%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU218+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 6.34s 1.85s
% Output : Refutation 7.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 26
% Syntax : Number of formulae : 296 ( 22 unt; 15 def)
% Number of atoms : 1153 ( 257 equ)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 1457 ( 600 ~; 671 |; 127 &)
% ( 35 <=>; 22 =>; 0 <=; 2 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 16 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 5 con; 0-2 aty)
% Number of variables : 322 ( 0 sgn 286 !; 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(f20,axiom,
! [X0] :
( relation(X0)
=> relation(relation_inverse(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f36,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f47,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(f48,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(f49,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)],[f48]) ).
fof(f59,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(f60,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,[],[f59]) ).
fof(f61,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(f62,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(f63,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(f64,plain,
! [X0] :
( function_inverse(X0) = relation_inverse(X0)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f65,plain,
! [X0] :
( function_inverse(X0) = relation_inverse(X0)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f64]) ).
fof(f68,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f78,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f82,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(relation_inverse(X0))
& relation_dom(X0) = relation_rng(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f83,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,[],[f49]) ).
fof(f84,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,[],[f83]) ).
fof(f91,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,[],[f60]) ).
fof(f92,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,[],[f61]) ).
fof(f93,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,[],[f92]) ).
fof(f94,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))],[f93]) ).
fof(f95,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,[],[f62]) ).
fof(f96,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,[],[f95]) ).
fof(f97,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))],[f96]) ).
fof(f98,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,[],[f63]) ).
fof(f99,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,[],[f98]) ).
fof(f100,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))],[f99]) ).
fof(f110,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,[],[f84]) ).
fof(f111,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,[],[f110]) ).
fof(f112,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,[],[f111]) ).
fof(f113,plain,
( ( relation_rng(sK19) != relation_dom(sK20)
| ( ( ~ in(sK22,relation_dom(sK19))
| sK21 != apply(sK19,sK22) )
& in(sK21,relation_rng(sK19))
& sK22 = apply(sK20,sK21) )
| ( ( ~ in(sK21,relation_rng(sK19))
| sK22 != apply(sK20,sK21) )
& in(sK22,relation_dom(sK19))
& sK21 = apply(sK19,sK22) )
| sK20 != function_inverse(sK19) )
& ( ( relation_rng(sK19) = relation_dom(sK20)
& ! [X4,X5] :
( ( ( in(X5,relation_dom(sK19))
& apply(sK19,X5) = X4 )
| ~ in(X4,relation_rng(sK19))
| apply(sK20,X4) != X5 )
& ( ( in(X4,relation_rng(sK19))
& apply(sK20,X4) = X5 )
| ~ in(X5,relation_dom(sK19))
| apply(sK19,X5) != X4 ) ) )
| sK20 = function_inverse(sK19) )
& relation(sK20)
& function(sK20)
& one_to_one(sK19)
& relation(sK19)
& function(sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20,sK21,sK22]),skolemize(X0,sK19),skolemize(X1,sK20),skolemize(X2,sK21),skolemize(X3,sK22)],[f112]) ).
fof(f120,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f125,plain,
! [X2,X0,X1] :
( empty_set = X2
| apply(X0,X1) != X2
| in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f127,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,[],[f91]) ).
fof(f128,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,[],[f91]) ).
fof(f129,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK4(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f130,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f134,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f137,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f138,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,[],[f100]) ).
fof(f139,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,[],[f100]) ).
fof(f140,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,[],[f100]) ).
fof(f141,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,[],[f100]) ).
fof(f142,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_inverse(X0) = function_inverse(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f145,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f166,plain,
! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(cnf_transformation,[],[f78]) ).
fof(f185,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) = relation_rng(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f186,plain,
! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_dom(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f187,plain,
function(sK19),
inference(cnf_transformation,[],[f113]) ).
fof(f188,plain,
relation(sK19),
inference(cnf_transformation,[],[f113]) ).
fof(f189,plain,
one_to_one(sK19),
inference(cnf_transformation,[],[f113]) ).
fof(f190,plain,
function(sK20),
inference(cnf_transformation,[],[f113]) ).
fof(f191,plain,
relation(sK20),
inference(cnf_transformation,[],[f113]) ).
fof(f192,plain,
! [X4,X5] :
( apply(sK20,X4) = X5
| ~ in(X5,relation_dom(sK19))
| apply(sK19,X5) != X4
| sK20 = function_inverse(sK19) ),
inference(cnf_transformation,[],[f113]) ).
fof(f194,plain,
! [X4,X5] :
( apply(sK19,X5) = X4
| ~ in(X4,relation_rng(sK19))
| apply(sK20,X4) != X5
| sK20 = function_inverse(sK19) ),
inference(cnf_transformation,[],[f113]) ).
fof(f195,plain,
! [X4,X5] :
( in(X5,relation_dom(sK19))
| ~ in(X4,relation_rng(sK19))
| apply(sK20,X4) != X5
| sK20 = function_inverse(sK19) ),
inference(cnf_transformation,[],[f113]) ).
fof(f196,plain,
( relation_rng(sK19) = relation_dom(sK20)
| sK20 = function_inverse(sK19) ),
inference(cnf_transformation,[],[f113]) ).
fof(f197,plain,
( relation_rng(sK19) != relation_dom(sK20)
| sK22 = apply(sK20,sK21)
| sK21 = apply(sK19,sK22)
| sK20 != function_inverse(sK19) ),
inference(cnf_transformation,[],[f113]) ).
fof(f198,plain,
( relation_rng(sK19) != relation_dom(sK20)
| sK22 = apply(sK20,sK21)
| in(sK22,relation_dom(sK19))
| sK20 != function_inverse(sK19) ),
inference(cnf_transformation,[],[f113]) ).
fof(f200,plain,
( relation_rng(sK19) != relation_dom(sK20)
| in(sK21,relation_rng(sK19))
| sK21 = apply(sK19,sK22)
| sK20 != function_inverse(sK19) ),
inference(cnf_transformation,[],[f113]) ).
fof(f201,plain,
( relation_rng(sK19) != relation_dom(sK20)
| in(sK21,relation_rng(sK19))
| in(sK22,relation_dom(sK19))
| sK20 != function_inverse(sK19) ),
inference(cnf_transformation,[],[f113]) ).
fof(f205,plain,
( relation_rng(sK19) != relation_dom(sK20)
| ~ in(sK22,relation_dom(sK19))
| sK21 != apply(sK19,sK22)
| ~ in(sK21,relation_rng(sK19))
| sK22 != apply(sK20,sK21)
| sK20 != function_inverse(sK19) ),
inference(cnf_transformation,[],[f113]) ).
fof(f213,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,[],[f128,f137]) ).
fof(f214,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,[],[f127,f137]) ).
fof(f217,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,[],[f130,f137]) ).
fof(f218,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK4(X0,X5)),singleton(X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f129,f137]) ).
fof(f221,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,[],[f134,f137]) ).
fof(f223,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ 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_inverse(X0) = X1 ),
inference(definition_unfolding,[],[f141,f137,f137]) ).
fof(f224,plain,
! [X0,X1] :
( ~ relation(X0)
| 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_inverse(X0) = X1 ),
inference(definition_unfolding,[],[f140,f137,f137]) ).
fof(f225,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,[],[f139,f137,f137]) ).
fof(f226,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,[],[f138,f137,f137]) ).
fof(f230,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f214]) ).
fof(f232,plain,
! [X0,X1] :
( ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) = empty_set
| ~ function(X0) ),
inference(equality_resolution,[],[f125]) ).
fof(f233,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f217]) ).
