%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU202+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:47:42 PM UTC 2026
% Result : Theorem 3.28s 1.32s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 158 ( 18 unt; 10 def)
% Number of atoms : 574 ( 46 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 736 ( 320 ~; 344 |; 46 &)
% ( 18 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 305 ( 0 sgn 290 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation(X2)
=> ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f5,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,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f12,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f25,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_relat_1) ).
fof(f26,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f34,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) ) ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f35,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,[],[f5]) ).
fof(f37,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f38,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f39,plain,
? [X0,X1,X2] :
( relation_dom_restriction(relation_rng_restriction(X0,X2),X1) != relation_rng_restriction(X0,relation_dom_restriction(X2,X1))
& relation(X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f46,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = relation_dom_restriction(X0,X1)
| ? [X3,X4] :
( ( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X0) )
& ( ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f34]) ).
fof(f47,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = relation_dom_restriction(X0,X1)
| ? [X3,X4] :
( ( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X0) )
& ( ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = relation_dom_restriction(X0,X1)
| ? [X3,X4] :
( ( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0) )
& ( ( in(X5,X1)
& in(ordered_pair(X5,X6),X0) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(rectify,[],[f47]) ).
fof(f49,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = relation_dom_restriction(X0,X1)
| ( ( ~ in(sK0(X0,X1,X2),X1)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2) )
& ( ( in(sK0(X0,X1,X2),X1)
& in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0) )
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0) )
& ( ( in(X5,X1)
& in(ordered_pair(X5,X6),X0) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X4,sK1(X0,X1,X2))],[f48]) ).
fof(f50,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,[],[f35]) ).
fof(f51,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,[],[f50]) ).
fof(f52,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,[],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = relation_rng_restriction(X0,X1)
| ( ( ~ in(sK3(X0,X1,X2),X0)
| ~ in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X2) )
& ( ( in(sK3(X0,X1,X2),X0)
& in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X1) )
| in(ordered_pair(sK2(X0,X1,X2),sK3(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,[sK2,sK3]),skolemize(X3,sK2(X0,X1,X2)),skolemize(X4,sK3(X0,X1,X2))],[f52]) ).
fof(f62,plain,
( relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12) != relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f39]) ).
fof(f66,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X5,X6),X2)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f67,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X2)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f68,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f72,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,[],[f53]) ).
fof(f73,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,[],[f53]) ).
fof(f74,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,[],[f53]) ).
fof(f75,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X1) = X2
| in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X1)
| in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f76,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X1) = X2
| in(sK3(X0,X1,X2),X0)
| in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f77,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X1) = X2
| ~ in(sK3(X0,X1,X2),X0)
| ~ in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f82,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f83,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f84,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f98,plain,
relation(sK13),
inference(cnf_transformation,[],[f62]) ).
fof(f99,plain,
relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12) != relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)),
inference(cnf_transformation,[],[f62]) ).
fof(f108,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| ~ in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f68,f82,f82]) ).
fof(f109,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f67,f82]) ).
fof(f110,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f66,f82,f82]) ).
fof(f111,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X1) = X2
| ~ in(sK3(X0,X1,X2),X0)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),singleton(sK2(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),singleton(sK2(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f77,f82,f82]) ).
fof(f112,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X1) = X2
| in(sK3(X0,X1,X2),X0)
| in(unordered_pair(unordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),singleton(sK2(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f76,f82]) ).
fof(f113,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X1) = X2
| in(unordered_pair(unordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),singleton(sK2(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),singleton(sK2(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f75,f82,f82]) ).
fof(f114,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,[],[f74,f82,f82]) ).
fof(f115,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,[],[f73,f82]) ).
fof(f116,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,[],[f72,f82,f82]) ).
fof(f122,plain,
! [X0,X1,X6,X5] :
( ~ relation(relation_dom_restriction(X0,X1))
| ~ in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f108]) ).
fof(f123,plain,
! [X0,X1,X6,X5] :
( ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_dom_restriction(X0,X1))
| in(X5,X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f109]) ).
fof(f124,plain,
! [X0,X1,X6,X5] :
( ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_dom_restriction(X0,X1))
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f110]) ).
fof(f125,plain,
! [X0,X1,X6,X5] :
( ~ relation(relation_rng_restriction(X0,X1))
| ~ in(X6,X0)
| ~ 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(equality_resolution,[],[f114]) ).
fof(f126,plain,
! [X0,X1,X6,X5] :
( ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_rng_restriction(X0,X1))
| in(X6,X0)
| ~ relation(X1) ),
inference(equality_resolution,[],[f115]) ).
