%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU043+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:47:07 PM UTC 2026
% Result : Theorem 6.85s 2.21s
% Output : Refutation 10.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 23
% Syntax : Number of formulae : 320 ( 16 unt; 15 def)
% Number of atoms : 1335 ( 225 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 1705 ( 690 ~; 842 |; 114 &)
% ( 40 <=>; 17 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 16 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 409 ( 0 sgn 374 !; 35 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,axiom,
! [X0,X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_rng_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X4,X0)
& in(ordered_pair(X3,X4),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f9,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f10,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f40,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_1) ).
fof(f41,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f43,axiom,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f45,plain,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( in(X4,relation_dom(X1))
=> apply(X2,X4) = apply(X1,X4) ) ) ) ) ),
inference(rectify,[],[f41]) ).
fof(f51,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = relation_rng_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X4,X0)
& in(ordered_pair(X3,X4),X1) ) ) )
| ~ relation(X2) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f52,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(f53,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,[],[f52]) ).
fof(f54,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(f55,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f70,plain,
? [X0,X1] :
( ? [X2] :
( ( X1 = relation_rng_restriction(X0,X2)
<~> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) ) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f71,plain,
? [X0,X1] :
( ? [X2] :
( ( X1 = relation_rng_restriction(X0,X2)
<~> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) ) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(flattening,[],[f70]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<=> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) )
| ~ relation(X2)
| ~ function(X2) ),
inference(ennf_transformation,[],[f43]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<=> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) )
| ~ relation(X2)
| ~ function(X2) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = relation_rng_restriction(X0,X1)
| ? [X3,X4] :
( ( ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(X4,X0)
& in(ordered_pair(X3,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X1) )
& ( ( in(X4,X0)
& in(ordered_pair(X3,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_rng_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f51]) ).
fof(f76,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = relation_rng_restriction(X0,X1)
| ? [X3,X4] :
( ( ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(X4,X0)
& in(ordered_pair(X3,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X1) )
& ( ( in(X4,X0)
& in(ordered_pair(X3,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_rng_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = relation_rng_restriction(X0,X1)
| ? [X3,X4] :
( ( ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(X4,X0)
& in(ordered_pair(X3,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(X6,X0)
| ~ in(ordered_pair(X5,X6),X1) )
& ( ( in(X6,X0)
& in(ordered_pair(X5,X6),X1) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| relation_rng_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) ),
inference(rectify,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = relation_rng_restriction(X0,X1)
| ( ( ~ in(sK1(X0,X1,X2),X0)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2) )
& ( ( in(sK1(X0,X1,X2),X0)
& in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X1) )
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(X6,X0)
| ~ in(ordered_pair(X5,X6),X1) )
& ( ( in(X6,X0)
& in(ordered_pair(X5,X6),X1) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| relation_rng_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X4,sK1(X0,X1,X2))],[f77]) ).
fof(f79,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,[],[f53]) ).
fof(f80,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,[],[f54]) ).
fof(f81,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,[],[f80]) ).
fof(f82,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))],[f81]) ).
fof(f95,plain,
? [X0,X1] :
( ? [X2] :
( ( ? [X3] :
( ( ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X1)) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) )
| in(X3,relation_dom(X1)) ) )
| ? [X4] :
( apply(X2,X4) != apply(X1,X4)
& in(X4,relation_dom(X1)) )
| relation_rng_restriction(X0,X2) != X1 )
& ( ( ! [X3] :
( ( in(X3,relation_dom(X1))
| ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X0) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) )
| ~ in(X3,relation_dom(X1)) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) )
| X1 = relation_rng_restriction(X0,X2) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(nnf_transformation,[],[f71]) ).
fof(f96,plain,
? [X0,X1] :
( ? [X2] :
( ( ? [X3] :
( ( ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X1)) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) )
| in(X3,relation_dom(X1)) ) )
| ? [X4] :
( apply(X2,X4) != apply(X1,X4)
& in(X4,relation_dom(X1)) )
| relation_rng_restriction(X0,X2) != X1 )
& ( ( ! [X3] :
( ( in(X3,relation_dom(X1))
| ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X0) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) )
| ~ in(X3,relation_dom(X1)) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) )
| X1 = relation_rng_restriction(X0,X2) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(flattening,[],[f95]) ).
fof(f97,plain,
? [X0,X1] :
( ? [X2] :
( ( ? [X3] :
( ( ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X1)) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) )
| in(X3,relation_dom(X1)) ) )
| ? [X4] :
( apply(X2,X4) != apply(X1,X4)
& in(X4,relation_dom(X1)) )
| relation_rng_restriction(X0,X2) != X1 )
& ( ( ! [X5] :
( ( in(X5,relation_dom(X1))
| ~ in(X5,relation_dom(X2))
| ~ in(apply(X2,X5),X0) )
& ( ( in(X5,relation_dom(X2))
& in(apply(X2,X5),X0) )
| ~ in(X5,relation_dom(X1)) ) )
& ! [X6] :
( apply(X2,X6) = apply(X1,X6)
| ~ in(X6,relation_dom(X1)) ) )
| X1 = relation_rng_restriction(X0,X2) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(rectify,[],[f96]) ).
fof(f98,plain,
( ( ( ( ~ in(sK19,relation_dom(sK18))
| ~ in(apply(sK18,sK19),sK16)
| ~ in(sK19,relation_dom(sK17)) )
& ( ( in(sK19,relation_dom(sK18))
& in(apply(sK18,sK19),sK16) )
| in(sK19,relation_dom(sK17)) ) )
| ( apply(sK18,sK20) != apply(sK17,sK20)
& in(sK20,relation_dom(sK17)) )
| sK17 != relation_rng_restriction(sK16,sK18) )
& ( ( ! [X5] :
( ( in(X5,relation_dom(sK17))
| ~ in(X5,relation_dom(sK18))
| ~ in(apply(sK18,X5),sK16) )
& ( ( in(X5,relation_dom(sK18))
& in(apply(sK18,X5),sK16) )
| ~ in(X5,relation_dom(sK17)) ) )
& ! [X6] :
( apply(sK18,X6) = apply(sK17,X6)
| ~ in(X6,relation_dom(sK17)) ) )
| sK17 = relation_rng_restriction(sK16,sK18) )
& relation(sK18)
& function(sK18)
& relation(sK17)
& function(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19,sK20]),skolemize(X0,sK16),skolemize(X1,sK17),skolemize(X2,sK18),skolemize(X3,sK19),skolemize(X4,sK20)],[f97]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ( ( in(ordered_pair(X0,X1),X2)
| ~ in(X0,relation_dom(X2))
| apply(X2,X0) != X1 )
& ( ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) )
| ~ in(ordered_pair(X0,X1),X2) ) )
| ~ relation(X2)
| ~ function(X2) ),
inference(nnf_transformation,[],[f74]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ( ( in(ordered_pair(X0,X1),X2)
| ~ in(X0,relation_dom(X2))
| apply(X2,X0) != X1 )
& ( ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) )
| ~ in(ordered_pair(X0,X1),X2) ) )
| ~ relation(X2)
| ~ function(X2) ),
inference(flattening,[],[f99]) ).
fof(f107,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f108,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X1)
| ~ in(ordered_pair(X5,X6),X2)
| relation_rng_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f109,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,X0)
| ~ in(ordered_pair(X5,X6),X2)
| relation_rng_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f110,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(X6,X0)
| ~ in(ordered_pair(X5,X6),X1)
| relation_rng_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f111,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X1) = X2
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X1)
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f112,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X1) = X2
| in(sK1(X0,X1,X2),X0)
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f113,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X1) = X2
| ~ in(sK1(X0,X1,X2),X0)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f114,plain,
! [X2,X0,X1] :
( empty_set = X2
| apply(X0,X1) != X2
| in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f118,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK4(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f119,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f122,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f123,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f169,plain,
function(sK17),
inference(cnf_transformation,[],[f98]) ).
fof(f170,plain,
relation(sK17),
inference(cnf_transformation,[],[f98]) ).
fof(f171,plain,
function(sK18),
inference(cnf_transformation,[],[f98]) ).
fof(f172,plain,
relation(sK18),
inference(cnf_transformation,[],[f98]) ).
fof(f173,plain,
! [X6] :
( apply(sK18,X6) = apply(sK17,X6)
| ~ in(X6,relation_dom(sK17))
| sK17 = relation_rng_restriction(sK16,sK18) ),
inference(cnf_transformation,[],[f98]) ).
fof(f174,plain,
! [X5] :
( in(apply(sK18,X5),sK16)
| ~ in(X5,relation_dom(sK17))
| sK17 = relation_rng_restriction(sK16,sK18) ),
inference(cnf_transformation,[],[f98]) ).
fof(f175,plain,
! [X5] :
( in(X5,relation_dom(sK18))
| ~ in(X5,relation_dom(sK17))
| sK17 = relation_rng_restriction(sK16,sK18) ),
inference(cnf_transformation,[],[f98]) ).
fof(f176,plain,
! [X5] :
( in(X5,relation_dom(sK17))
| ~ in(X5,relation_dom(sK18))
| ~ in(apply(sK18,X5),sK16)
| sK17 = relation_rng_restriction(sK16,sK18) ),
inference(cnf_transformation,[],[f98]) ).
fof(f177,plain,
( in(apply(sK18,sK19),sK16)
| in(sK19,relation_dom(sK17))
| in(sK20,relation_dom(sK17))
| sK17 != relation_rng_restriction(sK16,sK18) ),
inference(cnf_transformation,[],[f98]) ).
fof(f178,plain,
( in(apply(sK18,sK19),sK16)
| in(sK19,relation_dom(sK17))
| apply(sK18,sK20) != apply(sK17,sK20)
| sK17 != relation_rng_restriction(sK16,sK18) ),
inference(cnf_transformation,[],[f98]) ).
fof(f179,plain,
( in(sK19,relation_dom(sK18))
| in(sK19,relation_dom(sK17))
| in(sK20,relation_dom(sK17))
| sK17 != relation_rng_restriction(sK16,sK18) ),
inference(cnf_transformation,[],[f98]) ).
fof(f180,plain,
( in(sK19,relation_dom(sK18))
| in(sK19,relation_dom(sK17))
| apply(sK18,sK20) != apply(sK17,sK20)
| sK17 != relation_rng_restriction(sK16,sK18) ),
inference(cnf_transformation,[],[f98]) ).
