%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET990+1 : 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 : n005.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 12:42:29 PM UTC 2026
% Result : Theorem 10.47s 2.37s
% Output : Refutation 11.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 23
% Syntax : Number of formulae : 369 ( 26 unt; 16 def)
% Number of atoms : 1461 ( 335 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1734 ( 642 ~; 983 |; 65 &)
% ( 28 <=>; 14 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 15 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 5 con; 0-2 aty)
% Number of variables : 430 ( 0 sgn 398 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( in(X1,X0)
& ! [X2,X3] : X1 != ordered_pair(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f6,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(f7,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(f8,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(f28,axiom,
! [X0,X1] :
( ( ! [X2] :
~ ( in(X2,X0)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
& ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
& ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_zfmisc_1) ).
fof(f37,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( relation_dom(X0) = relation_dom(X1)
& ! [X2] :
( in(X2,relation_dom(X0))
=> apply(X0,X2) = apply(X1,X2) ) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
fof(f38,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( relation_dom(X0) = relation_dom(X1)
& ! [X2] :
( in(X2,relation_dom(X0))
=> apply(X0,X2) = apply(X1,X2) ) )
=> X0 = X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f40,plain,
! [X0,X1] :
( ( ! [X2] :
~ ( in(X2,X0)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
& ! [X5] :
~ ( in(X5,X1)
& ! [X6,X7] : ordered_pair(X6,X7) != X5 )
& ! [X8,X9] :
( in(ordered_pair(X8,X9),X0)
<=> in(ordered_pair(X8,X9),X1) ) )
=> X0 = X1 ),
inference(rectify,[],[f28]) ).
fof(f47,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| ? [X2,X3] : ordered_pair(X2,X3) = X1 ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f49,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,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f55,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
| ? [X5] :
( in(X5,X1)
& ! [X6,X7] : ordered_pair(X6,X7) != X5 )
| ? [X8,X9] :
( in(ordered_pair(X8,X9),X0)
<~> in(ordered_pair(X8,X9),X1) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f56,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
| ? [X5] :
( in(X5,X1)
& ! [X6,X7] : ordered_pair(X6,X7) != X5 )
| ? [X8,X9] :
( in(ordered_pair(X8,X9),X0)
<~> in(ordered_pair(X8,X9),X1) ) ),
inference(flattening,[],[f55]) ).
fof(f67,plain,
? [X0] :
( ? [X1] :
( X0 != X1
& relation_dom(X0) = relation_dom(X1)
& ! [X2] :
( apply(X0,X2) = apply(X1,X2)
| ~ in(X2,relation_dom(X0)) )
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f68,plain,
? [X0] :
( ? [X1] :
( X0 != X1
& relation_dom(X0) = relation_dom(X1)
& ! [X2] :
( apply(X0,X2) = apply(X1,X2)
| ~ in(X2,relation_dom(X0)) )
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( in(X1,X0)
& ! [X2,X3] : ordered_pair(X2,X3) != X1 ) )
& ( ! [X1] :
( ~ in(X1,X0)
| ? [X2,X3] : ordered_pair(X2,X3) = X1 )
| ~ relation(X0) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f70,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( in(X1,X0)
& ! [X2,X3] : ordered_pair(X2,X3) != X1 ) )
& ( ! [X4] :
( ~ in(X4,X0)
| ? [X5,X6] : ordered_pair(X5,X6) = X4 )
| ~ relation(X0) ) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ( relation(X0)
| ( in(sK0(X0),X0)
& ! [X2,X3] : ordered_pair(X2,X3) != sK0(X0) ) )
& ( ! [X4] :
( ~ in(X4,X0)
| ordered_pair(sK1(X4),sK2(X4)) = X4 )
| ~ relation(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X1,sK0(X0)),skolemize(X5,sK1(X4)),skolemize(X6,sK2(X4))],[f70]) ).
fof(f72,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,[],[f49]) ).
fof(f73,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,[],[f50]) ).
fof(f74,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,[],[f73]) ).
fof(f75,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))],[f74]) ).
fof(f85,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
| ? [X5] :
( in(X5,X1)
& ! [X6,X7] : ordered_pair(X6,X7) != X5 )
| ? [X8,X9] :
( ( ~ in(ordered_pair(X8,X9),X1)
| ~ in(ordered_pair(X8,X9),X0) )
& ( in(ordered_pair(X8,X9),X1)
| in(ordered_pair(X8,X9),X0) ) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f86,plain,
! [X0,X1] :
( X0 = X1
| ( in(sK15(X0),X0)
& ! [X3,X4] : ordered_pair(X3,X4) != sK15(X0) )
| ( in(sK16(X1),X1)
& ! [X6,X7] : ordered_pair(X6,X7) != sK16(X1) )
| ( ( ~ in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X1)
| ~ in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X0) )
& ( in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X1)
| in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18]),skolemize(X2,sK15(X0)),skolemize(X5,sK16(X1)),skolemize(X8,sK17(X0,X1)),skolemize(X9,sK18(X0,X1))],[f85]) ).
fof(f87,plain,
( sK19 != sK20
& relation_dom(sK19) = relation_dom(sK20)
& ! [X2] :
( apply(sK19,X2) = apply(sK20,X2)
| ~ in(X2,relation_dom(sK19)) )
& relation(sK20)
& function(sK20)
& relation(sK19)
& function(sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20]),skolemize(X0,sK19),skolemize(X1,sK20)],[f68]) ).
fof(f91,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f92,plain,
! [X0,X4] :
( ~ in(X4,X0)
| ordered_pair(sK1(X4),sK2(X4)) = X4
| ~ relation(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f95,plain,
! [X2,X0,X1] :
( empty_set = X2
| apply(X0,X1) != X2
| in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f97,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,[],[f72]) ).
fof(f98,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,[],[f72]) ).
fof(f100,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f103,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f8]) ).
fof(f131,plain,
! [X3,X0,X1,X6,X7,X4] :
( X0 = X1
| ordered_pair(X3,X4) != sK15(X0)
| ordered_pair(X6,X7) != sK16(X1)
| in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X1)
| in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f132,plain,
! [X3,X0,X1,X6,X7,X4] :
( X0 = X1
| ordered_pair(X3,X4) != sK15(X0)
| ordered_pair(X6,X7) != sK16(X1)
| ~ in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X1)
| ~ in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f133,plain,
! [X3,X0,X1,X4] :
( X0 = X1
| ordered_pair(X3,X4) != sK15(X0)
| in(sK16(X1),X1)
| in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X1)
| in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f134,plain,
! [X3,X0,X1,X4] :
( X0 = X1
| ordered_pair(X3,X4) != sK15(X0)
| in(sK16(X1),X1)
| ~ in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X1)
| ~ in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f135,plain,
! [X0,X1,X6,X7] :
( X0 = X1
| in(sK15(X0),X0)
| ordered_pair(X6,X7) != sK16(X1)
| in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X1)
| in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f136,plain,
! [X0,X1,X6,X7] :
( X0 = X1
| in(sK15(X0),X0)
| ordered_pair(X6,X7) != sK16(X1)
| ~ in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X1)
| ~ in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f137,plain,
! [X0,X1] :
( X0 = X1
| in(sK15(X0),X0)
| in(sK16(X1),X1)
| in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X1)
| in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f138,plain,
! [X0,X1] :
( X0 = X1
| in(sK15(X0),X0)
| in(sK16(X1),X1)
| ~ in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X1)
| ~ in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f147,plain,
function(sK19),
inference(cnf_transformation,[],[f87]) ).
fof(f148,plain,
relation(sK19),
inference(cnf_transformation,[],[f87]) ).
fof(f149,plain,
function(sK20),
inference(cnf_transformation,[],[f87]) ).
fof(f150,plain,
relation(sK20),
inference(cnf_transformation,[],[f87]) ).
fof(f151,plain,
! [X2] :
( apply(sK19,X2) = apply(sK20,X2)
| ~ in(X2,relation_dom(sK19)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f152,plain,
relation_dom(sK19) = relation_dom(sK20),
inference(cnf_transformation,[],[f87]) ).
fof(f153,plain,
sK19 != sK20,
inference(cnf_transformation,[],[f87]) ).
fof(f155,plain,
! [X0,X4] :
( ~ in(X4,X0)
| unordered_pair(unordered_pair(sK1(X4),sK2(X4)),singleton(sK1(X4))) = X4
| ~ relation(X0) ),
inference(definition_unfolding,[],[f92,f103]) ).
fof(f156,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,[],[f98,f103]) ).
fof(f157,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,[],[f97,f103]) ).
fof(f160,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,[],[f100,f103]) ).
fof(f163,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X1)
| in(sK15(X0),X0)
| in(sK16(X1),X1)
| X0 = X1
| ~ in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X0) ),
inference(definition_unfolding,[],[f138,f103,f103]) ).
fof(f164,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X0)
| in(sK16(X1),X1)
| in(sK15(X0),X0)
| X0 = X1 ),
inference(definition_unfolding,[],[f137,f103,f103]) ).
fof(f165,plain,
! [X0,X1,X6,X7] :
( sK16(X1) != unordered_pair(unordered_pair(X6,X7),singleton(X6))
| in(sK15(X0),X0)
| X0 = X1
| ~ in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X0) ),
inference(definition_unfolding,[],[f136,f103,f103,f103]) ).
fof(f166,plain,
! [X0,X1,X6,X7] :
( sK16(X1) != unordered_pair(unordered_pair(X6,X7),singleton(X6))
| in(sK15(X0),X0)
| X0 = X1
| in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X0) ),
inference(definition_unfolding,[],[f135,f103,f103,f103]) ).
fof(f167,plain,
! [X3,X0,X1,X4] :
( sK15(X0) != unordered_pair(unordered_pair(X3,X4),singleton(X3))
| X0 = X1
| in(sK16(X1),X1)
| ~ in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X0) ),
inference(definition_unfolding,[],[f134,f103,f103,f103]) ).
fof(f168,plain,
! [X3,X0,X1,X4] :
( sK15(X0) != unordered_pair(unordered_pair(X3,X4),singleton(X3))
| X0 = X1
| in(sK16(X1),X1)
| in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X0) ),
inference(definition_unfolding,[],[f133,f103,f103,f103]) ).
fof(f169,plain,
! [X3,X0,X1,X6,X7,X4] :
( sK16(X1) != unordered_pair(unordered_pair(X6,X7),singleton(X6))
| sK15(X0) != unordered_pair(unordered_pair(X3,X4),singleton(X3))
| X0 = X1
| ~ in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X0) ),
inference(definition_unfolding,[],[f132,f103,f103,f103,f103]) ).
fof(f170,plain,
! [X3,X0,X1,X6,X7,X4] :
( sK16(X1) != unordered_pair(unordered_pair(X6,X7),singleton(X6))
| sK15(X0) != unordered_pair(unordered_pair(X3,X4),singleton(X3))
| X0 = X1
| in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X0) ),
inference(definition_unfolding,[],[f131,f103,f103,f103,f103]) ).
fof(f171,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,[],[f157]) ).
fof(f173,plain,
! [X0,X1] :
( in(X1,relation_dom(X0))
| apply(X0,X1) = empty_set
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f95]) ).
fof(f174,plain,
! [X0,X6,X5] :
( ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f160]) ).
fof(f176,definition,
sF21 = relation_dom(sK19),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f177,plain,
relation_dom(sK19) = sF21,
inference(reorient_equations,[],[f176]) ).
fof(f178,definition,
sF22 = relation_dom(sK20),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f179,plain,
relation_dom(sK20) = sF22,
inference(reorient_equations,[],[f178]) ).
fof(f180,plain,
sF21 = sF22,
inference(definition_folding,[],[f152,f179,f177]) ).
fof(f181,plain,
! [X2] :
( ~ in(X2,sF21)
| apply(sK19,X2) = apply(sK20,X2) ),
inference(definition_folding,[],[f151,f177]) ).
