%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU218+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:47:48 PM UTC 2026
% Result : Theorem 11.09s 2.46s
% Output : Refutation 11.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 59
% Syntax : Number of formulae : 491 ( 44 unt; 48 def)
% Number of atoms : 1912 ( 307 equ)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 2521 (1100 ~;1202 |; 127 &)
% ( 68 <=>; 22 =>; 0 <=; 2 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 54 ( 52 usr; 49 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 5 con; 0-2 aty)
% Number of variables : 450 ( 0 sgn 414 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f7,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) )
& ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f8,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f10,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f11,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( X1 = relation_inverse(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
fof(f12,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> function_inverse(X0) = relation_inverse(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).
fof(f14,axiom,
! [X0] :
( relation(X0)
=> relation(relation_inverse(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f29,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f43,axiom,
! [X0] :
( relation(X0)
=> ( relation_rng(X0) = relation_dom(relation_inverse(X0))
& relation_dom(X0) = relation_rng(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f46,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
=> ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) )
& ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
=> ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f47,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
=> ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) )
& ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
=> ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f62,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f63,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_inverse(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f67,plain,
! [X0] :
( function_inverse(X0) = relation_inverse(X0)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f68,plain,
! [X0] :
( function_inverse(X0) = relation_inverse(X0)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f67]) ).
fof(f71,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f81,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f86,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(relation_inverse(X0))
& relation_dom(X0) = relation_rng(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f90,plain,
? [X0] :
( ? [X1] :
( ( X1 = function_inverse(X0)
<~> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ) ) )
& relation(X1)
& function(X1) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f91,plain,
? [X0] :
( ? [X1] :
( ( X1 = function_inverse(X0)
<~> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ) ) )
& relation(X1)
& function(X1) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(flattening,[],[f90]) ).
fof(f99,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( X2 = apply(X0,X1)
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) )
& ( ( ( X2 = apply(X0,X1)
| empty_set != X2 )
& ( X2 = empty_set
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f63]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f64]) ).
fof(f101,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,[],[f100]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK2(X0,X1),X3),X0)
| ~ in(sK2(X0,X1),X1) )
& ( in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK4(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X2,sK2(X0,X1)),skolemize(X4,sK3(X0,X1)),skolemize(X7,sK4(X0,X5))],[f101]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f65]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f103]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK5(X0,X1)),X0)
| ~ in(sK5(X0,X1),X1) )
& ( in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0)
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK7(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X2,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X7,sK7(X0,X5))],[f104]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = relation_inverse(X0)
| ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X0) )
& ( in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f66]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = relation_inverse(X0)
| ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0) )
& ( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f106]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = relation_inverse(X0)
| ( ( ~ in(ordered_pair(sK9(X0,X1),sK8(X0,X1)),X0)
| ~ in(ordered_pair(sK8(X0,X1),sK9(X0,X1)),X1) )
& ( in(ordered_pair(sK9(X0,X1),sK8(X0,X1)),X0)
| in(ordered_pair(sK8(X0,X1),sK9(X0,X1)),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0) )
& ( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X2,sK8(X0,X1)),skolemize(X3,sK9(X0,X1))],[f107]) ).
fof(f120,plain,
? [X0] :
( ? [X1] :
( ( relation_rng(X0) != relation_dom(X1)
| ? [X2,X3] :
( ( ( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
& in(X2,relation_rng(X0))
& apply(X1,X2) = X3 )
| ( ( ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& in(X3,relation_dom(X0))
& apply(X0,X3) = X2 ) )
| function_inverse(X0) != X1 )
& ( ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ) )
| X1 = function_inverse(X0) )
& relation(X1)
& function(X1) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(nnf_transformation,[],[f91]) ).
fof(f121,plain,
? [X0] :
( ? [X1] :
( ( relation_rng(X0) != relation_dom(X1)
| ? [X2,X3] :
( ( ( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
& in(X2,relation_rng(X0))
& apply(X1,X2) = X3 )
| ( ( ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& in(X3,relation_dom(X0))
& apply(X0,X3) = X2 ) )
| function_inverse(X0) != X1 )
& ( ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ) )
| X1 = function_inverse(X0) )
& relation(X1)
& function(X1) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(flattening,[],[f120]) ).
fof(f122,plain,
? [X0] :
( ? [X1] :
( ( relation_rng(X0) != relation_dom(X1)
| ? [X2,X3] :
( ( ( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
& in(X2,relation_rng(X0))
& apply(X1,X2) = X3 )
| ( ( ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& in(X3,relation_dom(X0))
& apply(X0,X3) = X2 ) )
| function_inverse(X0) != X1 )
& ( ( relation_dom(X1) = relation_rng(X0)
& ! [X4,X5] :
( ( ( in(X5,relation_dom(X0))
& apply(X0,X5) = X4 )
| ~ in(X4,relation_rng(X0))
| apply(X1,X4) != X5 )
& ( ( in(X4,relation_rng(X0))
& apply(X1,X4) = X5 )
| ~ in(X5,relation_dom(X0))
| apply(X0,X5) != X4 ) ) )
| X1 = function_inverse(X0) )
& relation(X1)
& function(X1) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(rectify,[],[f121]) ).
fof(f123,plain,
( ( relation_rng(sK21) != relation_dom(sK22)
| ( ( ~ in(sK24,relation_dom(sK21))
| sK23 != apply(sK21,sK24) )
& in(sK23,relation_rng(sK21))
& sK24 = apply(sK22,sK23) )
| ( ( ~ in(sK23,relation_rng(sK21))
| sK24 != apply(sK22,sK23) )
& in(sK24,relation_dom(sK21))
& sK23 = apply(sK21,sK24) )
| sK22 != function_inverse(sK21) )
& ( ( relation_rng(sK21) = relation_dom(sK22)
& ! [X4,X5] :
( ( ( in(X5,relation_dom(sK21))
& apply(sK21,X5) = X4 )
| ~ in(X4,relation_rng(sK21))
| apply(sK22,X4) != X5 )
& ( ( in(X4,relation_rng(sK21))
& apply(sK22,X4) = X5 )
| ~ in(X5,relation_dom(sK21))
| apply(sK21,X5) != X4 ) ) )
| sK22 = function_inverse(sK21) )
& relation(sK22)
& function(sK22)
& one_to_one(sK21)
& relation(sK21)
& function(sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22,sK23,sK24]),skolemize(X0,sK21),skolemize(X1,sK22),skolemize(X2,sK23),skolemize(X3,sK24)],[f122]) ).
fof(f130,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f137,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,[],[f99]) ).
fof(f138,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,[],[f99]) ).
fof(f140,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f144,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f147,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f148,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f149,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f150,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| in(ordered_pair(sK9(X0,X1),sK8(X0,X1)),X0)
| in(ordered_pair(sK8(X0,X1),sK9(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f151,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(ordered_pair(sK9(X0,X1),sK8(X0,X1)),X0)
| ~ in(ordered_pair(sK8(X0,X1),sK9(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f152,plain,
! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f155,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f176,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f200,plain,
! [X0] :
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f203,plain,
function(sK21),
inference(cnf_transformation,[],[f123]) ).
fof(f204,plain,
relation(sK21),
inference(cnf_transformation,[],[f123]) ).
fof(f205,plain,
one_to_one(sK21),
inference(cnf_transformation,[],[f123]) ).
fof(f206,plain,
function(sK22),
inference(cnf_transformation,[],[f123]) ).
fof(f207,plain,
relation(sK22),
inference(cnf_transformation,[],[f123]) ).
fof(f208,plain,
! [X4,X5] :
( apply(sK22,X4) = X5
| ~ in(X5,relation_dom(sK21))
| apply(sK21,X5) != X4
| sK22 = function_inverse(sK21) ),
inference(cnf_transformation,[],[f123]) ).
fof(f209,plain,
! [X4,X5] :
( in(X4,relation_rng(sK21))
| ~ in(X5,relation_dom(sK21))
| apply(sK21,X5) != X4
| sK22 = function_inverse(sK21) ),
inference(cnf_transformation,[],[f123]) ).
fof(f210,plain,
! [X4,X5] :
( apply(sK21,X5) = X4
| ~ in(X4,relation_rng(sK21))
| apply(sK22,X4) != X5
| sK22 = function_inverse(sK21) ),
inference(cnf_transformation,[],[f123]) ).
fof(f211,plain,
! [X4,X5] :
( in(X5,relation_dom(sK21))
| ~ in(X4,relation_rng(sK21))
| apply(sK22,X4) != X5
| sK22 = function_inverse(sK21) ),
inference(cnf_transformation,[],[f123]) ).
fof(f212,plain,
( relation_rng(sK21) = relation_dom(sK22)
| sK22 = function_inverse(sK21) ),
inference(cnf_transformation,[],[f123]) ).
fof(f213,plain,
( relation_rng(sK21) != relation_dom(sK22)
| sK24 = apply(sK22,sK23)
| sK23 = apply(sK21,sK24)
| sK22 != function_inverse(sK21) ),
inference(cnf_transformation,[],[f123]) ).
fof(f214,plain,
( relation_rng(sK21) != relation_dom(sK22)
| sK24 = apply(sK22,sK23)
| in(sK24,relation_dom(sK21))
| sK22 != function_inverse(sK21) ),
inference(cnf_transformation,[],[f123]) ).
fof(f216,plain,
( relation_rng(sK21) != relation_dom(sK22)
| in(sK23,relation_rng(sK21))
| sK23 = apply(sK21,sK24)
| sK22 != function_inverse(sK21) ),
inference(cnf_transformation,[],[f123]) ).
fof(f217,plain,
( relation_rng(sK21) != relation_dom(sK22)
| in(sK23,relation_rng(sK21))
| in(sK24,relation_dom(sK21))
| sK22 != function_inverse(sK21) ),
inference(cnf_transformation,[],[f123]) ).
fof(f221,plain,
( relation_rng(sK21) != relation_dom(sK22)
| ~ in(sK24,relation_dom(sK21))
| sK23 != apply(sK21,sK24)
| ~ in(sK23,relation_rng(sK21))
| sK24 != apply(sK22,sK23)
| sK22 != function_inverse(sK21) ),
inference(cnf_transformation,[],[f123]) ).
fof(f230,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,[],[f138,f147]) ).
fof(f231,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,[],[f137,f147]) ).
fof(f234,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,[],[f140,f147]) ).
fof(f238,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f144,f147]) ).
fof(f240,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK9(X0,X1),sK8(X0,X1)),singleton(sK9(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK8(X0,X1),sK9(X0,X1)),singleton(sK8(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f151,f147,f147]) ).
fof(f241,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK9(X0,X1),sK8(X0,X1)),singleton(sK9(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK8(X0,X1),sK9(X0,X1)),singleton(sK8(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f150,f147,f147]) ).
fof(f242,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1)
| ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f149,f147,f147]) ).
fof(f243,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f148,f147,f147]) ).
fof(f247,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,[],[f231]) ).
fof(f250,plain,
! [X0,X6,X5] :
( in(X5,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f234]) ).
fof(f252,plain,
! [X0,X6,X5] :
( in(X5,relation_rng(X0))
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f238]) ).
fof(f254,plain,
! [X0,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),relation_inverse(X0))
| ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0)
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f242]) ).
fof(f255,plain,
! [X0,X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),relation_inverse(X0))
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f243]) ).
fof(f256,plain,
! [X4] :
( in(apply(sK22,X4),relation_dom(sK21))
| ~ in(X4,relation_rng(sK21))
| sK22 = function_inverse(sK21) ),
inference(equality_resolution,[],[f211]) ).
fof(f257,plain,
! [X4] :
( apply(sK21,apply(sK22,X4)) = X4
| ~ in(X4,relation_rng(sK21))
| sK22 = function_inverse(sK21) ),
inference(equality_resolution,[],[f210]) ).
fof(f258,plain,
! [X5] :
( in(apply(sK21,X5),relation_rng(sK21))
| ~ in(X5,relation_dom(sK21))
| sK22 = function_inverse(sK21) ),
inference(equality_resolution,[],[f209]) ).
fof(f259,plain,
! [X5] :
( apply(sK22,apply(sK21,X5)) = X5
| ~ in(X5,relation_dom(sK21))
| sK22 = function_inverse(sK21) ),
inference(equality_resolution,[],[f208]) ).
fof(f265,definition,
( spl26_1
<=> sK22 = function_inverse(sK21) ),
introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition]) ).
fof(f266,plain,
( sK22 = function_inverse(sK21)
| ~ spl26_1 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f267,plain,
( sK22 != function_inverse(sK21)
| spl26_1 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f269,definition,
( spl26_2
<=> sK24 = apply(sK22,sK23) ),
introduced(definition,[new_symbols(definition,[spl26_2])],[avatar_definition]) ).
fof(f270,plain,
( sK24 = apply(sK22,sK23)
| ~ spl26_2 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f271,plain,
( sK24 != apply(sK22,sK23)
| spl26_2 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f273,definition,
( spl26_3
<=> in(sK23,relation_rng(sK21)) ),
introduced(definition,[new_symbols(definition,[spl26_3])],[avatar_definition]) ).
fof(f274,plain,
( in(sK23,relation_rng(sK21))
| ~ spl26_3 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f275,plain,
( ~ in(sK23,relation_rng(sK21))
| spl26_3 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f277,definition,
( spl26_4
<=> sK23 = apply(sK21,sK24) ),
introduced(definition,[new_symbols(definition,[spl26_4])],[avatar_definition]) ).