fof(f234,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(unordered_pair(unordered_pair(X5,sK4(X0,X5)),singleton(X5)),X0) ),
inference(equality_resolution,[],[f218]) ).
fof(f235,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f221]) ).
fof(f237,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,[],[f225]) ).
fof(f238,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,[],[f226]) ).
fof(f239,plain,
! [X4] :
( in(apply(sK20,X4),relation_dom(sK19))
| ~ in(X4,relation_rng(sK19))
| sK20 = function_inverse(sK19) ),
inference(equality_resolution,[],[f195]) ).
fof(f240,plain,
! [X4] :
( apply(sK19,apply(sK20,X4)) = X4
| ~ in(X4,relation_rng(sK19))
| sK20 = function_inverse(sK19) ),
inference(equality_resolution,[],[f194]) ).
fof(f242,plain,
! [X5] :
( apply(sK20,apply(sK19,X5)) = X5
| ~ in(X5,relation_dom(sK19))
| sK20 = function_inverse(sK19) ),
inference(equality_resolution,[],[f192]) ).
fof(f244,definition,
( spl23_1
<=> sK20 = function_inverse(sK19) ),
introduced(definition,[new_symbols(definition,[spl23_1])],[avatar_definition]) ).
fof(f245,plain,
( sK20 = function_inverse(sK19)
| ~ spl23_1 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f247,definition,
( spl23_2
<=> ! [X5] :
( apply(sK20,apply(sK19,X5)) = X5
| ~ in(X5,relation_dom(sK19)) ) ),
introduced(definition,[new_symbols(definition,[spl23_2])],[avatar_definition]) ).
fof(f248,plain,
( ! [X5] :
( ~ in(X5,relation_dom(sK19))
| apply(sK20,apply(sK19,X5)) = X5 )
| ~ spl23_2 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f249,plain,
( spl23_1
| spl23_2 ),
inference(avatar_split_clause,[],[f242,f247,f244]) ).
fof(f255,definition,
( spl23_4
<=> ! [X4] :
( apply(sK19,apply(sK20,X4)) = X4
| ~ in(X4,relation_rng(sK19)) ) ),
introduced(definition,[new_symbols(definition,[spl23_4])],[avatar_definition]) ).
fof(f256,plain,
( ! [X4] :
( ~ in(X4,relation_rng(sK19))
| apply(sK19,apply(sK20,X4)) = X4 )
| ~ spl23_4 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f257,plain,
( spl23_1
| spl23_4 ),
inference(avatar_split_clause,[],[f240,f255,f244]) ).
fof(f259,definition,
( spl23_5
<=> ! [X4] :
( in(apply(sK20,X4),relation_dom(sK19))
| ~ in(X4,relation_rng(sK19)) ) ),
introduced(definition,[new_symbols(definition,[spl23_5])],[avatar_definition]) ).
fof(f260,plain,
( ! [X4] :
( in(apply(sK20,X4),relation_dom(sK19))
| ~ in(X4,relation_rng(sK19)) )
| ~ spl23_5 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f261,plain,
( spl23_1
| spl23_5 ),
inference(avatar_split_clause,[],[f239,f259,f244]) ).
fof(f263,definition,
( spl23_6
<=> relation_rng(sK19) = relation_dom(sK20) ),
introduced(definition,[new_symbols(definition,[spl23_6])],[avatar_definition]) ).
fof(f264,plain,
( relation_rng(sK19) = relation_dom(sK20)
| ~ spl23_6 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f265,plain,
( spl23_1
| spl23_6 ),
inference(avatar_split_clause,[],[f196,f263,f244]) ).
fof(f266,plain,
( sK20 != function_inverse(sK19)
| spl23_1 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f268,definition,
( spl23_7
<=> sK21 = apply(sK19,sK22) ),
introduced(definition,[new_symbols(definition,[spl23_7])],[avatar_definition]) ).
fof(f269,plain,
( sK21 = apply(sK19,sK22)
| ~ spl23_7 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f271,definition,
( spl23_8
<=> sK22 = apply(sK20,sK21) ),
introduced(definition,[new_symbols(definition,[spl23_8])],[avatar_definition]) ).
fof(f272,plain,
( sK22 = apply(sK20,sK21)
| ~ spl23_8 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f273,plain,
( relation_rng(sK19) != relation_dom(sK20)
| spl23_6 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f274,plain,
( ~ spl23_1
| spl23_7
| spl23_8
| ~ spl23_6 ),
inference(avatar_split_clause,[],[f197,f263,f271,f268,f244]) ).
fof(f276,definition,
( spl23_9
<=> in(sK22,relation_dom(sK19)) ),
introduced(definition,[new_symbols(definition,[spl23_9])],[avatar_definition]) ).
fof(f277,plain,
( in(sK22,relation_dom(sK19))
| ~ spl23_9 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f278,plain,
( ~ spl23_1
| spl23_9
| spl23_8
| ~ spl23_6 ),
inference(avatar_split_clause,[],[f198,f263,f271,f276,f244]) ).
fof(f280,definition,
( spl23_10
<=> in(sK21,relation_rng(sK19)) ),
introduced(definition,[new_symbols(definition,[spl23_10])],[avatar_definition]) ).
fof(f281,plain,
( in(sK21,relation_rng(sK19))
| ~ spl23_10 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f282,plain,
( ~ spl23_1
| spl23_7
| spl23_10
| ~ spl23_6 ),
inference(avatar_split_clause,[],[f200,f263,f280,f268,f244]) ).
fof(f283,plain,
( ~ spl23_1
| spl23_9
| spl23_10
| ~ spl23_6 ),
inference(avatar_split_clause,[],[f201,f263,f280,f276,f244]) ).
fof(f284,plain,
( sK22 != apply(sK20,sK21)
| spl23_8 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f286,plain,
( sK21 != apply(sK19,sK22)
| spl23_7 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f287,plain,
( ~ in(sK22,relation_dom(sK19))
| spl23_9 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f288,plain,
( ~ spl23_1
| ~ spl23_8
| ~ spl23_10
| ~ spl23_7
| ~ spl23_9
| ~ spl23_6 ),
inference(avatar_split_clause,[],[f205,f263,f276,f268,f280,f271,f244]) ).
fof(f289,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(X0) ),
inference(forward_subsumption_resolution,[],[f238,f145]) ).
fof(f290,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(X0) ),
inference(forward_subsumption_resolution,[],[f237,f145]) ).
fof(f291,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f213,f233]) ).
fof(f292,plain,
! [X0,X4,X5] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),relation_inverse(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[],[f289,f120]) ).
fof(f293,plain,
! [X0,X4,X5] :
( in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),relation_inverse(X0))
| ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f290,f120]) ).
fof(f294,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| apply(X0,X1) = X2
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| ~ function(X0) ),
inference(forward_demodulation,[],[f291,f120]) ).
fof(f295,plain,
! [X0,X4,X5] :
( ~ relation(X0)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),X0)
| ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),relation_inverse(X0)) ),
inference(forward_demodulation,[],[f292,f120]) ).
fof(f296,plain,
! [X0,X4,X5] :
( ~ relation(X0)
| in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),relation_inverse(X0))
| ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),X0) ),
inference(forward_demodulation,[],[f293,f120]) ).
fof(f299,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK20))
| apply(sK19,apply(sK20,X0)) = X0 )
| ~ spl23_4
| ~ spl23_6 ),
inference(superposition,[],[f256,f264]) ).
fof(f302,plain,
( function_inverse(sK19) = relation_inverse(sK19)
| ~ relation(sK19)
| ~ function(sK19) ),
inference(resolution,[],[f142,f189]) ).