fof(f182,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f156,f174]) ).
fof(f183,plain,
relation_dom(sK20) = sF21,
inference(forward_demodulation,[],[f179,f180]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| apply(X0,X1) = X2
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_demodulation,[],[f182,f91]) ).
fof(f185,plain,
! [X0] :
( in(X0,sF21)
| empty_set = apply(sK20,X0)
| ~ relation(sK20)
| ~ function(sK20) ),
inference(superposition,[],[f173,f183]) ).
fof(f186,plain,
! [X0] :
( in(X0,sF21)
| empty_set = apply(sK19,X0)
| ~ relation(sK19)
| ~ function(sK19) ),
inference(superposition,[],[f173,f177]) ).
fof(f187,plain,
! [X0] :
( in(X0,sF21)
| empty_set = apply(sK19,X0)
| ~ function(sK19) ),
inference(forward_subsumption_resolution,[],[f186,f148]) ).
fof(f188,plain,
! [X0] :
( in(X0,sF21)
| empty_set = apply(sK20,X0)
| ~ function(sK20) ),
inference(forward_subsumption_resolution,[],[f185,f150]) ).
fof(f189,plain,
! [X0] :
( in(X0,sF21)
| empty_set = apply(sK19,X0) ),
inference(forward_subsumption_resolution,[],[f187,f147]) ).
fof(f190,plain,
! [X0] :
( in(X0,sF21)
| empty_set = apply(sK20,X0) ),
inference(forward_subsumption_resolution,[],[f188,f149]) ).
fof(f242,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X1)),X2)
| in(X1,relation_dom(X2))
| ~ relation(X2) ),
inference(superposition,[],[f174,f91]) ).
fof(f243,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),X2)
| apply(X2,X1) = X0
| ~ relation(X2)
| ~ function(X2) ),
inference(superposition,[],[f184,f91]) ).
fof(f244,plain,
! [X2,X3,X0,X1,X4,X5] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK16(X2)
| sK15(X3) != unordered_pair(unordered_pair(X4,X5),singleton(X4))
| X2 = X3
| ~ in(unordered_pair(unordered_pair(sK17(X3,X2),sK18(X3,X2)),singleton(sK17(X3,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK17(X3,X2),sK18(X3,X2)),singleton(sK17(X3,X2))),X3) ),
inference(superposition,[],[f169,f91]) ).
fof(f245,plain,
! [X2,X3,X0,X1] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK15(X2)
| X2 = X3
| in(sK16(X3),X3)
| ~ in(unordered_pair(unordered_pair(sK17(X2,X3),sK18(X2,X3)),singleton(sK17(X2,X3))),X3)
| ~ in(unordered_pair(unordered_pair(sK17(X2,X3),sK18(X2,X3)),singleton(sK17(X2,X3))),X2) ),
inference(superposition,[],[f167,f91]) ).
fof(f246,plain,
! [X2,X3,X0,X1] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK16(X2)
| in(sK15(X3),X3)
| X2 = X3
| ~ in(unordered_pair(unordered_pair(sK17(X3,X2),sK18(X3,X2)),singleton(sK17(X3,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK17(X3,X2),sK18(X3,X2)),singleton(sK17(X3,X2))),X3) ),
inference(superposition,[],[f165,f91]) ).
fof(f247,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| in(X0,relation_dom(X2))
| ~ relation(X2) ),
inference(superposition,[],[f174,f91]) ).
fof(f248,plain,
! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(X1,X0))),X1)
| ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(superposition,[],[f171,f91]) ).
fof(f250,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(sK17(X3,X2)),unordered_pair(sK17(X3,X2),sK18(X3,X2))),X2)
| unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK16(X2)
| in(sK15(X3),X3)
| X2 = X3
| ~ in(unordered_pair(unordered_pair(sK17(X3,X2),sK18(X3,X2)),singleton(sK17(X3,X2))),X3) ),
inference(forward_demodulation,[],[f246,f91]) ).
fof(f251,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(sK17(X2,X3)),unordered_pair(sK17(X2,X3),sK18(X2,X3))),X3)
| unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK15(X2)
| X2 = X3
| in(sK16(X3),X3)
| ~ in(unordered_pair(unordered_pair(sK17(X2,X3),sK18(X2,X3)),singleton(sK17(X2,X3))),X2) ),
inference(forward_demodulation,[],[f245,f91]) ).
fof(f252,plain,
! [X2,X3,X0,X1,X4,X5] :
( sK15(X3) != unordered_pair(singleton(X4),unordered_pair(X4,X5))
| unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK16(X2)
| X2 = X3
| ~ in(unordered_pair(unordered_pair(sK17(X3,X2),sK18(X3,X2)),singleton(sK17(X3,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK17(X3,X2),sK18(X3,X2)),singleton(sK17(X3,X2))),X3) ),
inference(forward_demodulation,[],[f244,f91]) ).
fof(f253,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),X2)
| in(X1,relation_dom(X2))
| ~ relation(X2) ),
inference(forward_demodulation,[],[f242,f91]) ).
fof(f264,plain,
! [X2,X3,X0,X1] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK16(X2)
| ~ in(unordered_pair(singleton(sK17(X3,X2)),unordered_pair(sK17(X3,X2),sK18(X3,X2))),X2)
| ~ in(unordered_pair(singleton(sK17(X3,X2)),unordered_pair(sK17(X3,X2),sK18(X3,X2))),X3)
| in(sK15(X3),X3)
| X2 = X3 ),
inference(forward_demodulation,[],[f250,f91]) ).
fof(f265,plain,
! [X2,X3,X0,X1] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK15(X2)
| ~ in(unordered_pair(singleton(sK17(X2,X3)),unordered_pair(sK17(X2,X3),sK18(X2,X3))),X3)
| ~ in(unordered_pair(singleton(sK17(X2,X3)),unordered_pair(sK17(X2,X3),sK18(X2,X3))),X2)
| X2 = X3
| in(sK16(X3),X3) ),
inference(forward_demodulation,[],[f251,f91]) ).
fof(f266,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(sK17(X3,X2)),unordered_pair(sK17(X3,X2),sK18(X3,X2))),X2)
| sK15(X3) != unordered_pair(singleton(X4),unordered_pair(X4,X5))
| unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK16(X2)
| X2 = X3
| ~ in(unordered_pair(unordered_pair(sK17(X3,X2),sK18(X3,X2)),singleton(sK17(X3,X2))),X3) ),
inference(forward_demodulation,[],[f252,f91]) ).
fof(f276,plain,
! [X2,X3,X0,X1,X4,X5] :
( sK15(X3) != unordered_pair(singleton(X4),unordered_pair(X4,X5))
| ~ in(unordered_pair(singleton(sK17(X3,X2)),unordered_pair(sK17(X3,X2),sK18(X3,X2))),X2)
| ~ in(unordered_pair(singleton(sK17(X3,X2)),unordered_pair(sK17(X3,X2),sK18(X3,X2))),X3)
| unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK16(X2)
| X2 = X3 ),
inference(forward_demodulation,[],[f266,f91]) ).
fof(f335,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK17(X0,X1)),unordered_pair(sK17(X0,X1),sK18(X0,X1))),X1)
| in(sK15(X0),X0)
| in(sK16(X1),X1)
| X0 = X1
| ~ in(unordered_pair(singleton(sK17(X0,X1)),unordered_pair(sK17(X0,X1),sK18(X0,X1))),X0) ),
inference(superposition,[],[f163,f91]) ).
fof(f342,plain,
! [X2,X3,X0,X1,X4,X5] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK16(X2)
| sK15(X3) != unordered_pair(unordered_pair(X4,X5),singleton(X4))
| X2 = X3
| in(unordered_pair(unordered_pair(sK17(X3,X2),sK18(X3,X2)),singleton(sK17(X3,X2))),X2)
| in(unordered_pair(unordered_pair(sK17(X3,X2),sK18(X3,X2)),singleton(sK17(X3,X2))),X3) ),
inference(superposition,[],[f170,f91]) ).
fof(f343,plain,
! [X2,X3,X0,X1,X4,X5] :
( sK15(X3) != unordered_pair(singleton(X4),unordered_pair(X4,X5))
| unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK16(X2)
| X2 = X3
| in(unordered_pair(unordered_pair(sK17(X3,X2),sK18(X3,X2)),singleton(sK17(X3,X2))),X2)
| in(unordered_pair(unordered_pair(sK17(X3,X2),sK18(X3,X2)),singleton(sK17(X3,X2))),X3) ),
inference(forward_demodulation,[],[f342,f91]) ).
fof(f347,plain,
! [X2,X3,X0,X1,X4,X5] :
( in(unordered_pair(singleton(sK17(X3,X2)),unordered_pair(sK17(X3,X2),sK18(X3,X2))),X2)
| sK15(X3) != unordered_pair(singleton(X4),unordered_pair(X4,X5))
| unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK16(X2)
| X2 = X3
| in(unordered_pair(unordered_pair(sK17(X3,X2),sK18(X3,X2)),singleton(sK17(X3,X2))),X3) ),
inference(forward_demodulation,[],[f343,f91]) ).
fof(f351,plain,
! [X2,X3,X0,X1,X4,X5] :
( sK15(X3) != unordered_pair(singleton(X4),unordered_pair(X4,X5))
| in(unordered_pair(singleton(sK17(X3,X2)),unordered_pair(sK17(X3,X2),sK18(X3,X2))),X2)
| in(unordered_pair(singleton(sK17(X3,X2)),unordered_pair(sK17(X3,X2),sK18(X3,X2))),X3)
| unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK16(X2)
| X2 = X3 ),
inference(forward_demodulation,[],[f347,f91]) ).
fof(f363,plain,
! [X0] :
( apply(sK20,X0) = apply(sK19,X0)
| empty_set = apply(sK20,X0) ),
inference(resolution,[],[f190,f181]) ).
fof(f383,plain,
! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK19,X0))),sK20)
| ~ in(X0,relation_dom(sK20))
| ~ relation(sK20)
| ~ function(sK20)
| empty_set = apply(sK20,X0) ),
inference(superposition,[],[f248,f363]) ).
fof(f387,plain,
! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK19,X0))),sK20)
| ~ in(X0,relation_dom(sK20))
| ~ function(sK20)
| empty_set = apply(sK20,X0) ),
inference(forward_subsumption_resolution,[],[f383,f150]) ).
fof(f389,plain,
! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK19,X0))),sK20)
| ~ in(X0,relation_dom(sK20))
| empty_set = apply(sK20,X0) ),
inference(forward_subsumption_resolution,[],[f387,f149]) ).
fof(f391,plain,
! [X0] :
( ~ in(X0,sF21)
| in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK19,X0))),sK20)
| empty_set = apply(sK20,X0) ),
inference(forward_demodulation,[],[f389,f183]) ).
fof(f393,plain,
! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK19,X0))),sK20)
| empty_set = apply(sK20,X0) ),
inference(forward_subsumption_resolution,[],[f391,f190]) ).
fof(f398,plain,
! [X2,X3,X0,X1] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK15(X2)
| X2 = X3
| in(sK16(X3),X3)
| in(unordered_pair(unordered_pair(sK17(X2,X3),sK18(X2,X3)),singleton(sK17(X2,X3))),X3)
| in(unordered_pair(unordered_pair(sK17(X2,X3),sK18(X2,X3)),singleton(sK17(X2,X3))),X2) ),
inference(superposition,[],[f168,f91]) ).
fof(f399,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK17(X2,X3)),unordered_pair(sK17(X2,X3),sK18(X2,X3))),X3)
| unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK15(X2)
| X2 = X3
| in(sK16(X3),X3)
| in(unordered_pair(unordered_pair(sK17(X2,X3),sK18(X2,X3)),singleton(sK17(X2,X3))),X2) ),
inference(forward_demodulation,[],[f398,f91]) ).