fof(f279,plain,
( sK23 != apply(sK21,sK24)
| spl26_4 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f281,definition,
( spl26_5
<=> in(sK24,relation_dom(sK21)) ),
introduced(definition,[new_symbols(definition,[spl26_5])],[avatar_definition]) ).
fof(f282,plain,
( in(sK24,relation_dom(sK21))
| ~ spl26_5 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f283,plain,
( ~ in(sK24,relation_dom(sK21))
| spl26_5 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f285,definition,
( spl26_6
<=> relation_rng(sK21) = relation_dom(sK22) ),
introduced(definition,[new_symbols(definition,[spl26_6])],[avatar_definition]) ).
fof(f286,plain,
( relation_rng(sK21) = relation_dom(sK22)
| ~ spl26_6 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f287,plain,
( relation_rng(sK21) != relation_dom(sK22)
| spl26_6 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f288,plain,
( ~ spl26_1
| ~ spl26_2
| ~ spl26_3
| ~ spl26_4
| ~ spl26_5
| ~ spl26_6 ),
inference(avatar_split_clause,[],[f221,f285,f281,f277,f273,f269,f265]) ).
fof(f289,plain,
( relation_rng(sK21) = relation_dom(sK22)
| spl26_1 ),
inference(backward_subsumption_resolution,[],[f212,f267]) ).
fof(f291,plain,
( ! [X4] :
( apply(sK21,apply(sK22,X4)) = X4
| ~ in(X4,relation_rng(sK21)) )
| spl26_1 ),
inference(backward_subsumption_resolution,[],[f257,f267]) ).
fof(f293,plain,
( ! [X5] :
( apply(sK22,apply(sK21,X5)) = X5
| ~ in(X5,relation_dom(sK21)) )
| spl26_1 ),
inference(backward_subsumption_resolution,[],[f259,f267]) ).
fof(f299,plain,
( ! [X4] :
( ~ in(X4,relation_dom(sK22))
| apply(sK21,apply(sK22,X4)) = X4 )
| spl26_1 ),
inference(forward_demodulation,[],[f291,f289]) ).
fof(f301,plain,
( spl26_6
| spl26_1 ),
inference(avatar_split_clause,[],[f289,f265,f285]) ).
fof(f328,definition,
( spl26_7
<=> relation(sK21) ),
introduced(definition,[new_symbols(definition,[spl26_7])],[avatar_definition]) ).
fof(f330,plain,
( relation(sK21)
| ~ spl26_7 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f331,plain,
spl26_7,
inference(avatar_split_clause,[],[f204,f328]) ).
fof(f333,definition,
( spl26_8
<=> relation(sK22) ),
introduced(definition,[new_symbols(definition,[spl26_8])],[avatar_definition]) ).
fof(f335,plain,
( relation(sK22)
| ~ spl26_8 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f336,plain,
spl26_8,
inference(avatar_split_clause,[],[f207,f333]) ).
fof(f353,plain,
( ! [X0,X1] :
( apply(sK22,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK22)
| ~ in(X0,relation_dom(sK22))
| ~ function(sK22) )
| ~ spl26_8 ),
inference(resolution,[],[f335,f230]) ).
fof(f362,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(X0,apply(sK22,X0)),singleton(X0)),sK22)
| ~ in(X0,relation_dom(sK22))
| ~ function(sK22) )
| ~ spl26_8 ),
inference(resolution,[],[f335,f247]) ).
fof(f365,plain,
( ! [X0,X1] :
( in(X0,relation_dom(sK22))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK22) )
| ~ spl26_8 ),
inference(resolution,[],[f335,f250]) ).
fof(f376,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK22)
| in(X0,relation_dom(sK22)) )
| ~ spl26_8 ),
inference(forward_demodulation,[],[f365,f130]) ).
fof(f379,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(X0,apply(sK22,X0)),singleton(X0)),sK22)
| ~ in(X0,relation_dom(sK22)) )
| ~ spl26_8 ),
inference(forward_subsumption_resolution,[],[f362,f206]) ).
fof(f388,plain,
( ! [X0,X1] :
( apply(sK22,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK22)
| ~ in(X0,relation_dom(sK22)) )
| ~ spl26_8 ),
inference(forward_subsumption_resolution,[],[f353,f206]) ).
fof(f402,plain,
( ! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK22,X0))),sK22)
| ~ in(X0,relation_dom(sK22)) )
| ~ spl26_8 ),
inference(forward_demodulation,[],[f379,f130]) ).
fof(f408,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK22)
| apply(sK22,X0) = X1
| ~ in(X0,relation_dom(sK22)) )
| ~ spl26_8 ),
inference(forward_demodulation,[],[f388,f130]) ).
fof(f419,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK22)
| apply(sK22,X0) = X1 )
| ~ spl26_8 ),
inference(forward_subsumption_resolution,[],[f408,f376]) ).
fof(f421,plain,
( function_inverse(sK21) = relation_inverse(sK21)
| ~ one_to_one(sK21)
| ~ function(sK21)
| ~ spl26_7 ),
inference(resolution,[],[f330,f152]) ).
fof(f424,plain,
( relation(relation_inverse(sK21))
| ~ spl26_7 ),
inference(resolution,[],[f330,f155]) ).
fof(f431,plain,
( relation_rng(sK21) = relation_dom(relation_inverse(sK21))
| ~ spl26_7 ),
inference(resolution,[],[f330,f200]) ).
fof(f436,plain,
( ! [X0,X1] :
( apply(sK21,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK21)
| ~ in(X0,relation_dom(sK21))
| ~ function(sK21) )
| ~ spl26_7 ),
inference(resolution,[],[f330,f230]) ).
fof(f442,plain,
( ! [X0] :
( relation_inverse(X0) = sK21
| ~ in(unordered_pair(unordered_pair(sK9(X0,sK21),sK8(X0,sK21)),singleton(sK9(X0,sK21))),X0)
| ~ in(unordered_pair(unordered_pair(sK8(X0,sK21),sK9(X0,sK21)),singleton(sK8(X0,sK21))),sK21)
| ~ relation(X0) )
| ~ spl26_7 ),
inference(resolution,[],[f330,f240]) ).
fof(f444,plain,
( ! [X0] :
( relation_inverse(X0) = sK21
| in(unordered_pair(unordered_pair(sK9(X0,sK21),sK8(X0,sK21)),singleton(sK9(X0,sK21))),X0)
| in(unordered_pair(unordered_pair(sK8(X0,sK21),sK9(X0,sK21)),singleton(sK8(X0,sK21))),sK21)
| ~ relation(X0) )
| ~ spl26_7 ),
inference(resolution,[],[f330,f241]) ).
fof(f448,plain,
( ! [X0,X1] :
( in(X0,relation_dom(sK21))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK21) )
| ~ spl26_7 ),
inference(resolution,[],[f330,f250]) ).
fof(f452,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_inverse(sK21))
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK21)
| ~ relation(relation_inverse(sK21)) )
| ~ spl26_7 ),
inference(resolution,[],[f330,f254]) ).
fof(f453,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK21)
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),relation_inverse(sK21))
| ~ relation(relation_inverse(sK21)) )
| ~ spl26_7 ),
inference(resolution,[],[f330,f255]) ).
fof(f454,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK21)
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),relation_inverse(sK21))
| ~ relation(relation_inverse(sK21)) )
| ~ spl26_7 ),
inference(forward_demodulation,[],[f453,f130]) ).
fof(f455,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_inverse(sK21))
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK21)
| ~ relation(relation_inverse(sK21)) )
| ~ spl26_7 ),
inference(forward_demodulation,[],[f452,f130]) ).
fof(f459,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK21)
| in(X0,relation_dom(sK21)) )
| ~ spl26_7 ),
inference(forward_demodulation,[],[f448,f130]) ).
fof(f463,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK9(X0,sK21)),unordered_pair(sK9(X0,sK21),sK8(X0,sK21))),X0)
| relation_inverse(X0) = sK21
| in(unordered_pair(unordered_pair(sK8(X0,sK21),sK9(X0,sK21)),singleton(sK8(X0,sK21))),sK21)
| ~ relation(X0) )
| ~ spl26_7 ),
inference(forward_demodulation,[],[f444,f130]) ).
fof(f465,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK9(X0,sK21)),unordered_pair(sK9(X0,sK21),sK8(X0,sK21))),X0)
| relation_inverse(X0) = sK21
| ~ in(unordered_pair(unordered_pair(sK8(X0,sK21),sK9(X0,sK21)),singleton(sK8(X0,sK21))),sK21)
| ~ relation(X0) )
| ~ spl26_7 ),
inference(forward_demodulation,[],[f442,f130]) ).
fof(f471,plain,
( ! [X0,X1] :
( apply(sK21,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK21)
| ~ in(X0,relation_dom(sK21)) )
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f436,f203]) ).
fof(f482,plain,
( function_inverse(sK21) = relation_inverse(sK21)
| ~ function(sK21)
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f421,f205]) ).
fof(f483,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK21)
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),relation_inverse(sK21)) )
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f454,f424]) ).
fof(f484,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_inverse(sK21))
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK21) )
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f455,f424]) ).
fof(f488,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK9(X0,sK21)),unordered_pair(sK8(X0,sK21),sK9(X0,sK21))),X0)
| relation_inverse(X0) = sK21
| in(unordered_pair(unordered_pair(sK8(X0,sK21),sK9(X0,sK21)),singleton(sK8(X0,sK21))),sK21)
| ~ relation(X0) )
| ~ spl26_7 ),
inference(forward_demodulation,[],[f463,f130]) ).
fof(f490,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK9(X0,sK21)),unordered_pair(sK8(X0,sK21),sK9(X0,sK21))),X0)
| relation_inverse(X0) = sK21
| ~ in(unordered_pair(unordered_pair(sK8(X0,sK21),sK9(X0,sK21)),singleton(sK8(X0,sK21))),sK21)
| ~ relation(X0) )
| ~ spl26_7 ),
inference(forward_demodulation,[],[f465,f130]) ).
fof(f494,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK21)
| apply(sK21,X0) = X1
| ~ in(X0,relation_dom(sK21)) )
| ~ spl26_7 ),
inference(forward_demodulation,[],[f471,f130]) ).
fof(f500,plain,
( function_inverse(sK21) = relation_inverse(sK21)
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f482,f203]) ).
fof(f501,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),relation_inverse(sK21))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK21) )
| ~ spl26_7 ),
inference(forward_demodulation,[],[f483,f130]) ).
fof(f502,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK21)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_inverse(sK21)) )
| ~ spl26_7 ),
inference(forward_demodulation,[],[f484,f130]) ).
fof(f504,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK8(X0,sK21)),unordered_pair(sK8(X0,sK21),sK9(X0,sK21))),sK21)
| in(unordered_pair(singleton(sK9(X0,sK21)),unordered_pair(sK8(X0,sK21),sK9(X0,sK21))),X0)
| relation_inverse(X0) = sK21
| ~ relation(X0) )
| ~ spl26_7 ),
inference(forward_demodulation,[],[f488,f130]) ).
fof(f506,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK8(X0,sK21)),unordered_pair(sK8(X0,sK21),sK9(X0,sK21))),sK21)
| ~ in(unordered_pair(singleton(sK9(X0,sK21)),unordered_pair(sK8(X0,sK21),sK9(X0,sK21))),X0)
| relation_inverse(X0) = sK21
| ~ relation(X0) )
| ~ spl26_7 ),
inference(forward_demodulation,[],[f490,f130]) ).
fof(f509,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK21)
| apply(sK21,X0) = X1 )
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f494,f459]) ).
fof(f510,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),function_inverse(sK21))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK21) )
| ~ spl26_7 ),
inference(forward_demodulation,[],[f501,f500]) ).
fof(f511,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),function_inverse(sK21))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK21) )
| ~ spl26_7 ),
inference(forward_demodulation,[],[f502,f500]) ).
fof(f515,definition,
( spl26_9
<=> ! [X5] :
( apply(sK22,apply(sK21,X5)) = X5
| ~ in(X5,relation_dom(sK21)) ) ),
introduced(definition,[new_symbols(definition,[spl26_9])],[avatar_definition]) ).
fof(f516,plain,
( ! [X5] :
( apply(sK22,apply(sK21,X5)) = X5
| ~ in(X5,relation_dom(sK21)) )
| ~ spl26_9 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f517,plain,
( spl26_9
| spl26_1 ),
inference(avatar_split_clause,[],[f293,f265,f515]) ).
fof(f520,plain,
( ! [X0,X1] :
( apply(sK22,X0) = X1
| ~ in(X1,relation_dom(sK21))
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK21)
| ~ in(X1,relation_dom(sK21))
| ~ relation(sK21)
| ~ function(sK21) )
| ~ spl26_9 ),
inference(superposition,[],[f516,f230]) ).
fof(f528,plain,
( ! [X0,X1] :
( apply(sK22,X0) = X1
| ~ in(X1,relation_dom(sK21))
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK21)
| ~ relation(sK21)
| ~ function(sK21) )
| ~ spl26_9 ),
inference(duplicate_literal_removal,[],[f520]) ).
fof(f532,plain,
( ! [X0,X1] :
( apply(sK22,X0) = X1
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK21)
| ~ relation(sK21)
| ~ function(sK21) )
| ~ spl26_9 ),
inference(forward_subsumption_resolution,[],[f528,f250]) ).
fof(f536,plain,
( ! [X0,X1] :
( apply(sK22,X0) = X1
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK21)
| ~ function(sK21) )
| ~ spl26_7
| ~ spl26_9 ),
inference(forward_subsumption_resolution,[],[f532,f330]) ).