fof(f303,plain,
( function_inverse(sK19) = relation_inverse(sK19)
| ~ function(sK19) ),
inference(forward_subsumption_resolution,[],[f302,f188]) ).
fof(f304,plain,
function_inverse(sK19) = relation_inverse(sK19),
inference(forward_subsumption_resolution,[],[f303,f187]) ).
fof(f305,plain,
( sK20 != relation_inverse(sK19)
| spl23_1 ),
inference(superposition,[],[f266,f304]) ).
fof(f306,plain,
! [X0,X1] :
( apply(sK19,X0) = X1
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK19)
| ~ function(sK19) ),
inference(resolution,[],[f294,f188]) ).
fof(f307,plain,
! [X0,X1] :
( apply(sK20,X0) = X1
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK20)
| ~ function(sK20) ),
inference(resolution,[],[f294,f191]) ).
fof(f308,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK20)
| apply(sK20,X0) = X1 ),
inference(forward_subsumption_resolution,[],[f307,f190]) ).
fof(f309,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK19)
| apply(sK19,X0) = X1 ),
inference(forward_subsumption_resolution,[],[f306,f187]) ).
fof(f311,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK19)
| apply(sK19,X1) = X0 ),
inference(superposition,[],[f309,f120]) ).
fof(f313,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK20)
| apply(sK20,X1) = X0 ),
inference(superposition,[],[f308,f120]) ).
fof(f314,plain,
relation_dom(sK19) = relation_rng(relation_inverse(sK19)),
inference(resolution,[],[f185,f188]) ).
fof(f325,plain,
relation_rng(sK19) = relation_dom(relation_inverse(sK19)),
inference(resolution,[],[f186,f188]) ).
fof(f328,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK19)
| in(X0,relation_dom(sK19)) ),
inference(resolution,[],[f233,f188]) ).
fof(f329,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK20)
| in(X0,relation_dom(sK20)) ),
inference(resolution,[],[f233,f191]) ).
fof(f330,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK20)
| in(X0,relation_dom(sK20)) ),
inference(forward_demodulation,[],[f329,f120]) ).
fof(f331,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK19)
| in(X0,relation_dom(sK19)) ),
inference(forward_demodulation,[],[f328,f120]) ).
fof(f333,plain,
! [X0] :
( in(X0,relation_dom(sK20))
| empty_set = apply(sK20,X0)
| ~ function(sK20) ),
inference(resolution,[],[f232,f191]) ).
fof(f334,plain,
! [X0] :
( in(X0,relation_dom(sK20))
| empty_set = apply(sK20,X0) ),
inference(forward_subsumption_resolution,[],[f333,f190]) ).
fof(f349,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK19)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_inverse(sK19)) ),
inference(resolution,[],[f296,f188]) ).
fof(f351,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK19)
| in(X1,relation_rng(sK19)) ),
inference(resolution,[],[f235,f188]) ).
fof(f352,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK20)
| in(X1,relation_rng(sK20)) ),
inference(resolution,[],[f235,f191]) ).
fof(f353,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK20)
| in(X1,relation_rng(sK20)) ),
inference(forward_demodulation,[],[f352,f120]) ).
fof(f354,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK19)
| in(X1,relation_rng(sK19)) ),
inference(forward_demodulation,[],[f351,f120]) ).
fof(f388,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),relation_inverse(sK19))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK19) ),
inference(resolution,[],[f295,f188]) ).
fof(f393,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK20)
| in(X1,relation_dom(sK20)) ),
inference(superposition,[],[f330,f120]) ).
fof(f426,plain,
sK20 = relation_inverse(relation_inverse(sK20)),
inference(resolution,[],[f166,f191]) ).
fof(f440,plain,
! [X0] :
( ~ in(X0,relation_dom(sK19))
| in(unordered_pair(unordered_pair(X0,sK4(sK19,X0)),singleton(X0)),sK19) ),
inference(resolution,[],[f234,f188]) ).
fof(f441,plain,
! [X0] :
( ~ in(X0,relation_dom(sK20))
| in(unordered_pair(unordered_pair(X0,sK4(sK20,X0)),singleton(X0)),sK20) ),
inference(resolution,[],[f234,f191]) ).
fof(f444,plain,
! [X0] :
( ~ in(X0,relation_dom(sK20))
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK4(sK20,X0))),sK20) ),
inference(forward_demodulation,[],[f441,f120]) ).
fof(f445,plain,
! [X0] :
( ~ in(X0,relation_dom(sK19))
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK4(sK19,X0))),sK19) ),
inference(forward_demodulation,[],[f440,f120]) ).
fof(f547,plain,
! [X0] :
( ~ in(unordered_pair(unordered_pair(sK9(sK20,X0),sK8(sK20,X0)),singleton(sK9(sK20,X0))),sK20)
| ~ in(unordered_pair(unordered_pair(sK8(sK20,X0),sK9(sK20,X0)),singleton(sK8(sK20,X0))),X0)
| ~ relation(X0)
| relation_inverse(sK20) = X0 ),
inference(resolution,[],[f223,f191]) ).
fof(f550,plain,
! [X0] :
( ~ in(unordered_pair(singleton(sK9(sK20,X0)),unordered_pair(sK9(sK20,X0),sK8(sK20,X0))),sK20)
| ~ in(unordered_pair(unordered_pair(sK8(sK20,X0),sK9(sK20,X0)),singleton(sK8(sK20,X0))),X0)
| ~ relation(X0)
| relation_inverse(sK20) = X0 ),
inference(forward_demodulation,[],[f547,f120]) ).
fof(f553,plain,
! [X0] :
( ~ in(unordered_pair(singleton(sK9(sK20,X0)),unordered_pair(sK8(sK20,X0),sK9(sK20,X0))),sK20)
| ~ in(unordered_pair(unordered_pair(sK8(sK20,X0),sK9(sK20,X0)),singleton(sK8(sK20,X0))),X0)
| ~ relation(X0)
| relation_inverse(sK20) = X0 ),
inference(forward_demodulation,[],[f550,f120]) ).
fof(f556,plain,
! [X0] :
( ~ relation(X0)
| ~ in(unordered_pair(singleton(sK9(sK20,X0)),unordered_pair(sK8(sK20,X0),sK9(sK20,X0))),sK20)
| ~ in(unordered_pair(singleton(sK8(sK20,X0)),unordered_pair(sK8(sK20,X0),sK9(sK20,X0))),X0)
| relation_inverse(sK20) = X0 ),
inference(forward_demodulation,[],[f553,f120]) ).
fof(f589,plain,
( ~ in(unordered_pair(singleton(sK9(sK20,sK19)),unordered_pair(sK8(sK20,sK19),sK9(sK20,sK19))),sK20)
| ~ in(unordered_pair(singleton(sK8(sK20,sK19)),unordered_pair(sK8(sK20,sK19),sK9(sK20,sK19))),sK19)
| sK19 = relation_inverse(sK20) ),
inference(resolution,[],[f556,f188]) ).
fof(f613,definition,
( spl23_44
<=> sK19 = relation_inverse(sK20) ),
introduced(definition,[new_symbols(definition,[spl23_44])],[avatar_definition]) ).
fof(f614,plain,
( sK19 = relation_inverse(sK20)
| ~ spl23_44 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f616,definition,
( spl23_45
<=> in(unordered_pair(singleton(sK8(sK20,sK19)),unordered_pair(sK8(sK20,sK19),sK9(sK20,sK19))),sK19) ),
introduced(definition,[new_symbols(definition,[spl23_45])],[avatar_definition]) ).