fof(f403,plain,
! [X2,X3,X0,X1] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK15(X2)
| in(unordered_pair(singleton(sK17(X2,X3)),unordered_pair(sK17(X2,X3),sK18(X2,X3))),X3)
| in(unordered_pair(singleton(sK17(X2,X3)),unordered_pair(sK17(X2,X3),sK18(X2,X3))),X2)
| X2 = X3
| in(sK16(X3),X3) ),
inference(forward_demodulation,[],[f399,f91]) ).
fof(f412,plain,
! [X2,X3,X0,X1] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK16(X2)
| in(sK15(X3),X3)
| X2 = X3
| in(unordered_pair(unordered_pair(sK17(X3,X2),sK18(X3,X2)),singleton(sK17(X3,X2))),X2)
| in(unordered_pair(unordered_pair(sK17(X3,X2),sK18(X3,X2)),singleton(sK17(X3,X2))),X3) ),
inference(superposition,[],[f166,f91]) ).
fof(f413,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(sK17(X3,X2)),unordered_pair(sK17(X3,X2),sK18(X3,X2))),X2)
| unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK16(X2)
| in(sK15(X3),X3)
| X2 = X3
| in(unordered_pair(unordered_pair(sK17(X3,X2),sK18(X3,X2)),singleton(sK17(X3,X2))),X3) ),
inference(forward_demodulation,[],[f412,f91]) ).
fof(f417,plain,
! [X2,X3,X0,X1] :
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK16(X2)
| in(unordered_pair(singleton(sK17(X3,X2)),unordered_pair(sK17(X3,X2),sK18(X3,X2))),X2)
| in(unordered_pair(singleton(sK17(X3,X2)),unordered_pair(sK17(X3,X2),sK18(X3,X2))),X3)
| in(sK15(X3),X3)
| X2 = X3 ),
inference(forward_demodulation,[],[f413,f91]) ).
fof(f436,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X0)
| in(sK16(X1),X1)
| in(sK15(X0),X0)
| X0 = X1
| in(sK17(X0,X1),relation_dom(X1))
| ~ relation(X1) ),
inference(resolution,[],[f164,f174]) ).
fof(f443,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X1)
| in(sK16(X1),X1)
| in(sK15(X0),X0)
| X0 = X1
| in(sK17(X0,X1),relation_dom(X0))
| ~ relation(X0) ),
inference(resolution,[],[f164,f174]) ).
fof(f453,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK17(X0,X1)),unordered_pair(sK17(X0,X1),sK18(X0,X1))),X1)
| in(unordered_pair(singleton(sK17(X0,X1)),unordered_pair(sK17(X0,X1),sK18(X0,X1))),X0)
| in(sK16(X1),X1)
| in(sK15(X0),X0)
| X0 = X1 ),
inference(superposition,[],[f164,f91]) ).
fof(f460,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK17(X0,X1)),unordered_pair(sK17(X0,X1),sK18(X0,X1))),X1)
| in(sK16(X1),X1)
| in(sK15(X0),X0)
| X0 = X1
| in(sK17(X0,X1),relation_dom(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[],[f443,f91]) ).
fof(f463,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK17(X0,X1)),unordered_pair(sK17(X0,X1),sK18(X0,X1))),X0)
| in(sK16(X1),X1)
| in(sK15(X0),X0)
| X0 = X1
| in(sK17(X0,X1),relation_dom(X1))
| ~ relation(X1) ),
inference(forward_demodulation,[],[f436,f91]) ).
fof(f550,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK17(X0,X1)),unordered_pair(sK17(X0,X1),sK18(X0,X1))),X1)
| in(sK16(X1),X1)
| in(sK15(X0),X0)
| X0 = X1
| sK18(X0,X1) = apply(X0,sK17(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(resolution,[],[f453,f184]) ).
fof(f584,plain,
! [X0,X1] :
( in(sK17(X1,X0),relation_dom(X1))
| in(sK16(X0),X0)
| X0 = X1
| in(sK15(X1),X1)
| ~ relation(X1)
| apply(X0,sK17(X1,X0)) = sK18(X1,X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(resolution,[],[f460,f184]) ).
fof(f594,plain,
! [X0,X1] :
( in(sK17(X1,X0),relation_dom(X0))
| in(sK15(X1),X1)
| X0 = X1
| in(sK16(X0),X0)
| ~ relation(X0)
| sK18(X1,X0) = apply(X1,sK17(X1,X0))
| ~ relation(X1)
| ~ function(X1) ),
inference(resolution,[],[f463,f184]) ).
fof(f757,plain,
! [X0] :
( in(sK17(sK19,X0),sF21)
| in(sK16(X0),X0)
| sK19 = X0
| in(sK15(sK19),sK19)
| ~ relation(sK19)
| apply(X0,sK17(sK19,X0)) = sK18(sK19,X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[],[f584,f177]) ).
fof(f760,plain,
! [X0] :
( in(sK17(sK19,X0),sF21)
| in(sK16(X0),X0)
| sK19 = X0
| in(sK15(sK19),sK19)
| apply(X0,sK17(sK19,X0)) = sK18(sK19,X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f757,f148]) ).
fof(f765,definition,
( spl23_13
<=> in(sK15(sK19),sK19) ),
introduced(definition,[new_symbols(definition,[spl23_13])],[avatar_definition]) ).
fof(f766,plain,
( ~ in(sK15(sK19),sK19)
| spl23_13 ),
inference(avatar_component_clause,[],[f765]) ).
fof(f767,plain,
( in(sK15(sK19),sK19)
| ~ spl23_13 ),
inference(avatar_component_clause,[],[f765]) ).
fof(f769,definition,
( spl23_14
<=> ! [X0] :
( in(sK17(sK19,X0),sF21)
| ~ function(X0)
| ~ relation(X0)
| apply(X0,sK17(sK19,X0)) = sK18(sK19,X0)
| sK19 = X0
| in(sK16(X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl23_14])],[avatar_definition]) ).
fof(f770,plain,
( ! [X0] :
( in(sK17(sK19,X0),sF21)
| in(sK16(X0),X0)
| ~ relation(X0)
| apply(X0,sK17(sK19,X0)) = sK18(sK19,X0)
| sK19 = X0
| ~ function(X0) )
| ~ spl23_14 ),
inference(avatar_component_clause,[],[f769]) ).
fof(f771,plain,
( spl23_13
| spl23_14 ),
inference(avatar_split_clause,[],[f760,f769,f765]) ).
fof(f984,plain,
! [X0] :
( in(sK17(X0,sK20),sF21)
| in(sK15(X0),X0)
| sK20 = X0
| in(sK16(sK20),sK20)
| ~ relation(sK20)
| sK18(X0,sK20) = apply(X0,sK17(X0,sK20))
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[],[f594,f183]) ).
fof(f989,plain,
! [X0] :
( in(sK17(X0,sK20),sF21)
| in(sK15(X0),X0)
| sK20 = X0
| in(sK16(sK20),sK20)
| sK18(X0,sK20) = apply(X0,sK17(X0,sK20))
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f984,f150]) ).
fof(f1001,definition,
( spl23_19
<=> in(sK16(sK20),sK20) ),
introduced(definition,[new_symbols(definition,[spl23_19])],[avatar_definition]) ).
fof(f1002,plain,
( ~ in(sK16(sK20),sK20)
| spl23_19 ),
inference(avatar_component_clause,[],[f1001]) ).
fof(f1003,plain,
( in(sK16(sK20),sK20)
| ~ spl23_19 ),
inference(avatar_component_clause,[],[f1001]) ).
fof(f1005,definition,
( spl23_20
<=> ! [X0] :
( in(sK17(X0,sK20),sF21)
| ~ function(X0)
| ~ relation(X0)
| sK18(X0,sK20) = apply(X0,sK17(X0,sK20))
| sK20 = X0
| in(sK15(X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl23_20])],[avatar_definition]) ).
fof(f1006,plain,
( ! [X0] :
( in(sK17(X0,sK20),sF21)
| in(sK15(X0),X0)
| ~ relation(X0)
| sK18(X0,sK20) = apply(X0,sK17(X0,sK20))
| sK20 = X0
| ~ function(X0) )
| ~ spl23_20 ),
inference(avatar_component_clause,[],[f1005]) ).
fof(f1007,plain,
( spl23_19
| spl23_20 ),
inference(avatar_split_clause,[],[f989,f1005,f1001]) ).
fof(f1451,plain,
( ! [X0] :
( in(sK16(X0),X0)
| ~ relation(X0)
| apply(X0,sK17(sK19,X0)) = sK18(sK19,X0)
| sK19 = X0
| ~ function(X0)
| apply(sK19,sK17(sK19,X0)) = apply(sK20,sK17(sK19,X0)) )
| ~ spl23_14 ),
inference(resolution,[],[f770,f181]) ).
fof(f1651,plain,
( ~ relation(sK20)
| apply(sK20,sK17(sK19,sK20)) = sK18(sK19,sK20)
| sK19 = sK20
| ~ function(sK20)
| apply(sK20,sK17(sK19,sK20)) = apply(sK19,sK17(sK19,sK20))
| ~ spl23_14
| spl23_19 ),
inference(resolution,[],[f1002,f1451]) ).
fof(f1653,plain,
( apply(sK20,sK17(sK19,sK20)) = sK18(sK19,sK20)
| sK19 = sK20
| ~ function(sK20)
| apply(sK20,sK17(sK19,sK20)) = apply(sK19,sK17(sK19,sK20))
| ~ spl23_14
| spl23_19 ),
inference(forward_subsumption_resolution,[],[f1651,f150]) ).
fof(f1654,plain,
( apply(sK20,sK17(sK19,sK20)) = sK18(sK19,sK20)
| ~ function(sK20)
| apply(sK20,sK17(sK19,sK20)) = apply(sK19,sK17(sK19,sK20))
| ~ spl23_14
| spl23_19 ),
inference(forward_subsumption_resolution,[],[f1653,f153]) ).
fof(f1655,plain,
( apply(sK20,sK17(sK19,sK20)) = sK18(sK19,sK20)
| apply(sK20,sK17(sK19,sK20)) = apply(sK19,sK17(sK19,sK20))
| ~ spl23_14
| spl23_19 ),
inference(forward_subsumption_resolution,[],[f1654,f149]) ).
fof(f1657,definition,
( spl23_30
<=> apply(sK20,sK17(sK19,sK20)) = apply(sK19,sK17(sK19,sK20)) ),
introduced(definition,[new_symbols(definition,[spl23_30])],[avatar_definition]) ).
fof(f1658,plain,
( apply(sK20,sK17(sK19,sK20)) != apply(sK19,sK17(sK19,sK20))
| spl23_30 ),
inference(avatar_component_clause,[],[f1657]) ).
fof(f1659,plain,
( apply(sK20,sK17(sK19,sK20)) = apply(sK19,sK17(sK19,sK20))
| ~ spl23_30 ),
inference(avatar_component_clause,[],[f1657]) ).
fof(f1661,definition,
( spl23_31
<=> apply(sK20,sK17(sK19,sK20)) = sK18(sK19,sK20) ),
introduced(definition,[new_symbols(definition,[spl23_31])],[avatar_definition]) ).
fof(f1662,plain,
( apply(sK20,sK17(sK19,sK20)) != sK18(sK19,sK20)
| spl23_31 ),
inference(avatar_component_clause,[],[f1661]) ).
fof(f1663,plain,
( apply(sK20,sK17(sK19,sK20)) = sK18(sK19,sK20)
| ~ spl23_31 ),
inference(avatar_component_clause,[],[f1661]) ).
fof(f1664,plain,
( spl23_30
| spl23_31
| ~ spl23_14
| spl23_19 ),
inference(avatar_split_clause,[],[f1655,f1001,f769,f1661,f1657]) ).