fof(f540,plain,
( ! [X0,X1] :
( apply(sK22,X0) = X1
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK21) )
| ~ spl26_7
| ~ spl26_9 ),
inference(forward_subsumption_resolution,[],[f536,f203]) ).
fof(f544,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK21)
| apply(sK22,X0) = X1 )
| ~ spl26_7
| ~ spl26_9 ),
inference(forward_demodulation,[],[f540,f130]) ).
fof(f547,definition,
( spl26_10
<=> ! [X4] :
( ~ in(X4,relation_dom(sK22))
| apply(sK21,apply(sK22,X4)) = X4 ) ),
introduced(definition,[new_symbols(definition,[spl26_10])],[avatar_definition]) ).
fof(f548,plain,
( ! [X4] :
( apply(sK21,apply(sK22,X4)) = X4
| ~ in(X4,relation_dom(sK22)) )
| ~ spl26_10 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f549,plain,
( spl26_10
| spl26_1 ),
inference(avatar_split_clause,[],[f299,f265,f547]) ).
fof(f550,plain,
( sK24 = apply(sK22,sK23)
| sK23 = apply(sK21,sK24)
| sK22 != function_inverse(sK21)
| ~ spl26_6 ),
inference(forward_subsumption_resolution,[],[f213,f286]) ).
fof(f551,plain,
( sK24 = apply(sK22,sK23)
| in(sK24,relation_dom(sK21))
| sK22 != function_inverse(sK21)
| ~ spl26_6 ),
inference(forward_subsumption_resolution,[],[f214,f286]) ).
fof(f552,plain,
( in(sK23,relation_rng(sK21))
| sK23 = apply(sK21,sK24)
| sK22 != function_inverse(sK21)
| ~ spl26_6 ),
inference(forward_subsumption_resolution,[],[f216,f286]) ).
fof(f553,plain,
( in(sK23,relation_rng(sK21))
| in(sK24,relation_dom(sK21))
| sK22 != function_inverse(sK21)
| ~ spl26_6 ),
inference(forward_subsumption_resolution,[],[f217,f286]) ).
fof(f560,plain,
( sK24 = apply(sK22,sK23)
| sK23 = apply(sK21,sK24)
| ~ spl26_1
| ~ spl26_6 ),
inference(forward_subsumption_resolution,[],[f550,f266]) ).
fof(f561,plain,
( sK24 = apply(sK22,sK23)
| sK22 != function_inverse(sK21)
| spl26_5
| ~ spl26_6 ),
inference(forward_subsumption_resolution,[],[f551,f283]) ).
fof(f562,plain,
( in(sK23,relation_rng(sK21))
| sK23 = apply(sK21,sK24)
| ~ spl26_1
| ~ spl26_6 ),
inference(forward_subsumption_resolution,[],[f552,f266]) ).
fof(f570,plain,
( sK24 = apply(sK22,sK23)
| ~ spl26_1
| spl26_5
| ~ spl26_6 ),
inference(forward_subsumption_resolution,[],[f561,f266]) ).
fof(f571,plain,
( in(sK23,relation_dom(sK22))
| sK23 = apply(sK21,sK24)
| ~ spl26_1
| ~ spl26_6 ),
inference(forward_demodulation,[],[f562,f286]) ).
fof(f580,plain,
( ! [X0] :
( ~ in(unordered_pair(unordered_pair(sK24,X0),singleton(sK24)),sK21)
| ~ relation(sK21) )
| spl26_5 ),
inference(resolution,[],[f283,f250]) ).
fof(f590,plain,
( ! [X0] : ~ in(unordered_pair(unordered_pair(sK24,X0),singleton(sK24)),sK21)
| spl26_5
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f580,f330]) ).
fof(f595,plain,
( ! [X0] : ~ in(unordered_pair(singleton(sK24),unordered_pair(sK24,X0)),sK21)
| spl26_5
| ~ spl26_7 ),
inference(forward_demodulation,[],[f590,f130]) ).
fof(f597,definition,
( spl26_11
<=> ! [X0] : ~ in(unordered_pair(singleton(sK24),unordered_pair(sK24,X0)),sK21) ),
introduced(definition,[new_symbols(definition,[spl26_11])],[avatar_definition]) ).
fof(f598,plain,
( ! [X0] : ~ in(unordered_pair(singleton(sK24),unordered_pair(sK24,X0)),sK21)
| ~ spl26_11 ),
inference(avatar_component_clause,[],[f597]) ).
fof(f599,plain,
( spl26_11
| spl26_5
| ~ spl26_7 ),
inference(avatar_split_clause,[],[f595,f328,f281,f597]) ).
fof(f600,plain,
( sK23 = apply(sK21,sK24)
| ~ spl26_1
| spl26_2
| ~ spl26_6 ),
inference(backward_subsumption_resolution,[],[f560,f271]) ).
fof(f646,plain,
( ! [X0] :
( sK23 != X0
| ~ in(unordered_pair(unordered_pair(sK24,X0),singleton(sK24)),sK21)
| ~ in(sK24,relation_dom(sK21))
| ~ relation(sK21)
| ~ function(sK21) )
| spl26_4 ),
inference(superposition,[],[f279,f230]) ).
fof(f647,plain,
( ! [X0] :
( sK23 != X0
| ~ in(unordered_pair(unordered_pair(sK24,X0),singleton(sK24)),sK21)
| ~ relation(sK21)
| ~ function(sK21) )
| spl26_4 ),
inference(forward_subsumption_resolution,[],[f646,f250]) ).
fof(f648,plain,
( ! [X0] :
( sK23 != X0
| ~ in(unordered_pair(unordered_pair(sK24,X0),singleton(sK24)),sK21)
| ~ function(sK21) )
| spl26_4
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f647,f330]) ).
fof(f649,plain,
( ! [X0] :
( sK23 != X0
| ~ in(unordered_pair(unordered_pair(sK24,X0),singleton(sK24)),sK21) )
| spl26_4
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f648,f203]) ).
fof(f650,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK24),unordered_pair(sK24,X0)),sK21)
| sK23 != X0 )
| spl26_4
| ~ spl26_7 ),
inference(forward_demodulation,[],[f649,f130]) ).
fof(f671,definition,
( spl26_13
<=> ! [X0] :
( ~ in(unordered_pair(singleton(sK24),unordered_pair(sK24,X0)),sK21)
| sK23 != X0 ) ),
introduced(definition,[new_symbols(definition,[spl26_13])],[avatar_definition]) ).
fof(f672,plain,
( ! [X0] :
( sK23 != X0
| ~ in(unordered_pair(singleton(sK24),unordered_pair(sK24,X0)),sK21) )
| ~ spl26_13 ),
inference(avatar_component_clause,[],[f671]) ).
fof(f673,plain,
( spl26_13
| spl26_4
| ~ spl26_7 ),
inference(avatar_split_clause,[],[f650,f328,f277,f671]) ).
fof(f674,plain,
( ~ in(sK23,relation_dom(sK22))
| spl26_3
| ~ spl26_6 ),
inference(forward_demodulation,[],[f275,f286]) ).
fof(f716,plain,
( in(sK23,relation_rng(sK21))
| sK22 != function_inverse(sK21)
| spl26_5
| ~ spl26_6 ),
inference(forward_subsumption_resolution,[],[f553,f283]) ).
fof(f721,plain,
( in(sK23,relation_rng(sK21))
| ~ spl26_1
| spl26_5
| ~ spl26_6 ),
inference(forward_subsumption_resolution,[],[f716,f266]) ).
fof(f726,plain,
( in(sK23,relation_dom(sK22))
| ~ spl26_1
| spl26_5
| ~ spl26_6 ),
inference(forward_demodulation,[],[f721,f286]) ).
fof(f731,plain,
( $false
| ~ spl26_1
| spl26_3
| spl26_5
| ~ spl26_6 ),
inference(forward_subsumption_resolution,[],[f726,f674]) ).
fof(f732,plain,
( ~ spl26_1
| spl26_3
| spl26_5
| ~ spl26_6 ),
inference(avatar_contradiction_clause,[],[f731]) ).
fof(f733,plain,
( in(sK23,relation_dom(sK22))
| ~ spl26_3
| ~ spl26_6 ),
inference(forward_demodulation,[],[f274,f286]) ).
fof(f761,plain,
( ! [X0] : ~ in(unordered_pair(singleton(sK24),unordered_pair(X0,sK24)),sK21)
| ~ spl26_11 ),
inference(superposition,[],[f598,f130]) ).
fof(f763,definition,
( spl26_15
<=> function(sK22) ),
introduced(definition,[new_symbols(definition,[spl26_15])],[avatar_definition]) ).
fof(f765,plain,
( function(sK22)
| ~ spl26_15 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f766,plain,
spl26_15,
inference(avatar_split_clause,[],[f206,f763]) ).
fof(f783,definition,
( spl26_16
<=> function(sK21) ),
introduced(definition,[new_symbols(definition,[spl26_16])],[avatar_definition]) ).
fof(f785,plain,
( function(sK21)
| ~ spl26_16 ),
inference(avatar_component_clause,[],[f783]) ).
fof(f786,plain,
spl26_16,
inference(avatar_split_clause,[],[f203,f783]) ).
fof(f803,definition,
( spl26_17
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK21)
| apply(sK22,X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[spl26_17])],[avatar_definition]) ).
fof(f804,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK21)
| apply(sK22,X0) = X1 )
| ~ spl26_17 ),
inference(avatar_component_clause,[],[f803]) ).
fof(f805,plain,
( spl26_17
| ~ spl26_7
| ~ spl26_9 ),
inference(avatar_split_clause,[],[f544,f515,f328,f803]) ).
fof(f807,definition,
( spl26_18
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK21)
| apply(sK21,X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[spl26_18])],[avatar_definition]) ).
fof(f808,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK21)
| apply(sK21,X0) = X1 )
| ~ spl26_18 ),
inference(avatar_component_clause,[],[f807]) ).
fof(f809,plain,
( spl26_18
| ~ spl26_7 ),
inference(avatar_split_clause,[],[f509,f328,f807]) ).
fof(f814,definition,
( spl26_19
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK22)
| apply(sK22,X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[spl26_19])],[avatar_definition]) ).
fof(f815,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK22)
| apply(sK22,X0) = X1 )
| ~ spl26_19 ),
inference(avatar_component_clause,[],[f814]) ).
fof(f816,plain,
( spl26_19
| ~ spl26_8 ),
inference(avatar_split_clause,[],[f419,f333,f814]) ).
fof(f845,plain,
( in(unordered_pair(unordered_pair(sK24,apply(sK21,sK24)),singleton(sK24)),sK21)
| ~ relation(sK21)
| ~ function(sK21)
| ~ spl26_5 ),
inference(resolution,[],[f282,f247]) ).
fof(f858,plain,
( in(unordered_pair(unordered_pair(sK24,apply(sK21,sK24)),singleton(sK24)),sK21)
| ~ function(sK21)
| ~ spl26_5
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f845,f330]) ).
fof(f863,plain,
( in(unordered_pair(unordered_pair(sK24,apply(sK21,sK24)),singleton(sK24)),sK21)
| ~ spl26_5
| ~ spl26_7
| ~ spl26_16 ),
inference(forward_subsumption_resolution,[],[f858,f785]) ).
fof(f866,plain,
( in(unordered_pair(singleton(sK24),unordered_pair(sK24,apply(sK21,sK24))),sK21)
| ~ spl26_5
| ~ spl26_7
| ~ spl26_16 ),
inference(forward_demodulation,[],[f863,f130]) ).
fof(f868,definition,
( spl26_22
<=> in(unordered_pair(singleton(sK24),unordered_pair(sK24,apply(sK21,sK24))),sK21) ),
introduced(definition,[new_symbols(definition,[spl26_22])],[avatar_definition]) ).
fof(f870,plain,
( in(unordered_pair(singleton(sK24),unordered_pair(sK24,apply(sK21,sK24))),sK21)
| ~ spl26_22 ),
inference(avatar_component_clause,[],[f868]) ).
fof(f871,plain,
( spl26_22
| ~ spl26_5
| ~ spl26_7
| ~ spl26_16 ),
inference(avatar_split_clause,[],[f866,f783,f328,f281,f868]) ).
fof(f894,plain,
( ~ in(unordered_pair(singleton(sK24),unordered_pair(sK24,sK23)),sK21)
| ~ spl26_13 ),
inference(equality_resolution,[],[f672]) ).
fof(f897,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK22)
| apply(sK22,X1) = X0 )
| ~ spl26_19 ),
inference(superposition,[],[f815,f130]) ).
fof(f899,definition,
( spl26_23
<=> one_to_one(sK21) ),
introduced(definition,[new_symbols(definition,[spl26_23])],[avatar_definition]) ).
fof(f901,plain,
( one_to_one(sK21)
| ~ spl26_23 ),
inference(avatar_component_clause,[],[f899]) ).
fof(f902,plain,
spl26_23,
inference(avatar_split_clause,[],[f205,f899]) ).
fof(f913,definition,
( spl26_25
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),function_inverse(sK21))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK21) ) ),
introduced(definition,[new_symbols(definition,[spl26_25])],[avatar_definition]) ).
fof(f914,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),function_inverse(sK21))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK21) )
| ~ spl26_25 ),
inference(avatar_component_clause,[],[f913]) ).
fof(f915,plain,
( spl26_25
| ~ spl26_7 ),
inference(avatar_split_clause,[],[f510,f328,f913]) ).