fof(f181,plain,
( ~ in(sK19,relation_dom(sK18))
| ~ in(apply(sK18,sK19),sK16)
| ~ in(sK19,relation_dom(sK17))
| in(sK20,relation_dom(sK17))
| sK17 != relation_rng_restriction(sK16,sK18) ),
inference(cnf_transformation,[],[f98]) ).
fof(f182,plain,
( ~ in(sK19,relation_dom(sK18))
| ~ in(apply(sK18,sK19),sK16)
| ~ in(sK19,relation_dom(sK17))
| apply(sK18,sK20) != apply(sK17,sK20)
| sK17 != relation_rng_restriction(sK16,sK18) ),
inference(cnf_transformation,[],[f98]) ).
fof(f184,plain,
! [X2,X0,X1] :
( apply(X2,X0) = X1
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f100]) ).
fof(f186,plain,
! [X2,X0,X1] :
( in(ordered_pair(X0,X1),X2)
| ~ in(X0,relation_dom(X2))
| apply(X2,X0) != X1
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f100]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ in(sK1(X0,X1,X2),X0)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X2)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f113,f122,f122]) ).
fof(f188,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| in(sK1(X0,X1,X2),X0)
| in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X2)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f112,f122]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X2)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f111,f122,f122]) ).
fof(f190,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| ~ in(X6,X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1)
| relation_rng_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f110,f122,f122]) ).
fof(f191,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| relation_rng_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f109,f122]) ).
fof(f192,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| relation_rng_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f108,f122,f122]) ).
fof(f197,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,[],[f119,f122]) ).
fof(f198,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,[],[f118,f122]) ).
fof(f200,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ in(X0,relation_dom(X2))
| apply(X2,X0) != X1
| ~ relation(X2)
| ~ function(X2) ),
inference(definition_unfolding,[],[f186,f122]) ).
fof(f202,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| apply(X2,X0) = X1
| ~ function(X2) ),
inference(definition_unfolding,[],[f184,f122]) ).
fof(f203,plain,
! [X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_rng_restriction(X0,X1))
| ~ in(X6,X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(equality_resolution,[],[f190]) ).
fof(f204,plain,
! [X0,X1,X6,X5] :
( in(X6,X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(equality_resolution,[],[f191]) ).
fof(f205,plain,
! [X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(equality_resolution,[],[f192]) ).
fof(f208,plain,
! [X0,X1] :
( ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) = empty_set
| ~ function(X0) ),
inference(equality_resolution,[],[f114]) ).
fof(f209,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f197]) ).
fof(f210,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,[],[f198]) ).
fof(f211,plain,
! [X2,X0] :
( ~ function(X2)
| ~ in(X0,relation_dom(X2))
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X0,apply(X2,X0)),singleton(X0)),X2) ),
inference(equality_resolution,[],[f200]) ).
fof(f213,definition,
( spl21_1
<=> sK17 = relation_rng_restriction(sK16,sK18) ),
introduced(definition,[new_symbols(definition,[spl21_1])],[avatar_definition]) ).
fof(f214,plain,
( sK17 = relation_rng_restriction(sK16,sK18)
| ~ spl21_1 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f216,definition,
( spl21_2
<=> ! [X6] :
( apply(sK18,X6) = apply(sK17,X6)
| ~ in(X6,relation_dom(sK17)) ) ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
fof(f217,plain,
( ! [X6] :
( ~ in(X6,relation_dom(sK17))
| apply(sK18,X6) = apply(sK17,X6) )
| ~ spl21_2 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f218,plain,
( spl21_1
| spl21_2 ),
inference(avatar_split_clause,[],[f173,f216,f213]) ).
fof(f220,definition,
( spl21_3
<=> ! [X5] :
( in(apply(sK18,X5),sK16)
| ~ in(X5,relation_dom(sK17)) ) ),
introduced(definition,[new_symbols(definition,[spl21_3])],[avatar_definition]) ).
fof(f221,plain,
( ! [X5] :
( in(apply(sK18,X5),sK16)
| ~ in(X5,relation_dom(sK17)) )
| ~ spl21_3 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f222,plain,
( spl21_1
| spl21_3 ),
inference(avatar_split_clause,[],[f174,f220,f213]) ).
fof(f224,definition,
( spl21_4
<=> ! [X5] :
( in(X5,relation_dom(sK18))
| ~ in(X5,relation_dom(sK17)) ) ),
introduced(definition,[new_symbols(definition,[spl21_4])],[avatar_definition]) ).
fof(f225,plain,
( ! [X5] :
( in(X5,relation_dom(sK18))
| ~ in(X5,relation_dom(sK17)) )
| ~ spl21_4 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f226,plain,
( spl21_1
| spl21_4 ),
inference(avatar_split_clause,[],[f175,f224,f213]) ).
fof(f228,definition,
( spl21_5
<=> ! [X5] :
( in(X5,relation_dom(sK17))
| ~ in(apply(sK18,X5),sK16)
| ~ in(X5,relation_dom(sK18)) ) ),
introduced(definition,[new_symbols(definition,[spl21_5])],[avatar_definition]) ).
fof(f229,plain,
( ! [X5] :
( ~ in(apply(sK18,X5),sK16)
| in(X5,relation_dom(sK17))
| ~ in(X5,relation_dom(sK18)) )
| ~ spl21_5 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f230,plain,
( spl21_1
| spl21_5 ),
inference(avatar_split_clause,[],[f176,f228,f213]) ).
fof(f231,plain,
( sK17 != relation_rng_restriction(sK16,sK18)
| spl21_1 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f233,definition,
( spl21_6
<=> in(sK20,relation_dom(sK17)) ),
introduced(definition,[new_symbols(definition,[spl21_6])],[avatar_definition]) ).
fof(f234,plain,
( in(sK20,relation_dom(sK17))
| ~ spl21_6 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f236,definition,
( spl21_7
<=> in(sK19,relation_dom(sK17)) ),
introduced(definition,[new_symbols(definition,[spl21_7])],[avatar_definition]) ).
fof(f237,plain,
( in(sK19,relation_dom(sK17))
| ~ spl21_7 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f239,definition,
( spl21_8
<=> in(apply(sK18,sK19),sK16) ),
introduced(definition,[new_symbols(definition,[spl21_8])],[avatar_definition]) ).
fof(f240,plain,
( in(apply(sK18,sK19),sK16)
| ~ spl21_8 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f241,plain,
( ~ spl21_1
| spl21_6
| spl21_7
| spl21_8 ),
inference(avatar_split_clause,[],[f177,f239,f236,f233,f213]) ).
fof(f243,definition,
( spl21_9
<=> apply(sK18,sK20) = apply(sK17,sK20) ),
introduced(definition,[new_symbols(definition,[spl21_9])],[avatar_definition]) ).
fof(f244,plain,
( apply(sK18,sK20) != apply(sK17,sK20)
| spl21_9 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f245,plain,
( ~ spl21_1
| ~ spl21_9
| spl21_7
| spl21_8 ),
inference(avatar_split_clause,[],[f178,f239,f236,f243,f213]) ).
fof(f247,definition,
( spl21_10
<=> in(sK19,relation_dom(sK18)) ),
introduced(definition,[new_symbols(definition,[spl21_10])],[avatar_definition]) ).
fof(f248,plain,
( in(sK19,relation_dom(sK18))
| ~ spl21_10 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f249,plain,
( ~ spl21_1
| spl21_6
| spl21_7
| spl21_10 ),
inference(avatar_split_clause,[],[f179,f247,f236,f233,f213]) ).
fof(f250,plain,
( ~ spl21_1
| ~ spl21_9
| spl21_7
| spl21_10 ),
inference(avatar_split_clause,[],[f180,f247,f236,f243,f213]) ).
fof(f251,plain,
( ~ in(sK19,relation_dom(sK17))
| spl21_7 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f252,plain,
( ~ in(apply(sK18,sK19),sK16)
| spl21_8 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f253,plain,
( ~ in(sK19,relation_dom(sK18))
| spl21_10 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f254,plain,
( ~ spl21_1
| spl21_6
| ~ spl21_7
| ~ spl21_8
| ~ spl21_10 ),
inference(avatar_split_clause,[],[f181,f247,f239,f236,f233,f213]) ).
fof(f255,plain,
( ~ spl21_1
| ~ spl21_9
| ~ spl21_7
| ~ spl21_8
| ~ spl21_10 ),
inference(avatar_split_clause,[],[f182,f247,f239,f236,f243,f213]) ).
fof(f256,plain,
! [X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(forward_subsumption_resolution,[],[f205,f123]) ).
fof(f257,plain,
! [X0,X1,X6,X5] :
( in(X6,X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(forward_subsumption_resolution,[],[f204,f123]) ).
fof(f258,plain,
! [X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_rng_restriction(X0,X1))
| ~ in(X6,X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1)
| ~ relation(X1) ),
inference(forward_subsumption_resolution,[],[f203,f123]) ).
fof(f259,plain,
! [X0,X1,X6,X5] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(forward_demodulation,[],[f256,f107]) ).
fof(f260,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| in(X6,X0)
| ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),relation_rng_restriction(X0,X1)) ),
inference(forward_demodulation,[],[f257,f107]) ).
fof(f261,plain,
! [X0,X1,X6,X5] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),relation_rng_restriction(X0,X1))
| ~ in(X6,X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1)
| ~ relation(X1) ),
inference(forward_demodulation,[],[f258,f107]) ).
fof(f262,plain,
! [X0,X1,X6,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),relation_rng_restriction(X0,X1))
| in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X1)
| ~ relation(X1) ),
inference(forward_demodulation,[],[f259,f107]) ).
fof(f263,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),relation_rng_restriction(X0,X1))
| ~ in(X6,X0)
| ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X1) ),
inference(forward_demodulation,[],[f261,f107]) ).
fof(f264,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK18)
| apply(sK18,X0) = X1
| ~ function(sK18) ),
inference(resolution,[],[f172,f202]) ).
fof(f267,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK18)
| apply(sK18,X0) = X1 ),
inference(forward_subsumption_resolution,[],[f264,f171]) ).
fof(f268,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18)
| apply(sK18,X0) = X1 ),
inference(forward_demodulation,[],[f267,f107]) ).
fof(f271,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK17)
| apply(sK17,X0) = X1
| ~ function(sK17) ),
inference(resolution,[],[f170,f202]) ).
