[f1367,f295]) ).
fof(f1376,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,[],[f1371,f374]) ).
fof(f1379,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,[],[f1376,f131]) ).
fof(f1381,plain,
( $false
| ~ spl22_5
| ~ spl22_7
| ~ spl22_19
| ~ spl22_30
| spl22_31
| ~ spl22_39
| ~ spl22_41 ),
inference(forward_subsumption_resolution,[],[f1379,f1143]) ).
fof(f1382,plain,
( ~ spl22_5
| ~ spl22_7
| ~ spl22_19
| ~ spl22_30
| spl22_31
| ~ spl22_39
| ~ spl22_41 ),
inference(avatar_contradiction_clause,[],[f1381]) ).
fof(f1383,plain,
( ~ relation(sK18)
| ~ spl22_14
| ~ spl22_17
| ~ spl22_31
| ~ spl22_37 ),
inference(forward_subsumption_resolution,[],[f1266,f1144]) ).
fof(f1387,plain,
( $false
| ~ spl22_5
| ~ spl22_14
| ~ spl22_17
| ~ spl22_31
| ~ spl22_37 ),
inference(forward_subsumption_resolution,[],[f1383,f295]) ).
fof(f1388,plain,
( ~ spl22_5
| ~ spl22_14
| ~ spl22_17
| ~ spl22_31
| ~ spl22_37 ),
inference(avatar_contradiction_clause,[],[f1387]) ).
fof(f1396,plain,
( in(unordered_pair(unordered_pair(sK20,sK5(sK18,sK20)),singleton(sK20)),sK18)
| ~ relation(sK18)
| ~ spl22_2 ),
inference(resolution,[],[f250,f237]) ).
fof(f1419,plain,
( in(unordered_pair(unordered_pair(sK20,sK5(sK18,sK20)),singleton(sK20)),sK18)
| ~ spl22_2
| ~ spl22_5 ),
inference(forward_subsumption_resolution,[],[f1396,f295]) ).
fof(f1425,plain,
( in(unordered_pair(singleton(sK20),unordered_pair(sK20,sK5(sK18,sK20))),sK18)
| ~ spl22_2
| ~ spl22_5 ),
inference(forward_demodulation,[],[f1419,f131]) ).
fof(f1514,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(f1516,plain,
( in(unordered_pair(singleton(sK20),unordered_pair(sK20,sK5(sK18,sK20))),sK18)
| ~ spl22_42 ),
inference(avatar_component_clause,[],[f1514]) ).
fof(f1517,plain,
( spl22_42
| ~ spl22_2
| ~ spl22_5 ),
inference(avatar_split_clause,[],[f1425,f293,f248,f1514]) ).
fof(f1520,plain,
( in(unordered_pair(singleton(sK20),unordered_pair(sK20,sK5(sK18,sK20))),sK19)
| ~ spl22_14
| ~ spl22_42 ),
inference(resolution,[],[f1516,f647]) ).
fof(f1522,plain,
( apply(sK18,sK20) = sK5(sK18,sK20)
| ~ spl22_12
| ~ spl22_42 ),
inference(resolution,[],[f1516,f623]) ).
fof(f1534,plain,
( in(unordered_pair(singleton(sK20),unordered_pair(sK20,apply(sK18,sK20))),sK19)
| ~ spl22_12
| ~ spl22_14
| ~ spl22_42 ),
inference(forward_demodulation,[],[f1520,f1522]) ).
fof(f1580,definition,
( spl22_46
<=> apply(sK18,sK20) = apply(sK19,sK20) ),
introduced(definition,[new_symbols(definition,[spl22_46])],[avatar_definition]) ).
fof(f1581,plain,
( apply(sK18,sK20) = apply(sK19,sK20)
| ~ spl22_46 ),
inference(avatar_component_clause,[],[f1580]) ).
fof(f1582,plain,
( apply(sK18,sK20) != apply(sK19,sK20)
| spl22_46 ),
inference(avatar_component_clause,[],[f1580]) ).
fof(f1588,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,[],[f1582,f220]) ).
fof(f1590,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,[],[f1588,f236]) ).
fof(f1593,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,[],[f1590,f290]) ).
fof(f1594,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,[],[f1593,f300]) ).
fof(f1595,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,[],[f1594,f131]) ).
fof(f1601,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(f1602,plain,
( ! [X0] :
( apply(sK18,sK20) != X0
| ~ in(unordered_pair(singleton(sK20),unordered_pair(sK20,X0)),sK19) )
| ~ spl22_47 ),
inference(avatar_component_clause,[],[f1601]) ).