fof(f916,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK22)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK21) )
| ~ spl26_1
| ~ spl26_25 ),
inference(forward_demodulation,[],[f914,f266]) ).
fof(f919,definition,
( spl26_26
<=> function_inverse(sK21) = relation_inverse(sK21) ),
introduced(definition,[new_symbols(definition,[spl26_26])],[avatar_definition]) ).
fof(f921,plain,
( function_inverse(sK21) = relation_inverse(sK21)
| ~ spl26_26 ),
inference(avatar_component_clause,[],[f919]) ).
fof(f922,plain,
( spl26_26
| ~ spl26_7 ),
inference(avatar_split_clause,[],[f500,f328,f919]) ).
fof(f923,plain,
( sK22 = relation_inverse(sK21)
| ~ spl26_1
| ~ spl26_26 ),
inference(forward_demodulation,[],[f921,f266]) ).
fof(f931,plain,
( ~ in(unordered_pair(singleton(sK24),unordered_pair(sK23,sK24)),sK21)
| ~ spl26_13 ),
inference(forward_demodulation,[],[f894,f130]) ).
fof(f937,plain,
( sK23 = apply(sK21,sK24)
| ~ spl26_1
| spl26_3
| ~ spl26_6 ),
inference(forward_subsumption_resolution,[],[f571,f674]) ).
fof(f1042,plain,
( relation_rng(sK21) = relation_dom(sK22)
| ~ spl26_1
| ~ spl26_7
| ~ spl26_26 ),
inference(forward_demodulation,[],[f431,f923]) ).
fof(f1057,plain,
( $false
| ~ spl26_1
| spl26_6
| ~ spl26_7
| ~ spl26_26 ),
inference(forward_subsumption_resolution,[],[f1042,f287]) ).
fof(f1058,plain,
( ~ spl26_1
| spl26_6
| ~ spl26_7
| ~ spl26_26 ),
inference(avatar_contradiction_clause,[],[f1057]) ).
fof(f1066,plain,
( ! [X0] :
( ~ in(unordered_pair(unordered_pair(X0,sK23),singleton(X0)),sK21)
| ~ relation(sK21) )
| spl26_3 ),
inference(resolution,[],[f275,f252]) ).
fof(f1073,plain,
( ! [X0] : ~ in(unordered_pair(unordered_pair(X0,sK23),singleton(X0)),sK21)
| spl26_3
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f1066,f330]) ).
fof(f1077,plain,
( ! [X0] : ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK23)),sK21)
| spl26_3
| ~ spl26_7 ),
inference(forward_demodulation,[],[f1073,f130]) ).
fof(f1116,definition,
( spl26_29
<=> ! [X0] : ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK23)),sK21) ),
introduced(definition,[new_symbols(definition,[spl26_29])],[avatar_definition]) ).
fof(f1117,plain,
( ! [X0] : ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK23)),sK21)
| ~ spl26_29 ),
inference(avatar_component_clause,[],[f1116]) ).
fof(f1118,plain,
( spl26_29
| spl26_3
| ~ spl26_7 ),
inference(avatar_split_clause,[],[f1077,f328,f273,f1116]) ).
fof(f1164,plain,
( in(unordered_pair(unordered_pair(sK23,sK24),singleton(sK23)),sK22)
| ~ in(sK23,relation_dom(sK22))
| ~ relation(sK22)
| ~ function(sK22)
| ~ spl26_2 ),
inference(superposition,[],[f247,f270]) ).
fof(f1167,plain,
( in(unordered_pair(unordered_pair(sK23,sK24),singleton(sK23)),sK22)
| ~ relation(sK22)
| ~ function(sK22)
| ~ spl26_2
| ~ spl26_3
| ~ spl26_6 ),
inference(forward_subsumption_resolution,[],[f1164,f733]) ).
fof(f1170,plain,
( in(unordered_pair(unordered_pair(sK23,sK24),singleton(sK23)),sK22)
| ~ function(sK22)
| ~ spl26_2
| ~ spl26_3
| ~ spl26_6
| ~ spl26_8 ),
inference(forward_subsumption_resolution,[],[f1167,f335]) ).
fof(f1173,plain,
( in(unordered_pair(unordered_pair(sK23,sK24),singleton(sK23)),sK22)
| ~ spl26_2
| ~ spl26_3
| ~ spl26_6
| ~ spl26_8
| ~ spl26_15 ),
inference(forward_subsumption_resolution,[],[f1170,f765]) ).
fof(f1176,plain,
( in(unordered_pair(singleton(sK23),unordered_pair(sK23,sK24)),sK22)
| ~ spl26_2
| ~ spl26_3
| ~ spl26_6
| ~ spl26_8
| ~ spl26_15 ),
inference(forward_demodulation,[],[f1173,f130]) ).
fof(f1197,definition,
( spl26_31
<=> in(unordered_pair(singleton(sK24),unordered_pair(sK23,sK24)),sK21) ),
introduced(definition,[new_symbols(definition,[spl26_31])],[avatar_definition]) ).
fof(f1199,plain,
( ~ in(unordered_pair(singleton(sK24),unordered_pair(sK23,sK24)),sK21)
| spl26_31 ),
inference(avatar_component_clause,[],[f1197]) ).
fof(f1200,plain,
( ~ spl26_31
| ~ spl26_13 ),
inference(avatar_split_clause,[],[f931,f671,f1197]) ).
fof(f1262,definition,
( spl26_35
<=> in(unordered_pair(singleton(sK23),unordered_pair(sK23,sK24)),sK22) ),
introduced(definition,[new_symbols(definition,[spl26_35])],[avatar_definition]) ).
fof(f1263,plain,
( ~ in(unordered_pair(singleton(sK23),unordered_pair(sK23,sK24)),sK22)
| spl26_35 ),
inference(avatar_component_clause,[],[f1262]) ).
fof(f1264,plain,
( in(unordered_pair(singleton(sK23),unordered_pair(sK23,sK24)),sK22)
| ~ spl26_35 ),
inference(avatar_component_clause,[],[f1262]) ).
fof(f1265,plain,
( spl26_35
| ~ spl26_2
| ~ spl26_3
| ~ spl26_6
| ~ spl26_8
| ~ spl26_15 ),
inference(avatar_split_clause,[],[f1176,f763,f333,f285,f273,f269,f1262]) ).
fof(f1272,definition,
( spl26_37
<=> ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),function_inverse(sK21))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK21) ) ),
introduced(definition,[new_symbols(definition,[spl26_37])],[avatar_definition]) ).
fof(f1273,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),function_inverse(sK21))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK21) )
| ~ spl26_37 ),
inference(avatar_component_clause,[],[f1272]) ).
fof(f1274,plain,
( spl26_37
| ~ spl26_7 ),
inference(avatar_split_clause,[],[f511,f328,f1272]) ).
fof(f1275,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK22)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK21) )
| ~ spl26_1
| ~ spl26_37 ),
inference(forward_demodulation,[],[f1273,f266]) ).
fof(f1315,definition,
( spl26_43
<=> ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK22)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK21) ) ),
introduced(definition,[new_symbols(definition,[spl26_43])],[avatar_definition]) ).
fof(f1316,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK21)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK22) )
| ~ spl26_43 ),
inference(avatar_component_clause,[],[f1315]) ).
fof(f1317,plain,
( spl26_43
| ~ spl26_1
| ~ spl26_37 ),
inference(avatar_split_clause,[],[f1275,f1272,f265,f1315]) ).
fof(f1319,plain,
( in(unordered_pair(singleton(apply(sK21,sK24)),unordered_pair(apply(sK21,sK24),sK24)),sK22)
| ~ spl26_22
| ~ spl26_43 ),
inference(resolution,[],[f1316,f870]) ).
fof(f1326,plain,
( in(unordered_pair(singleton(apply(sK21,sK24)),unordered_pair(sK24,apply(sK21,sK24))),sK22)
| ~ spl26_22
| ~ spl26_43 ),
inference(forward_demodulation,[],[f1319,f130]) ).
fof(f1358,definition,
( spl26_46
<=> ! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK22,X0))),sK22)
| ~ in(X0,relation_dom(sK22)) ) ),
introduced(definition,[new_symbols(definition,[spl26_46])],[avatar_definition]) ).
fof(f1359,plain,
( ! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK22,X0))),sK22)
| ~ in(X0,relation_dom(sK22)) )
| ~ spl26_46 ),
inference(avatar_component_clause,[],[f1358]) ).
fof(f1360,plain,
( spl26_46
| ~ spl26_8 ),
inference(avatar_split_clause,[],[f402,f333,f1358]) ).
fof(f1378,definition,
( spl26_47
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK21)
| in(X0,relation_dom(sK21)) ) ),
introduced(definition,[new_symbols(definition,[spl26_47])],[avatar_definition]) ).
fof(f1379,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK21)
| in(X0,relation_dom(sK21)) )
| ~ spl26_47 ),
inference(avatar_component_clause,[],[f1378]) ).
fof(f1380,plain,
( spl26_47
| ~ spl26_7 ),
inference(avatar_split_clause,[],[f459,f328,f1378]) ).
fof(f1458,plain,
( sK24 = apply(sK22,sK23)
| ~ spl26_19
| ~ spl26_35 ),
inference(resolution,[],[f1264,f815]) ).
fof(f1569,definition,
( spl26_57
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK22)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK21) ) ),
introduced(definition,[new_symbols(definition,[spl26_57])],[avatar_definition]) ).
fof(f1570,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK22)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK21) )
| ~ spl26_57 ),
inference(avatar_component_clause,[],[f1569]) ).
fof(f1571,plain,
( spl26_57
| ~ spl26_1
| ~ spl26_25 ),
inference(avatar_split_clause,[],[f916,f913,f265,f1569]) ).
fof(f1572,plain,
( ! [X0] :
( in(unordered_pair(singleton(apply(sK22,X0)),unordered_pair(apply(sK22,X0),X0)),sK21)
| ~ in(X0,relation_dom(sK22)) )
| ~ spl26_46
| ~ spl26_57 ),
inference(resolution,[],[f1570,f1359]) ).
fof(f1574,plain,
( in(unordered_pair(singleton(sK24),unordered_pair(sK24,sK23)),sK21)
| ~ spl26_35
| ~ spl26_57 ),
inference(resolution,[],[f1570,f1264]) ).
fof(f1579,plain,
( in(unordered_pair(singleton(sK24),unordered_pair(sK23,sK24)),sK21)
| ~ spl26_35
| ~ spl26_57 ),
inference(forward_demodulation,[],[f1574,f130]) ).
fof(f1581,plain,
( ! [X0] :
( in(unordered_pair(singleton(apply(sK22,X0)),unordered_pair(X0,apply(sK22,X0))),sK21)
| ~ in(X0,relation_dom(sK22)) )
| ~ spl26_46
| ~ spl26_57 ),
inference(forward_demodulation,[],[f1572,f130]) ).
fof(f1582,plain,
( $false
| spl26_31
| ~ spl26_35
| ~ spl26_57 ),
inference(forward_subsumption_resolution,[],[f1579,f1199]) ).
fof(f1583,plain,
( spl26_31
| ~ spl26_35
| ~ spl26_57 ),
inference(avatar_contradiction_clause,[],[f1582]) ).
fof(f1635,plain,
( ! [X5] :
( in(apply(sK21,X5),relation_rng(sK21))
| ~ in(X5,relation_dom(sK21)) )
| spl26_1 ),
inference(forward_subsumption_resolution,[],[f258,f267]) ).
fof(f1637,plain,
( ! [X4] :
( in(apply(sK22,X4),relation_dom(sK21))
| ~ in(X4,relation_rng(sK21)) )
| spl26_1 ),
inference(forward_subsumption_resolution,[],[f256,f267]) ).
fof(f1646,plain,
( ! [X5] :
( in(apply(sK21,X5),relation_dom(sK22))
| ~ in(X5,relation_dom(sK21)) )
| spl26_1
| ~ spl26_6 ),
inference(forward_demodulation,[],[f1635,f286]) ).
fof(f1648,plain,
( ! [X4] :
( ~ in(X4,relation_dom(sK22))
| in(apply(sK22,X4),relation_dom(sK21)) )
| spl26_1
| ~ spl26_6 ),
inference(forward_demodulation,[],[f1637,f286]) ).
fof(f1740,plain,
( ! [X0,X1] :
( apply(sK21,X0) = X1
| ~ in(X1,relation_dom(sK22))
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK22)
| ~ in(X1,relation_dom(sK22))
| ~ relation(sK22)
| ~ function(sK22) )
| ~ spl26_10 ),
inference(superposition,[],[f548,f230]) ).
fof(f1750,plain,
( ! [X0,X1] :
( apply(sK21,X0) = X1
| ~ in(X1,relation_dom(sK22))
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK22)
| ~ relation(sK22)
| ~ function(sK22) )
| ~ spl26_10 ),
inference(duplicate_literal_removal,[],[f1740]) ).
fof(f1756,plain,
( ! [X0,X1] :
( apply(sK21,X0) = X1
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK22)
| ~ relation(sK22)
| ~ function(sK22) )
| ~ spl26_10 ),
inference(forward_subsumption_resolution,[],[f1750,f250]) ).
fof(f1762,plain,
( ! [X0,X1] :
( apply(sK21,X0) = X1
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK22)
| ~ function(sK22) )
| ~ spl26_8
| ~ spl26_10 ),
inference(forward_subsumption_resolution,[],[f1756,f335]) ).