fof(f127,plain,
! [X0,X1,X6,X5] :
( ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_rng_restriction(X0,X1))
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f116]) ).
fof(f130,definition,
! [X0,X1] :
( sQ14_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ14_eqProxy])],[equality_proxy_definition]) ).
fof(f135,plain,
! [X2,X0,X1] :
( sQ14_eqProxy(relation_rng_restriction(X0,X1),X2)
| ~ in(sK3(X0,X1,X2),X0)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),singleton(sK2(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),singleton(sK2(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(equality_proxy_replacement,[],[f111,f130]) ).
fof(f136,plain,
! [X2,X0,X1] :
( sQ14_eqProxy(relation_rng_restriction(X0,X1),X2)
| in(sK3(X0,X1,X2),X0)
| in(unordered_pair(unordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),singleton(sK2(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(equality_proxy_replacement,[],[f112,f130]) ).
fof(f137,plain,
! [X2,X0,X1] :
( sQ14_eqProxy(relation_rng_restriction(X0,X1),X2)
| in(unordered_pair(unordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),singleton(sK2(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),singleton(sK2(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(equality_proxy_replacement,[],[f113,f130]) ).
fof(f140,plain,
~ sQ14_eqProxy(relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12),relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),
inference(equality_proxy_replacement,[],[f99,f130]) ).
fof(f144,plain,
! [X0,X1] :
( sQ14_eqProxy(X1,X0)
| ~ sQ14_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f130]) ).
fof(f154,plain,
~ sQ14_eqProxy(relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),
inference(resolution,[],[f144,f140]) ).
fof(f168,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(X2,X3))
| in(X0,X3)
| ~ relation(X2)
| ~ relation(X2) ),
inference(resolution,[],[f123,f83]) ).
fof(f169,plain,
! [X2,X3,X0,X1] :
( ~ relation(X2)
| in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(X2,X3)) ),
inference(duplicate_literal_removal,[],[f168]) ).
fof(f179,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,X3))
| in(X1,X2)
| ~ relation(X3)
| ~ relation(X3) ),
inference(resolution,[],[f126,f84]) ).
fof(f180,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,X3)) ),
inference(duplicate_literal_removal,[],[f179]) ).
fof(f183,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(X2,X3))
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2)
| ~ relation(X2) ),
inference(resolution,[],[f124,f83]) ).
fof(f184,plain,
! [X2,X3,X0,X1] :
( ~ relation(X2)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(X2,X3)) ),
inference(duplicate_literal_removal,[],[f183]) ).
fof(f187,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,X3))
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X3)
| ~ relation(X3)
| ~ relation(X3) ),
inference(resolution,[],[f127,f84]) ).
fof(f188,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,X3)) ),
inference(duplicate_literal_removal,[],[f187]) ).
fof(f189,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,X1)
| ~ in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),X3)
| in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),relation_dom_restriction(X3,X1))
| ~ relation(X3)
| ~ relation(X3) ),
inference(resolution,[],[f122,f83]) ).
fof(f190,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),X3)
| in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),relation_dom_restriction(X3,X1))
| ~ in(X0,X1) ),
inference(duplicate_literal_removal,[],[f189]) ).
fof(f191,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,X1)
| ~ in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X3)
| in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),relation_rng_restriction(X1,X3))
| ~ relation(X3)
| ~ relation(X3) ),
inference(resolution,[],[f125,f84]) ).
fof(f192,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X3)
| in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),relation_rng_restriction(X1,X3))
| ~ in(X0,X1) ),
inference(duplicate_literal_removal,[],[f191]) ).
fof(f195,definition,
( spl15_3
<=> relation(relation_rng_restriction(sK11,sK13)) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f196,plain,
( ~ relation(relation_rng_restriction(sK11,sK13))
| spl15_3 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f207,plain,
( ~ relation(sK13)
| spl15_3 ),
inference(resolution,[],[f196,f84]) ).
fof(f208,plain,
( $false
| spl15_3 ),
inference(resolution,[],[f207,f98]) ).
fof(f209,plain,
spl15_3,
inference(avatar_contradiction_clause,[],[f208]) ).
fof(f216,plain,
( in(sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK11)
| in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))
| ~ relation(relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))
| ~ relation(relation_dom_restriction(sK13,sK12)) ),
inference(resolution,[],[f136,f154]) ).