fof(f272,plain,
! [X0] :
( in(X0,relation_dom(sK17))
| empty_set = apply(sK17,X0)
| ~ function(sK17) ),
inference(resolution,[],[f170,f208]) ).
fof(f273,plain,
! [X0] :
( in(X0,relation_dom(sK17))
| empty_set = apply(sK17,X0) ),
inference(forward_subsumption_resolution,[],[f272,f169]) ).
fof(f274,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK17)
| apply(sK17,X0) = X1 ),
inference(forward_subsumption_resolution,[],[f271,f169]) ).
fof(f275,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK17)
| apply(sK17,X0) = X1 ),
inference(forward_demodulation,[],[f274,f107]) ).
fof(f292,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),relation_rng_restriction(X1,sK18))
| in(X0,X1) ),
inference(resolution,[],[f260,f172]) ).
fof(f293,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),relation_rng_restriction(X1,sK17))
| in(X0,X1) ),
inference(resolution,[],[f260,f170]) ).
fof(f301,plain,
! [X0] :
( ~ in(X0,relation_dom(sK18))
| ~ relation(sK18)
| in(unordered_pair(unordered_pair(X0,apply(sK18,X0)),singleton(X0)),sK18) ),
inference(resolution,[],[f211,f171]) ).
fof(f302,plain,
! [X0] :
( ~ in(X0,relation_dom(sK17))
| ~ relation(sK17)
| in(unordered_pair(unordered_pair(X0,apply(sK17,X0)),singleton(X0)),sK17) ),
inference(resolution,[],[f211,f169]) ).
fof(f305,plain,
! [X0] :
( ~ in(X0,relation_dom(sK17))
| in(unordered_pair(unordered_pair(X0,apply(sK17,X0)),singleton(X0)),sK17) ),
inference(forward_subsumption_resolution,[],[f302,f170]) ).
fof(f306,plain,
! [X0] :
( ~ in(X0,relation_dom(sK18))
| in(unordered_pair(unordered_pair(X0,apply(sK18,X0)),singleton(X0)),sK18) ),
inference(forward_subsumption_resolution,[],[f301,f172]) ).
fof(f308,plain,
! [X0] :
( ~ in(X0,relation_dom(sK17))
| in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK17,X0))),sK17) ),
inference(forward_demodulation,[],[f305,f107]) ).
fof(f309,plain,
! [X0] :
( ~ in(X0,relation_dom(sK18))
| in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK18,X0))),sK18) ),
inference(forward_demodulation,[],[f306,f107]) ).
fof(f313,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18)
| ~ in(X1,X2)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_rng_restriction(X2,sK18)) ),
inference(resolution,[],[f263,f172]) ).
fof(f317,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK18)
| in(X0,relation_dom(sK18)) ),
inference(resolution,[],[f209,f172]) ).
fof(f318,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK17)
| in(X0,relation_dom(sK17)) ),
inference(resolution,[],[f209,f170]) ).
fof(f323,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK17)
| in(X0,relation_dom(sK17)) ),
inference(forward_demodulation,[],[f318,f107]) ).
fof(f324,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18)
| in(X0,relation_dom(sK18)) ),
inference(forward_demodulation,[],[f317,f107]) ).
fof(f339,plain,
! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK17,X0))),sK17)
| empty_set = apply(sK17,X0) ),
inference(resolution,[],[f308,f273]) ).
fof(f350,plain,
! [X0] :
( ~ in(X0,relation_dom(sK18))
| in(unordered_pair(unordered_pair(X0,sK4(sK18,X0)),singleton(X0)),sK18) ),
inference(resolution,[],[f210,f172]) ).
fof(f351,plain,
! [X0] :
( ~ in(X0,relation_dom(sK17))
| in(unordered_pair(unordered_pair(X0,sK4(sK17,X0)),singleton(X0)),sK17) ),
inference(resolution,[],[f210,f170]) ).
fof(f356,plain,
! [X0] :
( ~ in(X0,relation_dom(sK17))
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK4(sK17,X0))),sK17) ),
inference(forward_demodulation,[],[f351,f107]) ).
fof(f357,plain,
! [X0] :
( ~ in(X0,relation_dom(sK18))
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK4(sK18,X0))),sK18) ),
inference(forward_demodulation,[],[f350,f107]) ).
fof(f362,plain,
! [X0,X1] :
( ~ in(sK1(X0,sK18,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK0(X0,sK18,X1),sK1(X0,sK18,X1)),singleton(sK0(X0,sK18,X1))),sK18)
| ~ in(unordered_pair(unordered_pair(sK0(X0,sK18,X1),sK1(X0,sK18,X1)),singleton(sK0(X0,sK18,X1))),X1)
| ~ relation(X1)
| relation_rng_restriction(X0,sK18) = X1 ),
inference(resolution,[],[f187,f172]) ).
fof(f363,plain,
! [X0,X1] :
( ~ in(sK1(X0,sK17,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK0(X0,sK17,X1),sK1(X0,sK17,X1)),singleton(sK0(X0,sK17,X1))),sK17)
| ~ in(unordered_pair(unordered_pair(sK0(X0,sK17,X1),sK1(X0,sK17,X1)),singleton(sK0(X0,sK17,X1))),X1)
| ~ relation(X1)
| relation_rng_restriction(X0,sK17) = X1 ),
inference(resolution,[],[f187,f170]) ).
fof(f368,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK0(X0,sK17,X1)),unordered_pair(sK0(X0,sK17,X1),sK1(X0,sK17,X1))),sK17)
| ~ in(sK1(X0,sK17,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK0(X0,sK17,X1),sK1(X0,sK17,X1)),singleton(sK0(X0,sK17,X1))),X1)
| ~ relation(X1)
| relation_rng_restriction(X0,sK17) = X1 ),
inference(forward_demodulation,[],[f363,f107]) ).
fof(f369,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK0(X0,sK18,X1)),unordered_pair(sK0(X0,sK18,X1),sK1(X0,sK18,X1))),sK18)
| ~ in(sK1(X0,sK18,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK0(X0,sK18,X1),sK1(X0,sK18,X1)),singleton(sK0(X0,sK18,X1))),X1)
| ~ relation(X1)
| relation_rng_restriction(X0,sK18) = X1 ),
inference(forward_demodulation,[],[f362,f107]) ).
fof(f372,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK0(X0,sK17,X1)),unordered_pair(sK0(X0,sK17,X1),sK1(X0,sK17,X1))),sK17)
| ~ in(unordered_pair(singleton(sK0(X0,sK17,X1)),unordered_pair(sK0(X0,sK17,X1),sK1(X0,sK17,X1))),X1)
| ~ in(sK1(X0,sK17,X1),X0)
| ~ relation(X1)
| relation_rng_restriction(X0,sK17) = X1 ),
inference(forward_demodulation,[],[f368,f107]) ).
fof(f373,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK0(X0,sK18,X1)),unordered_pair(sK0(X0,sK18,X1),sK1(X0,sK18,X1))),sK18)
| ~ in(unordered_pair(singleton(sK0(X0,sK18,X1)),unordered_pair(sK0(X0,sK18,X1),sK1(X0,sK18,X1))),X1)
| ~ in(sK1(X0,sK18,X1),X0)
| ~ relation(X1)
| relation_rng_restriction(X0,sK18) = X1 ),
inference(forward_demodulation,[],[f369,f107]) ).
fof(f393,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK0(X0,sK18,X1),sK1(X0,sK18,X1)),singleton(sK0(X0,sK18,X1))),sK18)
| in(unordered_pair(unordered_pair(sK0(X0,sK18,X1),sK1(X0,sK18,X1)),singleton(sK0(X0,sK18,X1))),X1)
| ~ relation(X1)
| relation_rng_restriction(X0,sK18) = X1 ),
inference(resolution,[],[f189,f172]) ).
fof(f394,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK0(X0,sK17,X1),sK1(X0,sK17,X1)),singleton(sK0(X0,sK17,X1))),sK17)
| in(unordered_pair(unordered_pair(sK0(X0,sK17,X1),sK1(X0,sK17,X1)),singleton(sK0(X0,sK17,X1))),X1)
| ~ relation(X1)
| relation_rng_restriction(X0,sK17) = X1 ),
inference(resolution,[],[f189,f170]) ).
fof(f399,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK0(X0,sK17,X1)),unordered_pair(sK0(X0,sK17,X1),sK1(X0,sK17,X1))),sK17)
| in(unordered_pair(unordered_pair(sK0(X0,sK17,X1),sK1(X0,sK17,X1)),singleton(sK0(X0,sK17,X1))),X1)
| ~ relation(X1)
| relation_rng_restriction(X0,sK17) = X1 ),
inference(forward_demodulation,[],[f394,f107]) ).
fof(f400,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK0(X0,sK18,X1)),unordered_pair(sK0(X0,sK18,X1),sK1(X0,sK18,X1))),sK18)
| in(unordered_pair(unordered_pair(sK0(X0,sK18,X1),sK1(X0,sK18,X1)),singleton(sK0(X0,sK18,X1))),X1)
| ~ relation(X1)
| relation_rng_restriction(X0,sK18) = X1 ),
inference(forward_demodulation,[],[f393,f107]) ).
fof(f403,plain,
! [X0,X1] :
( ~ relation(X1)
| in(unordered_pair(singleton(sK0(X0,sK17,X1)),unordered_pair(sK0(X0,sK17,X1),sK1(X0,sK17,X1))),sK17)
| in(unordered_pair(singleton(sK0(X0,sK17,X1)),unordered_pair(sK0(X0,sK17,X1),sK1(X0,sK17,X1))),X1)
| relation_rng_restriction(X0,sK17) = X1 ),
inference(forward_demodulation,[],[f399,f107]) ).
fof(f404,plain,
! [X0,X1] :
( ~ relation(X1)
| in(unordered_pair(singleton(sK0(X0,sK18,X1)),unordered_pair(sK0(X0,sK18,X1),sK1(X0,sK18,X1))),sK18)
| in(unordered_pair(singleton(sK0(X0,sK18,X1)),unordered_pair(sK0(X0,sK18,X1),sK1(X0,sK18,X1))),X1)
| relation_rng_restriction(X0,sK18) = X1 ),
inference(forward_demodulation,[],[f400,f107]) ).