fof(f1603,plain,
( spl22_47
| ~ spl22_4
| ~ spl22_6
| spl22_46 ),
inference(avatar_split_clause,[],[f1595,f1580,f298,f288,f1601]) ).
fof(f1641,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(f1643,plain,
( in(unordered_pair(singleton(sK20),unordered_pair(sK20,apply(sK18,sK20))),sK19)
| ~ spl22_49 ),
inference(avatar_component_clause,[],[f1641]) ).
fof(f1644,plain,
( spl22_49
| ~ spl22_12
| ~ spl22_14
| ~ spl22_42 ),
inference(avatar_split_clause,[],[f1534,f1514,f646,f622,f1641]) ).
fof(f1773,plain,
( ~ in(unordered_pair(singleton(sK20),unordered_pair(sK20,apply(sK18,sK20))),sK19)
| ~ spl22_47 ),
inference(equality_resolution,[],[f1602]) ).
fof(f1774,plain,
( $false
| ~ spl22_47
| ~ spl22_49 ),
inference(forward_subsumption_resolution,[],[f1773,f1643]) ).
fof(f1775,plain,
( ~ spl22_47
| ~ spl22_49 ),
inference(avatar_contradiction_clause,[],[f1774]) ).
fof(f1780,plain,
( relation_dom(sK18) != relation_dom(relation_dom_restriction(sK19,sK17))
| spl22_3
| ~ spl22_15 ),
inference(forward_demodulation,[],[f254,f791]) ).
fof(f1781,plain,
( relation_dom(sK18) != set_intersection2(sK17,relation_dom(sK19))
| sK18 != relation_dom_restriction(sK19,sK17)
| ~ spl22_46 ),
inference(forward_subsumption_resolution,[],[f242,f1581]) ).
fof(f1782,plain,
( relation_dom(sK18) != relation_dom(sK18)
| ~ spl22_1
| spl22_3
| ~ spl22_15 ),
inference(forward_demodulation,[],[f1780,f245]) ).
fof(f1783,plain,
( $false
| ~ spl22_1
| spl22_3
| ~ spl22_15 ),
inference(trivial_inequality_removal,[],[f1782]) ).
fof(f1784,plain,
( ~ spl22_1
| spl22_3
| ~ spl22_15 ),
inference(avatar_contradiction_clause,[],[f1783]) ).
fof(f1785,plain,
( relation_dom(sK18) != set_intersection2(sK17,relation_dom(sK19))
| ~ spl22_1
| ~ spl22_46 ),
inference(forward_subsumption_resolution,[],[f1781,f245]) ).
fof(f1786,plain,
( relation_dom(sK18) != relation_dom(relation_dom_restriction(sK19,sK17))
| ~ spl22_1
| ~ spl22_15
| ~ spl22_46 ),
inference(forward_demodulation,[],[f1785,f791]) ).
fof(f1787,plain,
( relation_dom(sK18) != relation_dom(sK18)
| ~ spl22_1
| ~ spl22_15
| ~ spl22_46 ),
inference(forward_demodulation,[],[f1786,f245]) ).
fof(f1788,plain,
( $false
| ~ spl22_1
| ~ spl22_15
| ~ spl22_46 ),
inference(trivial_inequality_removal,[],[f1787]) ).
fof(f1789,plain,
( ~ spl22_1
| ~ spl22_15
| ~ spl22_46 ),
inference(avatar_contradiction_clause,[],[f1788]) ).
cnf(s1,plain,
( ~ spl22_1
| spl22_2
| ~ spl22_3 ),
inference(sat_conversion,[],[f255]) ).
cnf(s2,plain,
( spl22_1
| spl22_3 ),
inference(sat_conversion,[],[f270]) ).
cnf(s3,plain,
spl22_4,
inference(sat_conversion,[],[f291]) ).
cnf(s4,plain,
spl22_5,
inference(sat_conversion,[],[f296]) ).
cnf(s5,plain,
spl22_6,
inference(sat_conversion,[],[f301]) ).
cnf(s6,plain,
spl22_7,
inference(sat_conversion,[],[f375]) ).
cnf(s7,plain,
( ~ spl22_3
| spl22_8 ),
inference(sat_conversion,[],[f393]) ).
cnf(s8,plain,
( ~ spl22_3
| spl22_9 ),
inference(sat_conversion,[],[f451]) ).
cnf(s10,plain,
( spl22_1
| spl22_11 ),
inference(sat_conversion,[],[f554]) ).
cnf(s11,plain,
( ~ spl22_5
| ~ spl22_7
| spl22_12 ),
inference(sat_conversion,[],[f624]) ).