fof(f218,definition,
( spl15_7
<=> relation(relation_dom_restriction(sK13,sK12)) ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
fof(f219,plain,
( ~ relation(relation_dom_restriction(sK13,sK12))
| spl15_7 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f221,definition,
( spl15_8
<=> relation(relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)) ),
introduced(definition,[new_symbols(definition,[spl15_8])],[avatar_definition]) ).
fof(f222,plain,
( ~ relation(relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))
| spl15_8 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f224,definition,
( spl15_9
<=> in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)) ),
introduced(definition,[new_symbols(definition,[spl15_9])],[avatar_definition]) ).
fof(f225,plain,
( in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))
| ~ spl15_9 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f227,definition,
( spl15_10
<=> in(sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK11) ),
introduced(definition,[new_symbols(definition,[spl15_10])],[avatar_definition]) ).
fof(f229,plain,
( ~ spl15_7
| ~ spl15_8
| spl15_9
| spl15_10 ),
inference(avatar_split_clause,[],[f216,f227,f224,f221,f218]) ).
fof(f230,plain,
( ~ relation(sK13)
| spl15_7 ),
inference(resolution,[],[f219,f83]) ).
fof(f231,plain,
( $false
| spl15_7 ),
inference(resolution,[],[f230,f98]) ).
fof(f232,plain,
spl15_7,
inference(avatar_contradiction_clause,[],[f231]) ).
fof(f233,plain,
( ~ relation(relation_rng_restriction(sK11,sK13))
| spl15_8 ),
inference(resolution,[],[f222,f83]) ).
fof(f234,plain,
( ~ spl15_3
| spl15_8 ),
inference(avatar_split_clause,[],[f233,f221,f195]) ).
fof(f274,plain,
( in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),relation_dom_restriction(sK13,sK12))
| in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))
| ~ relation(relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))
| ~ relation(relation_dom_restriction(sK13,sK12)) ),
inference(resolution,[],[f137,f154]) ).
fof(f296,plain,
( ~ in(sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK11)
| ~ in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),relation_dom_restriction(sK13,sK12))
| ~ in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))
| ~ relation(relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))
| ~ relation(relation_dom_restriction(sK13,sK12)) ),
inference(resolution,[],[f135,f154]) ).
fof(f297,plain,
( ~ in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))
| spl15_9 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f299,definition,
( spl15_16
<=> in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),relation_dom_restriction(sK13,sK12)) ),
introduced(definition,[new_symbols(definition,[spl15_16])],[avatar_definition]) ).
fof(f300,plain,
( ~ in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),relation_dom_restriction(sK13,sK12))
| spl15_16 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f302,plain,
( ~ spl15_7
| ~ spl15_8
| ~ spl15_9
| ~ spl15_16
| ~ spl15_10 ),
inference(avatar_split_clause,[],[f296,f227,f299,f224,f221,f218]) ).
fof(f305,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),relation_dom_restriction(relation_rng_restriction(X3,X4),X1))
| in(X0,X1) ),
inference(resolution,[],[f169,f84]) ).
fof(f310,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),relation_dom_restriction(sK13,X1))
| in(X0,X1) ),
inference(resolution,[],[f169,f98]) ).
fof(f318,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),relation_rng_restriction(X1,sK13))
| in(X0,X1) ),
inference(resolution,[],[f180,f98]) ).
fof(f321,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(relation_rng_restriction(X2,X3),X4))
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,X3)) ),
inference(resolution,[],[f184,f84]) ).
fof(f326,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(sK13,X2))
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK13) ),
inference(resolution,[],[f184,f98]) ).
fof(f334,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,sK13))
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK13) ),
inference(resolution,[],[f188,f98]) ).
fof(f337,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X3)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(relation_rng_restriction(X2,X3),X4))
| ~ in(X0,X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,X3)) ),
inference(resolution,[],[f190,f84]) ).
fof(f342,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(sK13,X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK13)
| ~ in(X0,X2) ),
inference(resolution,[],[f190,f98]) ).
fof(f355,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,sK13))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK13)
| ~ in(X1,X2) ),
inference(resolution,[],[f192,f98]) ).
fof(f393,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(relation_rng_restriction(X2,sK13),X3))
| in(X0,X3) ),
inference(resolution,[],[f305,f98]) ).
fof(f394,plain,
( in(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK12)
| ~ spl15_9 ),
inference(resolution,[],[f393,f225]) ).
fof(f493,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(relation_rng_restriction(X2,sK13),X3))
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,sK13)) ),
inference(resolution,[],[f321,f98]) ).
fof(f494,plain,
( in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),relation_rng_restriction(sK11,sK13))
| ~ spl15_9 ),
inference(resolution,[],[f493,f225]) ).