fof(f406,plain,
! [X0] :
( in(unordered_pair(singleton(sK0(X0,sK17,sK17)),unordered_pair(sK0(X0,sK17,sK17),sK1(X0,sK17,sK17))),sK17)
| in(unordered_pair(singleton(sK0(X0,sK17,sK17)),unordered_pair(sK0(X0,sK17,sK17),sK1(X0,sK17,sK17))),sK17)
| sK17 = relation_rng_restriction(X0,sK17) ),
inference(resolution,[],[f403,f170]) ).
fof(f409,plain,
! [X0] :
( in(unordered_pair(singleton(sK0(X0,sK17,sK17)),unordered_pair(sK0(X0,sK17,sK17),sK1(X0,sK17,sK17))),sK17)
| sK17 = relation_rng_restriction(X0,sK17) ),
inference(duplicate_literal_removal,[],[f406]) ).
fof(f410,plain,
! [X0] :
( sK17 = relation_rng_restriction(X0,sK17)
| ~ in(unordered_pair(singleton(sK0(X0,sK17,sK17)),unordered_pair(sK0(X0,sK17,sK17),sK1(X0,sK17,sK17))),sK17)
| ~ in(sK1(X0,sK17,sK17),X0)
| ~ relation(sK17)
| sK17 = relation_rng_restriction(X0,sK17) ),
inference(resolution,[],[f409,f372]) ).
fof(f411,plain,
! [X0] :
( in(sK0(X0,sK17,sK17),relation_dom(sK17))
| sK17 = relation_rng_restriction(X0,sK17) ),
inference(resolution,[],[f409,f323]) ).
fof(f413,plain,
! [X0] :
( sK1(X0,sK17,sK17) = apply(sK17,sK0(X0,sK17,sK17))
| sK17 = relation_rng_restriction(X0,sK17) ),
inference(resolution,[],[f409,f275]) ).
fof(f414,plain,
! [X0] :
( sK17 = relation_rng_restriction(X0,sK17)
| ~ in(unordered_pair(singleton(sK0(X0,sK17,sK17)),unordered_pair(sK0(X0,sK17,sK17),sK1(X0,sK17,sK17))),sK17)
| ~ in(sK1(X0,sK17,sK17),X0)
| ~ relation(sK17) ),
inference(duplicate_literal_removal,[],[f410]) ).
fof(f415,plain,
! [X0] :
( sK17 = relation_rng_restriction(X0,sK17)
| ~ in(sK1(X0,sK17,sK17),X0)
| ~ relation(sK17) ),
inference(forward_subsumption_resolution,[],[f414,f409]) ).
fof(f416,plain,
! [X0] :
( ~ in(sK1(X0,sK17,sK17),X0)
| sK17 = relation_rng_restriction(X0,sK17) ),
inference(forward_subsumption_resolution,[],[f415,f170]) ).
fof(f465,definition,
( spl21_17
<=> sK17 = relation_rng_restriction(sK16,sK17) ),
introduced(definition,[new_symbols(definition,[spl21_17])],[avatar_definition]) ).
fof(f466,plain,
( sK17 = relation_rng_restriction(sK16,sK17)
| ~ spl21_17 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f473,plain,
( in(unordered_pair(singleton(sK20),unordered_pair(sK20,sK4(sK17,sK20))),sK17)
| ~ spl21_6 ),
inference(resolution,[],[f234,f356]) ).
fof(f475,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK17)
| in(X1,sK16) )
| ~ spl21_1 ),
inference(superposition,[],[f292,f214]) ).
fof(f480,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK17)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18)
| ~ relation(sK18) )
| ~ spl21_1 ),
inference(superposition,[],[f262,f214]) ).
fof(f487,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK17)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK18) )
| ~ spl21_1 ),
inference(forward_subsumption_resolution,[],[f480,f172]) ).
fof(f493,plain,
( in(unordered_pair(singleton(sK20),unordered_pair(sK20,sK4(sK17,sK20))),sK18)
| ~ spl21_1
| ~ spl21_6 ),
inference(resolution,[],[f473,f487]) ).
fof(f497,plain,
( apply(sK17,sK20) = sK4(sK17,sK20)
| ~ spl21_6 ),
inference(resolution,[],[f473,f275]) ).
fof(f500,plain,
( in(unordered_pair(singleton(sK20),unordered_pair(sK20,apply(sK17,sK20))),sK18)
| ~ spl21_1
| ~ spl21_6 ),
inference(forward_demodulation,[],[f493,f497]) ).
fof(f508,plain,
( apply(sK18,sK20) = apply(sK17,sK20)
| ~ spl21_1
| ~ spl21_6 ),
inference(resolution,[],[f500,f268]) ).
fof(f510,plain,
( $false
| ~ spl21_1
| ~ spl21_6
| spl21_9 ),
inference(forward_subsumption_resolution,[],[f508,f244]) ).
fof(f511,plain,
( ~ spl21_1
| ~ spl21_6
| spl21_9 ),
inference(avatar_contradiction_clause,[],[f510]) ).
fof(f514,plain,
( in(unordered_pair(singleton(sK19),unordered_pair(sK19,sK4(sK17,sK19))),sK17)
| ~ spl21_7 ),
inference(resolution,[],[f237,f356]) ).
fof(f529,plain,
( in(unordered_pair(singleton(sK19),unordered_pair(sK19,sK4(sK17,sK19))),sK18)
| ~ spl21_1
| ~ spl21_7 ),
inference(resolution,[],[f514,f487]) ).
fof(f533,plain,
( apply(sK17,sK19) = sK4(sK17,sK19)
| ~ spl21_7 ),
inference(resolution,[],[f514,f275]) ).
fof(f536,plain,
( in(unordered_pair(singleton(sK19),unordered_pair(sK19,apply(sK17,sK19))),sK18)
| ~ spl21_1
| ~ spl21_7 ),
inference(forward_demodulation,[],[f529,f533]) ).
fof(f540,plain,
( in(sK19,relation_dom(sK18))
| ~ spl21_1
| ~ spl21_7 ),
inference(resolution,[],[f536,f324]) ).
fof(f545,plain,
( $false
| ~ spl21_1
| ~ spl21_7
| spl21_10 ),
inference(forward_subsumption_resolution,[],[f540,f253]) ).
fof(f546,plain,
( ~ spl21_1
| ~ spl21_7
| spl21_10 ),
inference(avatar_contradiction_clause,[],[f545]) ).
fof(f547,plain,
( in(unordered_pair(singleton(sK19),unordered_pair(sK19,sK4(sK18,sK19))),sK18)
| ~ spl21_10 ),
inference(resolution,[],[f248,f357]) ).
fof(f555,plain,
( ! [X0] :
( ~ in(sK4(sK18,sK19),X0)
| in(unordered_pair(singleton(sK19),unordered_pair(sK19,sK4(sK18,sK19))),relation_rng_restriction(X0,sK18)) )
| ~ spl21_10 ),
inference(resolution,[],[f547,f313]) ).
fof(f556,plain,
( apply(sK18,sK19) = sK4(sK18,sK19)
| ~ spl21_10 ),
inference(resolution,[],[f547,f268]) ).
fof(f557,plain,
( ! [X0] :
( ~ in(apply(sK18,sK19),X0)
| in(unordered_pair(singleton(sK19),unordered_pair(sK19,sK4(sK18,sK19))),relation_rng_restriction(X0,sK18)) )
| ~ spl21_10 ),
inference(forward_demodulation,[],[f555,f556]) ).
fof(f558,plain,
( ! [X0] :
( ~ in(apply(sK18,sK19),X0)
| in(unordered_pair(singleton(sK19),unordered_pair(sK19,apply(sK18,sK19))),relation_rng_restriction(X0,sK18)) )
| ~ spl21_10 ),
inference(forward_demodulation,[],[f557,f556]) ).
fof(f569,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK17)
| in(X1,sK16) )
| ~ spl21_17 ),
inference(superposition,[],[f293,f466]) ).
fof(f581,plain,
! [X0] :
( in(unordered_pair(singleton(sK0(X0,sK18,sK17)),unordered_pair(sK0(X0,sK18,sK17),sK1(X0,sK18,sK17))),sK18)
| in(unordered_pair(singleton(sK0(X0,sK18,sK17)),unordered_pair(sK0(X0,sK18,sK17),sK1(X0,sK18,sK17))),sK17)
| sK17 = relation_rng_restriction(X0,sK18) ),
inference(resolution,[],[f404,f170]) ).
fof(f765,plain,
( in(unordered_pair(singleton(sK19),unordered_pair(sK19,apply(sK18,sK19))),relation_rng_restriction(sK16,sK18))
| ~ spl21_8
| ~ spl21_10 ),
inference(resolution,[],[f558,f240]) ).
fof(f776,plain,
( in(unordered_pair(singleton(sK19),unordered_pair(sK19,apply(sK18,sK19))),sK17)
| ~ spl21_1
| ~ spl21_8
| ~ spl21_10 ),
inference(forward_demodulation,[],[f765,f214]) ).
fof(f781,plain,
( in(sK19,relation_dom(sK17))
| ~ spl21_1
| ~ spl21_8
| ~ spl21_10 ),
inference(resolution,[],[f776,f323]) ).
fof(f786,plain,
( $false
| ~ spl21_1
| spl21_7
| ~ spl21_8
| ~ spl21_10 ),
inference(forward_subsumption_resolution,[],[f781,f251]) ).
fof(f787,plain,
( ~ spl21_1
| spl21_7
| ~ spl21_8
| ~ spl21_10 ),
inference(avatar_contradiction_clause,[],[f786]) ).
fof(f790,plain,
( in(unordered_pair(singleton(sK19),unordered_pair(sK19,sK4(sK17,sK19))),sK17)
| ~ spl21_7 ),
inference(resolution,[],[f237,f356]) ).
fof(f797,plain,
( in(sK4(sK17,sK19),sK16)
| ~ spl21_1
| ~ spl21_7 ),
inference(resolution,[],[f790,f475]) ).
fof(f798,plain,
( in(unordered_pair(singleton(sK19),unordered_pair(sK19,sK4(sK17,sK19))),sK18)
| ~ spl21_1
| ~ spl21_7 ),
inference(resolution,[],[f790,f487]) ).
fof(f802,plain,
( apply(sK17,sK19) = sK4(sK17,sK19)
| ~ spl21_7 ),
inference(resolution,[],[f790,f275]) ).