fof(f617,plain,
( ~ in(unordered_pair(singleton(sK8(sK20,sK19)),unordered_pair(sK8(sK20,sK19),sK9(sK20,sK19))),sK19)
| spl23_45 ),
inference(avatar_component_clause,[],[f616]) ).
fof(f619,definition,
( spl23_46
<=> in(unordered_pair(singleton(sK9(sK20,sK19)),unordered_pair(sK8(sK20,sK19),sK9(sK20,sK19))),sK20) ),
introduced(definition,[new_symbols(definition,[spl23_46])],[avatar_definition]) ).
fof(f620,plain,
( ~ in(unordered_pair(singleton(sK9(sK20,sK19)),unordered_pair(sK8(sK20,sK19),sK9(sK20,sK19))),sK20)
| spl23_46 ),
inference(avatar_component_clause,[],[f619]) ).
fof(f621,plain,
( spl23_44
| ~ spl23_45
| ~ spl23_46 ),
inference(avatar_split_clause,[],[f589,f619,f616,f613]) ).
fof(f1120,plain,
( sK20 = relation_inverse(sK19)
| ~ spl23_1 ),
inference(superposition,[],[f245,f304]) ).
fof(f1203,definition,
( spl23_67
<=> sK20 = relation_inverse(sK19) ),
introduced(definition,[new_symbols(definition,[spl23_67])],[avatar_definition]) ).
fof(f1204,plain,
( sK20 = relation_inverse(sK19)
| ~ spl23_67 ),
inference(avatar_component_clause,[],[f1203]) ).
fof(f1239,plain,
( spl23_67
| ~ spl23_1 ),
inference(avatar_split_clause,[],[f1120,f244,f1203]) ).
fof(f1244,plain,
( in(unordered_pair(unordered_pair(sK22,apply(sK19,sK22)),singleton(sK22)),sK19)
| ~ relation(sK19)
| ~ function(sK19)
| ~ spl23_9 ),
inference(resolution,[],[f277,f230]) ).
fof(f1245,plain,
( in(unordered_pair(unordered_pair(sK22,apply(sK19,sK22)),singleton(sK22)),sK19)
| ~ function(sK19)
| ~ spl23_9 ),
inference(forward_subsumption_resolution,[],[f1244,f188]) ).
fof(f1249,plain,
( in(unordered_pair(unordered_pair(sK22,apply(sK19,sK22)),singleton(sK22)),sK19)
| ~ spl23_9 ),
inference(forward_subsumption_resolution,[],[f1245,f187]) ).
fof(f1252,plain,
( in(unordered_pair(singleton(sK22),unordered_pair(sK22,apply(sK19,sK22))),sK19)
| ~ spl23_9 ),
inference(forward_demodulation,[],[f1249,f120]) ).
fof(f1270,plain,
( in(sK21,relation_dom(sK20))
| ~ spl23_6
| ~ spl23_10 ),
inference(forward_demodulation,[],[f281,f264]) ).
fof(f1283,plain,
( in(unordered_pair(singleton(apply(sK19,sK22)),unordered_pair(apply(sK19,sK22),sK22)),relation_inverse(sK19))
| ~ spl23_9 ),
inference(resolution,[],[f1252,f349]) ).
fof(f1286,plain,
( in(unordered_pair(singleton(apply(sK19,sK22)),unordered_pair(apply(sK19,sK22),sK22)),sK20)
| ~ spl23_9
| ~ spl23_67 ),
inference(forward_demodulation,[],[f1283,f1204]) ).
fof(f1287,plain,
( in(unordered_pair(singleton(apply(sK19,sK22)),unordered_pair(sK22,apply(sK19,sK22))),sK20)
| ~ spl23_9
| ~ spl23_67 ),
inference(forward_demodulation,[],[f1286,f120]) ).
fof(f1288,plain,
( in(unordered_pair(singleton(sK21),unordered_pair(sK21,sK4(sK20,sK21))),sK20)
| ~ spl23_6
| ~ spl23_10 ),
inference(resolution,[],[f1270,f444]) ).
fof(f1294,plain,
( sK22 = apply(sK20,apply(sK19,sK22))
| ~ spl23_9
| ~ spl23_67 ),
inference(resolution,[],[f1287,f313]) ).
fof(f1295,plain,
( in(sK4(sK20,sK21),relation_rng(sK20))
| ~ spl23_6
| ~ spl23_10 ),
inference(resolution,[],[f1288,f353]) ).
fof(f1298,plain,
( apply(sK20,sK21) = sK4(sK20,sK21)
| ~ spl23_6
| ~ spl23_10 ),
inference(resolution,[],[f1288,f308]) ).
fof(f1299,plain,
( sK22 = sK4(sK20,sK21)
| ~ spl23_6
| ~ spl23_8
| ~ spl23_10 ),
inference(forward_demodulation,[],[f1298,f272]) ).
fof(f1317,plain,
( relation_dom(sK19) = relation_rng(sK20)
| ~ spl23_67 ),
inference(superposition,[],[f314,f1204]) ).
fof(f1319,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK20)
| in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK19) )
| ~ spl23_67 ),
inference(superposition,[],[f388,f1204]) ).
fof(f1330,plain,
( sK20 = relation_inverse(sK19)
| ~ spl23_44 ),
inference(superposition,[],[f426,f614]) ).
fof(f1345,plain,
( in(sK22,relation_rng(sK20))
| ~ spl23_6
| ~ spl23_8
| ~ spl23_10 ),
inference(superposition,[],[f1295,f1299]) ).
fof(f1573,plain,
( relation_rng(sK19) = relation_dom(sK20)
| ~ spl23_67 ),
inference(superposition,[],[f325,f1204]) ).
fof(f1654,plain,
( in(unordered_pair(singleton(sK4(sK20,sK21)),unordered_pair(sK4(sK20,sK21),sK21)),sK19)
| ~ spl23_6
| ~ spl23_10
| ~ spl23_67 ),
inference(resolution,[],[f1319,f1288]) ).
fof(f1659,plain,
( in(unordered_pair(singleton(sK4(sK20,sK21)),unordered_pair(sK21,sK4(sK20,sK21))),sK19)
| ~ spl23_6
| ~ spl23_10
| ~ spl23_67 ),
inference(forward_demodulation,[],[f1654,f120]) ).
fof(f1665,plain,
( in(unordered_pair(singleton(sK22),unordered_pair(sK21,sK22)),sK19)
| ~ spl23_6
| ~ spl23_8
| ~ spl23_10
| ~ spl23_67 ),
inference(forward_demodulation,[],[f1659,f1299]) ).
fof(f1683,plain,
( sK21 = apply(sK19,sK22)
| ~ spl23_6
| ~ spl23_8
| ~ spl23_10
| ~ spl23_67 ),
inference(resolution,[],[f1665,f311]) ).
fof(f1685,plain,
( $false
| ~ spl23_6
| spl23_7
| ~ spl23_8
| ~ spl23_10
| ~ spl23_67 ),
inference(forward_subsumption_resolution,[],[f1683,f286]) ).
fof(f1686,plain,
( ~ spl23_6
| spl23_7
| ~ spl23_8
| ~ spl23_10
| ~ spl23_67 ),
inference(avatar_contradiction_clause,[],[f1685]) ).
fof(f1695,plain,
( sK22 = apply(sK20,sK21)
| ~ spl23_7
| ~ spl23_9
| ~ spl23_67 ),
inference(forward_demodulation,[],[f1294,f269]) ).
fof(f1701,plain,
( $false
| ~ spl23_7
| spl23_8
| ~ spl23_9
| ~ spl23_67 ),
inference(forward_subsumption_resolution,[],[f1695,f284]) ).