fof(f496,plain,
( in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),sK13)
| ~ spl15_9 ),
inference(resolution,[],[f494,f334]) ).
fof(f497,plain,
( in(sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK11)
| ~ spl15_9 ),
inference(resolution,[],[f494,f318]) ).
fof(f501,plain,
( spl15_10
| ~ spl15_9 ),
inference(avatar_split_clause,[],[f497,f224,f227]) ).
fof(f505,plain,
( ~ in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),sK13)
| ~ in(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK12)
| spl15_16 ),
inference(resolution,[],[f300,f342]) ).
fof(f507,definition,
( spl15_17
<=> in(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK12) ),
introduced(definition,[new_symbols(definition,[spl15_17])],[avatar_definition]) ).
fof(f508,plain,
( ~ in(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK12)
| spl15_17 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f510,definition,
( spl15_18
<=> in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),sK13) ),
introduced(definition,[new_symbols(definition,[spl15_18])],[avatar_definition]) ).
fof(f511,plain,
( ~ in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),sK13)
| spl15_18 ),
inference(avatar_component_clause,[],[f510]) ).
fof(f512,plain,
( ~ spl15_17
| ~ spl15_18
| spl15_16 ),
inference(avatar_split_clause,[],[f505,f299,f510,f507]) ).
fof(f513,plain,
( $false
| ~ spl15_9
| spl15_17 ),
inference(resolution,[],[f508,f394]) ).
fof(f514,plain,
( ~ spl15_9
| spl15_17 ),
inference(avatar_contradiction_clause,[],[f513]) ).
fof(f515,plain,
( $false
| ~ spl15_9
| spl15_18 ),
inference(resolution,[],[f496,f511]) ).
fof(f521,plain,
( ~ spl15_9
| spl15_18 ),
inference(avatar_contradiction_clause,[],[f515]) ).
fof(f522,plain,
( in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),relation_dom_restriction(sK13,sK12))
| ~ spl15_16 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f523,plain,
( ~ spl15_7
| ~ spl15_8
| spl15_9
| spl15_16 ),
inference(avatar_split_clause,[],[f274,f299,f224,f221,f218]) ).
fof(f524,plain,
( in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),sK13)
| ~ spl15_16 ),
inference(resolution,[],[f522,f326]) ).
fof(f525,plain,
( in(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK12)
| ~ spl15_16 ),
inference(resolution,[],[f522,f310]) ).
fof(f532,plain,
( $false
| ~ spl15_16
| spl15_18 ),
inference(resolution,[],[f524,f511]) ).
fof(f538,plain,
( ~ spl15_16
| spl15_18 ),
inference(avatar_contradiction_clause,[],[f532]) ).
fof(f661,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(relation_rng_restriction(X2,sK13),X3))
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,sK13)) ),
inference(resolution,[],[f337,f98]) ).
fof(f664,plain,
( ~ in(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK12)
| ~ in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),relation_rng_restriction(sK11,sK13))
| spl15_9 ),
inference(resolution,[],[f661,f297]) ).
fof(f691,definition,
( spl15_23
<=> in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),relation_rng_restriction(sK11,sK13)) ),
introduced(definition,[new_symbols(definition,[spl15_23])],[avatar_definition]) ).
fof(f692,plain,
( ~ in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),relation_rng_restriction(sK11,sK13))
| spl15_23 ),
inference(avatar_component_clause,[],[f691]) ).
fof(f693,plain,
( ~ spl15_23
| ~ spl15_17
| spl15_9 ),
inference(avatar_split_clause,[],[f664,f224,f507,f691]) ).
fof(f694,plain,
( ~ in(unordered_pair(unordered_pair(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12))),singleton(sK2(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)))),sK13)
| ~ in(sK3(sK11,relation_dom_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12)),sK11)
| spl15_23 ),
inference(resolution,[],[f692,f355]) ).
fof(f695,plain,
( ~ spl15_10
| ~ spl15_18
| spl15_23 ),
inference(avatar_split_clause,[],[f694,f691,f510,f227]) ).
fof(f696,plain,
( $false
| ~ spl15_16
| spl15_17 ),
inference(resolution,[],[f508,f525]) ).
fof(f697,plain,
( ~ spl15_16
| spl15_17 ),
inference(avatar_contradiction_clause,[],[f696]) ).
cnf(s4,plain,
spl15_3,
inference(sat_conversion,[],[f209]) ).