fof(f1740,plain,
( ! [X0] :
( in(sK15(X0),X0)
| ~ relation(X0)
| sK18(X0,sK20) = apply(X0,sK17(X0,sK20))
| sK20 = X0
| ~ function(X0)
| apply(sK19,sK17(X0,sK20)) = apply(sK20,sK17(X0,sK20)) )
| ~ spl23_20 ),
inference(resolution,[],[f1006,f181]) ).
fof(f2037,plain,
( sK16(sK20) = unordered_pair(unordered_pair(sK1(sK16(sK20)),sK2(sK16(sK20))),singleton(sK1(sK16(sK20))))
| ~ relation(sK20)
| ~ spl23_19 ),
inference(resolution,[],[f1003,f155]) ).
fof(f2038,plain,
( sK16(sK20) = unordered_pair(unordered_pair(sK1(sK16(sK20)),sK2(sK16(sK20))),singleton(sK1(sK16(sK20))))
| ~ spl23_19 ),
inference(forward_subsumption_resolution,[],[f2037,f150]) ).
fof(f2039,plain,
( sK16(sK20) = unordered_pair(singleton(sK1(sK16(sK20))),unordered_pair(sK1(sK16(sK20)),sK2(sK16(sK20))))
| ~ spl23_19 ),
inference(forward_demodulation,[],[f2038,f91]) ).
fof(f2042,plain,
( ! [X0,X1] :
( sK16(X0) != sK16(sK20)
| ~ in(unordered_pair(singleton(sK17(X1,X0)),unordered_pair(sK17(X1,X0),sK18(X1,X0))),X0)
| ~ in(unordered_pair(singleton(sK17(X1,X0)),unordered_pair(sK17(X1,X0),sK18(X1,X0))),X1)
| in(sK15(X1),X1)
| X0 = X1 )
| ~ spl23_19 ),
inference(superposition,[],[f264,f2039]) ).
fof(f2047,plain,
( ! [X0,X1] :
( sK16(X0) != sK16(sK20)
| in(unordered_pair(singleton(sK17(X1,X0)),unordered_pair(sK17(X1,X0),sK18(X1,X0))),X0)
| in(unordered_pair(singleton(sK17(X1,X0)),unordered_pair(sK17(X1,X0),sK18(X1,X0))),X1)
| in(sK15(X1),X1)
| X0 = X1 )
| ~ spl23_19 ),
inference(superposition,[],[f417,f2039]) ).
fof(f2178,plain,
( ~ relation(sK19)
| sK18(sK19,sK20) = apply(sK19,sK17(sK19,sK20))
| sK19 = sK20
| ~ function(sK19)
| apply(sK20,sK17(sK19,sK20)) = apply(sK19,sK17(sK19,sK20))
| spl23_13
| ~ spl23_20 ),
inference(resolution,[],[f766,f1740]) ).
fof(f2179,plain,
( sK18(sK19,sK20) = apply(sK19,sK17(sK19,sK20))
| sK19 = sK20
| ~ function(sK19)
| apply(sK20,sK17(sK19,sK20)) = apply(sK19,sK17(sK19,sK20))
| spl23_13
| ~ spl23_20 ),
inference(forward_subsumption_resolution,[],[f2178,f148]) ).
fof(f2180,plain,
( sK18(sK19,sK20) = apply(sK19,sK17(sK19,sK20))
| ~ function(sK19)
| apply(sK20,sK17(sK19,sK20)) = apply(sK19,sK17(sK19,sK20))
| spl23_13
| ~ spl23_20 ),
inference(forward_subsumption_resolution,[],[f2179,f153]) ).
fof(f2181,plain,
( sK18(sK19,sK20) = apply(sK19,sK17(sK19,sK20))
| apply(sK20,sK17(sK19,sK20)) = apply(sK19,sK17(sK19,sK20))
| spl23_13
| ~ spl23_20 ),
inference(forward_subsumption_resolution,[],[f2180,f147]) ).
fof(f2183,definition,
( spl23_34
<=> sK18(sK19,sK20) = apply(sK19,sK17(sK19,sK20)) ),
introduced(definition,[new_symbols(definition,[spl23_34])],[avatar_definition]) ).
fof(f2184,plain,
( sK18(sK19,sK20) != apply(sK19,sK17(sK19,sK20))
| spl23_34 ),
inference(avatar_component_clause,[],[f2183]) ).
fof(f2185,plain,
( sK18(sK19,sK20) = apply(sK19,sK17(sK19,sK20))
| ~ spl23_34 ),
inference(avatar_component_clause,[],[f2183]) ).
fof(f2236,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK17(X0,sK20)),unordered_pair(sK17(X0,sK20),sK18(X0,sK20))),sK20)
| ~ in(unordered_pair(singleton(sK17(X0,sK20)),unordered_pair(sK17(X0,sK20),sK18(X0,sK20))),X0)
| in(sK15(X0),X0)
| sK20 = X0 )
| ~ spl23_19 ),
inference(equality_resolution,[],[f2042]) ).
fof(f2837,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK17(X0,sK20)),unordered_pair(sK17(X0,sK20),sK18(X0,sK20))),sK20)
| in(unordered_pair(singleton(sK17(X0,sK20)),unordered_pair(sK17(X0,sK20),sK18(X0,sK20))),X0)
| in(sK15(X0),X0)
| sK20 = X0 )
| ~ spl23_19 ),
inference(equality_resolution,[],[f2047]) ).
fof(f2840,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK17(X0,sK20)),unordered_pair(sK17(X0,sK20),sK18(X0,sK20))),X0)
| in(sK15(X0),X0)
| sK20 = X0
| in(sK17(X0,sK20),relation_dom(sK20))
| ~ relation(sK20) )
| ~ spl23_19 ),
inference(resolution,[],[f2837,f247]) ).
fof(f2862,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK17(X0,sK20)),unordered_pair(sK17(X0,sK20),sK18(X0,sK20))),X0)
| in(sK15(X0),X0)
| sK20 = X0
| in(sK17(X0,sK20),relation_dom(sK20)) )
| ~ spl23_19 ),
inference(forward_subsumption_resolution,[],[f2840,f150]) ).
fof(f2865,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK17(X0,sK20)),unordered_pair(sK17(X0,sK20),sK18(X0,sK20))),X0)
| in(sK17(X0,sK20),sF21)
| in(sK15(X0),X0)
| sK20 = X0 )
| ~ spl23_19 ),
inference(forward_demodulation,[],[f2862,f183]) ).
fof(f2868,plain,
( ! [X0] :
( in(sK17(X0,sK20),sF21)
| in(sK15(X0),X0)
| sK20 = X0
| sK18(X0,sK20) = apply(X0,sK17(X0,sK20))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl23_19 ),
inference(resolution,[],[f2865,f184]) ).
fof(f2883,plain,
( spl23_20
| ~ spl23_19 ),
inference(avatar_split_clause,[],[f2868,f1001,f1005]) ).
fof(f2884,plain,
( spl23_30
| spl23_34
| spl23_13
| ~ spl23_20 ),
inference(avatar_split_clause,[],[f2181,f1005,f765,f2183,f1657]) ).
fof(f2888,plain,
( in(unordered_pair(unordered_pair(sK17(sK19,sK20),apply(sK19,sK17(sK19,sK20))),singleton(sK17(sK19,sK20))),sK20)
| ~ in(sK17(sK19,sK20),relation_dom(sK20))
| ~ relation(sK20)
| ~ function(sK20)
| ~ spl23_30 ),
inference(superposition,[],[f171,f1659]) ).
fof(f2889,plain,
( in(unordered_pair(unordered_pair(sK17(sK19,sK20),apply(sK19,sK17(sK19,sK20))),singleton(sK17(sK19,sK20))),sK20)
| ~ in(sK17(sK19,sK20),relation_dom(sK20))
| ~ function(sK20)
| ~ spl23_30 ),
inference(forward_subsumption_resolution,[],[f2888,f150]) ).
fof(f2891,plain,
( in(unordered_pair(unordered_pair(sK17(sK19,sK20),apply(sK19,sK17(sK19,sK20))),singleton(sK17(sK19,sK20))),sK20)
| ~ in(sK17(sK19,sK20),relation_dom(sK20))
| ~ spl23_30 ),
inference(forward_subsumption_resolution,[],[f2889,f149]) ).
fof(f2893,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),apply(sK19,sK17(sK19,sK20)))),sK20)
| ~ in(sK17(sK19,sK20),relation_dom(sK20))
| ~ spl23_30 ),
inference(forward_demodulation,[],[f2891,f91]) ).
fof(f2895,plain,
( ~ in(sK17(sK19,sK20),sF21)
| in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),apply(sK19,sK17(sK19,sK20)))),sK20)
| ~ spl23_30 ),
inference(forward_demodulation,[],[f2893,f183]) ).
fof(f2897,definition,
( spl23_53
<=> in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),apply(sK19,sK17(sK19,sK20)))),sK20) ),
introduced(definition,[new_symbols(definition,[spl23_53])],[avatar_definition]) ).
fof(f2899,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),apply(sK19,sK17(sK19,sK20)))),sK20)
| ~ spl23_53 ),
inference(avatar_component_clause,[],[f2897]) ).
fof(f2901,definition,
( spl23_54
<=> in(sK17(sK19,sK20),sF21) ),
introduced(definition,[new_symbols(definition,[spl23_54])],[avatar_definition]) ).
fof(f2902,plain,
( in(sK17(sK19,sK20),sF21)
| ~ spl23_54 ),
inference(avatar_component_clause,[],[f2901]) ).
fof(f2903,plain,
( ~ in(sK17(sK19,sK20),sF21)
| spl23_54 ),
inference(avatar_component_clause,[],[f2901]) ).
fof(f2905,plain,
( spl23_53
| ~ spl23_54
| ~ spl23_30 ),
inference(avatar_split_clause,[],[f2895,f1657,f2901,f2897]) ).
fof(f2992,definition,
( spl23_55
<=> in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(empty_set,sK17(sK19,sK20))),sK20) ),
introduced(definition,[new_symbols(definition,[spl23_55])],[avatar_definition]) ).
fof(f2993,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(empty_set,sK17(sK19,sK20))),sK20)
| ~ spl23_55 ),
inference(avatar_component_clause,[],[f2992]) ).
fof(f2996,definition,
( spl23_56
<=> in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(empty_set,sK17(sK19,sK20))),sK19) ),
introduced(definition,[new_symbols(definition,[spl23_56])],[avatar_definition]) ).
fof(f2997,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(empty_set,sK17(sK19,sK20))),sK19)
| ~ spl23_56 ),
inference(avatar_component_clause,[],[f2996]) ).
fof(f2998,plain,
( ~ in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(empty_set,sK17(sK19,sK20))),sK19)
| spl23_56 ),
inference(avatar_component_clause,[],[f2996]) ).
fof(f3003,plain,
( in(sK17(sK19,sK20),relation_dom(sK19))
| ~ relation(sK19)
| ~ spl23_56 ),
inference(resolution,[],[f2997,f253]) ).
fof(f3004,plain,
( empty_set = apply(sK19,sK17(sK19,sK20))
| ~ relation(sK19)
| ~ function(sK19)
| ~ spl23_56 ),
inference(resolution,[],[f2997,f243]) ).
fof(f3008,plain,
( in(sK17(sK19,sK20),relation_dom(sK19))
| ~ spl23_56 ),
inference(forward_subsumption_resolution,[],[f3003,f148]) ).
fof(f3010,plain,
( in(sK17(sK19,sK20),sF21)
| ~ spl23_56 ),
inference(forward_demodulation,[],[f3008,f177]) ).
fof(f3011,plain,
( $false
| spl23_54
| ~ spl23_56 ),
inference(forward_subsumption_resolution,[],[f3010,f2903]) ).