fof(f805,plain,
( in(unordered_pair(singleton(sK19),unordered_pair(sK19,apply(sK17,sK19))),sK18)
| ~ spl21_1
| ~ spl21_7 ),
inference(forward_demodulation,[],[f798,f802]) ).
fof(f806,plain,
( in(apply(sK17,sK19),sK16)
| ~ spl21_1
| ~ spl21_7 ),
inference(forward_demodulation,[],[f797,f802]) ).
fof(f813,plain,
( apply(sK18,sK19) = apply(sK17,sK19)
| ~ spl21_1
| ~ spl21_7 ),
inference(resolution,[],[f805,f268]) ).
fof(f814,plain,
( ~ in(apply(sK17,sK19),sK16)
| ~ spl21_1
| ~ spl21_7
| spl21_8 ),
inference(superposition,[],[f252,f813]) ).
fof(f819,plain,
( $false
| ~ spl21_1
| ~ spl21_7
| spl21_8 ),
inference(forward_subsumption_resolution,[],[f814,f806]) ).
fof(f820,plain,
( ~ spl21_1
| ~ spl21_7
| spl21_8 ),
inference(avatar_contradiction_clause,[],[f819]) ).
fof(f824,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK17))
| in(unordered_pair(singleton(X0),unordered_pair(X0,apply(sK18,X0))),sK18) )
| ~ spl21_4 ),
inference(resolution,[],[f225,f309]) ).
fof(f833,plain,
( ! [X0] :
( apply(sK17,sK0(X0,sK17,sK17)) = apply(sK18,sK0(X0,sK17,sK17))
| sK17 = relation_rng_restriction(X0,sK17) )
| ~ spl21_2 ),
inference(resolution,[],[f217,f411]) ).
fof(f861,plain,
! [X0] :
( in(unordered_pair(singleton(sK0(X0,sK18,sK17)),unordered_pair(sK0(X0,sK18,sK17),sK1(X0,sK18,sK17))),sK17)
| sK17 = relation_rng_restriction(X0,sK18)
| in(sK0(X0,sK18,sK17),relation_dom(sK18)) ),
inference(resolution,[],[f581,f324]) ).
fof(f863,plain,
! [X0] :
( in(unordered_pair(singleton(sK0(X0,sK18,sK17)),unordered_pair(sK0(X0,sK18,sK17),sK1(X0,sK18,sK17))),sK17)
| sK17 = relation_rng_restriction(X0,sK18)
| sK1(X0,sK18,sK17) = apply(sK18,sK0(X0,sK18,sK17)) ),
inference(resolution,[],[f581,f268]) ).
fof(f874,plain,
( ! [X0] :
( in(apply(sK17,sK0(X0,sK17,sK17)),sK16)
| ~ in(sK0(X0,sK17,sK17),relation_dom(sK17))
| sK17 = relation_rng_restriction(X0,sK17) )
| ~ spl21_2
| ~ spl21_3 ),
inference(superposition,[],[f221,f833]) ).
fof(f875,plain,
( ! [X0] :
( in(apply(sK17,sK0(X0,sK17,sK17)),sK16)
| sK17 = relation_rng_restriction(X0,sK17) )
| ~ spl21_2
| ~ spl21_3 ),
inference(forward_subsumption_resolution,[],[f874,f411]) ).
fof(f876,plain,
( ! [X0] :
( in(sK1(X0,sK17,sK17),sK16)
| sK17 = relation_rng_restriction(X0,sK17)
| sK17 = relation_rng_restriction(X0,sK17) )
| ~ spl21_2
| ~ spl21_3 ),
inference(superposition,[],[f875,f413]) ).
fof(f877,plain,
( ! [X0] :
( in(sK1(X0,sK17,sK17),sK16)
| sK17 = relation_rng_restriction(X0,sK17) )
| ~ spl21_2
| ~ spl21_3 ),
inference(duplicate_literal_removal,[],[f876]) ).
fof(f878,plain,
( sK17 = relation_rng_restriction(sK16,sK17)
| sK17 = relation_rng_restriction(sK16,sK17)
| ~ spl21_2
| ~ spl21_3 ),
inference(resolution,[],[f877,f416]) ).
fof(f879,plain,
( sK17 = relation_rng_restriction(sK16,sK17)
| ~ spl21_2
| ~ spl21_3 ),
inference(duplicate_literal_removal,[],[f878]) ).
fof(f898,plain,
! [X0] :
( in(sK0(X0,sK18,sK17),relation_dom(sK17))
| sK1(X0,sK18,sK17) = apply(sK18,sK0(X0,sK18,sK17))
| sK17 = relation_rng_restriction(X0,sK18) ),
inference(resolution,[],[f863,f323]) ).
fof(f900,plain,
! [X0] :
( sK1(X0,sK18,sK17) = apply(sK18,sK0(X0,sK18,sK17))
| sK17 = relation_rng_restriction(X0,sK18)
| sK1(X0,sK18,sK17) = apply(sK17,sK0(X0,sK18,sK17)) ),
inference(resolution,[],[f863,f275]) ).
fof(f1005,plain,
( ! [X0] :
( ~ in(sK1(X0,sK18,sK17),sK16)
| in(sK0(X0,sK18,sK17),relation_dom(sK17))
| ~ in(sK0(X0,sK18,sK17),relation_dom(sK18))
| sK17 = relation_rng_restriction(X0,sK18)
| sK1(X0,sK18,sK17) = apply(sK17,sK0(X0,sK18,sK17)) )
| ~ spl21_5 ),
inference(superposition,[],[f229,f900]) ).
fof(f1374,plain,
( ! [X0] :
( apply(sK18,sK0(X0,sK18,sK17)) = apply(sK17,sK0(X0,sK18,sK17))
| sK17 = relation_rng_restriction(X0,sK18)
| sK1(X0,sK18,sK17) = apply(sK18,sK0(X0,sK18,sK17)) )
| ~ spl21_2 ),
inference(resolution,[],[f898,f217]) ).
fof(f1384,plain,
( ! [X0] :
( sK1(X0,sK18,sK17) != apply(sK17,sK0(X0,sK18,sK17))
| sK17 = relation_rng_restriction(X0,sK18)
| sK1(X0,sK18,sK17) = apply(sK18,sK0(X0,sK18,sK17)) )
| ~ spl21_2 ),
inference(equality_factoring,[],[f1374]) ).
fof(f1386,plain,
( ! [X0] :
( sK1(X0,sK18,sK17) = apply(sK18,sK0(X0,sK18,sK17))
| sK17 = relation_rng_restriction(X0,sK18) )
| ~ spl21_2 ),
inference(forward_subsumption_resolution,[],[f1384,f900]) ).
fof(f1392,plain,
( ! [X0] :
( ~ in(sK1(X0,sK18,sK17),sK16)
| in(sK0(X0,sK18,sK17),relation_dom(sK17))
| ~ in(sK0(X0,sK18,sK17),relation_dom(sK18))
| sK17 = relation_rng_restriction(X0,sK18) )
| ~ spl21_2
| ~ spl21_5 ),
inference(superposition,[],[f229,f1386]) ).
fof(f1393,plain,
( ! [X0] :
( ~ in(sK0(X0,sK18,sK17),relation_dom(sK17))
| in(sK1(X0,sK18,sK17),sK16)
| sK17 = relation_rng_restriction(X0,sK18) )
| ~ spl21_2
| ~ spl21_3 ),
inference(superposition,[],[f221,f1386]) ).
fof(f1883,plain,
! [X0] :
( sK17 = relation_rng_restriction(X0,sK18)
| in(sK0(X0,sK18,sK17),relation_dom(sK18))
| in(sK0(X0,sK18,sK17),relation_dom(sK17)) ),
inference(resolution,[],[f861,f323]) ).
fof(f1885,plain,
! [X0] :
( in(sK0(X0,sK18,sK17),relation_dom(sK18))
| sK17 = relation_rng_restriction(X0,sK18)
| sK1(X0,sK18,sK17) = apply(sK17,sK0(X0,sK18,sK17)) ),
inference(resolution,[],[f861,f275]) ).
fof(f1886,plain,
( ! [X0] :
( in(sK0(X0,sK18,sK17),relation_dom(sK18))
| sK17 = relation_rng_restriction(X0,sK18) )
| ~ spl21_4 ),
inference(forward_subsumption_resolution,[],[f1883,f225]) ).
fof(f1989,plain,
! [X0,X1] :
( in(sK1(X0,sK18,X1),X0)
| in(unordered_pair(unordered_pair(sK0(X0,sK18,X1),sK1(X0,sK18,X1)),singleton(sK0(X0,sK18,X1))),X1)
| ~ relation(X1)
| relation_rng_restriction(X0,sK18) = X1 ),
inference(resolution,[],[f188,f172]) ).
fof(f1990,plain,
! [X0,X1] :
( ~ relation(X1)
| in(sK1(X0,sK18,X1),X0)
| in(unordered_pair(singleton(sK0(X0,sK18,X1)),unordered_pair(sK0(X0,sK18,X1),sK1(X0,sK18,X1))),X1)
| relation_rng_restriction(X0,sK18) = X1 ),
inference(forward_demodulation,[],[f1989,f107]) ).
fof(f1998,plain,
! [X0] :
( in(unordered_pair(singleton(sK0(X0,sK18,sK17)),unordered_pair(sK0(X0,sK18,sK17),sK1(X0,sK18,sK17))),sK17)
| in(sK1(X0,sK18,sK17),X0)
| sK17 = relation_rng_restriction(X0,sK18) ),
inference(resolution,[],[f1990,f170]) ).
fof(f2005,plain,
! [X0] :
( in(sK1(X0,sK18,sK17),X0)
| sK17 = relation_rng_restriction(X0,sK18)
| sK1(X0,sK18,sK17) = apply(sK17,sK0(X0,sK18,sK17)) ),
inference(resolution,[],[f1998,f275]) ).
fof(f2007,plain,
( sK17 = relation_rng_restriction(sK16,sK18)
| apply(sK17,sK0(sK16,sK18,sK17)) = sK1(sK16,sK18,sK17)
| in(sK0(sK16,sK18,sK17),relation_dom(sK17))
| ~ in(sK0(sK16,sK18,sK17),relation_dom(sK18))
| sK17 = relation_rng_restriction(sK16,sK18)
| apply(sK17,sK0(sK16,sK18,sK17)) = sK1(sK16,sK18,sK17)
| ~ spl21_5 ),
inference(resolution,[],[f2005,f1005]) ).