fof(f1702,plain,
( ~ spl23_7
| spl23_8
| ~ spl23_9
| ~ spl23_67 ),
inference(avatar_contradiction_clause,[],[f1701]) ).
fof(f1705,plain,
( in(sK22,relation_dom(sK19))
| ~ spl23_6
| ~ spl23_8
| ~ spl23_10
| ~ spl23_67 ),
inference(forward_demodulation,[],[f1345,f1317]) ).
fof(f1711,plain,
( $false
| ~ spl23_6
| ~ spl23_8
| spl23_9
| ~ spl23_10
| ~ spl23_67 ),
inference(forward_subsumption_resolution,[],[f1705,f287]) ).
fof(f1712,plain,
( ~ spl23_6
| ~ spl23_8
| spl23_9
| ~ spl23_10
| ~ spl23_67 ),
inference(avatar_contradiction_clause,[],[f1711]) ).
fof(f1785,plain,
( in(unordered_pair(singleton(sK22),unordered_pair(sK22,sK4(sK19,sK22))),sK19)
| ~ spl23_9 ),
inference(resolution,[],[f277,f445]) ).
fof(f1817,plain,
( in(sK4(sK19,sK22),relation_rng(sK19))
| ~ spl23_9 ),
inference(resolution,[],[f1785,f354]) ).
fof(f1820,plain,
( apply(sK19,sK22) = sK4(sK19,sK22)
| ~ spl23_9 ),
inference(resolution,[],[f1785,f309]) ).
fof(f1821,plain,
( sK21 = sK4(sK19,sK22)
| ~ spl23_7
| ~ spl23_9 ),
inference(forward_demodulation,[],[f1820,f269]) ).
fof(f1836,plain,
( $false
| spl23_6
| ~ spl23_67 ),
inference(forward_subsumption_resolution,[],[f1573,f273]) ).
fof(f1837,plain,
( spl23_6
| ~ spl23_67 ),
inference(avatar_contradiction_clause,[],[f1836]) ).
fof(f1839,plain,
( in(sK21,relation_rng(sK19))
| ~ spl23_7
| ~ spl23_9 ),
inference(forward_demodulation,[],[f1817,f1821]) ).
fof(f1841,plain,
( spl23_10
| ~ spl23_7
| ~ spl23_9 ),
inference(avatar_split_clause,[],[f1839,f276,f268,f280]) ).
fof(f2001,plain,
( ! [X0] :
( apply(sK19,apply(sK20,X0)) = X0
| empty_set = apply(sK20,X0) )
| ~ spl23_4
| ~ spl23_6 ),
inference(resolution,[],[f299,f334]) ).
fof(f2852,plain,
! [X0] :
( in(unordered_pair(unordered_pair(sK9(sK20,X0),sK8(sK20,X0)),singleton(sK9(sK20,X0))),sK20)
| in(unordered_pair(unordered_pair(sK8(sK20,X0),sK9(sK20,X0)),singleton(sK8(sK20,X0))),X0)
| ~ relation(X0)
| relation_inverse(sK20) = X0 ),
inference(resolution,[],[f224,f191]) ).
fof(f2853,plain,
! [X0] :
( in(unordered_pair(singleton(sK9(sK20,X0)),unordered_pair(sK9(sK20,X0),sK8(sK20,X0))),sK20)
| in(unordered_pair(unordered_pair(sK8(sK20,X0),sK9(sK20,X0)),singleton(sK8(sK20,X0))),X0)
| ~ relation(X0)
| relation_inverse(sK20) = X0 ),
inference(forward_demodulation,[],[f2852,f120]) ).
fof(f2857,plain,
! [X0] :
( in(unordered_pair(singleton(sK9(sK20,X0)),unordered_pair(sK8(sK20,X0),sK9(sK20,X0))),sK20)
| in(unordered_pair(unordered_pair(sK8(sK20,X0),sK9(sK20,X0)),singleton(sK8(sK20,X0))),X0)
| ~ relation(X0)
| relation_inverse(sK20) = X0 ),
inference(forward_demodulation,[],[f2853,f120]) ).
fof(f2861,plain,
! [X0] :
( ~ relation(X0)
| in(unordered_pair(singleton(sK9(sK20,X0)),unordered_pair(sK8(sK20,X0),sK9(sK20,X0))),sK20)
| in(unordered_pair(singleton(sK8(sK20,X0)),unordered_pair(sK8(sK20,X0),sK9(sK20,X0))),X0)
| relation_inverse(sK20) = X0 ),
inference(forward_demodulation,[],[f2857,f120]) ).
fof(f3067,plain,
( in(unordered_pair(singleton(sK9(sK20,sK19)),unordered_pair(sK8(sK20,sK19),sK9(sK20,sK19))),sK20)
| in(unordered_pair(singleton(sK8(sK20,sK19)),unordered_pair(sK8(sK20,sK19),sK9(sK20,sK19))),sK19)
| sK19 = relation_inverse(sK20) ),
inference(resolution,[],[f2861,f188]) ).
fof(f3074,plain,
( in(unordered_pair(singleton(sK8(sK20,sK19)),unordered_pair(sK8(sK20,sK19),sK9(sK20,sK19))),sK19)
| ~ spl23_45 ),
inference(avatar_component_clause,[],[f616]) ).
fof(f3082,plain,
( $false
| spl23_1
| ~ spl23_44 ),
inference(forward_subsumption_resolution,[],[f1330,f305]) ).
fof(f3083,plain,
( spl23_1
| ~ spl23_44 ),
inference(avatar_contradiction_clause,[],[f3082]) ).
fof(f3089,plain,
( in(sK9(sK20,sK19),relation_rng(sK19))
| ~ spl23_45 ),
inference(resolution,[],[f3074,f354]) ).
fof(f3091,plain,
( in(sK8(sK20,sK19),relation_dom(sK19))
| ~ spl23_45 ),
inference(resolution,[],[f3074,f331]) ).
fof(f3092,plain,
( sK9(sK20,sK19) = apply(sK19,sK8(sK20,sK19))
| ~ spl23_45 ),
inference(resolution,[],[f3074,f309]) ).
fof(f3094,plain,
( in(sK9(sK20,sK19),relation_dom(sK20))
| ~ spl23_6
| ~ spl23_45 ),
inference(forward_demodulation,[],[f3089,f264]) ).
fof(f3445,plain,
( in(unordered_pair(singleton(sK9(sK20,sK19)),unordered_pair(sK9(sK20,sK19),sK4(sK20,sK9(sK20,sK19)))),sK20)
| ~ spl23_6
| ~ spl23_45 ),
inference(resolution,[],[f3094,f444]) ).
fof(f3527,plain,
( sK8(sK20,sK19) = apply(sK20,apply(sK19,sK8(sK20,sK19)))
| ~ spl23_2
| ~ spl23_45 ),
inference(resolution,[],[f3091,f248]) ).
fof(f3531,plain,
( sK8(sK20,sK19) = apply(sK20,sK9(sK20,sK19))
| ~ spl23_2
| ~ spl23_45 ),
inference(forward_demodulation,[],[f3527,f3092]) ).
fof(f3856,plain,
( apply(sK20,sK9(sK20,sK19)) = sK4(sK20,sK9(sK20,sK19))
| ~ spl23_6
| ~ spl23_45 ),
inference(resolution,[],[f3445,f308]) ).
fof(f3857,plain,
( sK8(sK20,sK19) = sK4(sK20,sK9(sK20,sK19))
| ~ spl23_2
| ~ spl23_6
| ~ spl23_45 ),
inference(forward_demodulation,[],[f3856,f3531]) ).