fof(f3012,plain,
( spl23_54
| ~ spl23_56 ),
inference(avatar_contradiction_clause,[],[f3011]) ).
fof(f3013,plain,
( empty_set = apply(sK19,sK17(sK19,sK20))
| ~ function(sK19)
| ~ spl23_56 ),
inference(forward_subsumption_resolution,[],[f3004,f148]) ).
fof(f3014,plain,
( empty_set = apply(sK19,sK17(sK19,sK20))
| ~ spl23_56 ),
inference(forward_subsumption_resolution,[],[f3013,f147]) ).
fof(f3018,plain,
( apply(sK20,sK17(sK19,sK20)) = apply(sK19,sK17(sK19,sK20))
| ~ spl23_54 ),
inference(resolution,[],[f2902,f181]) ).
fof(f3034,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),empty_set)),sK20)
| ~ spl23_53
| ~ spl23_56 ),
inference(superposition,[],[f2899,f3014]) ).
fof(f3043,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(empty_set,sK17(sK19,sK20))),sK20)
| ~ spl23_53
| ~ spl23_56 ),
inference(forward_demodulation,[],[f3034,f91]) ).
fof(f3061,plain,
( apply(sK20,sK17(sK19,sK20)) = sK18(sK19,sK20)
| ~ spl23_34
| ~ spl23_54 ),
inference(forward_demodulation,[],[f3018,f2185]) ).
fof(f3063,plain,
( spl23_31
| ~ spl23_34
| ~ spl23_54 ),
inference(avatar_split_clause,[],[f3061,f2901,f2183,f1661]) ).
fof(f3069,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK20)
| empty_set = apply(sK20,sK17(sK19,sK20))
| ~ spl23_34 ),
inference(superposition,[],[f393,f2185]) ).
fof(f3070,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| ~ in(sK17(sK19,sK20),relation_dom(sK19))
| ~ relation(sK19)
| ~ function(sK19)
| ~ spl23_34 ),
inference(superposition,[],[f248,f2185]) ).
fof(f3073,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| ~ in(sK17(sK19,sK20),relation_dom(sK19))
| ~ function(sK19)
| ~ spl23_34 ),
inference(forward_subsumption_resolution,[],[f3070,f148]) ).
fof(f3074,plain,
( empty_set = sK18(sK19,sK20)
| in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK20)
| ~ spl23_31
| ~ spl23_34 ),
inference(forward_demodulation,[],[f3069,f1663]) ).
fof(f3076,definition,
( spl23_57
<=> empty_set = sK18(sK19,sK20) ),
introduced(definition,[new_symbols(definition,[spl23_57])],[avatar_definition]) ).
fof(f3078,plain,
( empty_set = sK18(sK19,sK20)
| ~ spl23_57 ),
inference(avatar_component_clause,[],[f3076]) ).
fof(f3080,definition,
( spl23_58
<=> in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK20) ),
introduced(definition,[new_symbols(definition,[spl23_58])],[avatar_definition]) ).
fof(f3081,plain,
( ~ in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK20)
| spl23_58 ),
inference(avatar_component_clause,[],[f3080]) ).
fof(f3082,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK20)
| ~ spl23_58 ),
inference(avatar_component_clause,[],[f3080]) ).
fof(f3086,definition,
( spl23_59
<=> in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19) ),
introduced(definition,[new_symbols(definition,[spl23_59])],[avatar_definition]) ).
fof(f3087,plain,
( ~ in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| spl23_59 ),
inference(avatar_component_clause,[],[f3086]) ).
fof(f3088,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| ~ spl23_59 ),
inference(avatar_component_clause,[],[f3086]) ).
fof(f3091,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| ~ in(sK17(sK19,sK20),relation_dom(sK19))
| ~ spl23_34 ),
inference(forward_subsumption_resolution,[],[f3073,f147]) ).
fof(f3092,plain,
( spl23_58
| spl23_57
| ~ spl23_31
| ~ spl23_34 ),
inference(avatar_split_clause,[],[f3074,f2183,f1661,f3076,f3080]) ).
fof(f3095,plain,
( ~ in(sK17(sK19,sK20),sF21)
| in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| ~ spl23_34 ),
inference(forward_demodulation,[],[f3091,f177]) ).
fof(f3097,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| ~ spl23_34
| ~ spl23_54 ),
inference(forward_subsumption_resolution,[],[f3095,f2902]) ).
fof(f3099,plain,
( spl23_59
| ~ spl23_34
| ~ spl23_54 ),
inference(avatar_split_clause,[],[f3097,f2901,f2183,f3086]) ).
fof(f3100,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),empty_set)),sK19)
| ~ spl23_57
| ~ spl23_59 ),
inference(forward_demodulation,[],[f3088,f3078]) ).
fof(f3101,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(empty_set,sK17(sK19,sK20))),sK19)
| ~ spl23_57
| ~ spl23_59 ),
inference(forward_demodulation,[],[f3100,f91]) ).
fof(f3102,plain,
( $false
| spl23_56
| ~ spl23_57
| ~ spl23_59 ),
inference(forward_subsumption_resolution,[],[f3101,f2998]) ).
fof(f3103,plain,
( spl23_56
| ~ spl23_57
| ~ spl23_59 ),
inference(avatar_contradiction_clause,[],[f3102]) ).
fof(f3104,plain,
( ~ in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| in(sK15(sK19),sK19)
| sK19 = sK20
| ~ spl23_19
| ~ spl23_58 ),
inference(resolution,[],[f3082,f2236]) ).
fof(f3106,plain,
( in(sK17(sK19,sK20),relation_dom(sK20))
| ~ relation(sK20)
| ~ spl23_58 ),
inference(resolution,[],[f3082,f247]) ).
fof(f3107,plain,
( apply(sK20,sK17(sK19,sK20)) = sK18(sK19,sK20)
| ~ relation(sK20)
| ~ function(sK20)
| ~ spl23_58 ),
inference(resolution,[],[f3082,f184]) ).
fof(f3111,plain,
( in(sK17(sK19,sK20),relation_dom(sK20))
| ~ spl23_58 ),
inference(forward_subsumption_resolution,[],[f3106,f150]) ).
fof(f3112,plain,
( in(sK15(sK19),sK19)
| sK19 = sK20
| ~ spl23_19
| ~ spl23_58
| ~ spl23_59 ),
inference(forward_subsumption_resolution,[],[f3104,f3088]) ).
fof(f3114,plain,
( in(sK17(sK19,sK20),sF21)
| ~ spl23_58 ),
inference(forward_demodulation,[],[f3111,f183]) ).
fof(f3115,plain,
( sK19 = sK20
| spl23_13
| ~ spl23_19
| ~ spl23_58
| ~ spl23_59 ),
inference(forward_subsumption_resolution,[],[f3112,f766]) ).
fof(f3116,plain,
( $false
| spl23_13
| ~ spl23_19
| ~ spl23_58
| ~ spl23_59 ),
inference(forward_subsumption_resolution,[],[f3115,f153]) ).
fof(f3117,plain,
( spl23_13
| ~ spl23_19
| ~ spl23_58
| ~ spl23_59 ),
inference(avatar_contradiction_clause,[],[f3116]) ).
fof(f3118,plain,
( sK18(sK19,sK20) = apply(sK19,sK17(sK19,sK20))
| ~ spl23_30
| ~ spl23_31 ),
inference(forward_demodulation,[],[f1659,f1663]) ).
fof(f3119,plain,
( sK18(sK19,sK20) = apply(sK19,sK17(sK19,sK20))
| ~ spl23_31
| ~ spl23_54 ),
inference(forward_demodulation,[],[f3018,f1663]) ).
fof(f3123,plain,
( $false
| ~ spl23_31
| spl23_34
| ~ spl23_54 ),
inference(forward_subsumption_resolution,[],[f3119,f2184]) ).
fof(f3124,plain,
( ~ spl23_31
| spl23_34
| ~ spl23_54 ),
inference(avatar_contradiction_clause,[],[f3123]) ).
fof(f3135,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| in(sK15(sK19),sK19)
| sK19 = sK20
| ~ spl23_19
| spl23_58 ),
inference(resolution,[],[f3081,f2837]) ).
fof(f3140,plain,
( sK18(sK19,sK20) = apply(sK19,sK17(sK19,sK20))
| ~ relation(sK19)
| ~ function(sK19)
| ~ spl23_59 ),
inference(resolution,[],[f3088,f184]) ).
fof(f3144,plain,
( ~ relation(sK19)
| ~ function(sK19)
| spl23_34
| ~ spl23_59 ),
inference(forward_subsumption_resolution,[],[f3140,f2184]) ).
fof(f3147,plain,
( ~ function(sK19)
| spl23_34
| ~ spl23_59 ),
inference(forward_subsumption_resolution,[],[f3144,f148]) ).
fof(f3149,plain,
( $false
| spl23_34
| ~ spl23_59 ),
inference(forward_subsumption_resolution,[],[f3147,f147]) ).
fof(f3150,plain,
( spl23_34
| ~ spl23_59 ),
inference(avatar_contradiction_clause,[],[f3149]) ).
fof(f3151,plain,
( in(sK15(sK19),sK19)
| sK19 = sK20
| ~ spl23_19
| spl23_58
| spl23_59 ),
inference(forward_subsumption_resolution,[],[f3135,f3087]) ).
fof(f3152,plain,
( sK19 = sK20
| spl23_13
| ~ spl23_19
| spl23_58
| spl23_59 ),
inference(forward_subsumption_resolution,[],[f3151,f766]) ).
fof(f3153,plain,
( $false
| spl23_13
| ~ spl23_19
| spl23_58
| spl23_59 ),
inference(forward_subsumption_resolution,[],[f3152,f153]) ).
fof(f3154,plain,
( spl23_13
| ~ spl23_19
| spl23_58
| spl23_59 ),
inference(avatar_contradiction_clause,[],[f3153]) ).
fof(f3155,plain,
( ~ relation(sK20)
| ~ function(sK20)
| spl23_31
| ~ spl23_58 ),
inference(forward_subsumption_resolution,[],[f3107,f1662]) ).
fof(f3156,plain,
( ~ function(sK20)
| spl23_31
| ~ spl23_58 ),
inference(forward_subsumption_resolution,[],[f3155,f150]) ).
fof(f3157,plain,
( $false
| spl23_31
| ~ spl23_58 ),
inference(forward_subsumption_resolution,[],[f3156,f149]) ).
fof(f3158,plain,
( spl23_31
| ~ spl23_58 ),
inference(avatar_contradiction_clause,[],[f3157]) ).
fof(f3164,plain,
( sK15(sK19) = unordered_pair(unordered_pair(sK1(sK15(sK19)),sK2(sK15(sK19))),singleton(sK1(sK15(sK19))))
| ~ relation(sK19)
| ~ spl23_13 ),
inference(resolution,[],[f767,f155]) ).
fof(f3165,plain,
( sK15(sK19) = unordered_pair(unordered_pair(sK1(sK15(sK19)),sK2(sK15(sK19))),singleton(sK1(sK15(sK19))))
| ~ spl23_13 ),
inference(forward_subsumption_resolution,[],[f3164,f148]) ).
fof(f3166,plain,
( sK15(sK19) = unordered_pair(singleton(sK1(sK15(sK19))),unordered_pair(sK1(sK15(sK19)),sK2(sK15(sK19))))
| ~ spl23_13 ),
inference(forward_demodulation,[],[f3165,f91]) ).
fof(f3185,plain,
( ! [X0,X1] :
( sK15(X0) != sK15(sK19)
| ~ in(unordered_pair(singleton(sK17(X0,X1)),unordered_pair(sK17(X0,X1),sK18(X0,X1))),X1)
| ~ in(unordered_pair(singleton(sK17(X0,X1)),unordered_pair(sK17(X0,X1),sK18(X0,X1))),X0)
| X0 = X1
| in(sK16(X1),X1) )
| ~ spl23_13 ),
inference(superposition,[],[f265,f3166]) ).