fof(f2018,plain,
( sK17 = relation_rng_restriction(sK16,sK18)
| apply(sK17,sK0(sK16,sK18,sK17)) = sK1(sK16,sK18,sK17)
| in(sK0(sK16,sK18,sK17),relation_dom(sK17))
| ~ in(sK0(sK16,sK18,sK17),relation_dom(sK18))
| ~ spl21_5 ),
inference(duplicate_literal_removal,[],[f2007]) ).
fof(f2020,plain,
( sK17 = relation_rng_restriction(sK16,sK18)
| apply(sK17,sK0(sK16,sK18,sK17)) = sK1(sK16,sK18,sK17)
| in(sK0(sK16,sK18,sK17),relation_dom(sK17))
| ~ spl21_5 ),
inference(forward_subsumption_resolution,[],[f2018,f1885]) ).
fof(f2022,plain,
( apply(sK17,sK0(sK16,sK18,sK17)) = sK1(sK16,sK18,sK17)
| in(sK0(sK16,sK18,sK17),relation_dom(sK17))
| spl21_1
| ~ spl21_5 ),
inference(forward_subsumption_resolution,[],[f2020,f231]) ).
fof(f2025,definition,
( spl21_76
<=> in(sK0(sK16,sK18,sK17),relation_dom(sK17)) ),
introduced(definition,[new_symbols(definition,[spl21_76])],[avatar_definition]) ).
fof(f2026,plain,
( in(sK0(sK16,sK18,sK17),relation_dom(sK17))
| ~ spl21_76 ),
inference(avatar_component_clause,[],[f2025]) ).
fof(f2028,definition,
( spl21_77
<=> apply(sK17,sK0(sK16,sK18,sK17)) = sK1(sK16,sK18,sK17) ),
introduced(definition,[new_symbols(definition,[spl21_77])],[avatar_definition]) ).
fof(f2029,plain,
( apply(sK17,sK0(sK16,sK18,sK17)) = sK1(sK16,sK18,sK17)
| ~ spl21_77 ),
inference(avatar_component_clause,[],[f2028]) ).
fof(f2030,plain,
( spl21_76
| spl21_77
| spl21_1
| ~ spl21_5 ),
inference(avatar_split_clause,[],[f2022,f228,f213,f2028,f2025]) ).
fof(f2032,plain,
( in(sK1(sK16,sK18,sK17),sK16)
| sK17 = relation_rng_restriction(sK16,sK18)
| ~ spl21_2
| ~ spl21_3
| ~ spl21_76 ),
inference(resolution,[],[f2026,f1393]) ).
fof(f2034,plain,
( in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(sK0(sK16,sK18,sK17),apply(sK18,sK0(sK16,sK18,sK17)))),sK18)
| ~ spl21_4
| ~ spl21_76 ),
inference(resolution,[],[f2026,f824]) ).
fof(f2036,plain,
( apply(sK17,sK0(sK16,sK18,sK17)) = apply(sK18,sK0(sK16,sK18,sK17))
| ~ spl21_2
| ~ spl21_76 ),
inference(resolution,[],[f2026,f217]) ).
fof(f2038,plain,
( in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(sK0(sK16,sK18,sK17),apply(sK17,sK0(sK16,sK18,sK17)))),sK17)
| ~ spl21_76 ),
inference(resolution,[],[f2026,f308]) ).
fof(f2039,plain,
( in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(sK0(sK16,sK18,sK17),apply(sK17,sK0(sK16,sK18,sK17)))),sK18)
| ~ spl21_2
| ~ spl21_4
| ~ spl21_76 ),
inference(forward_demodulation,[],[f2034,f2036]) ).
fof(f2040,plain,
( in(sK1(sK16,sK18,sK17),sK16)
| spl21_1
| ~ spl21_2
| ~ spl21_3
| ~ spl21_76 ),
inference(forward_subsumption_resolution,[],[f2032,f231]) ).
fof(f2044,plain,
( apply(sK17,sK0(sK16,sK18,sK17)) = sK1(sK16,sK18,sK17)
| sK17 = relation_rng_restriction(sK16,sK18)
| apply(sK17,sK0(sK16,sK18,sK17)) = sK1(sK16,sK18,sK17)
| ~ spl21_2
| ~ spl21_76 ),
inference(superposition,[],[f900,f2036]) ).
fof(f2050,plain,
( apply(sK17,sK0(sK16,sK18,sK17)) = sK1(sK16,sK18,sK17)
| sK17 = relation_rng_restriction(sK16,sK18)
| ~ spl21_2
| ~ spl21_76 ),
inference(duplicate_literal_removal,[],[f2044]) ).
fof(f2053,plain,
( apply(sK17,sK0(sK16,sK18,sK17)) = sK1(sK16,sK18,sK17)
| spl21_1
| ~ spl21_2
| ~ spl21_76 ),
inference(forward_subsumption_resolution,[],[f2050,f231]) ).
fof(f2057,plain,
( spl21_77
| spl21_1
| ~ spl21_2
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f2053,f2025,f216,f213,f2028]) ).
fof(f2059,plain,
( in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(sK0(sK16,sK18,sK17),sK1(sK16,sK18,sK17))),sK17)
| empty_set = sK1(sK16,sK18,sK17)
| ~ spl21_77 ),
inference(superposition,[],[f339,f2029]) ).
fof(f2062,definition,
( spl21_78
<=> empty_set = sK1(sK16,sK18,sK17) ),
introduced(definition,[new_symbols(definition,[spl21_78])],[avatar_definition]) ).
fof(f2063,plain,
( empty_set = sK1(sK16,sK18,sK17)
| ~ spl21_78 ),
inference(avatar_component_clause,[],[f2062]) ).
fof(f2065,definition,
( spl21_79
<=> in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(sK0(sK16,sK18,sK17),sK1(sK16,sK18,sK17))),sK17) ),
introduced(definition,[new_symbols(definition,[spl21_79])],[avatar_definition]) ).
fof(f2066,plain,
( in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(sK0(sK16,sK18,sK17),sK1(sK16,sK18,sK17))),sK17)
| ~ spl21_79 ),
inference(avatar_component_clause,[],[f2065]) ).
fof(f2067,plain,
( spl21_78
| spl21_79
| ~ spl21_77 ),
inference(avatar_split_clause,[],[f2059,f2028,f2065,f2062]) ).
fof(f2088,plain,
( in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(sK0(sK16,sK18,sK17),sK1(sK16,sK18,sK17))),sK18)
| ~ spl21_2
| ~ spl21_4
| ~ spl21_76
| ~ spl21_77 ),
inference(superposition,[],[f2039,f2029]) ).
fof(f2113,plain,
( in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(sK0(sK16,sK18,sK17),sK1(sK16,sK18,sK17))),sK17)
| ~ spl21_76
| ~ spl21_77 ),
inference(superposition,[],[f2038,f2029]) ).
fof(f2138,plain,
( ~ in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(sK0(sK16,sK18,sK17),sK1(sK16,sK18,sK17))),sK17)
| ~ in(sK1(sK16,sK18,sK17),sK16)
| ~ relation(sK17)
| sK17 = relation_rng_restriction(sK16,sK18)
| ~ spl21_2
| ~ spl21_4
| ~ spl21_76
| ~ spl21_77 ),
inference(resolution,[],[f2088,f373]) ).
fof(f2143,plain,
( ~ in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(sK0(sK16,sK18,sK17),sK1(sK16,sK18,sK17))),sK17)
| ~ relation(sK17)
| sK17 = relation_rng_restriction(sK16,sK18)
| ~ spl21_2
| ~ spl21_4
| ~ spl21_17
| ~ spl21_76
| ~ spl21_77 ),
inference(forward_subsumption_resolution,[],[f2138,f569]) ).
fof(f2144,plain,
( ~ relation(sK17)
| sK17 = relation_rng_restriction(sK16,sK18)
| ~ spl21_2
| ~ spl21_4
| ~ spl21_17
| ~ spl21_76
| ~ spl21_77
| ~ spl21_79 ),
inference(forward_subsumption_resolution,[],[f2143,f2066]) ).
fof(f2145,plain,
( sK17 = relation_rng_restriction(sK16,sK18)
| ~ spl21_2
| ~ spl21_4
| ~ spl21_17
| ~ spl21_76
| ~ spl21_77
| ~ spl21_79 ),
inference(forward_subsumption_resolution,[],[f2144,f170]) ).
fof(f2146,plain,
( $false
| spl21_1
| ~ spl21_2
| ~ spl21_4
| ~ spl21_17
| ~ spl21_76
| ~ spl21_77
| ~ spl21_79 ),
inference(forward_subsumption_resolution,[],[f2145,f231]) ).
fof(f2147,plain,
( spl21_1
| ~ spl21_2
| ~ spl21_4
| ~ spl21_17
| ~ spl21_76
| ~ spl21_77
| ~ spl21_79 ),
inference(avatar_contradiction_clause,[],[f2146]) ).
fof(f2148,plain,
( in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(sK0(sK16,sK18,sK17),empty_set)),sK17)
| ~ spl21_76
| ~ spl21_77
| ~ spl21_78 ),
inference(forward_demodulation,[],[f2113,f2063]) ).
fof(f2149,plain,
( spl21_17
| ~ spl21_2
| ~ spl21_3 ),
inference(avatar_split_clause,[],[f879,f220,f216,f465]) ).
fof(f2150,plain,
( ~ in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(sK0(sK16,sK18,sK17),sK1(sK16,sK18,sK17))),sK17)
| ~ relation(sK17)
| sK17 = relation_rng_restriction(sK16,sK18)
| spl21_1
| ~ spl21_2
| ~ spl21_3
| ~ spl21_4
| ~ spl21_76
| ~ spl21_77 ),
inference(forward_subsumption_resolution,[],[f2138,f2040]) ).
fof(f2151,plain,
( in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(empty_set,sK0(sK16,sK18,sK17))),sK17)
| ~ spl21_76
| ~ spl21_77
| ~ spl21_78 ),
inference(forward_demodulation,[],[f2148,f107]) ).