fof(f1766,plain,
( ! [X0,X1] :
( apply(sK21,X0) = X1
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK22) )
| ~ spl26_8
| ~ spl26_10
| ~ spl26_15 ),
inference(forward_subsumption_resolution,[],[f1762,f765]) ).
fof(f1770,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK22)
| apply(sK21,X0) = X1 )
| ~ spl26_8
| ~ spl26_10
| ~ spl26_15 ),
inference(forward_demodulation,[],[f1766,f130]) ).
fof(f1878,definition,
( spl26_62
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK22)
| apply(sK21,X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[spl26_62])],[avatar_definition]) ).
fof(f1879,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK22)
| apply(sK21,X0) = X1 )
| ~ spl26_62 ),
inference(avatar_component_clause,[],[f1878]) ).
fof(f1880,plain,
( spl26_62
| ~ spl26_8
| ~ spl26_10
| ~ spl26_15 ),
inference(avatar_split_clause,[],[f1770,f763,f547,f333,f1878]) ).
fof(f1884,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK22)
| apply(sK21,X0) = X1 )
| ~ spl26_62 ),
inference(superposition,[],[f1879,f130]) ).
fof(f1939,definition,
( spl26_67
<=> ! [X4] :
( ~ in(X4,relation_dom(sK22))
| in(apply(sK22,X4),relation_dom(sK21)) ) ),
introduced(definition,[new_symbols(definition,[spl26_67])],[avatar_definition]) ).
fof(f1940,plain,
( ! [X4] :
( in(apply(sK22,X4),relation_dom(sK21))
| ~ in(X4,relation_dom(sK22)) )
| ~ spl26_67 ),
inference(avatar_component_clause,[],[f1939]) ).
fof(f1941,plain,
( spl26_67
| spl26_1
| ~ spl26_6 ),
inference(avatar_split_clause,[],[f1648,f285,f265,f1939]) ).
fof(f1955,plain,
( ! [X0,X1] :
( in(X0,relation_dom(sK21))
| ~ in(X1,relation_dom(sK22))
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK22)
| ~ in(X1,relation_dom(sK22))
| ~ relation(sK22)
| ~ function(sK22) )
| ~ spl26_67 ),
inference(superposition,[],[f1940,f230]) ).
fof(f1958,plain,
( ! [X0,X1] :
( in(X0,relation_dom(sK21))
| ~ in(X1,relation_dom(sK22))
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK22)
| ~ relation(sK22)
| ~ function(sK22) )
| ~ spl26_67 ),
inference(duplicate_literal_removal,[],[f1955]) ).
fof(f1961,plain,
( ! [X0,X1] :
( in(X0,relation_dom(sK21))
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK22)
| ~ relation(sK22)
| ~ function(sK22) )
| ~ spl26_67 ),
inference(forward_subsumption_resolution,[],[f1958,f250]) ).
fof(f1967,plain,
( ! [X0,X1] :
( in(X0,relation_dom(sK21))
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK22)
| ~ function(sK22) )
| ~ spl26_8
| ~ spl26_67 ),
inference(forward_subsumption_resolution,[],[f1961,f335]) ).
fof(f1971,plain,
( ! [X0,X1] :
( in(X0,relation_dom(sK21))
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK22) )
| ~ spl26_8
| ~ spl26_15
| ~ spl26_67 ),
inference(forward_subsumption_resolution,[],[f1967,f765]) ).
fof(f1974,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK22)
| in(X0,relation_dom(sK21)) )
| ~ spl26_8
| ~ spl26_15
| ~ spl26_67 ),
inference(forward_demodulation,[],[f1971,f130]) ).
fof(f1976,definition,
( spl26_68
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK22)
| in(X0,relation_dom(sK21)) ) ),
introduced(definition,[new_symbols(definition,[spl26_68])],[avatar_definition]) ).
fof(f1977,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK22)
| in(X0,relation_dom(sK21)) )
| ~ spl26_68 ),
inference(avatar_component_clause,[],[f1976]) ).
fof(f1978,plain,
( spl26_68
| ~ spl26_8
| ~ spl26_15
| ~ spl26_67 ),
inference(avatar_split_clause,[],[f1974,f1939,f763,f333,f1976]) ).
fof(f1983,definition,
( spl26_69
<=> ! [X5] :
( in(apply(sK21,X5),relation_dom(sK22))
| ~ in(X5,relation_dom(sK21)) ) ),
introduced(definition,[new_symbols(definition,[spl26_69])],[avatar_definition]) ).
fof(f1984,plain,
( ! [X5] :
( in(apply(sK21,X5),relation_dom(sK22))
| ~ in(X5,relation_dom(sK21)) )
| ~ spl26_69 ),
inference(avatar_component_clause,[],[f1983]) ).
fof(f1985,plain,
( spl26_69
| spl26_1
| ~ spl26_6 ),
inference(avatar_split_clause,[],[f1646,f285,f265,f1983]) ).
fof(f1987,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK21))
| in(unordered_pair(unordered_pair(apply(sK21,X0),apply(sK22,apply(sK21,X0))),singleton(apply(sK21,X0))),sK22)
| ~ relation(sK22)
| ~ function(sK22) )
| ~ spl26_69 ),
inference(resolution,[],[f1984,f247]) ).
fof(f2007,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK21))
| in(unordered_pair(unordered_pair(apply(sK21,X0),apply(sK22,apply(sK21,X0))),singleton(apply(sK21,X0))),sK22)
| ~ function(sK22) )
| ~ spl26_8
| ~ spl26_69 ),
inference(forward_subsumption_resolution,[],[f1987,f335]) ).
fof(f2013,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK21))
| in(unordered_pair(unordered_pair(apply(sK21,X0),apply(sK22,apply(sK21,X0))),singleton(apply(sK21,X0))),sK22) )
| ~ spl26_8
| ~ spl26_15
| ~ spl26_69 ),
inference(forward_subsumption_resolution,[],[f2007,f765]) ).
fof(f2017,plain,
( ! [X0] :
( in(unordered_pair(singleton(apply(sK21,X0)),unordered_pair(apply(sK21,X0),apply(sK22,apply(sK21,X0)))),sK22)
| ~ in(X0,relation_dom(sK21)) )
| ~ spl26_8
| ~ spl26_15
| ~ spl26_69 ),
inference(forward_demodulation,[],[f2013,f130]) ).
fof(f2022,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK22)
| in(X0,relation_dom(sK21)) )
| ~ spl26_68 ),
inference(superposition,[],[f1977,f130]) ).
fof(f2298,definition,
( spl26_83
<=> ! [X0] :
( in(unordered_pair(singleton(apply(sK21,X0)),unordered_pair(apply(sK21,X0),apply(sK22,apply(sK21,X0)))),sK22)
| ~ in(X0,relation_dom(sK21)) ) ),
introduced(definition,[new_symbols(definition,[spl26_83])],[avatar_definition]) ).
fof(f2299,plain,
( ! [X0] :
( in(unordered_pair(singleton(apply(sK21,X0)),unordered_pair(apply(sK21,X0),apply(sK22,apply(sK21,X0)))),sK22)
| ~ in(X0,relation_dom(sK21)) )
| ~ spl26_83 ),
inference(avatar_component_clause,[],[f2298]) ).
fof(f2300,plain,
( spl26_83
| ~ spl26_8
| ~ spl26_15
| ~ spl26_69 ),
inference(avatar_split_clause,[],[f2017,f1983,f763,f333,f2298]) ).
fof(f2316,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK22,X0))),sK22)
| ~ in(X1,relation_dom(sK21))
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK21)
| ~ in(X1,relation_dom(sK21))
| ~ relation(sK21)
| ~ function(sK21) )
| ~ spl26_83 ),
inference(superposition,[],[f2299,f230]) ).
fof(f2322,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK22,X0))),sK22)
| ~ in(X1,relation_dom(sK21))
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK21)
| ~ relation(sK21)
| ~ function(sK21) )
| ~ spl26_83 ),
inference(duplicate_literal_removal,[],[f2316]) ).
fof(f2325,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK22,X0))),sK22)
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK21)
| ~ relation(sK21)
| ~ function(sK21) )
| ~ spl26_83 ),
inference(forward_subsumption_resolution,[],[f2322,f250]) ).
fof(f2328,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK22,X0))),sK22)
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK21)
| ~ function(sK21) )
| ~ spl26_7
| ~ spl26_83 ),
inference(forward_subsumption_resolution,[],[f2325,f330]) ).
fof(f2330,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK22,X0))),sK22)
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK21) )
| ~ spl26_7
| ~ spl26_16
| ~ spl26_83 ),
inference(forward_subsumption_resolution,[],[f2328,f785]) ).
fof(f2332,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK21)
| in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK22,X0))),sK22) )
| ~ spl26_7
| ~ spl26_16
| ~ spl26_83 ),
inference(forward_demodulation,[],[f2330,f130]) ).
fof(f2347,definition,
( spl26_87
<=> ! [X0] :
( in(unordered_pair(singleton(apply(sK22,X0)),unordered_pair(X0,apply(sK22,X0))),sK21)
| ~ in(X0,relation_dom(sK22)) ) ),
introduced(definition,[new_symbols(definition,[spl26_87])],[avatar_definition]) ).
fof(f2348,plain,
( ! [X0] :
( in(unordered_pair(singleton(apply(sK22,X0)),unordered_pair(X0,apply(sK22,X0))),sK21)
| ~ in(X0,relation_dom(sK22)) )
| ~ spl26_87 ),
inference(avatar_component_clause,[],[f2347]) ).
fof(f2349,plain,
( spl26_87
| ~ spl26_46
| ~ spl26_57 ),
inference(avatar_split_clause,[],[f1581,f1569,f1358,f2347]) ).
fof(f2524,definition,
( spl26_97
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK21)
| in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK22,X0))),sK22) ) ),
introduced(definition,[new_symbols(definition,[spl26_97])],[avatar_definition]) ).
fof(f2525,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK22,X0))),sK22)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK21) )
| ~ spl26_97 ),
inference(avatar_component_clause,[],[f2524]) ).
fof(f2526,plain,
( spl26_97
| ~ spl26_7
| ~ spl26_16
| ~ spl26_83 ),
inference(avatar_split_clause,[],[f2332,f2298,f783,f328,f2524]) ).
fof(f2670,definition,
( spl26_108
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK22)
| apply(sK22,X1) = X0 ) ),
introduced(definition,[new_symbols(definition,[spl26_108])],[avatar_definition]) ).
fof(f2671,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK22)
| apply(sK22,X1) = X0 )
| ~ spl26_108 ),
inference(avatar_component_clause,[],[f2670]) ).
fof(f2672,plain,
( spl26_108
| ~ spl26_19 ),
inference(avatar_split_clause,[],[f897,f814,f2670]) ).
fof(f2822,definition,
( spl26_115
<=> ! [X0] :
( ~ in(unordered_pair(singleton(sK8(X0,sK21)),unordered_pair(sK8(X0,sK21),sK9(X0,sK21))),sK21)
| ~ in(unordered_pair(singleton(sK9(X0,sK21)),unordered_pair(sK8(X0,sK21),sK9(X0,sK21))),X0)
| relation_inverse(X0) = sK21
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[spl26_115])],[avatar_definition]) ).
fof(f2823,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK9(X0,sK21)),unordered_pair(sK8(X0,sK21),sK9(X0,sK21))),X0)
| ~ in(unordered_pair(singleton(sK8(X0,sK21)),unordered_pair(sK8(X0,sK21),sK9(X0,sK21))),sK21)
| relation_inverse(X0) = sK21
| ~ relation(X0) )
| ~ spl26_115 ),
inference(avatar_component_clause,[],[f2822]) ).
fof(f2824,plain,
( spl26_115
| ~ spl26_7 ),
inference(avatar_split_clause,[],[f506,f328,f2822]) ).
fof(f2915,definition,
( spl26_118
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK22)
| apply(sK21,X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[spl26_118])],[avatar_definition]) ).
fof(f2916,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK22)
| apply(sK21,X0) = X1 )
| ~ spl26_118 ),
inference(avatar_component_clause,[],[f2915]) ).
fof(f2917,plain,
( spl26_118
| ~ spl26_62 ),
inference(avatar_split_clause,[],[f1884,f1878,f2915]) ).
fof(f3637,definition,
( spl26_142
<=> ! [X0] :
( in(unordered_pair(singleton(sK8(X0,sK21)),unordered_pair(sK8(X0,sK21),sK9(X0,sK21))),sK21)
| in(unordered_pair(singleton(sK9(X0,sK21)),unordered_pair(sK8(X0,sK21),sK9(X0,sK21))),X0)
| relation_inverse(X0) = sK21
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[spl26_142])],[avatar_definition]) ).
fof(f3638,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK9(X0,sK21)),unordered_pair(sK8(X0,sK21),sK9(X0,sK21))),X0)
| in(unordered_pair(singleton(sK8(X0,sK21)),unordered_pair(sK8(X0,sK21),sK9(X0,sK21))),sK21)
| relation_inverse(X0) = sK21
| ~ relation(X0) )
| ~ spl26_142 ),
inference(avatar_component_clause,[],[f3637]) ).
fof(f3639,plain,
( spl26_142
| ~ spl26_7 ),
inference(avatar_split_clause,[],[f504,f328,f3637]) ).
fof(f3657,plain,
( in(unordered_pair(singleton(sK8(sK22,sK21)),unordered_pair(sK8(sK22,sK21),sK9(sK22,sK21))),sK21)
| sK21 = relation_inverse(sK22)
| ~ relation(sK22)
| sK9(sK22,sK21) = apply(sK21,sK8(sK22,sK21))
| ~ spl26_118
| ~ spl26_142 ),
inference(resolution,[],[f3638,f2916]) ).