fof(f3186,plain,
( ! [X2,X3,X0,X1] :
( sK16(X1) != unordered_pair(singleton(X2),unordered_pair(X2,X3))
| ~ in(unordered_pair(singleton(sK17(X0,X1)),unordered_pair(sK17(X0,X1),sK18(X0,X1))),X1)
| ~ in(unordered_pair(singleton(sK17(X0,X1)),unordered_pair(sK17(X0,X1),sK18(X0,X1))),X0)
| sK15(X0) != sK15(sK19)
| X0 = X1 )
| ~ spl23_13 ),
inference(superposition,[],[f276,f3166]) ).
fof(f3187,plain,
( ! [X2,X3,X0,X1] :
( sK16(X1) != unordered_pair(singleton(X2),unordered_pair(X2,X3))
| in(unordered_pair(singleton(sK17(X0,X1)),unordered_pair(sK17(X0,X1),sK18(X0,X1))),X1)
| in(unordered_pair(singleton(sK17(X0,X1)),unordered_pair(sK17(X0,X1),sK18(X0,X1))),X0)
| sK15(X0) != sK15(sK19)
| X0 = X1 )
| ~ spl23_13 ),
inference(superposition,[],[f351,f3166]) ).
fof(f3188,plain,
( ! [X0,X1] :
( sK15(X0) != sK15(sK19)
| in(unordered_pair(singleton(sK17(X0,X1)),unordered_pair(sK17(X0,X1),sK18(X0,X1))),X1)
| in(unordered_pair(singleton(sK17(X0,X1)),unordered_pair(sK17(X0,X1),sK18(X0,X1))),X0)
| X0 = X1
| in(sK16(X1),X1) )
| ~ spl23_13 ),
inference(superposition,[],[f403,f3166]) ).
fof(f3268,plain,
( sK18(sK19,sK20) != apply(sK19,sK17(sK19,sK20))
| ~ spl23_30
| spl23_31 ),
inference(superposition,[],[f1662,f1659]) ).
fof(f3382,plain,
( ! [X0,X1] :
( sK16(X0) != sK16(sK20)
| ~ in(unordered_pair(singleton(sK17(X1,X0)),unordered_pair(sK17(X1,X0),sK18(X1,X0))),X0)
| ~ in(unordered_pair(singleton(sK17(X1,X0)),unordered_pair(sK17(X1,X0),sK18(X1,X0))),X1)
| sK15(X1) != sK15(sK19)
| X0 = X1 )
| ~ spl23_13
| ~ spl23_19 ),
inference(superposition,[],[f3186,f2039]) ).
fof(f3387,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK17(sK19,X0)),unordered_pair(sK17(sK19,X0),sK18(sK19,X0))),sK19)
| ~ in(unordered_pair(singleton(sK17(sK19,X0)),unordered_pair(sK17(sK19,X0),sK18(sK19,X0))),X0)
| sK19 = X0
| in(sK16(X0),X0) )
| ~ spl23_13 ),
inference(equality_resolution,[],[f3185]) ).
fof(f3424,plain,
( ! [X0] :
( sK15(X0) != sK15(sK19)
| ~ in(unordered_pair(singleton(sK17(X0,sK20)),unordered_pair(sK17(X0,sK20),sK18(X0,sK20))),X0)
| ~ in(unordered_pair(singleton(sK17(X0,sK20)),unordered_pair(sK17(X0,sK20),sK18(X0,sK20))),sK20)
| sK20 = X0 )
| ~ spl23_13
| ~ spl23_19 ),
inference(equality_resolution,[],[f3382]) ).
fof(f3425,plain,
( ~ in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| ~ in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK20)
| sK19 = sK20
| ~ spl23_13
| ~ spl23_19 ),
inference(equality_resolution,[],[f3424]) ).
fof(f3609,plain,
( ! [X0,X1] :
( sK16(X0) != sK16(sK20)
| in(unordered_pair(singleton(sK17(X1,X0)),unordered_pair(sK17(X1,X0),sK18(X1,X0))),X0)
| in(unordered_pair(singleton(sK17(X1,X0)),unordered_pair(sK17(X1,X0),sK18(X1,X0))),X1)
| sK15(X1) != sK15(sK19)
| X0 = X1 )
| ~ spl23_13
| ~ spl23_19 ),
inference(superposition,[],[f3187,f2039]) ).
fof(f3694,plain,
( ! [X0] :
( sK15(X0) != sK15(sK19)
| in(unordered_pair(singleton(sK17(X0,sK20)),unordered_pair(sK17(X0,sK20),sK18(X0,sK20))),X0)
| in(unordered_pair(singleton(sK17(X0,sK20)),unordered_pair(sK17(X0,sK20),sK18(X0,sK20))),sK20)
| sK20 = X0 )
| ~ spl23_13
| ~ spl23_19 ),
inference(equality_resolution,[],[f3609]) ).
fof(f3695,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK20)
| sK19 = sK20
| ~ spl23_13
| ~ spl23_19 ),
inference(equality_resolution,[],[f3694]) ).
fof(f3696,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK20)
| sK19 = sK20
| ~ spl23_13
| ~ spl23_19
| spl23_59 ),
inference(forward_subsumption_resolution,[],[f3695,f3087]) ).
fof(f3697,plain,
( sK19 = sK20
| ~ spl23_13
| ~ spl23_19
| spl23_58
| spl23_59 ),
inference(forward_subsumption_resolution,[],[f3696,f3081]) ).
fof(f3698,plain,
( $false
| ~ spl23_13
| ~ spl23_19
| spl23_58
| spl23_59 ),
inference(forward_subsumption_resolution,[],[f3697,f153]) ).
fof(f3699,plain,
( ~ spl23_13
| ~ spl23_19
| spl23_58
| spl23_59 ),
inference(avatar_contradiction_clause,[],[f3698]) ).
fof(f3700,plain,
( spl23_34
| ~ spl23_30
| ~ spl23_31 ),
inference(avatar_split_clause,[],[f3118,f1661,f1657,f2183]) ).
fof(f3703,plain,
( ~ in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK20)
| sK19 = sK20
| ~ spl23_13
| ~ spl23_19
| ~ spl23_59 ),
inference(forward_subsumption_resolution,[],[f3425,f3088]) ).
fof(f3704,plain,
( sK19 = sK20
| ~ spl23_13
| ~ spl23_19
| ~ spl23_58
| ~ spl23_59 ),
inference(forward_subsumption_resolution,[],[f3703,f3082]) ).
fof(f3705,plain,
( $false
| ~ spl23_13
| ~ spl23_19
| ~ spl23_58
| ~ spl23_59 ),
inference(forward_subsumption_resolution,[],[f3704,f153]) ).
fof(f3706,plain,
( ~ spl23_13
| ~ spl23_19
| ~ spl23_58
| ~ spl23_59 ),
inference(avatar_contradiction_clause,[],[f3705]) ).
fof(f3708,plain,
( ~ in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),empty_set)),sK20)
| ~ spl23_57
| spl23_58 ),
inference(forward_demodulation,[],[f3081,f3078]) ).
fof(f3710,plain,
( ~ in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(empty_set,sK17(sK19,sK20))),sK20)
| ~ spl23_57
| spl23_58 ),
inference(forward_demodulation,[],[f3708,f91]) ).
fof(f3712,plain,
( $false
| ~ spl23_55
| ~ spl23_57
| spl23_58 ),
inference(forward_subsumption_resolution,[],[f3710,f2993]) ).
fof(f3713,plain,
( ~ spl23_55
| ~ spl23_57
| spl23_58 ),
inference(avatar_contradiction_clause,[],[f3712]) ).
fof(f3717,plain,
( sK18(sK19,sK20) != apply(sK19,sK17(sK19,sK20))
| spl23_30
| ~ spl23_31 ),
inference(forward_demodulation,[],[f1658,f1663]) ).
fof(f3719,plain,
( $false
| spl23_54
| ~ spl23_58 ),
inference(forward_subsumption_resolution,[],[f3114,f2903]) ).
fof(f3720,plain,
( spl23_54
| ~ spl23_58 ),
inference(avatar_contradiction_clause,[],[f3719]) ).
fof(f3857,plain,
( empty_set = apply(sK19,sK17(sK19,sK20))
| spl23_54 ),
inference(resolution,[],[f2903,f189]) ).
fof(f3858,plain,
( empty_set = apply(sK20,sK17(sK19,sK20))
| spl23_54 ),
inference(resolution,[],[f2903,f190]) ).
fof(f4095,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK17(sK19,X0)),unordered_pair(sK17(sK19,X0),sK18(sK19,X0))),sK19)
| in(unordered_pair(singleton(sK17(sK19,X0)),unordered_pair(sK17(sK19,X0),sK18(sK19,X0))),X0)
| sK19 = X0
| in(sK16(X0),X0) )
| ~ spl23_13 ),
inference(equality_resolution,[],[f3188]) ).
fof(f4141,plain,
( ~ spl23_34
| spl23_30
| ~ spl23_31 ),
inference(avatar_split_clause,[],[f3717,f1661,f1657,f2183]) ).
fof(f4158,plain,
( empty_set != apply(sK20,sK17(sK19,sK20))
| spl23_30
| spl23_54 ),
inference(forward_demodulation,[],[f1658,f3857]) ).
fof(f4160,plain,
( $false
| spl23_30
| spl23_54 ),
inference(forward_subsumption_resolution,[],[f4158,f3858]) ).
fof(f4161,plain,
( spl23_30
| spl23_54 ),
inference(avatar_contradiction_clause,[],[f4160]) ).
fof(f4168,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| sK19 = sK20
| in(sK16(sK20),sK20)
| ~ spl23_13
| spl23_58 ),
inference(resolution,[],[f3081,f4095]) ).
fof(f4172,plain,
( sK19 = sK20
| in(sK16(sK20),sK20)
| ~ spl23_13
| spl23_58
| spl23_59 ),
inference(forward_subsumption_resolution,[],[f4168,f3087]) ).
fof(f4173,plain,
( in(sK16(sK20),sK20)
| ~ spl23_13
| spl23_58
| spl23_59 ),
inference(forward_subsumption_resolution,[],[f4172,f153]) ).
fof(f4174,plain,
( $false
| ~ spl23_13
| spl23_19
| spl23_58
| spl23_59 ),
inference(forward_subsumption_resolution,[],[f4173,f1002]) ).
fof(f4175,plain,
( ~ spl23_13
| spl23_19
| spl23_58
| spl23_59 ),
inference(avatar_contradiction_clause,[],[f4174]) ).
fof(f4179,plain,
( spl23_55
| ~ spl23_53
| ~ spl23_56 ),
inference(avatar_split_clause,[],[f3043,f2996,f2897,f2992]) ).
fof(f4274,plain,
( in(sK15(sK19),sK19)
| in(sK16(sK20),sK20)
| sK19 = sK20
| ~ in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| ~ spl23_58 ),
inference(resolution,[],[f3082,f335]) ).
fof(f4292,plain,
( ~ in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK20)
| sK19 = sK20
| in(sK16(sK20),sK20)
| ~ spl23_13
| ~ spl23_59 ),
inference(resolution,[],[f3088,f3387]) ).
fof(f4299,plain,
( sK19 = sK20
| in(sK16(sK20),sK20)
| ~ spl23_13
| ~ spl23_58
| ~ spl23_59 ),
inference(forward_subsumption_resolution,[],[f4292,f3082]) ).
fof(f4302,plain,
( in(sK16(sK20),sK20)
| ~ spl23_13
| ~ spl23_58
| ~ spl23_59 ),
inference(forward_subsumption_resolution,[],[f4299,f153]) ).