cnf(s13,plain,
( ~ spl22_1
| ~ spl22_4
| ~ spl22_5
| spl22_14 ),
inference(sat_conversion,[],[f648]) ).
cnf(s14,plain,
( ~ spl22_4
| spl22_15 ),
inference(sat_conversion,[],[f701]) ).
cnf(s17,plain,
( ~ spl22_5
| ~ spl22_8
| spl22_17 ),
inference(sat_conversion,[],[f768]) ).
cnf(s18,plain,
( ~ spl22_4
| ~ spl22_6
| ~ spl22_11
| spl22_18 ),
inference(sat_conversion,[],[f772]) ).
cnf(s19,plain,
( ~ spl22_3
| spl22_19 ),
inference(sat_conversion,[],[f806]) ).
cnf(s21,plain,
( ~ spl22_4
| ~ spl22_6
| ~ spl22_9
| ~ spl22_11
| spl22_21 ),
inference(sat_conversion,[],[f960]) ).
cnf(s28,plain,
( spl22_1
| ~ spl22_4
| spl22_28 ),
inference(sat_conversion,[],[f1094]) ).
cnf(s30,plain,
( ~ spl22_5
| ~ spl22_7
| ~ spl22_21
| ~ spl22_28
| spl22_29 ),
inference(sat_conversion,[],[f1105]) ).
cnf(s31,plain,
( ~ spl22_5
| ~ spl22_7
| spl22_14
| ~ spl22_21 ),
inference(sat_conversion,[],[f1126]) ).
cnf(s33,plain,
( spl22_1
| ~ spl22_4
| ~ spl22_5
| spl22_30
| spl22_31 ),
inference(sat_conversion,[],[f1157]) ).
cnf(s40,plain,
( spl22_1
| ~ spl22_4
| spl22_37 ),
inference(sat_conversion,[],[f1263]) ).
cnf(s41,plain,
( ~ spl22_4
| spl22_38 ),
inference(sat_conversion,[],[f1270]) ).
cnf(s42,plain,
( ~ spl22_29
| ~ spl22_38
| spl22_39 ),
inference(sat_conversion,[],[f1288]) ).
cnf(s44,plain,
( ~ spl22_18
| ~ spl22_19
| ~ spl22_29
| ~ spl22_30
| ~ spl22_39
| spl22_41 ),
inference(sat_conversion,[],[f1354]) ).
cnf(s46,plain,
( ~ spl22_5
| ~ spl22_7
| ~ spl22_19
| ~ spl22_30
| spl22_31
| ~ spl22_39
| ~ spl22_41 ),
inference(sat_conversion,[],[f1382]) ).
cnf(s47,plain,
( ~ spl22_5
| ~ spl22_14
| ~ spl22_17
| ~ spl22_31
| ~ spl22_37 ),
inference(sat_conversion,[],[f1388]) ).
cnf(s49,plain,
( ~ spl22_2
| ~ spl22_5
| spl22_42 ),
inference(sat_conversion,[],[f1517]) ).
cnf(s55,plain,
( ~ spl22_4
| ~ spl22_6
| spl22_46
| spl22_47 ),
inference(sat_conversion,[],[f1603]) ).
cnf(s57,plain,
( ~ spl22_12
| ~ spl22_14
| ~ spl22_42
| spl22_49 ),
inference(sat_conversion,[],[f1644]) ).
cnf(s60,plain,
( ~ spl22_47
| ~ spl22_49 ),
inference(sat_conversion,[],[f1775]) ).
cnf(s61,plain,
( ~ spl22_1
| spl22_3
| ~ spl22_15 ),
inference(sat_conversion,[],[f1784]) ).
cnf(s62,plain,
( ~ spl22_1
| ~ spl22_15
| ~ spl22_46 ),
inference(sat_conversion,[],[f1789]) ).
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(f1790,plain,
$false,
inference(avatar_sat_refutation,[],[s97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU222+1 : TPTP v9.3.1. Released v3.3.0.
% 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 04:13:48 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 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
% 8.65/2.11 % (3249584)Detected formulas, will run a generic FOF schedule.
% 8.65/2.11 % (3249590)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=476026281:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.65/2.11 % (3249589)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=481212126:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.65/2.11 % (3249592)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2589032586:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.65/2.11 % (3249593)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=632559648:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.65/2.11 % (3249591)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=1478127774:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.65/2.11 % (3249595)dis-21_1_sil=8000:lcm=predicate:random_seed=1715734683: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)
% 8.65/2.11 % (3249594)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1457437232:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.65/2.11 % (3249592)Refutation not found, incomplete strategy
% 8.65/2.11 % (3249592)------------------------------
% 8.65/2.11 % (3249592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.11 % (3249592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.11 % (3249592)CaDiCaL version: 2.1.3
% 8.65/2.11 % (3249592)Termination reason: Refutation not found, incomplete strategy
% 8.65/2.11 % (3249592)Time elapsed: 0.008 s
% 8.65/2.11 % (3249592)Peak memory usage: 89 MB
% 8.65/2.11 % (3249592)Instructions burned: 11 (million)
% 8.65/2.11 % (3249593)Instruction limit reached!