fof(f3861,plain,
( in(unordered_pair(singleton(sK9(sK20,sK19)),unordered_pair(sK9(sK20,sK19),sK8(sK20,sK19))),sK20)
| ~ spl23_2
| ~ spl23_6
| ~ spl23_45 ),
inference(superposition,[],[f3445,f3857]) ).
fof(f3862,plain,
( in(unordered_pair(singleton(sK9(sK20,sK19)),unordered_pair(sK8(sK20,sK19),sK9(sK20,sK19))),sK20)
| ~ spl23_2
| ~ spl23_6
| ~ spl23_45 ),
inference(forward_demodulation,[],[f3861,f120]) ).
fof(f3863,plain,
( $false
| ~ spl23_2
| ~ spl23_6
| ~ spl23_45
| spl23_46 ),
inference(forward_subsumption_resolution,[],[f3862,f620]) ).
fof(f3864,plain,
( ~ spl23_2
| ~ spl23_6
| ~ spl23_45
| spl23_46 ),
inference(avatar_contradiction_clause,[],[f3863]) ).
fof(f3865,plain,
( in(unordered_pair(singleton(sK9(sK20,sK19)),unordered_pair(sK8(sK20,sK19),sK9(sK20,sK19))),sK20)
| sK19 = relation_inverse(sK20)
| spl23_45 ),
inference(forward_subsumption_resolution,[],[f3067,f617]) ).
fof(f3866,plain,
( in(unordered_pair(singleton(sK9(sK20,sK19)),unordered_pair(sK8(sK20,sK19),sK9(sK20,sK19))),sK20)
| ~ spl23_46 ),
inference(avatar_component_clause,[],[f619]) ).
fof(f3867,plain,
( spl23_44
| spl23_46
| spl23_45 ),
inference(avatar_split_clause,[],[f3865,f616,f619,f613]) ).
fof(f3868,plain,
( in(sK9(sK20,sK19),relation_dom(sK20))
| ~ spl23_46 ),
inference(resolution,[],[f3866,f393]) ).
fof(f3869,plain,
( sK8(sK20,sK19) = apply(sK20,sK9(sK20,sK19))
| ~ spl23_46 ),
inference(resolution,[],[f3866,f313]) ).
fof(f3870,plain,
( sK9(sK20,sK19) = apply(sK19,sK8(sK20,sK19))
| empty_set = sK8(sK20,sK19)
| ~ spl23_4
| ~ spl23_6
| ~ spl23_46 ),
inference(superposition,[],[f2001,f3869]) ).
fof(f3873,plain,
( in(sK8(sK20,sK19),relation_dom(sK19))
| ~ in(sK9(sK20,sK19),relation_rng(sK19))
| ~ spl23_5
| ~ spl23_46 ),
inference(superposition,[],[f260,f3869]) ).
fof(f3874,plain,
( ~ in(sK9(sK20,sK19),relation_dom(sK20))
| in(sK8(sK20,sK19),relation_dom(sK19))
| ~ spl23_5
| ~ spl23_6
| ~ spl23_46 ),
inference(forward_demodulation,[],[f3873,f264]) ).
fof(f3878,definition,
( spl23_96
<=> empty_set = sK8(sK20,sK19) ),
introduced(definition,[new_symbols(definition,[spl23_96])],[avatar_definition]) ).
fof(f3879,plain,
( empty_set = sK8(sK20,sK19)
| ~ spl23_96 ),
inference(avatar_component_clause,[],[f3878]) ).
fof(f3881,definition,
( spl23_97
<=> sK9(sK20,sK19) = apply(sK19,sK8(sK20,sK19)) ),
introduced(definition,[new_symbols(definition,[spl23_97])],[avatar_definition]) ).
fof(f3882,plain,
( sK9(sK20,sK19) = apply(sK19,sK8(sK20,sK19))
| ~ spl23_97 ),
inference(avatar_component_clause,[],[f3881]) ).
fof(f3883,plain,
( spl23_96
| spl23_97
| ~ spl23_4
| ~ spl23_6
| ~ spl23_46 ),
inference(avatar_split_clause,[],[f3870,f619,f263,f255,f3881,f3878]) ).
fof(f3884,plain,
( in(sK8(sK20,sK19),relation_dom(sK19))
| ~ spl23_5
| ~ spl23_6
| ~ spl23_46 ),
inference(forward_subsumption_resolution,[],[f3874,f3868]) ).
fof(f3890,plain,
( in(unordered_pair(unordered_pair(sK8(sK20,sK19),apply(sK19,sK8(sK20,sK19))),singleton(sK8(sK20,sK19))),sK19)
| ~ relation(sK19)
| ~ function(sK19)
| ~ spl23_5
| ~ spl23_6
| ~ spl23_46 ),
inference(resolution,[],[f3884,f230]) ).
fof(f3891,plain,
( in(unordered_pair(unordered_pair(sK8(sK20,sK19),apply(sK19,sK8(sK20,sK19))),singleton(sK8(sK20,sK19))),sK19)
| ~ function(sK19)
| ~ spl23_5
| ~ spl23_6
| ~ spl23_46 ),
inference(forward_subsumption_resolution,[],[f3890,f188]) ).
fof(f3896,plain,
( in(unordered_pair(unordered_pair(sK8(sK20,sK19),apply(sK19,sK8(sK20,sK19))),singleton(sK8(sK20,sK19))),sK19)
| ~ spl23_5
| ~ spl23_6
| ~ spl23_46 ),
inference(forward_subsumption_resolution,[],[f3891,f187]) ).
fof(f3897,plain,
( in(unordered_pair(singleton(sK8(sK20,sK19)),unordered_pair(sK8(sK20,sK19),apply(sK19,sK8(sK20,sK19)))),sK19)
| ~ spl23_5
| ~ spl23_6
| ~ spl23_46 ),
inference(forward_demodulation,[],[f3896,f120]) ).
fof(f3898,plain,
( in(unordered_pair(singleton(empty_set),unordered_pair(empty_set,apply(sK19,empty_set))),sK19)
| ~ spl23_5
| ~ spl23_6
| ~ spl23_46
| ~ spl23_96 ),
inference(forward_demodulation,[],[f3897,f3879]) ).
fof(f3918,plain,
( sK9(sK20,sK19) = apply(sK19,apply(sK20,sK9(sK20,sK19)))
| ~ spl23_4
| ~ spl23_6
| ~ spl23_46 ),
inference(resolution,[],[f3868,f299]) ).
fof(f3927,plain,
( sK9(sK20,sK19) = apply(sK19,sK8(sK20,sK19))
| ~ spl23_4
| ~ spl23_6
| ~ spl23_46 ),
inference(forward_demodulation,[],[f3918,f3869]) ).
fof(f3931,plain,
( sK9(sK20,sK19) = apply(sK19,empty_set)
| ~ spl23_4
| ~ spl23_6
| ~ spl23_46
| ~ spl23_96 ),
inference(forward_demodulation,[],[f3927,f3879]) ).
fof(f5853,plain,
( ~ in(unordered_pair(singleton(empty_set),unordered_pair(empty_set,sK9(sK20,sK19))),sK19)
| spl23_45
| ~ spl23_96 ),
inference(superposition,[],[f617,f3879]) ).
fof(f5856,plain,
( ~ in(unordered_pair(singleton(empty_set),unordered_pair(empty_set,apply(sK19,empty_set))),sK19)
| ~ spl23_4
| ~ spl23_6
| spl23_45
| ~ spl23_46
| ~ spl23_96 ),
inference(forward_demodulation,[],[f5853,f3931]) ).