fof(f3658,plain,
( in(unordered_pair(singleton(sK8(sK22,sK21)),unordered_pair(sK8(sK22,sK21),sK9(sK22,sK21))),sK21)
| sK21 = relation_inverse(sK22)
| ~ relation(sK22)
| sK8(sK22,sK21) = apply(sK22,sK9(sK22,sK21))
| ~ spl26_108
| ~ spl26_142 ),
inference(resolution,[],[f3638,f2671]) ).
fof(f3662,plain,
( sK21 = relation_inverse(sK22)
| ~ relation(sK22)
| sK8(sK22,sK21) = apply(sK22,sK9(sK22,sK21))
| ~ spl26_17
| ~ spl26_108
| ~ spl26_142 ),
inference(forward_subsumption_resolution,[],[f3658,f804]) ).
fof(f3663,plain,
( sK21 = relation_inverse(sK22)
| ~ relation(sK22)
| sK9(sK22,sK21) = apply(sK21,sK8(sK22,sK21))
| ~ spl26_18
| ~ spl26_118
| ~ spl26_142 ),
inference(forward_subsumption_resolution,[],[f3657,f808]) ).
fof(f3673,plain,
( sK21 = relation_inverse(sK22)
| sK8(sK22,sK21) = apply(sK22,sK9(sK22,sK21))
| ~ spl26_8
| ~ spl26_17
| ~ spl26_108
| ~ spl26_142 ),
inference(forward_subsumption_resolution,[],[f3662,f335]) ).
fof(f3674,plain,
( sK21 = relation_inverse(sK22)
| sK9(sK22,sK21) = apply(sK21,sK8(sK22,sK21))
| ~ spl26_8
| ~ spl26_18
| ~ spl26_118
| ~ spl26_142 ),
inference(forward_subsumption_resolution,[],[f3663,f335]) ).
fof(f4498,plain,
( in(unordered_pair(singleton(sK24),unordered_pair(sK23,sK24)),sK21)
| ~ in(sK23,relation_dom(sK22))
| ~ spl26_2
| ~ spl26_87 ),
inference(superposition,[],[f2348,f270]) ).
fof(f5461,definition,
( spl26_172
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK22)
| in(X0,relation_dom(sK21)) ) ),
introduced(definition,[new_symbols(definition,[spl26_172])],[avatar_definition]) ).
fof(f5462,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK22)
| in(X0,relation_dom(sK21)) )
| ~ spl26_172 ),
inference(avatar_component_clause,[],[f5461]) ).
fof(f5463,plain,
( spl26_172
| ~ spl26_68 ),
inference(avatar_split_clause,[],[f2022,f1976,f5461]) ).
fof(f5470,plain,
( in(sK8(sK22,sK21),relation_dom(sK21))
| in(unordered_pair(singleton(sK8(sK22,sK21)),unordered_pair(sK8(sK22,sK21),sK9(sK22,sK21))),sK21)
| sK21 = relation_inverse(sK22)
| ~ relation(sK22)
| ~ spl26_142
| ~ spl26_172 ),
inference(resolution,[],[f5462,f3638]) ).
fof(f5475,plain,
( in(sK8(sK22,sK21),relation_dom(sK21))
| sK21 = relation_inverse(sK22)
| ~ relation(sK22)
| ~ spl26_47
| ~ spl26_142
| ~ spl26_172 ),
inference(forward_subsumption_resolution,[],[f5470,f1379]) ).
fof(f5476,plain,
( in(sK8(sK22,sK21),relation_dom(sK21))
| sK21 = relation_inverse(sK22)
| ~ spl26_8
| ~ spl26_47
| ~ spl26_142
| ~ spl26_172 ),
inference(forward_subsumption_resolution,[],[f5475,f335]) ).
fof(f5533,definition,
( spl26_174
<=> sK21 = relation_inverse(sK22) ),
introduced(definition,[new_symbols(definition,[spl26_174])],[avatar_definition]) ).
fof(f5534,plain,
( sK21 != relation_inverse(sK22)
| spl26_174 ),
inference(avatar_component_clause,[],[f5533]) ).
fof(f5535,plain,
( sK21 = relation_inverse(sK22)
| ~ spl26_174 ),
inference(avatar_component_clause,[],[f5533]) ).
fof(f5537,definition,
( spl26_175
<=> in(sK8(sK22,sK21),relation_dom(sK21)) ),
introduced(definition,[new_symbols(definition,[spl26_175])],[avatar_definition]) ).
fof(f5539,plain,
( in(sK8(sK22,sK21),relation_dom(sK21))
| ~ spl26_175 ),
inference(avatar_component_clause,[],[f5537]) ).
fof(f5540,plain,
( spl26_174
| spl26_175
| ~ spl26_8
| ~ spl26_47
| ~ spl26_142
| ~ spl26_172 ),
inference(avatar_split_clause,[],[f5476,f5461,f3637,f1378,f333,f5537,f5533]) ).
fof(f5553,plain,
( sK22 = relation_inverse(sK21)
| ~ relation(sK22)
| ~ spl26_174 ),
inference(superposition,[],[f176,f5535]) ).
fof(f5569,plain,
( sK22 = relation_inverse(sK21)
| ~ spl26_8
| ~ spl26_174 ),
inference(forward_subsumption_resolution,[],[f5553,f335]) ).
fof(f5796,definition,
( spl26_185
<=> sK22 = relation_inverse(sK21) ),
introduced(definition,[new_symbols(definition,[spl26_185])],[avatar_definition]) ).
fof(f5798,plain,
( sK22 = relation_inverse(sK21)
| ~ spl26_185 ),
inference(avatar_component_clause,[],[f5796]) ).
fof(f5799,plain,
( spl26_185
| ~ spl26_8
| ~ spl26_174 ),
inference(avatar_split_clause,[],[f5569,f5533,f333,f5796]) ).
fof(f5801,plain,
( sK22 = function_inverse(sK21)
| ~ one_to_one(sK21)
| ~ relation(sK21)
| ~ function(sK21)
| ~ spl26_185 ),
inference(superposition,[],[f5798,f152]) ).
fof(f5831,plain,
( ~ one_to_one(sK21)
| ~ relation(sK21)
| ~ function(sK21)
| spl26_1
| ~ spl26_185 ),
inference(forward_subsumption_resolution,[],[f5801,f267]) ).
fof(f5843,plain,
( ~ relation(sK21)
| ~ function(sK21)
| spl26_1
| ~ spl26_23
| ~ spl26_185 ),
inference(forward_subsumption_resolution,[],[f5831,f901]) ).
fof(f5853,plain,
( ~ function(sK21)
| spl26_1
| ~ spl26_7
| ~ spl26_23
| ~ spl26_185 ),
inference(forward_subsumption_resolution,[],[f5843,f330]) ).
fof(f5864,plain,
( $false
| spl26_1
| ~ spl26_7
| ~ spl26_16
| ~ spl26_23
| ~ spl26_185 ),
inference(forward_subsumption_resolution,[],[f5853,f785]) ).
fof(f5865,plain,
( spl26_1
| ~ spl26_7
| ~ spl26_16
| ~ spl26_23
| ~ spl26_185 ),
inference(avatar_contradiction_clause,[],[f5864]) ).
fof(f5866,plain,
( sK9(sK22,sK21) = apply(sK21,sK8(sK22,sK21))
| ~ spl26_8
| ~ spl26_18
| ~ spl26_118
| ~ spl26_142
| spl26_174 ),
inference(backward_subsumption_resolution,[],[f3674,f5534]) ).
fof(f5867,plain,
( sK8(sK22,sK21) = apply(sK22,sK9(sK22,sK21))
| ~ spl26_8
| ~ spl26_17
| ~ spl26_108
| ~ spl26_142
| spl26_174 ),
inference(backward_subsumption_resolution,[],[f3673,f5534]) ).
fof(f5871,plain,
( in(unordered_pair(unordered_pair(sK8(sK22,sK21),apply(sK21,sK8(sK22,sK21))),singleton(sK8(sK22,sK21))),sK21)
| ~ relation(sK21)
| ~ function(sK21)
| ~ spl26_175 ),
inference(resolution,[],[f5539,f247]) ).
fof(f5884,plain,
( in(unordered_pair(unordered_pair(sK8(sK22,sK21),apply(sK21,sK8(sK22,sK21))),singleton(sK8(sK22,sK21))),sK21)
| ~ function(sK21)
| ~ spl26_7
| ~ spl26_175 ),
inference(forward_subsumption_resolution,[],[f5871,f330]) ).
fof(f5889,plain,
( in(unordered_pair(unordered_pair(sK8(sK22,sK21),apply(sK21,sK8(sK22,sK21))),singleton(sK8(sK22,sK21))),sK21)
| ~ spl26_7
| ~ spl26_16
| ~ spl26_175 ),
inference(forward_subsumption_resolution,[],[f5884,f785]) ).
fof(f5892,plain,
( in(unordered_pair(singleton(sK8(sK22,sK21)),unordered_pair(sK8(sK22,sK21),apply(sK21,sK8(sK22,sK21)))),sK21)
| ~ spl26_7
| ~ spl26_16
| ~ spl26_175 ),
inference(forward_demodulation,[],[f5889,f130]) ).
fof(f5894,plain,
( in(unordered_pair(singleton(sK8(sK22,sK21)),unordered_pair(sK8(sK22,sK21),sK9(sK22,sK21))),sK21)
| ~ spl26_7
| ~ spl26_8
| ~ spl26_16
| ~ spl26_18
| ~ spl26_118
| ~ spl26_142
| spl26_174
| ~ spl26_175 ),
inference(forward_demodulation,[],[f5892,f5866]) ).
fof(f5901,definition,
( spl26_187
<=> in(unordered_pair(singleton(sK8(sK22,sK21)),unordered_pair(sK8(sK22,sK21),sK9(sK22,sK21))),sK21) ),
introduced(definition,[new_symbols(definition,[spl26_187])],[avatar_definition]) ).
fof(f5903,plain,
( in(unordered_pair(singleton(sK8(sK22,sK21)),unordered_pair(sK8(sK22,sK21),sK9(sK22,sK21))),sK21)
| ~ spl26_187 ),
inference(avatar_component_clause,[],[f5901]) ).
fof(f5904,plain,
( spl26_187
| ~ spl26_7
| ~ spl26_8
| ~ spl26_16
| ~ spl26_18
| ~ spl26_118
| ~ spl26_142
| spl26_174
| ~ spl26_175 ),
inference(avatar_split_clause,[],[f5894,f5537,f5533,f3637,f2915,f807,f783,f333,f328,f5901]) ).
fof(f5948,definition,
( spl26_188
<=> sK9(sK22,sK21) = apply(sK21,sK8(sK22,sK21)) ),
introduced(definition,[new_symbols(definition,[spl26_188])],[avatar_definition]) ).
fof(f5950,plain,
( sK9(sK22,sK21) = apply(sK21,sK8(sK22,sK21))
| ~ spl26_188 ),
inference(avatar_component_clause,[],[f5948]) ).
fof(f5951,plain,
( spl26_188
| ~ spl26_8
| ~ spl26_18
| ~ spl26_118
| ~ spl26_142
| spl26_174 ),
inference(avatar_split_clause,[],[f5866,f5533,f3637,f2915,f807,f333,f5948]) ).
fof(f5994,definition,
( spl26_190
<=> sK8(sK22,sK21) = apply(sK22,sK9(sK22,sK21)) ),
introduced(definition,[new_symbols(definition,[spl26_190])],[avatar_definition]) ).
fof(f5996,plain,
( sK8(sK22,sK21) = apply(sK22,sK9(sK22,sK21))
| ~ spl26_190 ),
inference(avatar_component_clause,[],[f5994]) ).
fof(f5997,plain,
( spl26_190
| ~ spl26_8
| ~ spl26_17
| ~ spl26_108
| ~ spl26_142
| spl26_174 ),
inference(avatar_split_clause,[],[f5867,f5533,f3637,f2670,f803,f333,f5994]) ).
fof(f6008,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK9(sK22,sK21)),unordered_pair(sK9(sK22,sK21),sK8(sK22,sK21))),sK22)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK22,sK21))),sK21) )
| ~ spl26_97
| ~ spl26_190 ),
inference(superposition,[],[f2525,f5996]) ).
fof(f6018,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK9(sK22,sK21)),unordered_pair(sK8(sK22,sK21),sK9(sK22,sK21))),sK22)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK22,sK21))),sK21) )
| ~ spl26_97
| ~ spl26_190 ),
inference(forward_demodulation,[],[f6008,f130]) ).
fof(f6049,definition,
( spl26_191
<=> in(unordered_pair(singleton(sK9(sK22,sK21)),unordered_pair(sK8(sK22,sK21),sK9(sK22,sK21))),sK22) ),
introduced(definition,[new_symbols(definition,[spl26_191])],[avatar_definition]) ).
fof(f6050,plain,
( ~ in(unordered_pair(singleton(sK9(sK22,sK21)),unordered_pair(sK8(sK22,sK21),sK9(sK22,sK21))),sK22)
| spl26_191 ),
inference(avatar_component_clause,[],[f6049]) ).
fof(f6051,plain,
( in(unordered_pair(singleton(sK9(sK22,sK21)),unordered_pair(sK8(sK22,sK21),sK9(sK22,sK21))),sK22)
| ~ spl26_191 ),
inference(avatar_component_clause,[],[f6049]) ).