% 8.65/2.11 % (3249593)------------------------------
% 8.65/2.11 % (3249593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.11 % (3249593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.11 % (3249593)CaDiCaL version: 2.1.3
% 8.65/2.11 % (3249593)Termination reason: Instruction limit
% 8.65/2.11 % (3249593)Termination phase: Saturation
% 8.65/2.11 % (3249593)Time elapsed: 0.070 s
% 8.65/2.11 % (3249593)Peak memory usage: 88 MB
% 8.65/2.11 % (3249593)Instructions burned: 120 (million)
% 8.65/2.11 % (3249595)Instruction limit reached!
% 8.65/2.11 % (3249595)------------------------------
% 8.65/2.11 % (3249595)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.11 % (3249595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.11 % (3249595)CaDiCaL version: 2.1.3
% 8.65/2.11 % (3249595)Termination reason: Instruction limit
% 8.65/2.11 % (3249595)Termination phase: Saturation
% 8.65/2.11 % (3249595)Time elapsed: 0.080 s
% 8.65/2.11 % (3249595)Peak memory usage: 90 MB
% 8.65/2.11 % (3249595)Instructions burned: 130 (million)
% 8.65/2.11 % (3249594)Instruction limit reached!
% 8.65/2.11 % (3249594)------------------------------
% 8.65/2.11 % (3249594)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.11 % (3249594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.11 % (3249594)CaDiCaL version: 2.1.3
% 8.65/2.11 % (3249594)Termination reason: Instruction limit
% 8.65/2.11 % (3249594)Termination phase: Saturation
% 8.65/2.11 % (3249594)Time elapsed: 0.094 s
% 8.65/2.11 % (3249594)Peak memory usage: 90 MB
% 8.65/2.11 % (3249594)Instructions burned: 140 (million)
% 8.65/2.11 % (3249603)lrs+10_1_sil=8000:sp=occurrence:random_seed=1937622097:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 8.65/2.11 % (3249604)lrs+10_1_sil=32000:urr=on:br=off:random_seed=334048166:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.65/2.11 % (3249592)------------------------------
% 8.65/2.11 % (3249592)------------------------------
% 8.65/2.11 % (3249605)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4049124432:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.65/2.11 % (3249604)Instruction limit reached!
% 8.65/2.11 % (3249604)------------------------------
% 8.65/2.11 % (3249604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.11 % (3249604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.11 % (3249604)CaDiCaL version: 2.1.3
% 8.65/2.11 % (3249604)Termination reason: Instruction limit
% 8.65/2.11 % (3249604)Termination phase: Saturation
% 8.65/2.11 % (3249604)Time elapsed: 0.086 s
% 8.65/2.11 % (3249604)Peak memory usage: 90 MB
% 8.65/2.11 % (3249604)Instructions burned: 159 (million)
% 8.65/2.11 % (3249603)Instruction limit reached!
% 8.65/2.11 % (3249603)------------------------------
% 8.65/2.11 % (3249603)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.11 % (3249603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.11 % (3249603)CaDiCaL version: 2.1.3
% 8.65/2.11 % (3249603)Termination reason: Instruction limit
% 8.65/2.11 % (3249603)Termination phase: Saturation
% 8.65/2.11 % (3249603)Time elapsed: 0.175 s
% 8.65/2.11 % (3249603)Peak memory usage: 91 MB
% 8.65/2.11 % (3249603)Instructions burned: 286 (million)
% 8.65/2.11 % (3249608)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=3012692408:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 8.65/2.11 % (3249610)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4077123695:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 8.65/2.11 % (3249605)Instruction limit reached!
% 8.65/2.11 % (3249605)------------------------------
% 8.65/2.11 % (3249605)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.11 % (3249605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.11 % (3249605)CaDiCaL version: 2.1.3
% 8.65/2.11 % (3249605)Termination reason: Instruction limit
% 8.65/2.11 % (3249605)Termination phase: Saturation
% 8.65/2.11 % (3249605)Time elapsed: 0.215 s
% 8.65/2.11 % (3249605)Peak memory usage: 92 MB
% 8.65/2.11 % (3249605)Instructions burned: 326 (million)
% 8.65/2.11 % (3249611)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3308880206:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 8.65/2.11 % (3249608)Instruction limit reached!