fof(f2152,plain,
( ~ in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(sK0(sK16,sK18,sK17),sK1(sK16,sK18,sK17))),sK17)
| sK17 = relation_rng_restriction(sK16,sK18)
| spl21_1
| ~ spl21_2
| ~ spl21_3
| ~ spl21_4
| ~ spl21_76
| ~ spl21_77 ),
inference(forward_subsumption_resolution,[],[f2150,f170]) ).
fof(f2153,plain,
( ~ in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(sK0(sK16,sK18,sK17),sK1(sK16,sK18,sK17))),sK17)
| spl21_1
| ~ spl21_2
| ~ spl21_3
| ~ spl21_4
| ~ spl21_76
| ~ spl21_77 ),
inference(forward_subsumption_resolution,[],[f2152,f231]) ).
fof(f2154,plain,
( ~ in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(sK0(sK16,sK18,sK17),empty_set)),sK17)
| spl21_1
| ~ spl21_2
| ~ spl21_3
| ~ spl21_4
| ~ spl21_76
| ~ spl21_77
| ~ spl21_78 ),
inference(forward_demodulation,[],[f2153,f2063]) ).
fof(f2155,plain,
( ~ in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(empty_set,sK0(sK16,sK18,sK17))),sK17)
| spl21_1
| ~ spl21_2
| ~ spl21_3
| ~ spl21_4
| ~ spl21_76
| ~ spl21_77
| ~ spl21_78 ),
inference(forward_demodulation,[],[f2154,f107]) ).
fof(f2156,plain,
( $false
| spl21_1
| ~ spl21_2
| ~ spl21_3
| ~ spl21_4
| ~ spl21_76
| ~ spl21_77
| ~ spl21_78 ),
inference(forward_subsumption_resolution,[],[f2155,f2151]) ).
fof(f2157,plain,
( spl21_1
| ~ spl21_2
| ~ spl21_3
| ~ spl21_4
| ~ spl21_76
| ~ spl21_77
| ~ spl21_78 ),
inference(avatar_contradiction_clause,[],[f2156]) ).
fof(f2176,plain,
( in(sK0(sK16,sK18,sK17),relation_dom(sK17))
| ~ spl21_79 ),
inference(resolution,[],[f2066,f323]) ).
fof(f2180,plain,
( spl21_76
| ~ spl21_79 ),
inference(avatar_split_clause,[],[f2176,f2065,f2025]) ).
fof(f2188,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK17)
| in(X1,sK16) )
| ~ spl21_17 ),
inference(superposition,[],[f293,f466]) ).
fof(f2210,plain,
( ~ in(empty_set,sK16)
| in(sK0(sK16,sK18,sK17),relation_dom(sK17))
| ~ in(sK0(sK16,sK18,sK17),relation_dom(sK18))
| sK17 = relation_rng_restriction(sK16,sK18)
| ~ spl21_2
| ~ spl21_5
| ~ spl21_78 ),
inference(superposition,[],[f1392,f2063]) ).
fof(f2212,plain,
( in(unordered_pair(singleton(sK0(sK16,sK18,sK17)),unordered_pair(sK0(sK16,sK18,sK17),empty_set)),sK17)
| in(empty_set,sK16)
| sK17 = relation_rng_restriction(sK16,sK18)
| ~ spl21_78 ),
inference(superposition,[],[f1998,f2063]) ).
fof(f2217,plain,
( in(empty_set,sK16)
| sK17 = relation_rng_restriction(sK16,sK18)
| ~ spl21_17
| ~ spl21_78 ),
inference(forward_subsumption_resolution,[],[f2212,f2188]) ).
fof(f2245,plain,
( ~ in(empty_set,sK16)
| in(sK0(sK16,sK18,sK17),relation_dom(sK17))
| sK17 = relation_rng_restriction(sK16,sK18)
| ~ spl21_2
| ~ spl21_4
| ~ spl21_5
| ~ spl21_78 ),
inference(forward_subsumption_resolution,[],[f2210,f1886]) ).
fof(f2247,plain,
( in(empty_set,sK16)
| spl21_1
| ~ spl21_17
| ~ spl21_78 ),
inference(forward_subsumption_resolution,[],[f2217,f231]) ).
fof(f2250,plain,
( ~ in(empty_set,sK16)
| in(sK0(sK16,sK18,sK17),relation_dom(sK17))
| spl21_1
| ~ spl21_2
| ~ spl21_4
| ~ spl21_5
| ~ spl21_78 ),
inference(forward_subsumption_resolution,[],[f2245,f231]) ).
fof(f2251,plain,
( in(sK0(sK16,sK18,sK17),relation_dom(sK17))
| spl21_1
| ~ spl21_2
| ~ spl21_4
| ~ spl21_5
| ~ spl21_17
| ~ spl21_78 ),
inference(forward_subsumption_resolution,[],[f2250,f2247]) ).
fof(f2252,plain,
( spl21_76
| spl21_1
| ~ spl21_2
| ~ spl21_4
| ~ spl21_5
| ~ spl21_17
| ~ spl21_78 ),
inference(avatar_split_clause,[],[f2251,f2062,f465,f228,f224,f216,f213,f2025]) ).
cnf(s1,plain,
( spl21_1
| spl21_2 ),
inference(sat_conversion,[],[f218]) ).
cnf(s2,plain,
( spl21_1
| spl21_3 ),
inference(sat_conversion,[],[f222]) ).
cnf(s3,plain,
( spl21_1
| spl21_4 ),
inference(sat_conversion,[],[f226]) ).
cnf(s4,plain,
( spl21_1
| spl21_5 ),
inference(sat_conversion,[],[f230]) ).
cnf(s5,plain,
( ~ spl21_1
| spl21_6
| spl21_7
| spl21_8 ),
inference(sat_conversion,[],[f241]) ).
cnf(s6,plain,
( ~ spl21_1
| spl21_7
| spl21_8
| ~ spl21_9 ),
inference(sat_conversion,[],[f245]) ).
cnf(s7,plain,
( ~ spl21_1
| spl21_6
| spl21_7
| spl21_10 ),
inference(sat_conversion,[],[f249]) ).
cnf(s8,plain,
( ~ spl21_1
| spl21_7
| ~ spl21_9
| spl21_10 ),
inference(sat_conversion,[],[f250]) ).
cnf(s9,plain,
( ~ spl21_1
| spl21_6
| ~ spl21_7
| ~ spl21_8
| ~ spl21_10 ),
inference(sat_conversion,[],[f254]) ).
cnf(s10,plain,
( ~ spl21_1
| ~ spl21_7
| ~ spl21_8
| ~ spl21_9
| ~ spl21_10 ),
inference(sat_conversion,[],[f255]) ).
cnf(s17,plain,
( ~ spl21_1
| ~ spl21_6
| spl21_9 ),
inference(sat_conversion,[],[f511]) ).
cnf(s21,plain,
( ~ spl21_1
| ~ spl21_7
| spl21_10 ),
inference(sat_conversion,[],[f546]) ).
cnf(s31,plain,
( ~ spl21_1
| spl21_7
| ~ spl21_8
| ~ spl21_10 ),
inference(sat_conversion,[],[f787]) ).
cnf(s34,plain,
( ~ spl21_1
| ~ spl21_7
| spl21_8 ),
inference(sat_conversion,[],[f820]) ).
cnf(s105,plain,
( spl21_1
| ~ spl21_5
| spl21_76
| spl21_77 ),
inference(sat_conversion,[],[f2030]) ).
cnf(s107,plain,
( spl21_1
| ~ spl21_2
| ~ spl21_76
| spl21_77 ),
inference(sat_conversion,[],[f2057]) ).
cnf(s111,plain,
( ~ spl21_77
| spl21_78
| spl21_79 ),
inference(sat_conversion,[],[f2067]) ).
cnf(s115,plain,
( spl21_1
| ~ spl21_2
| ~ spl21_4
| ~ spl21_17
| ~ spl21_76
| ~ spl21_77
| ~ spl21_79 ),
inference(sat_conversion,[],[f2147]) ).
cnf(s116,plain,
( ~ spl21_2
| ~ spl21_3
| spl21_17 ),
inference(sat_conversion,[],[f2149]) ).
cnf(s117,plain,
( spl21_1
| ~ spl21_2
| ~ spl21_3
| ~ spl21_4
| ~ spl21_76
| ~ spl21_77
| ~ spl21_78 ),
inference(sat_conversion,[],[f2157]) ).
cnf(s120,plain,
( spl21_76
| ~ spl21_79 ),
inference(sat_conversion,[],[f2180]) ).
cnf(s124,plain,
( spl21_1
| ~ spl21_2
| ~ spl21_4
| ~ spl21_5
| ~ spl21_17
| spl21_76
| ~ spl21_78 ),
inference(sat_conversion,[],[f2252]) ).
cnf(s125,plain,
( spl21_76
| spl21_1 ),
inference(rat,[],[s111,s105,s124,s120,s4,s3,s116,s1,s2]) ).
cnf(s126,plain,
spl21_1,
inference(rat,[],[s111,s115,s117,s107,s125,s116,s1,s2,s3]) ).
cnf(s132,plain,
( spl21_8
| spl21_7 ),
inference(rat,[],[s17,s5,s6,s126]) ).
cnf(s133,plain,
( spl21_10
| spl21_7 ),
inference(rat,[],[s17,s8,s7,s126]) ).
cnf(s134,plain,
( ~ spl21_8
| spl21_7 ),
inference(rat,[],[s133,s31,s126]) ).
cnf(s135,plain,
spl21_7,
inference(rat,[],[s134,s132]) ).
cnf(s136,plain,
spl21_8,
inference(rat,[],[s34,s126,s135]) ).
cnf(s137,plain,
spl21_10,
inference(rat,[],[s21,s126,s135]) ).
cnf(s138,plain,
~ spl21_9,
inference(rat,[],[s10,s137,s135,s126,s136]) ).
cnf(s139,plain,
spl21_6,
inference(rat,[],[s9,s137,s135,s126,s136]) ).
cnf(s140,plain,
$false,
inference(rat,[],[s17,s126,s138,s139]) ).
fof(f2253,plain,
$false,
inference(avatar_sat_refutation,[],[s140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU043+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n016.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 03:32:27 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.85/2.20 % (3232673)Detected formulas, will run a generic FOF schedule.