fof(f6058,plain,
( ~ in(unordered_pair(singleton(sK8(sK22,sK21)),unordered_pair(sK8(sK22,sK21),sK9(sK22,sK21))),sK21)
| sK21 = relation_inverse(sK22)
| ~ relation(sK22)
| ~ spl26_115
| ~ spl26_191 ),
inference(resolution,[],[f6051,f2823]) ).
fof(f6065,plain,
( sK21 = relation_inverse(sK22)
| ~ relation(sK22)
| ~ spl26_115
| ~ spl26_187
| ~ spl26_191 ),
inference(forward_subsumption_resolution,[],[f6058,f5903]) ).
fof(f6067,plain,
( ~ relation(sK22)
| ~ spl26_115
| spl26_174
| ~ spl26_187
| ~ spl26_191 ),
inference(forward_subsumption_resolution,[],[f6065,f5534]) ).
fof(f6069,plain,
( $false
| ~ spl26_8
| ~ spl26_115
| spl26_174
| ~ spl26_187
| ~ spl26_191 ),
inference(forward_subsumption_resolution,[],[f6067,f335]) ).
fof(f6070,plain,
( ~ spl26_8
| ~ spl26_115
| spl26_174
| ~ spl26_187
| ~ spl26_191 ),
inference(avatar_contradiction_clause,[],[f6069]) ).
fof(f6081,plain,
( ! [X0] : ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK22,sK21))),sK21)
| ~ spl26_97
| ~ spl26_190
| spl26_191 ),
inference(forward_subsumption_resolution,[],[f6018,f6050]) ).
fof(f6138,plain,
( in(unordered_pair(singleton(sK8(sK22,sK21)),unordered_pair(sK8(sK22,sK21),sK9(sK22,sK21))),sK21)
| ~ spl26_7
| ~ spl26_16
| ~ spl26_175
| ~ spl26_188 ),
inference(forward_demodulation,[],[f5892,f5950]) ).
fof(f6209,plain,
( $false
| ~ spl26_7
| ~ spl26_16
| ~ spl26_97
| ~ spl26_175
| ~ spl26_188
| ~ spl26_190
| spl26_191 ),
inference(forward_subsumption_resolution,[],[f6138,f6081]) ).
fof(f6210,plain,
( ~ spl26_7
| ~ spl26_16
| ~ spl26_97
| ~ spl26_175
| ~ spl26_188
| ~ spl26_190
| spl26_191 ),
inference(avatar_contradiction_clause,[],[f6209]) ).
fof(f6258,plain,
( $false
| ~ spl26_1
| spl26_2
| spl26_5
| ~ spl26_6 ),
inference(forward_subsumption_resolution,[],[f271,f570]) ).
fof(f6259,plain,
( ~ spl26_1
| spl26_2
| spl26_5
| ~ spl26_6 ),
inference(avatar_contradiction_clause,[],[f6258]) ).
fof(f6297,plain,
( in(unordered_pair(singleton(sK23),unordered_pair(sK24,sK23)),sK22)
| ~ spl26_1
| spl26_2
| ~ spl26_6
| ~ spl26_22
| ~ spl26_43 ),
inference(forward_demodulation,[],[f1326,f600]) ).
fof(f6323,plain,
( in(unordered_pair(singleton(sK23),unordered_pair(sK23,sK24)),sK22)
| ~ spl26_1
| spl26_2
| ~ spl26_6
| ~ spl26_22
| ~ spl26_43 ),
inference(forward_demodulation,[],[f6297,f130]) ).
fof(f6448,plain,
( $false
| ~ spl26_1
| spl26_2
| ~ spl26_6
| ~ spl26_22
| spl26_35
| ~ spl26_43 ),
inference(forward_subsumption_resolution,[],[f6323,f1263]) ).
fof(f6449,plain,
( ~ spl26_1
| spl26_2
| ~ spl26_6
| ~ spl26_22
| spl26_35
| ~ spl26_43 ),
inference(avatar_contradiction_clause,[],[f6448]) ).
fof(f6520,plain,
( $false
| spl26_2
| ~ spl26_19
| ~ spl26_35 ),
inference(forward_subsumption_resolution,[],[f1458,f271]) ).
fof(f6521,plain,
( spl26_2
| ~ spl26_19
| ~ spl26_35 ),
inference(avatar_contradiction_clause,[],[f6520]) ).
fof(f6577,plain,
( in(unordered_pair(singleton(sK24),unordered_pair(sK24,sK23)),sK21)
| ~ spl26_1
| spl26_3
| ~ spl26_6
| ~ spl26_22 ),
inference(forward_demodulation,[],[f870,f937]) ).
fof(f6616,plain,
( $false
| ~ spl26_1
| spl26_3
| ~ spl26_6
| ~ spl26_22
| ~ spl26_29 ),
inference(forward_subsumption_resolution,[],[f6577,f1117]) ).
fof(f6617,plain,
( ~ spl26_1
| spl26_3
| ~ spl26_6
| ~ spl26_22
| ~ spl26_29 ),
inference(avatar_contradiction_clause,[],[f6616]) ).
fof(f6678,plain,
( ~ in(sK23,relation_dom(sK22))
| ~ spl26_2
| ~ spl26_11
| ~ spl26_87 ),
inference(forward_subsumption_resolution,[],[f4498,f761]) ).
fof(f6734,plain,
( $false
| ~ spl26_2
| ~ spl26_3
| ~ spl26_6
| ~ spl26_11
| ~ spl26_87 ),
inference(forward_subsumption_resolution,[],[f6678,f733]) ).
fof(f6735,plain,
( ~ spl26_2
| ~ spl26_3
| ~ spl26_6
| ~ spl26_11
| ~ spl26_87 ),
inference(avatar_contradiction_clause,[],[f6734]) ).
cnf(s1,plain,
( ~ spl26_1
| ~ spl26_2
| ~ spl26_3
| ~ spl26_4
| ~ spl26_5
| ~ spl26_6 ),
inference(sat_conversion,[],[f288]) ).
cnf(s2,plain,
( spl26_1
| spl26_6 ),
inference(sat_conversion,[],[f301]) ).
cnf(s3,plain,
spl26_7,
inference(sat_conversion,[],[f331]) ).
cnf(s4,plain,
spl26_8,
inference(sat_conversion,[],[f336]) ).
cnf(s5,plain,
( spl26_1
| spl26_9 ),
inference(sat_conversion,[],[f517]) ).
cnf(s6,plain,
( spl26_1
| spl26_10 ),
inference(sat_conversion,[],[f549]) ).
cnf(s7,plain,
( spl26_5
| ~ spl26_7
| spl26_11 ),
inference(sat_conversion,[],[f599]) ).
cnf(s9,plain,
( spl26_4
| ~ spl26_7
| spl26_13 ),
inference(sat_conversion,[],[f673]) ).
cnf(s12,plain,
( ~ spl26_1
| spl26_3
| spl26_5
| ~ spl26_6 ),
inference(sat_conversion,[],[f732]) ).
cnf(s13,plain,
spl26_15,
inference(sat_conversion,[],[f766]) ).
cnf(s14,plain,
spl26_16,
inference(sat_conversion,[],[f786]) ).
cnf(s15,plain,
( ~ spl26_7
| ~ spl26_9
| spl26_17 ),
inference(sat_conversion,[],[f805]) ).
cnf(s16,plain,
( ~ spl26_7
| spl26_18 ),
inference(sat_conversion,[],[f809]) ).
cnf(s17,plain,
( ~ spl26_8
| spl26_19 ),
inference(sat_conversion,[],[f816]) ).
cnf(s21,plain,
( ~ spl26_5
| ~ spl26_7
| ~ spl26_16
| spl26_22 ),
inference(sat_conversion,[],[f871]) ).
cnf(s22,plain,
spl26_23,
inference(sat_conversion,[],[f902]) ).
cnf(s24,plain,
( ~ spl26_7
| spl26_25 ),
inference(sat_conversion,[],[f915]) ).
cnf(s26,plain,
( ~ spl26_7
| spl26_26 ),
inference(sat_conversion,[],[f922]) ).
cnf(s36,plain,
( ~ spl26_1
| spl26_6
| ~ spl26_7
| ~ spl26_26 ),
inference(sat_conversion,[],[f1058]) ).
cnf(s37,plain,
( spl26_3
| ~ spl26_7
| spl26_29 ),
inference(sat_conversion,[],[f1118]) ).
cnf(s43,plain,
( ~ spl26_13
| ~ spl26_31 ),
inference(sat_conversion,[],[f1200]) ).
cnf(s48,plain,
( ~ spl26_2
| ~ spl26_3
| ~ spl26_6
| ~ spl26_8
| ~ spl26_15
| spl26_35 ),
inference(sat_conversion,[],[f1265]) ).
cnf(s50,plain,
( ~ spl26_7
| spl26_37 ),
inference(sat_conversion,[],[f1274]) ).
cnf(s56,plain,
( ~ spl26_1
| ~ spl26_37
| spl26_43 ),
inference(sat_conversion,[],[f1317]) ).
cnf(s59,plain,
( ~ spl26_8
| spl26_46 ),
inference(sat_conversion,[],[f1360]) ).
cnf(s60,plain,
( ~ spl26_7
| spl26_47 ),
inference(sat_conversion,[],[f1380]) ).
cnf(s70,plain,
( ~ spl26_1
| ~ spl26_25
| spl26_57 ),
inference(sat_conversion,[],[f1571]) ).
cnf(s71,plain,
( spl26_31
| ~ spl26_35
| ~ spl26_57 ),
inference(sat_conversion,[],[f1583]) ).
cnf(s83,plain,
( ~ spl26_8
| ~ spl26_10
| ~ spl26_15
| spl26_62 ),
inference(sat_conversion,[],[f1880]) ).
cnf(s90,plain,
( spl26_1
| ~ spl26_6
| spl26_67 ),
inference(sat_conversion,[],[f1941]) ).
cnf(s91,plain,
( ~ spl26_8
| ~ spl26_15
| ~ spl26_67
| spl26_68 ),
inference(sat_conversion,[],[f1978]) ).
cnf(s92,plain,
( spl26_1
| ~ spl26_6
| spl26_69 ),
inference(sat_conversion,[],[f1985]) ).
cnf(s105,plain,
( ~ spl26_8
| ~ spl26_15
| ~ spl26_69
| spl26_83 ),
inference(sat_conversion,[],[f2300]) ).
cnf(s109,plain,
( ~ spl26_46
| ~ spl26_57
| spl26_87 ),
inference(sat_conversion,[],[f2349]) ).
cnf(s119,plain,
( ~ spl26_7
| ~ spl26_16
| ~ spl26_83
| spl26_97 ),
inference(sat_conversion,[],[f2526]) ).
cnf(s130,plain,
( ~ spl26_19
| spl26_108 ),
inference(sat_conversion,[],[f2672]) ).
cnf(s137,plain,
( ~ spl26_7
| spl26_115 ),
inference(sat_conversion,[],[f2824]) ).
cnf(s140,plain,
( ~ spl26_62
| spl26_118 ),
inference(sat_conversion,[],[f2917]) ).
cnf(s164,plain,
( ~ spl26_7
| spl26_142 ),
inference(sat_conversion,[],[f3639]) ).
cnf(s207,plain,
( ~ spl26_68
| spl26_172 ),
inference(sat_conversion,[],[f5463]) ).
cnf(s209,plain,
( ~ spl26_8
| ~ spl26_47
| ~ spl26_142
| ~ spl26_172
| spl26_174
| spl26_175 ),
inference(sat_conversion,[],[f5540]) ).
cnf(s219,plain,
( ~ spl26_8
| ~ spl26_174
| spl26_185 ),
inference(sat_conversion,[],[f5799]) ).
cnf(s223,plain,
( spl26_1
| ~ spl26_7
| ~ spl26_16
| ~ spl26_23
| ~ spl26_185 ),
inference(sat_conversion,[],[f5865]) ).
cnf(s225,plain,
( ~ spl26_7
| ~ spl26_8
| ~ spl26_16
| ~ spl26_18
| ~ spl26_118
| ~ spl26_142
| spl26_174
| ~ spl26_175
| spl26_187 ),
inference(sat_conversion,[],[f5904]) ).
cnf(s226,plain,
( ~ spl26_8
| ~ spl26_18
| ~ spl26_118
| ~ spl26_142
| spl26_174
| spl26_188 ),
inference(sat_conversion,[],[f5951]) ).
cnf(s228,plain,
( ~ spl26_8
| ~ spl26_17
| ~ spl26_108
| ~ spl26_142
| spl26_174
| spl26_190 ),
inference(sat_conversion,[],[f5997]) ).
cnf(s230,plain,
( ~ spl26_8
| ~ spl26_115
| spl26_174
| ~ spl26_187
| ~ spl26_191 ),
inference(sat_conversion,[],[f6070]) ).
cnf(s255,plain,
( ~ spl26_7
| ~ spl26_16
| ~ spl26_97
| ~ spl26_175
| ~ spl26_188
| ~ spl26_190
| spl26_191 ),
inference(sat_conversion,[],[f6210]) ).
cnf(s259,plain,
( ~ spl26_1
| spl26_2
| spl26_5
| ~ spl26_6 ),
inference(sat_conversion,[],[f6259]) ).
cnf(s279,plain,
( ~ spl26_1
| spl26_2
| ~ spl26_6
| ~ spl26_22
| spl26_35
| ~ spl26_43 ),
inference(sat_conversion,[],[f6449]) ).