% 8.65/2.11 % (3249608)------------------------------
% 8.65/2.11 % (3249608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.11 % (3249608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.11 % (3249608)CaDiCaL version: 2.1.3
% 8.65/2.11 % (3249608)Termination reason: Instruction limit
% 8.65/2.11 % (3249608)Termination phase: Saturation
% 8.65/2.11 % (3249608)Time elapsed: 0.143 s
% 8.65/2.11 % (3249608)Peak memory usage: 95 MB
% 8.65/2.11 % (3249608)Instructions burned: 249 (million)
% 8.65/2.11 % (3249614)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=831543083:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 8.65/2.11 % (3249610)Instruction limit reached!
% 8.65/2.11 % (3249610)------------------------------
% 8.65/2.11 % (3249610)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.11 % (3249610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.11 % (3249610)CaDiCaL version: 2.1.3
% 8.65/2.11 % (3249610)Termination reason: Instruction limit
% 8.65/2.11 % (3249610)Termination phase: Saturation
% 8.65/2.11 % (3249610)Time elapsed: 0.182 s
% 8.65/2.11 % (3249610)Peak memory usage: 91 MB
% 8.65/2.11 % (3249610)Instructions burned: 295 (million)
% 8.65/2.11 % (3249614)Instruction limit reached!
% 8.65/2.11 % (3249614)------------------------------
% 8.65/2.11 % (3249614)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.11 % (3249614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.11 % (3249614)CaDiCaL version: 2.1.3
% 8.65/2.11 % (3249614)Termination reason: Instruction limit
% 8.65/2.11 % (3249614)Termination phase: Saturation
% 8.65/2.11 % (3249614)Time elapsed: 0.078 s
% 8.65/2.11 % (3249614)Peak memory usage: 90 MB
% 8.65/2.11 % (3249614)Instructions burned: 113 (million)
% 8.65/2.11 % (3249616)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3037045022:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 8.65/2.11 % (3249616)Instruction limit reached!
% 8.65/2.11 % (3249616)------------------------------
% 8.65/2.11 % (3249616)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.11 % (3249616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.11 % (3249616)CaDiCaL version: 2.1.3
% 8.65/2.11 % (3249616)Termination reason: Instruction limit
% 8.65/2.11 % (3249616)Termination phase: Saturation
% 8.65/2.11 % (3249616)Time elapsed: 0.066 s
% 8.65/2.11 % (3249616)Peak memory usage: 89 MB
% 8.65/2.11 % (3249616)Instructions burned: 127 (million)
% 8.65/2.11 % (3249591)First to succeed.
% 8.65/2.11 % (3249618)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2522374621:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 8.65/2.11 % (3249591)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3249584"
% 8.65/2.11 % (3249619)lrs+10_1_sil=8000:sp=occurrence:random_seed=1512370012:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 8.65/2.11 % (3249618)Instruction limit reached!
% 8.65/2.11 % (3249618)------------------------------
% 8.65/2.11 % (3249618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.11 % (3249618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.11 % (3249618)CaDiCaL version: 2.1.3
% 8.65/2.11 % (3249618)Termination reason: Instruction limit
% 8.65/2.11 % (3249618)Termination phase: Saturation
% 8.65/2.11 % (3249618)Time elapsed: 0.072 s
% 8.65/2.11 % (3249618)Peak memory usage: 90 MB
% 8.65/2.11 % (3249618)Instructions burned: 115 (million)
% 8.65/2.11 % (3249590)Also succeeded, but the first one will report.
% 8.65/2.11 % (3249621)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2925143900:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 8.65/2.11 % (3249624)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1308193620:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 8.65/2.11 % (3249591)Refutation found. Thanks to Tanya!
% 8.65/2.11 % SZS status Theorem for theBenchmark
% 8.65/2.11 % SZS output start Proof for theBenchmark
% See solution above
% 9.45/2.32 % (3249591)------------------------------
% 9.45/2.32 % (3249591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.32 % (3249591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.32 % (3249591)CaDiCaL version: 2.1.3
% 9.45/2.32 % (3249591)Termination reason: Refutation
% 9.45/2.32 % (3249591)Time elapsed: 0.807 s
% 9.45/2.32 % (3249591)Peak memory usage: 131 MB
% 9.45/2.32 % (3249591)Instructions burned: 1199 (million)
% 9.45/2.32 % (3249591)------------------------------
% 9.45/2.32 % (3249591)------------------------------
% 9.45/2.32 % (3249584)Success in time 1.243 s
% 9.45/2.32 % Vampire exiting
%------------------------------------------------------------------------------