fof(f5858,plain,
( $false
| ~ spl23_4
| ~ spl23_5
| ~ spl23_6
| spl23_45
| ~ spl23_46
| ~ spl23_96 ),
inference(forward_subsumption_resolution,[],[f5856,f3898]) ).
fof(f5859,plain,
( ~ spl23_4
| ~ spl23_5
| ~ spl23_6
| spl23_45
| ~ spl23_46
| ~ spl23_96 ),
inference(avatar_contradiction_clause,[],[f5858]) ).
fof(f5863,plain,
( in(unordered_pair(singleton(sK8(sK20,sK19)),unordered_pair(sK8(sK20,sK19),sK9(sK20,sK19))),sK19)
| ~ spl23_5
| ~ spl23_6
| ~ spl23_46
| ~ spl23_97 ),
inference(forward_demodulation,[],[f3897,f3882]) ).
fof(f5879,plain,
( $false
| ~ spl23_5
| ~ spl23_6
| spl23_45
| ~ spl23_46
| ~ spl23_97 ),
inference(forward_subsumption_resolution,[],[f5863,f617]) ).
fof(f5880,plain,
( ~ spl23_5
| ~ spl23_6
| spl23_45
| ~ spl23_46
| ~ spl23_97 ),
inference(avatar_contradiction_clause,[],[f5879]) ).
cnf(s1,plain,
( spl23_1
| spl23_2 ),
inference(sat_conversion,[],[f249]) ).
cnf(s3,plain,
( spl23_1
| spl23_4 ),
inference(sat_conversion,[],[f257]) ).
cnf(s4,plain,
( spl23_1
| spl23_5 ),
inference(sat_conversion,[],[f261]) ).
cnf(s5,plain,
( spl23_1
| spl23_6 ),
inference(sat_conversion,[],[f265]) ).
cnf(s6,plain,
( ~ spl23_1
| ~ spl23_6
| spl23_7
| spl23_8 ),
inference(sat_conversion,[],[f274]) ).
cnf(s7,plain,
( ~ spl23_1
| ~ spl23_6
| spl23_8
| spl23_9 ),
inference(sat_conversion,[],[f278]) ).
cnf(s8,plain,
( ~ spl23_1
| ~ spl23_6
| spl23_7
| spl23_10 ),
inference(sat_conversion,[],[f282]) ).
cnf(s9,plain,
( ~ spl23_1
| ~ spl23_6
| spl23_9
| spl23_10 ),
inference(sat_conversion,[],[f283]) ).
cnf(s10,plain,
( ~ spl23_1
| ~ spl23_6
| ~ spl23_7
| ~ spl23_8
| ~ spl23_9
| ~ spl23_10 ),
inference(sat_conversion,[],[f288]) ).
cnf(s28,plain,
( spl23_44
| ~ spl23_45
| ~ spl23_46 ),
inference(sat_conversion,[],[f621]) ).
cnf(s68,plain,
( ~ spl23_1
| spl23_67 ),
inference(sat_conversion,[],[f1239]) ).
cnf(s79,plain,
( ~ spl23_6
| spl23_7
| ~ spl23_8
| ~ spl23_10
| ~ spl23_67 ),
inference(sat_conversion,[],[f1686]) ).
cnf(s81,plain,
( ~ spl23_7
| spl23_8
| ~ spl23_9
| ~ spl23_67 ),
inference(sat_conversion,[],[f1702]) ).
cnf(s84,plain,
( ~ spl23_6
| ~ spl23_8
| spl23_9
| ~ spl23_10
| ~ spl23_67 ),
inference(sat_conversion,[],[f1712]) ).
cnf(s92,plain,
( spl23_6
| ~ spl23_67 ),
inference(sat_conversion,[],[f1837]) ).
cnf(s93,plain,
( ~ spl23_7
| ~ spl23_9
| spl23_10 ),
inference(sat_conversion,[],[f1841]) ).
cnf(s116,plain,
( spl23_1
| ~ spl23_44 ),
inference(sat_conversion,[],[f3083]) ).
cnf(s130,plain,
( ~ spl23_2
| ~ spl23_6
| ~ spl23_45
| spl23_46 ),
inference(sat_conversion,[],[f3864]) ).
cnf(s131,plain,
( spl23_44
| spl23_45
| spl23_46 ),
inference(sat_conversion,[],[f3867]) ).
cnf(s132,plain,
( ~ spl23_4
| ~ spl23_6
| ~ spl23_46
| spl23_96
| spl23_97 ),
inference(sat_conversion,[],[f3883]) ).
cnf(s160,plain,
( ~ spl23_4
| ~ spl23_5
| ~ spl23_6
| spl23_45
| ~ spl23_46
| ~ spl23_96 ),
inference(sat_conversion,[],[f5859]) ).
cnf(s161,plain,
( ~ spl23_5
| ~ spl23_6
| spl23_45
| ~ spl23_46
| ~ spl23_97 ),
inference(sat_conversion,[],[f5880]) ).
cnf(s166,plain,
( spl23_45
| spl23_1 ),
inference(rat,[],[s132,s160,s161,s131,s116,s5,s4,s3]) ).
cnf(s167,plain,
spl23_1,
inference(rat,[],[s28,s130,s166,s1,s5,s116]) ).
cnf(s168,plain,
spl23_67,
inference(rat,[],[s68,s167]) ).
cnf(s169,plain,
spl23_6,
inference(rat,[],[s92,s168]) ).
cnf(s173,plain,
spl23_7,
inference(rat,[],[s79,s6,s8,s169,s168,s167]) ).
cnf(s174,plain,
spl23_8,
inference(rat,[],[s81,s7,s173,s168,s167,s169]) ).
cnf(s175,plain,
spl23_9,
inference(rat,[],[s84,s9,s169,s174,s168,s167]) ).
cnf(s176,plain,
spl23_10,
inference(rat,[],[s93,s173,s175]) ).
cnf(s178,plain,
$false,
inference(rat,[],[s10,s174,s173,s169,s167,s176,s175]) ).
fof(f5892,plain,
$false,
inference(avatar_sat_refutation,[],[s178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU218+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:06:56 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 6.34/1.85 % (3568689)Detected formulas, will run a generic FOF schedule.
% 6.34/1.85 % (3568695)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=456010257:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.34/1.85 % (3568699)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=20170464:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.34/1.85 % (3568700)dis-21_1_sil=8000:lcm=predicate:random_seed=2337531677: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)
% 6.34/1.85 % (3568697)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1024776410:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.34/1.85 % (3568698)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1159512396:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.34/1.85 % (3568696)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=1148708774:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.34/1.85 % (3568694)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=1384645457:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.34/1.85 % (3568697)Refutation not found, incomplete strategy
% 6.34/1.85 % (3568697)------------------------------
% 6.34/1.85 % (3568697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.85 % (3568697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.85 % (3568697)CaDiCaL version: 2.1.3
% 6.34/1.85 % (3568697)Termination reason: Refutation not found, incomplete strategy
% 6.34/1.85 % (3568697)Time elapsed: 0.015 s
% 6.34/1.85 % (3568697)Peak memory usage: 89 MB
% 6.34/1.85 % (3568697)Instructions burned: 20 (million)
% 6.34/1.85 % (3568700)Instruction limit reached!
% 6.34/1.85 % (3568700)------------------------------
% 6.34/1.85 % (3568700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.85 % (3568700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.85 % (3568700)CaDiCaL version: 2.1.3
% 6.34/1.85 % (3568700)Termination reason: Instruction limit
% 6.34/1.85 % (3568700)Termination phase: Saturation
% 6.34/1.85 % (3568700)Time elapsed: 0.065 s
% 6.34/1.85 % (3568700)Peak memory usage: 90 MB
% 6.34/1.85 % (3568700)Instructions burned: 130 (million)
% 6.34/1.85 % (3568698)Instruction limit reached!