cnf(s293,plain,
( spl26_2
| ~ spl26_19
| ~ spl26_35 ),
inference(sat_conversion,[],[f6521]) ).
cnf(s303,plain,
( ~ spl26_1
| spl26_3
| ~ spl26_6
| ~ spl26_22
| ~ spl26_29 ),
inference(sat_conversion,[],[f6617]) ).
cnf(s327,plain,
( ~ spl26_2
| ~ spl26_3
| ~ spl26_6
| ~ spl26_11
| ~ spl26_87 ),
inference(sat_conversion,[],[f6735]) ).
cnf(s346,plain,
spl26_46,
inference(rat,[],[s59,s4]) ).
cnf(s350,plain,
spl26_19,
inference(rat,[],[s17,s4]) ).
cnf(s354,plain,
spl26_108,
inference(rat,[],[s130,s350]) ).
cnf(s357,plain,
spl26_142,
inference(rat,[],[s164,s3]) ).
cnf(s359,plain,
spl26_115,
inference(rat,[],[s137,s3]) ).
cnf(s367,plain,
spl26_47,
inference(rat,[],[s60,s3]) ).
cnf(s371,plain,
spl26_37,
inference(rat,[],[s50,s3]) ).
cnf(s373,plain,
spl26_26,
inference(rat,[],[s26,s3]) ).
cnf(s374,plain,
spl26_25,
inference(rat,[],[s24,s3]) ).
cnf(s376,plain,
spl26_18,
inference(rat,[],[s16,s3]) ).
cnf(s381,plain,
spl26_1,
inference(rat,[],[s230,s225,s255,s209,s207,s119,s226,s91,s105,s228,s140,s90,s92,s15,s83,s219,s2,s5,s6,s223,s4,s359,s14,s3,s357,s376,s367,s13,s354,s22]) ).
cnf(s382,plain,
spl26_57,
inference(rat,[],[s70,s374,s381]) ).
cnf(s383,plain,
spl26_43,
inference(rat,[],[s56,s371,s381]) ).
cnf(s384,plain,
spl26_6,
inference(rat,[],[s36,s373,s3,s381]) ).
cnf(s386,plain,
spl26_87,
inference(rat,[],[s109,s346,s382]) ).
cnf(s396,plain,
spl26_2,
inference(rat,[],[s21,s279,s259,s293,s14,s3,s381,s384,s383,s350]) ).
cnf(s398,plain,
spl26_3,
inference(rat,[],[s21,s303,s12,s37,s14,s3,s381,s384]) ).
cnf(s400,plain,
~ spl26_11,
inference(rat,[],[s327,s386,s396,s384,s398]) ).
cnf(s401,plain,
spl26_35,
inference(rat,[],[s48,s396,s13,s4,s384,s398]) ).
cnf(s404,plain,
spl26_5,
inference(rat,[],[s7,s3,s400]) ).
cnf(s405,plain,
spl26_31,
inference(rat,[],[s71,s382,s401]) ).
cnf(s412,plain,
~ spl26_4,
inference(rat,[],[s1,s384,s398,s396,s381,s404]) ).
cnf(s414,plain,
~ spl26_13,
inference(rat,[],[s43,s405]) ).
cnf(s417,plain,
$false,
inference(rat,[],[s9,s3,s414,s412]) ).
fof(f6756,plain,
$false,
inference(avatar_sat_refutation,[],[s417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU218+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n013.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
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Mon Sep 28 04:06:51 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.09/2.46 % (792608)Detected formulas, will run a generic FOF schedule.
% 11.09/2.46 % (792613)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=2335179514:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.09/2.46 % (792617)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=712958851:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.09/2.46 % (792614)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=3986718549:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.09/2.46 % (792618)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3355974598:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.09/2.46 % (792619)dis-21_1_sil=8000:lcm=predicate:random_seed=443041699: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)
% 11.09/2.46 % (792616)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2866649073:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.09/2.46 % (792615)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=3597941825:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.09/2.46 % (792616)Refutation not found, incomplete strategy
% 11.09/2.46 % (792616)------------------------------
% 11.09/2.46 % (792616)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.46 % (792616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.46 % (792616)CaDiCaL version: 2.1.3
% 11.09/2.46 % (792616)Termination reason: Refutation not found, incomplete strategy
% 11.09/2.46 % (792616)Time elapsed: 0.015 s
% 11.09/2.46 % (792616)Peak memory usage: 89 MB
% 11.09/2.46 % (792616)Instructions burned: 20 (million)
% 11.09/2.46 % (792619)Instruction limit reached!
% 11.09/2.46 % (792619)------------------------------
% 11.09/2.46 % (792619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.46 % (792619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.46 % (792619)CaDiCaL version: 2.1.3
% 11.09/2.46 % (792619)Termination reason: Instruction limit
% 11.09/2.46 % (792619)Termination phase: Saturation
% 11.09/2.46 % (792619)Time elapsed: 0.065 s
% 11.09/2.46 % (792619)Peak memory usage: 90 MB
% 11.09/2.46 % (792619)Instructions burned: 129 (million)
% 11.09/2.46 % (792617)Instruction limit reached!
% 11.09/2.46 % (792617)------------------------------
% 11.09/2.46 % (792617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.46 % (792617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.46 % (792617)CaDiCaL version: 2.1.3
% 11.09/2.46 % (792617)Termination reason: Instruction limit
% 11.09/2.46 % (792617)Termination phase: Saturation
% 11.09/2.46 % (792617)Time elapsed: 0.069 s
% 11.09/2.46 % (792617)Peak memory usage: 88 MB
% 11.09/2.46 % (792617)Instructions burned: 119 (million)
% 11.09/2.46 % (792618)Instruction limit reached!
% 11.09/2.46 % (792618)------------------------------
% 11.09/2.46 % (792618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.46 % (792618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.46 % (792618)CaDiCaL version: 2.1.3
% 11.09/2.46 % (792618)Termination reason: Instruction limit
% 11.09/2.46 % (792618)Termination phase: Saturation
% 11.09/2.46 % (792618)Time elapsed: 0.081 s
% 11.09/2.46 % (792618)Peak memory usage: 90 MB
% 11.09/2.46 % (792618)Instructions burned: 140 (million)
% 11.09/2.46 % (792629)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4125281015:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 11.09/2.46 % (792628)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2407775446:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 11.09/2.46 % (792627)lrs+10_1_sil=8000:sp=occurrence:random_seed=3918138573:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 11.09/2.46 % (792616)------------------------------
% 11.09/2.46 % (792616)------------------------------
% 11.09/2.46 % (792628)Instruction limit reached!
% 11.09/2.46 % (792628)------------------------------
% 11.09/2.46 % (792628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.46 % (792628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.46 % (792628)CaDiCaL version: 2.1.3
% 11.09/2.46 % (792628)Termination reason: Instruction limit
% 11.09/2.46 % (792628)Termination phase: Saturation
% 11.09/2.46 % (792628)Time elapsed: 0.091 s
% 11.09/2.46 % (792628)Peak memory usage: 90 MB
% 11.09/2.46 % (792628)Instructions burned: 158 (million)
% 11.09/2.46 % (792627)Instruction limit reached!
% 11.09/2.46 % (792627)------------------------------
% 11.09/2.46 % (792627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.46 % (792627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.46 % (792627)CaDiCaL version: 2.1.3
% 11.09/2.46 % (792627)Termination reason: Instruction limit
% 11.09/2.46 % (792627)Termination phase: Saturation
% 11.09/2.46 % (792627)Time elapsed: 0.179 s
% 11.09/2.46 % (792627)Peak memory usage: 92 MB
% 11.09/2.46 % (792627)Instructions burned: 286 (million)
% 11.09/2.46 % (792633)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=4127077798:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 11.09/2.46 % (792629)Instruction limit reached!
% 11.09/2.46 % (792629)------------------------------
% 11.09/2.46 % (792629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.46 % (792629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.46 % (792629)CaDiCaL version: 2.1.3
% 11.09/2.46 % (792629)Termination reason: Instruction limit
% 11.09/2.46 % (792629)Termination phase: Saturation
% 11.09/2.46 % (792629)Time elapsed: 0.226 s
% 11.09/2.46 % (792629)Peak memory usage: 92 MB
% 11.09/2.46 % (792629)Instructions burned: 326 (million)
% 11.09/2.46 % (792635)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3003682182:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 11.09/2.46 % (792635)Refutation not found, incomplete strategy
% 11.09/2.46 % (792635)------------------------------
% 11.09/2.46 % (792635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.46 % (792635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.46 % (792635)CaDiCaL version: 2.1.3
% 11.09/2.46 % (792635)Termination reason: Refutation not found, incomplete strategy
% 11.09/2.46 % (792635)Time elapsed: 0.014 s
% 11.09/2.46 % (792635)Peak memory usage: 89 MB
% 11.09/2.46 % (792635)Instructions burned: 19 (million)
% 11.09/2.46 % (792636)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3474068750:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 11.09/2.46 % (792633)Instruction limit reached!
% 11.09/2.46 % (792633)------------------------------
% 11.09/2.46 % (792633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.46 % (792633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.46 % (792633)CaDiCaL version: 2.1.3
% 11.09/2.46 % (792633)Termination reason: Instruction limit
% 11.09/2.46 % (792633)Termination phase: Saturation
% 11.09/2.46 % (792633)Time elapsed: 0.149 s
% 11.09/2.46 % (792633)Peak memory usage: 91 MB
% 11.09/2.46 % (792633)Instructions burned: 248 (million)
% 11.09/2.46 % (792638)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2823989696:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 11.09/2.46 % (792638)Instruction limit reached!
% 11.09/2.46 % (792638)------------------------------
% 11.09/2.46 % (792638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.46 % (792638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.46 % (792638)CaDiCaL version: 2.1.3
% 11.09/2.46 % (792638)Termination reason: Instruction limit
% 11.09/2.46 % (792638)Termination phase: Saturation
% 11.09/2.46 % (792638)Time elapsed: 0.078 s
% 11.09/2.46 % (792638)Peak memory usage: 90 MB
% 11.09/2.46 % (792638)Instructions burned: 113 (million)
% 11.09/2.46 % (792635)------------------------------
% 11.09/2.46 % (792635)------------------------------
% 11.09/2.46 % (792641)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1161506095:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 11.09/2.46 % (792641)Instruction limit reached!
% 11.09/2.46 % (792641)------------------------------
% 11.09/2.46 % (792641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.46 % (792641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.46 % (792641)CaDiCaL version: 2.1.3
% 11.09/2.46 % (792641)Termination reason: Instruction limit
% 11.09/2.46 % (792641)Termination phase: Saturation
% 11.09/2.46 % (792641)Time elapsed: 0.061 s
% 11.09/2.46 % (792641)Peak memory usage: 89 MB
% 11.09/2.46 % (792641)Instructions burned: 127 (million)
% 11.09/2.46 % (792643)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=835418742:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 11.09/2.46 % (792645)lrs+10_1_sil=8000:sp=occurrence:random_seed=282720840:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 11.09/2.46 % (792643)Instruction limit reached!
% 11.09/2.46 % (792643)------------------------------
% 11.09/2.46 % (792643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.46 % (792643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.46 % (792643)CaDiCaL version: 2.1.3
% 11.09/2.46 % (792643)Termination reason: Instruction limit
% 11.09/2.46 % (792643)Termination phase: Saturation
% 11.09/2.46 % (792643)Time elapsed: 0.069 s
% 11.09/2.46 % (792643)Peak memory usage: 89 MB
% 11.09/2.46 % (792643)Instructions burned: 114 (million)
% 11.09/2.46 % (792646)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2636356578:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 11.09/2.46 % (792646)Refutation not found, incomplete strategy
% 11.09/2.46 % (792646)------------------------------
% 11.09/2.46 % (792646)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.46 % (792646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.46 % (792646)CaDiCaL version: 2.1.3
% 11.09/2.46 % (792646)Termination reason: Refutation not found, incomplete strategy
% 11.09/2.46 % (792646)Time elapsed: 0.013 s
% 11.09/2.46 % (792646)Peak memory usage: 89 MB
% 11.09/2.46 % (792646)Instructions burned: 16 (million)
% 11.09/2.46 % (792649)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=831254437:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 11.09/2.46 % (792615)First to succeed.
% 11.09/2.46 % (792615)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-792608"
% 11.09/2.46 % (792646)------------------------------
% 11.09/2.46 % (792646)------------------------------
% 11.09/2.46 % (792652)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2887212207:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2986 on theBenchmark for (2986ds/134Mi)
% 11.09/2.46 % (792615)Refutation found. Thanks to Tanya!
% 11.09/2.46 % SZS status Theorem for theBenchmark
% 11.09/2.46 % SZS output start Proof for theBenchmark
% See solution above
% 11.85/2.68 % (792615)------------------------------
% 11.85/2.68 % (792615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.85/2.68 % (792615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.85/2.68 % (792615)CaDiCaL version: 2.1.3
% 11.85/2.68 % (792615)Termination reason: Refutation
% 11.85/2.68 % (792615)Time elapsed: 1.164 s
% 11.85/2.68 % (792615)Peak memory usage: 135 MB
% 11.85/2.68 % (792615)Instructions burned: 1701 (million)
% 11.85/2.68 % (792615)------------------------------
% 11.85/2.68 % (792615)------------------------------
% 11.85/2.68 % (792608)Success in time 1.594 s
% 11.85/2.68 % Vampire exiting
%------------------------------------------------------------------------------