fof(f4303,plain,
( $false
| ~ spl23_13
| spl23_19
| ~ spl23_58
| ~ spl23_59 ),
inference(forward_subsumption_resolution,[],[f4302,f1002]) ).
fof(f4304,plain,
( ~ spl23_13
| spl23_19
| ~ spl23_58
| ~ spl23_59 ),
inference(avatar_contradiction_clause,[],[f4303]) ).
fof(f4312,plain,
( in(sK16(sK20),sK20)
| sK19 = sK20
| ~ in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| spl23_13
| ~ spl23_58 ),
inference(forward_subsumption_resolution,[],[f4274,f766]) ).
fof(f4318,plain,
( sK19 = sK20
| ~ in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| spl23_13
| spl23_19
| ~ spl23_58 ),
inference(forward_subsumption_resolution,[],[f4312,f1002]) ).
fof(f4323,plain,
( ~ in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| spl23_13
| spl23_19
| ~ spl23_58 ),
inference(forward_subsumption_resolution,[],[f4318,f153]) ).
fof(f4324,plain,
( $false
| spl23_13
| spl23_19
| ~ spl23_58
| ~ spl23_59 ),
inference(forward_subsumption_resolution,[],[f4323,f3088]) ).
fof(f4325,plain,
( spl23_13
| spl23_19
| ~ spl23_58
| ~ spl23_59 ),
inference(avatar_contradiction_clause,[],[f4324]) ).
fof(f4327,plain,
( ~ spl23_34
| ~ spl23_30
| spl23_31 ),
inference(avatar_split_clause,[],[f3268,f1661,f1657,f2183]) ).
fof(f4402,plain,
( in(sK16(sK20),sK20)
| in(sK15(sK19),sK19)
| sK19 = sK20
| sK18(sK19,sK20) = apply(sK19,sK17(sK19,sK20))
| ~ relation(sK19)
| ~ function(sK19)
| spl23_58 ),
inference(resolution,[],[f3081,f550]) ).
fof(f4404,plain,
( in(unordered_pair(singleton(sK17(sK19,sK20)),unordered_pair(sK17(sK19,sK20),sK18(sK19,sK20))),sK19)
| in(sK16(sK20),sK20)
| in(sK15(sK19),sK19)
| sK19 = sK20
| spl23_58 ),
inference(resolution,[],[f3081,f453]) ).
fof(f4405,plain,
( in(sK16(sK20),sK20)
| in(sK15(sK19),sK19)
| sK19 = sK20
| spl23_58
| spl23_59 ),
inference(forward_subsumption_resolution,[],[f4404,f3087]) ).
fof(f4407,plain,
( in(sK15(sK19),sK19)
| sK19 = sK20
| sK18(sK19,sK20) = apply(sK19,sK17(sK19,sK20))
| ~ relation(sK19)
| ~ function(sK19)
| spl23_19
| spl23_58 ),
inference(forward_subsumption_resolution,[],[f4402,f1002]) ).
fof(f4408,plain,
( in(sK15(sK19),sK19)
| sK19 = sK20
| spl23_19
| spl23_58
| spl23_59 ),
inference(forward_subsumption_resolution,[],[f4405,f1002]) ).
fof(f4410,plain,
( sK19 = sK20
| sK18(sK19,sK20) = apply(sK19,sK17(sK19,sK20))
| ~ relation(sK19)
| ~ function(sK19)
| spl23_13
| spl23_19
| spl23_58 ),
inference(forward_subsumption_resolution,[],[f4407,f766]) ).
fof(f4411,plain,
( sK19 = sK20
| spl23_13
| spl23_19
| spl23_58
| spl23_59 ),
inference(forward_subsumption_resolution,[],[f4408,f766]) ).
fof(f4413,plain,
( sK18(sK19,sK20) = apply(sK19,sK17(sK19,sK20))
| ~ relation(sK19)
| ~ function(sK19)
| spl23_13
| spl23_19
| spl23_58 ),
inference(forward_subsumption_resolution,[],[f4410,f153]) ).
fof(f4414,plain,
( $false
| spl23_13
| spl23_19
| spl23_58
| spl23_59 ),
inference(forward_subsumption_resolution,[],[f4411,f153]) ).
fof(f4415,plain,
( spl23_13
| spl23_19
| spl23_58
| spl23_59 ),
inference(avatar_contradiction_clause,[],[f4414]) ).
fof(f4417,plain,
( ~ relation(sK19)
| ~ function(sK19)
| spl23_13
| spl23_19
| spl23_34
| spl23_58 ),
inference(forward_subsumption_resolution,[],[f4413,f2184]) ).
fof(f4419,plain,
( ~ function(sK19)
| spl23_13
| spl23_19
| spl23_34
| spl23_58 ),
inference(forward_subsumption_resolution,[],[f4417,f148]) ).
fof(f4420,plain,
( $false
| spl23_13
| spl23_19
| spl23_34
| spl23_58 ),
inference(forward_subsumption_resolution,[],[f4419,f147]) ).
fof(f4421,plain,
( spl23_13
| spl23_19
| spl23_34
| spl23_58 ),
inference(avatar_contradiction_clause,[],[f4420]) ).
cnf(s11,plain,
( spl23_13
| spl23_14 ),
inference(sat_conversion,[],[f771]) ).
cnf(s14,plain,
( spl23_19
| spl23_20 ),
inference(sat_conversion,[],[f1007]) ).
cnf(s25,plain,
( ~ spl23_14
| spl23_19
| spl23_30
| spl23_31 ),
inference(sat_conversion,[],[f1664]) ).
cnf(s53,plain,
( ~ spl23_19
| spl23_20 ),
inference(sat_conversion,[],[f2883]) ).
cnf(s54,plain,
( spl23_13
| ~ spl23_20
| spl23_30
| spl23_34 ),
inference(sat_conversion,[],[f2884]) ).
cnf(s56,plain,
( ~ spl23_30
| spl23_53
| ~ spl23_54 ),
inference(sat_conversion,[],[f2905]) ).
cnf(s61,plain,
( spl23_54
| ~ spl23_56 ),
inference(sat_conversion,[],[f3012]) ).
cnf(s64,plain,
( spl23_31
| ~ spl23_34
| ~ spl23_54 ),
inference(sat_conversion,[],[f3063]) ).
cnf(s68,plain,
( ~ spl23_31
| ~ spl23_34
| spl23_57
| spl23_58 ),
inference(sat_conversion,[],[f3092]) ).
cnf(s70,plain,
( ~ spl23_34
| ~ spl23_54
| spl23_59 ),
inference(sat_conversion,[],[f3099]) ).
cnf(s72,plain,
( spl23_56
| ~ spl23_57
| ~ spl23_59 ),
inference(sat_conversion,[],[f3103]) ).
cnf(s73,plain,
( spl23_13
| ~ spl23_19
| ~ spl23_58
| ~ spl23_59 ),
inference(sat_conversion,[],[f3117]) ).
cnf(s75,plain,
( ~ spl23_31
| spl23_34
| ~ spl23_54 ),
inference(sat_conversion,[],[f3124]) ).
cnf(s77,plain,
( spl23_34
| ~ spl23_59 ),
inference(sat_conversion,[],[f3150]) ).
cnf(s78,plain,
( spl23_13
| ~ spl23_19
| spl23_58
| spl23_59 ),
inference(sat_conversion,[],[f3154]) ).
cnf(s79,plain,
( spl23_31
| ~ spl23_58 ),
inference(sat_conversion,[],[f3158]) ).
cnf(s83,plain,
( ~ spl23_13
| ~ spl23_19
| spl23_58
| spl23_59 ),
inference(sat_conversion,[],[f3699]) ).
cnf(s84,plain,
( ~ spl23_30
| ~ spl23_31
| spl23_34 ),
inference(sat_conversion,[],[f3700]) ).
cnf(s87,plain,
( ~ spl23_13
| ~ spl23_19
| ~ spl23_58
| ~ spl23_59 ),
inference(sat_conversion,[],[f3706]) ).
cnf(s89,plain,
( ~ spl23_55
| ~ spl23_57
| spl23_58 ),
inference(sat_conversion,[],[f3713]) ).
cnf(s91,plain,
( spl23_54
| ~ spl23_58 ),
inference(sat_conversion,[],[f3720]) ).
cnf(s114,plain,
( spl23_30
| ~ spl23_31
| ~ spl23_34 ),
inference(sat_conversion,[],[f4141]) ).
cnf(s117,plain,
( spl23_30
| spl23_54 ),
inference(sat_conversion,[],[f4161]) ).
cnf(s118,plain,
( ~ spl23_13
| spl23_19
| spl23_58
| spl23_59 ),
inference(sat_conversion,[],[f4175]) ).
cnf(s124,plain,
( ~ spl23_53
| spl23_55
| ~ spl23_56 ),
inference(sat_conversion,[],[f4179]) ).
cnf(s128,plain,
( ~ spl23_13
| spl23_19
| ~ spl23_58
| ~ spl23_59 ),
inference(sat_conversion,[],[f4304]) ).
cnf(s131,plain,
( spl23_13
| spl23_19
| ~ spl23_58
| ~ spl23_59 ),
inference(sat_conversion,[],[f4325]) ).
cnf(s132,plain,
( ~ spl23_30
| spl23_31
| ~ spl23_34 ),
inference(sat_conversion,[],[f4327]) ).
cnf(s141,plain,
( spl23_13
| spl23_19
| spl23_58
| spl23_59 ),
inference(sat_conversion,[],[f4415]) ).
cnf(s142,plain,
( spl23_13
| spl23_19
| spl23_34
| spl23_58 ),
inference(sat_conversion,[],[f4421]) ).
cnf(s143,plain,
( spl23_30
| spl23_19
| spl23_13 ),
inference(rat,[],[s114,s54,s25,s11,s14]) ).
cnf(s144,plain,
( spl23_54
| ~ spl23_31
| spl23_19
| spl23_13 ),
inference(rat,[],[s72,s68,s141,s61,s91,s84,s143]) ).
cnf(s145,plain,
( ~ spl23_31
| spl23_19
| spl23_13 ),
inference(rat,[],[s124,s72,s89,s68,s131,s56,s70,s144,s84,s143]) ).
cnf(s146,plain,
( spl23_19
| spl23_13 ),
inference(rat,[],[s142,s79,s132,s145,s143]) ).
cnf(s147,plain,
( spl23_58
| ~ spl23_31
| ~ spl23_30
| spl23_13 ),
inference(rat,[],[s56,s124,s61,s72,s89,s68,s78,s146,s84]) ).
cnf(s148,plain,
( ~ spl23_31
| ~ spl23_30
| spl23_13 ),
inference(rat,[],[s70,s73,s91,s147,s84,s146]) ).
cnf(s149,plain,
( ~ spl23_30
| spl23_13 ),
inference(rat,[],[s78,s77,s79,s132,s148,s146]) ).
cnf(s150,plain,
spl23_13,
inference(rat,[],[s64,s114,s54,s117,s149,s53,s146]) ).
cnf(s151,plain,
( spl23_58
| ~ spl23_31
| ~ spl23_30
| spl23_19 ),
inference(rat,[],[s56,s124,s61,s72,s89,s68,s118,s84,s150]) ).
cnf(s152,plain,
( ~ spl23_31
| ~ spl23_30
| spl23_19 ),
inference(rat,[],[s70,s128,s91,s151,s84,s150]) ).
cnf(s153,plain,
( ~ spl23_30
| spl23_19 ),
inference(rat,[],[s118,s77,s79,s132,s152,s150]) ).
cnf(s154,plain,
( ~ spl23_31
| spl23_30 ),
inference(rat,[],[s75,s114,s117]) ).
cnf(s155,plain,
spl23_19,
inference(rat,[],[s77,s118,s64,s79,s154,s117,s153,s150]) ).
cnf(s158,plain,
( spl23_58
| ~ spl23_31
| ~ spl23_30 ),
inference(rat,[],[s56,s124,s61,s72,s89,s68,s83,s84,s150,s155]) ).
cnf(s159,plain,
( ~ spl23_31
| ~ spl23_30 ),
inference(rat,[],[s70,s87,s91,s158,s84,s155,s150]) ).
cnf(s160,plain,
( spl23_31
| ~ spl23_30 ),
inference(rat,[],[s83,s77,s79,s132,s155,s150]) ).
cnf(s161,plain,
~ spl23_30,
inference(rat,[],[s160,s159]) ).
cnf(s162,plain,
spl23_54,
inference(rat,[],[s117,s161]) ).
cnf(s163,plain,
~ spl23_31,
inference(rat,[],[s154,s161]) ).
cnf(s164,plain,
~ spl23_58,
inference(rat,[],[s79,s163]) ).
cnf(s165,plain,
~ spl23_34,
inference(rat,[],[s64,s162,s163]) ).
cnf(s166,plain,
spl23_59,
inference(rat,[],[s83,s155,s150,s164]) ).
cnf(s167,plain,
$false,
inference(rat,[],[s77,s166,s165]) ).
fof(f4422,plain,
$false,
inference(avatar_sat_refutation,[],[s167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET990+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:19:17 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 10.47/2.37 % (402823)Detected formulas, will run a generic FOF schedule.