% 6.34/1.85 % (3568698)------------------------------
% 6.34/1.85 % (3568698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.85 % (3568698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.85 % (3568698)CaDiCaL version: 2.1.3
% 6.34/1.85 % (3568698)Termination reason: Instruction limit
% 6.34/1.85 % (3568698)Termination phase: Saturation
% 6.34/1.85 % (3568698)Time elapsed: 0.069 s
% 6.34/1.85 % (3568698)Peak memory usage: 88 MB
% 6.34/1.85 % (3568698)Instructions burned: 120 (million)
% 6.34/1.85 % (3568699)Instruction limit reached!
% 6.34/1.85 % (3568699)------------------------------
% 6.34/1.85 % (3568699)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.85 % (3568699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.85 % (3568699)CaDiCaL version: 2.1.3
% 6.34/1.85 % (3568699)Termination reason: Instruction limit
% 6.34/1.85 % (3568699)Termination phase: Saturation
% 6.34/1.85 % (3568699)Time elapsed: 0.098 s
% 6.34/1.85 % (3568699)Peak memory usage: 90 MB
% 6.34/1.85 % (3568699)Instructions burned: 140 (million)
% 6.34/1.85 % (3568709)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1045962395:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.34/1.85 % (3568708)lrs+10_1_sil=8000:sp=occurrence:random_seed=2077546717:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.34/1.85 % (3568710)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4074098706:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.34/1.85 % (3568697)------------------------------
% 6.34/1.85 % (3568697)------------------------------
% 6.34/1.85 % (3568709)Instruction limit reached!
% 6.34/1.85 % (3568709)------------------------------
% 6.34/1.85 % (3568709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.85 % (3568709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.85 % (3568709)CaDiCaL version: 2.1.3
% 6.34/1.85 % (3568709)Termination reason: Instruction limit
% 6.34/1.85 % (3568709)Termination phase: Saturation
% 6.34/1.85 % (3568709)Time elapsed: 0.091 s
% 6.34/1.85 % (3568709)Peak memory usage: 90 MB
% 6.34/1.85 % (3568709)Instructions burned: 157 (million)
% 6.34/1.85 % (3568708)Instruction limit reached!
% 6.34/1.85 % (3568708)------------------------------
% 6.34/1.85 % (3568708)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.85 % (3568708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.85 % (3568708)CaDiCaL version: 2.1.3
% 6.34/1.85 % (3568708)Termination reason: Instruction limit
% 6.34/1.85 % (3568708)Termination phase: Saturation
% 6.34/1.85 % (3568708)Time elapsed: 0.172 s
% 6.34/1.85 % (3568708)Peak memory usage: 91 MB
% 6.34/1.85 % (3568708)Instructions burned: 286 (million)
% 6.34/1.85 % (3568714)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=280853538:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.34/1.85 % (3568715)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3169870935:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.34/1.85 % (3568715)Refutation not found, incomplete strategy
% 6.34/1.85 % (3568715)------------------------------
% 6.34/1.85 % (3568715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.85 % (3568715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.85 % (3568715)CaDiCaL version: 2.1.3
% 6.34/1.85 % (3568715)Termination reason: Refutation not found, incomplete strategy
% 6.34/1.85 % (3568715)Time elapsed: 0.013 s
% 6.34/1.85 % (3568715)Peak memory usage: 89 MB
% 6.34/1.85 % (3568715)Instructions burned: 19 (million)
% 6.34/1.85 % (3568710)Instruction limit reached!
% 6.34/1.85 % (3568710)------------------------------
% 6.34/1.85 % (3568710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.85 % (3568710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.85 % (3568710)CaDiCaL version: 2.1.3
% 6.34/1.85 % (3568710)Termination reason: Instruction limit
% 6.34/1.85 % (3568710)Termination phase: Saturation
% 6.34/1.85 % (3568710)Time elapsed: 0.223 s
% 6.34/1.85 % (3568710)Peak memory usage: 92 MB
% 6.34/1.85 % (3568710)Instructions burned: 326 (million)
% 6.34/1.85 % (3568717)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2619619314:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.34/1.85 % (3568714)Instruction limit reached!
% 6.34/1.85 % (3568714)------------------------------
% 6.34/1.85 % (3568714)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.85 % (3568714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.85 % (3568714)CaDiCaL version: 2.1.3
% 6.34/1.85 % (3568714)Termination reason: Instruction limit
% 6.34/1.85 % (3568714)Termination phase: Saturation
% 6.34/1.85 % (3568714)Time elapsed: 0.148 s
% 6.34/1.85 % (3568714)Peak memory usage: 91 MB
% 6.34/1.85 % (3568714)Instructions burned: 248 (million)
% 6.34/1.85 % (3568720)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3980615921:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 6.34/1.85 % (3568715)------------------------------
% 6.34/1.85 % (3568715)------------------------------
% 6.34/1.85 % (3568722)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=922969330:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.34/1.85 % (3568720)Instruction limit reached!
% 6.34/1.85 % (3568720)------------------------------
% 6.34/1.85 % (3568720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.85 % (3568720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.85 % (3568720)CaDiCaL version: 2.1.3
% 6.34/1.85 % (3568720)Termination reason: Instruction limit
% 6.34/1.85 % (3568720)Termination phase: Saturation
% 6.34/1.85 % (3568720)Time elapsed: 0.076 s
% 6.34/1.85 % (3568720)Peak memory usage: 90 MB
% 6.34/1.85 % (3568720)Instructions burned: 113 (million)
% 6.34/1.85 % (3568695)First to succeed.
% 6.34/1.85 % (3568695)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3568689"
% 6.34/1.85 % (3568722)Instruction limit reached!
% 6.34/1.85 % (3568722)------------------------------
% 6.34/1.85 % (3568722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.85 % (3568722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.85 % (3568722)CaDiCaL version: 2.1.3
% 6.34/1.85 % (3568722)Termination reason: Instruction limit
% 6.34/1.85 % (3568722)Termination phase: Saturation
% 6.34/1.85 % (3568722)Time elapsed: 0.063 s
% 6.34/1.85 % (3568722)Peak memory usage: 89 MB
% 6.34/1.85 % (3568722)Instructions burned: 129 (million)
% 6.34/1.85 % (3568725)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1856784355:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 6.34/1.85 % (3568726)lrs+10_1_sil=8000:sp=occurrence:random_seed=4205319265:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.34/1.85 % (3568727)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1394337016:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.34/1.85 % (3568695)Refutation found. Thanks to Tanya!
% 6.34/1.85 % SZS status Theorem for theBenchmark
% 6.34/1.85 % SZS output start Proof for theBenchmark
% See solution above
% 7.70/2.05 % (3568695)------------------------------
% 7.70/2.05 % (3568695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.70/2.05 % (3568695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.70/2.05 % (3568695)CaDiCaL version: 2.1.3
% 7.70/2.05 % (3568695)Termination reason: Refutation
% 7.70/2.05 % (3568695)Time elapsed: 0.723 s
% 7.70/2.05 % (3568695)Peak memory usage: 136 MB
% 7.70/2.05 % (3568695)Instructions burned: 1792 (million)
% 7.70/2.05 % (3568695)------------------------------
% 7.70/2.05 % (3568695)------------------------------
% 7.70/2.05 % (3568689)Success in time 1.001 s
% 7.70/2.05 % Vampire exiting
%------------------------------------------------------------------------------