% 6.85/2.20 % (3232678)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=3219370278:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.85/2.20 % (3232684)dis-21_1_sil=8000:lcm=predicate:random_seed=548532242: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)
% 6.85/2.20 % (3232680)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=1568273223:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.85/2.20 % (3232682)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3028376646:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.85/2.20 % (3232681)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=109136055:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.85/2.20 % (3232679)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=335653896:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.85/2.20 % (3232683)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2185324033:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.85/2.20 % (3232681)Refutation not found, incomplete strategy
% 6.85/2.20 % (3232681)------------------------------
% 6.85/2.20 % (3232681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/2.20 % (3232681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/2.20 % (3232681)CaDiCaL version: 2.1.3
% 6.85/2.20 % (3232681)Termination reason: Refutation not found, incomplete strategy
% 6.85/2.20 % (3232681)Time elapsed: 0.004 s
% 6.85/2.20 % (3232681)Peak memory usage: 88 MB
% 6.85/2.20 % (3232681)Instructions burned: 4 (million)
% 6.85/2.20 % (3232684)Instruction limit reached!
% 6.85/2.20 % (3232684)------------------------------
% 6.85/2.20 % (3232684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/2.20 % (3232684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/2.20 % (3232684)CaDiCaL version: 2.1.3
% 6.85/2.20 % (3232684)Termination reason: Instruction limit
% 6.85/2.20 % (3232684)Termination phase: Saturation
% 6.85/2.20 % (3232684)Time elapsed: 0.071 s
% 6.85/2.20 % (3232684)Peak memory usage: 89 MB
% 6.85/2.20 % (3232684)Instructions burned: 130 (million)
% 6.85/2.20 % (3232682)Instruction limit reached!
% 6.85/2.20 % (3232682)------------------------------
% 6.85/2.20 % (3232682)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/2.20 % (3232682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/2.20 % (3232682)CaDiCaL version: 2.1.3
% 6.85/2.20 % (3232682)Termination reason: Instruction limit
% 6.85/2.20 % (3232682)Termination phase: Saturation
% 6.85/2.20 % (3232682)Time elapsed: 0.070 s
% 6.85/2.20 % (3232682)Peak memory usage: 88 MB
% 6.85/2.20 % (3232682)Instructions burned: 120 (million)
% 6.85/2.20 % (3232683)Instruction limit reached!
% 6.85/2.20 % (3232683)------------------------------
% 6.85/2.20 % (3232683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/2.20 % (3232683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/2.20 % (3232683)CaDiCaL version: 2.1.3
% 6.85/2.20 % (3232683)Termination reason: Instruction limit
% 6.85/2.20 % (3232683)Termination phase: Saturation
% 6.85/2.20 % (3232683)Time elapsed: 0.096 s
% 6.85/2.20 % (3232683)Peak memory usage: 90 MB
% 6.85/2.20 % (3232683)Instructions burned: 140 (million)
% 6.85/2.20 % (3232692)lrs+10_1_sil=8000:sp=occurrence:random_seed=3317407923:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.85/2.20 % (3232693)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1904926512:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.85/2.20 % (3232694)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3468367873:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.85/2.20 % (3232681)------------------------------
% 6.85/2.20 % (3232681)------------------------------
% 6.85/2.20 % (3232693)Instruction limit reached!
% 6.85/2.20 % (3232693)------------------------------
% 6.85/2.20 % (3232693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/2.20 % (3232693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/2.20 % (3232693)CaDiCaL version: 2.1.3
% 6.85/2.20 % (3232693)Termination reason: Instruction limit
% 6.85/2.20 % (3232693)Termination phase: Saturation
% 6.85/2.20 % (3232693)Time elapsed: 0.079 s
% 6.85/2.20 % (3232693)Peak memory usage: 89 MB
% 6.85/2.20 % (3232693)Instructions burned: 159 (million)
% 6.85/2.20 % (3232692)Instruction limit reached!
% 6.85/2.20 % (3232692)------------------------------
% 6.85/2.20 % (3232692)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/2.20 % (3232692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/2.20 % (3232692)CaDiCaL version: 2.1.3
% 6.85/2.20 % (3232692)Termination reason: Instruction limit
% 6.85/2.20 % (3232692)Termination phase: Saturation
% 6.85/2.20 % (3232692)Time elapsed: 0.182 s
% 6.85/2.20 % (3232692)Peak memory usage: 91 MB
% 6.85/2.20 % (3232692)Instructions burned: 285 (million)
% 6.85/2.20 % (3232698)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=1287319223:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 6.85/2.20 % (3232699)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1684413319:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.85/2.20 % (3232694)Instruction limit reached!
% 6.85/2.20 % (3232694)------------------------------
% 6.85/2.20 % (3232694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/2.20 % (3232694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/2.20 % (3232694)CaDiCaL version: 2.1.3
% 6.85/2.20 % (3232694)Termination reason: Instruction limit
% 6.85/2.20 % (3232694)Termination phase: Saturation
% 6.85/2.20 % (3232694)Time elapsed: 0.213 s
% 6.85/2.20 % (3232694)Peak memory usage: 91 MB
% 6.85/2.20 % (3232694)Instructions burned: 326 (million)
% 6.85/2.20 % (3232700)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2184108187:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.85/2.20 % (3232698)Instruction limit reached!
% 6.85/2.20 % (3232698)------------------------------
% 6.85/2.20 % (3232698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/2.20 % (3232698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/2.20 % (3232698)CaDiCaL version: 2.1.3
% 6.85/2.20 % (3232698)Termination reason: Instruction limit
% 6.85/2.20 % (3232698)Termination phase: Saturation
% 6.85/2.20 % (3232698)Time elapsed: 0.135 s
% 6.85/2.20 % (3232698)Peak memory usage: 92 MB
% 6.85/2.20 % (3232698)Instructions burned: 249 (million)
% 6.85/2.20 % (3232703)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2933147930:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.85/2.20 % (3232699)Instruction limit reached!
% 6.85/2.20 % (3232699)------------------------------
% 6.85/2.20 % (3232699)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/2.20 % (3232699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/2.20 % (3232699)CaDiCaL version: 2.1.3
% 6.85/2.20 % (3232699)Termination reason: Instruction limit
% 6.85/2.20 % (3232699)Termination phase: Saturation
% 6.85/2.20 % (3232699)Time elapsed: 0.179 s
% 6.85/2.20 % (3232699)Peak memory usage: 89 MB
% 6.85/2.21 % (3232699)Instructions burned: 294 (million)
% 6.85/2.21 % (3232705)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3707703454:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.85/2.21 % (3232703)Instruction limit reached!
% 6.85/2.21 % (3232703)------------------------------
% 6.85/2.21 % (3232703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/2.21 % (3232703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/2.21 % (3232703)CaDiCaL version: 2.1.3
% 6.85/2.21 % (3232703)Termination reason: Instruction limit
% 6.85/2.21 % (3232703)Termination phase: Saturation
% 6.85/2.21 % (3232703)Time elapsed: 0.078 s
% 6.85/2.21 % (3232703)Peak memory usage: 90 MB
% 6.85/2.21 % (3232703)Instructions burned: 113 (million)
% 6.85/2.21 % (3232705)Instruction limit reached!
% 6.85/2.21 % (3232705)------------------------------
% 6.85/2.21 % (3232705)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/2.21 % (3232705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/2.21 % (3232705)CaDiCaL version: 2.1.3
% 6.85/2.21 % (3232705)Termination reason: Instruction limit
% 6.85/2.21 % (3232705)Termination phase: Saturation
% 6.85/2.21 % (3232705)Time elapsed: 0.067 s
% 6.85/2.21 % (3232705)Peak memory usage: 89 MB
% 6.85/2.21 % (3232705)Instructions burned: 127 (million)
% 6.85/2.21 % (3232707)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1383231734:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.85/2.21 % (3232709)lrs+10_1_sil=8000:sp=occurrence:random_seed=4092096131:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.85/2.21 % (3232707)Instruction limit reached!
% 6.85/2.21 % (3232707)------------------------------
% 6.85/2.21 % (3232707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/2.21 % (3232707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/2.21 % (3232707)CaDiCaL version: 2.1.3
% 6.85/2.21 % (3232707)Termination reason: Instruction limit
% 6.85/2.21 % (3232707)Termination phase: Saturation
% 6.85/2.21 % (3232707)Time elapsed: 0.073 s
% 6.85/2.21 % (3232707)Peak memory usage: 89 MB
% 6.85/2.21 % (3232707)Instructions burned: 114 (million)
% 6.85/2.21 % (3232710)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3323468285:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.85/2.21 % (3232710)Refutation not found, incomplete strategy
% 6.85/2.21 % (3232710)------------------------------
% 6.85/2.21 % (3232710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.85/2.21 % (3232710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.85/2.21 % (3232710)CaDiCaL version: 2.1.3
% 6.85/2.21 % (3232710)Termination reason: Refutation not found, incomplete strategy
% 6.85/2.21 % (3232710)Time elapsed: 0.003 s
% 6.85/2.21 % (3232710)Peak memory usage: 88 MB
% 6.85/2.21 % (3232710)Instructions burned: 4 (million)
% 6.85/2.21 % (3232679)First to succeed.
% 6.85/2.21 % (3232679)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3232673"
% 6.85/2.21 % (3232713)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2547630567:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 6.85/2.21 % (3232680)Also succeeded, but the first one will report.
% 6.85/2.21 % (3232710)------------------------------
% 6.85/2.21 % (3232710)------------------------------
% 6.85/2.21 % (3232679)Refutation found. Thanks to Tanya!
% 6.85/2.21 % SZS status Theorem for theBenchmark
% 6.85/2.21 % SZS output start Proof for theBenchmark
% See solution above
% 10.11/2.40 % (3232679)------------------------------
% 10.11/2.40 % (3232679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.40 % (3232679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.40 % (3232679)CaDiCaL version: 2.1.3
% 10.11/2.40 % (3232679)Termination reason: Refutation
% 10.11/2.40 % (3232679)Time elapsed: 0.932 s
% 10.11/2.40 % (3232679)Peak memory usage: 133 MB
% 10.11/2.40 % (3232679)Instructions burned: 1350 (million)
% 10.11/2.40 % (3232679)------------------------------
% 10.11/2.40 % (3232679)------------------------------
% 10.11/2.40 % (3232673)Success in time 1.339 s
% 10.11/2.40 % Vampire exiting
%------------------------------------------------------------------------------