% 10.47/2.37 % (402832)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2854393116:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.47/2.37 % (402832)Instruction limit reached!
% 10.47/2.37 % (402832)------------------------------
% 10.47/2.37 % (402832)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.47/2.37 % (402832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.47/2.37 % (402832)CaDiCaL version: 2.1.3
% 10.47/2.37 % (402832)Termination reason: Instruction limit
% 10.47/2.37 % (402832)Termination phase: Saturation
% 10.47/2.37 % (402832)Time elapsed: 0.037 s
% 10.47/2.37 % (402832)Peak memory usage: 88 MB
% 10.47/2.37 % (402832)Instructions burned: 119 (million)
% 10.47/2.37 % (402828)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=4077856511:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.47/2.37 % (402829)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=1537228519:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.47/2.37 % (402830)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=3711552972:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.47/2.37 % (402831)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3566481271:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.47/2.37 % (402831)Refutation not found, incomplete strategy
% 10.47/2.37 % (402831)------------------------------
% 10.47/2.37 % (402831)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.47/2.37 % (402831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.47/2.37 % (402831)CaDiCaL version: 2.1.3
% 10.47/2.37 % (402831)Termination reason: Refutation not found, incomplete strategy
% 10.47/2.37 % (402831)Time elapsed: 0.003 s
% 10.47/2.37 % (402831)Peak memory usage: 88 MB
% 10.47/2.37 % (402831)Instructions burned: 3 (million)
% 10.47/2.37 % (402833)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=691617712:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.47/2.37 % (402834)dis-21_1_sil=8000:lcm=predicate:random_seed=1627287368: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)
% 10.47/2.37 % (402834)Instruction limit reached!
% 10.47/2.37 % (402834)------------------------------
% 10.47/2.37 % (402834)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.47/2.37 % (402834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.47/2.37 % (402834)CaDiCaL version: 2.1.3
% 10.47/2.37 % (402834)Termination reason: Instruction limit
% 10.47/2.37 % (402834)Termination phase: Saturation
% 10.47/2.37 % (402834)Time elapsed: 0.073 s
% 10.47/2.37 % (402834)Peak memory usage: 89 MB
% 10.47/2.37 % (402834)Instructions burned: 129 (million)
% 10.47/2.37 % (402833)Instruction limit reached!
% 10.47/2.37 % (402833)------------------------------
% 10.47/2.37 % (402833)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.47/2.37 % (402833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.47/2.37 % (402833)CaDiCaL version: 2.1.3
% 10.47/2.37 % (402833)Termination reason: Instruction limit
% 10.47/2.37 % (402833)Termination phase: Saturation
% 10.47/2.37 % (402833)Time elapsed: 0.092 s
% 10.47/2.37 % (402833)Peak memory usage: 89 MB
% 10.47/2.37 % (402833)Instructions burned: 139 (million)
% 10.47/2.37 % (402836)lrs+10_1_sil=8000:sp=occurrence:random_seed=3822856224:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 10.47/2.37 % (402836)Instruction limit reached!
% 10.47/2.37 % (402836)------------------------------
% 10.47/2.37 % (402836)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.47/2.37 % (402836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.47/2.37 % (402836)CaDiCaL version: 2.1.3
% 10.47/2.37 % (402836)Termination reason: Instruction limit
% 10.47/2.37 % (402836)Termination phase: Saturation
% 10.47/2.37 % (402836)Time elapsed: 0.090 s
% 10.47/2.37 % (402836)Peak memory usage: 91 MB
% 10.47/2.37 % (402836)Instructions burned: 288 (million)
% 10.47/2.37 % (402843)lrs+10_1_sil=32000:urr=on:br=off:random_seed=227101044:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.47/2.37 % (402843)Refutation not found, incomplete strategy
% 10.47/2.37 % (402843)------------------------------
% 10.47/2.37 % (402843)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.47/2.37 % (402843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.47/2.37 % (402843)CaDiCaL version: 2.1.3
% 10.47/2.37 % (402843)Termination reason: Refutation not found, incomplete strategy
% 10.47/2.37 % (402843)Time elapsed: 0.004 s
% 10.47/2.37 % (402843)Peak memory usage: 89 MB
% 10.47/2.37 % (402843)Instructions burned: 3 (million)
% 10.47/2.37 % (402831)------------------------------
% 10.47/2.37 % (402831)------------------------------
% 10.47/2.37 % (402844)lrs+1011_1_sil=32000:sp=occurrence:random_seed=989258192:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 10.47/2.37 % (402846)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=3412348726:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 10.47/2.37 % (402846)Instruction limit reached!
% 10.47/2.37 % (402846)------------------------------
% 10.47/2.37 % (402846)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.47/2.37 % (402846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.47/2.37 % (402846)CaDiCaL version: 2.1.3
% 10.47/2.37 % (402846)Termination reason: Instruction limit
% 10.47/2.37 % (402846)Termination phase: Saturation
% 10.47/2.37 % (402846)Time elapsed: 0.072 s
% 10.47/2.37 % (402846)Peak memory usage: 90 MB
% 10.47/2.37 % (402846)Instructions burned: 251 (million)
% 10.47/2.37 % (402848)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2080709715:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 10.47/2.37 % (402848)Refutation not found, incomplete strategy
% 10.47/2.37 % (402848)------------------------------
% 10.47/2.37 % (402848)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.47/2.37 % (402848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.47/2.37 % (402848)CaDiCaL version: 2.1.3
% 10.47/2.37 % (402848)Termination reason: Refutation not found, incomplete strategy
% 10.47/2.37 % (402848)Time elapsed: 0.004 s
% 10.47/2.37 % (402848)Peak memory usage: 89 MB
% 10.47/2.37 % (402848)Instructions burned: 4 (million)
% 10.47/2.37 % (402844)Instruction limit reached!
% 10.47/2.37 % (402844)------------------------------
% 10.47/2.37 % (402844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.47/2.37 % (402844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.47/2.37 % (402844)CaDiCaL version: 2.1.3
% 10.47/2.37 % (402844)Termination reason: Instruction limit
% 10.47/2.37 % (402844)Termination phase: Saturation
% 10.47/2.37 % (402844)Time elapsed: 0.207 s
% 10.47/2.37 % (402844)Peak memory usage: 91 MB
% 10.47/2.37 % (402844)Instructions burned: 326 (million)
% 10.47/2.37 % (402843)------------------------------
% 10.47/2.37 % (402843)------------------------------
% 10.47/2.37 % (402851)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2193616240:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 10.47/2.37 % (402853)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=714980178:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 10.47/2.37 % (402848)------------------------------
% 10.47/2.37 % (402848)------------------------------
% 10.47/2.37 % (402854)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3403207677:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 10.47/2.37 % (402853)Instruction limit reached!
% 10.47/2.37 % (402853)------------------------------
% 10.47/2.37 % (402853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.47/2.37 % (402853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.47/2.37 % (402853)CaDiCaL version: 2.1.3
% 10.47/2.37 % (402853)Termination reason: Instruction limit
% 10.47/2.37 % (402853)Termination phase: Saturation
% 10.47/2.37 % (402853)Time elapsed: 0.079 s
% 10.47/2.37 % (402853)Peak memory usage: 90 MB
% 10.47/2.37 % (402853)Instructions burned: 114 (million)
% 10.47/2.37 % (402854)Instruction limit reached!
% 10.47/2.37 % (402854)------------------------------
% 10.47/2.37 % (402854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.47/2.37 % (402854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.47/2.37 % (402854)CaDiCaL version: 2.1.3
% 10.47/2.37 % (402854)Termination reason: Instruction limit
% 10.47/2.37 % (402854)Termination phase: Saturation
% 10.47/2.37 % (402854)Time elapsed: 0.064 s
% 10.47/2.37 % (402854)Peak memory usage: 89 MB
% 10.47/2.37 % (402854)Instructions burned: 128 (million)
% 10.47/2.37 % (402858)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3695003718:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 10.47/2.37 % (402859)lrs+10_1_sil=8000:sp=occurrence:random_seed=2353435743:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 10.47/2.37 % (402860)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=606078386:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 10.47/2.37 % (402860)Refutation not found, incomplete strategy
% 10.47/2.37 % (402860)------------------------------
% 10.47/2.37 % (402860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.47/2.37 % (402860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.47/2.37 % (402860)CaDiCaL version: 2.1.3
% 10.47/2.37 % (402860)Termination reason: Refutation not found, incomplete strategy
% 10.47/2.37 % (402860)Time elapsed: 0.004 s
% 10.47/2.37 % (402860)Peak memory usage: 88 MB
% 10.47/2.37 % (402860)Instructions burned: 5 (million)
% 10.47/2.37 % (402858)Instruction limit reached!
% 10.47/2.37 % (402858)------------------------------
% 10.47/2.37 % (402858)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.47/2.37 % (402858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.47/2.37 % (402858)CaDiCaL version: 2.1.3
% 10.47/2.37 % (402858)Termination reason: Instruction limit
% 10.47/2.37 % (402858)Termination phase: Saturation
% 10.47/2.37 % (402858)Time elapsed: 0.071 s
% 10.47/2.37 % (402858)Peak memory usage: 89 MB
% 10.47/2.37 % (402858)Instructions burned: 115 (million)
% 10.47/2.37 % (402864)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2090087944:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 10.47/2.37 % (402860)------------------------------
% 10.47/2.37 % (402860)------------------------------
% 10.47/2.37 % (402851)First to succeed.
% 10.47/2.37 % (402851)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-402823"
% 10.47/2.37 % (402866)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2721741185:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 10.47/2.37 % (402851)Refutation found. Thanks to Tanya!
% 10.47/2.37 % SZS status Theorem for theBenchmark
% 10.47/2.37 % SZS output start Proof for theBenchmark
% See solution above
% 11.14/2.46 % (402851)------------------------------
% 11.14/2.46 % (402851)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.14/2.46 % (402851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.14/2.46 % (402851)CaDiCaL version: 2.1.3
% 11.14/2.46 % (402851)Termination reason: Refutation
% 11.14/2.46 % (402851)Time elapsed: 0.612 s
% 11.14/2.46 % (402851)Peak memory usage: 135 MB
% 11.14/2.46 % (402851)Instructions burned: 1663 (million)
% 11.14/2.46 % (402851)------------------------------
% 11.14/2.46 % (402851)------------------------------
% 11.14/2.46 % (402823)Success in time 1.509 s
% 11.14/2.46 % Vampire exiting
%------------------------------------------------------------------------------