cnf(s6,plain,
( ~ spl15_7
| ~ spl15_8
| spl15_9
| spl15_10 ),
inference(sat_conversion,[],[f229]) ).
cnf(s7,plain,
spl15_7,
inference(sat_conversion,[],[f232]) ).
cnf(s8,plain,
( ~ spl15_3
| spl15_8 ),
inference(sat_conversion,[],[f234]) ).
cnf(s14,plain,
( ~ spl15_7
| ~ spl15_8
| ~ spl15_9
| ~ spl15_10
| ~ spl15_16 ),
inference(sat_conversion,[],[f302]) ).
cnf(s15,plain,
( ~ spl15_9
| spl15_10 ),
inference(sat_conversion,[],[f501]) ).
cnf(s16,plain,
( spl15_16
| ~ spl15_17
| ~ spl15_18 ),
inference(sat_conversion,[],[f512]) ).
cnf(s17,plain,
( ~ spl15_9
| spl15_17 ),
inference(sat_conversion,[],[f514]) ).
cnf(s18,plain,
( ~ spl15_9
| spl15_18 ),
inference(sat_conversion,[],[f521]) ).
cnf(s19,plain,
( ~ spl15_7
| ~ spl15_8
| spl15_9
| spl15_16 ),
inference(sat_conversion,[],[f523]) ).
cnf(s20,plain,
( ~ spl15_16
| spl15_18 ),
inference(sat_conversion,[],[f538]) ).
cnf(s27,plain,
( spl15_9
| ~ spl15_17
| ~ spl15_23 ),
inference(sat_conversion,[],[f693]) ).
cnf(s28,plain,
( ~ spl15_10
| ~ spl15_18
| spl15_23 ),
inference(sat_conversion,[],[f695]) ).
cnf(s29,plain,
( ~ spl15_16
| spl15_17 ),
inference(sat_conversion,[],[f697]) ).
cnf(s30,plain,
( ~ spl15_8
| spl15_9
| spl15_10 ),
inference(rat,[],[s6,s7]) ).
cnf(s31,plain,
spl15_8,
inference(rat,[],[s8,s4]) ).
cnf(s33,plain,
spl15_9,
inference(rat,[],[s27,s28,s20,s29,s30,s19,s31,s7]) ).
cnf(s34,plain,
spl15_18,
inference(rat,[],[s18,s33]) ).
cnf(s35,plain,
spl15_17,
inference(rat,[],[s17,s33]) ).
cnf(s36,plain,
spl15_10,
inference(rat,[],[s15,s33]) ).
cnf(s37,plain,
spl15_16,
inference(rat,[],[s16,s34,s35]) ).
cnf(s39,plain,
$false,
inference(rat,[],[s14,s33,s31,s7,s37,s36]) ).
fof(f698,plain,
$false,
inference(avatar_sat_refutation,[],[s39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU202+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n007.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
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:59:10 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.28/1.32 % (2012712)Detected formulas, will run a generic FOF schedule.
% 3.28/1.32 % (2012722)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1572645611:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.28/1.32 % (2012717)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=2996608151:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.28/1.32 % (2012718)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=2951765378:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.28/1.32 % (2012720)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=443419904:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.28/1.32 % (2012719)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=3409081542:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.28/1.32 % (2012720)Refutation not found, incomplete strategy
% 3.28/1.32 % (2012720)------------------------------
% 3.28/1.32 % (2012720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.28/1.32 % (2012720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.28/1.32 % (2012720)CaDiCaL version: 2.1.3
% 3.28/1.32 % (2012720)Termination reason: Refutation not found, incomplete strategy
% 3.28/1.32 % (2012720)Time elapsed: 0.002 s
% 3.28/1.32 % (2012720)Peak memory usage: 88 MB
% 3.28/1.32 % (2012720)Instructions burned: 2 (million)
% 3.28/1.32 % (2012722)Instruction limit reached!
% 3.28/1.32 % (2012722)------------------------------
% 3.28/1.32 % (2012722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.28/1.32 % (2012722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.28/1.32 % (2012721)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2560725296:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.28/1.32 % (2012722)CaDiCaL version: 2.1.3
% 3.28/1.32 % (2012722)Termination reason: Instruction limit
% 3.28/1.32 % (2012722)Termination phase: Saturation
% 3.28/1.32 % (2012722)Time elapsed: 0.053 s
% 3.28/1.32 % (2012722)Peak memory usage: 90 MB
% 3.28/1.32 % (2012722)Instructions burned: 141 (million)
% 3.28/1.32 % (2012723)dis-21_1_sil=8000:lcm=predicate:random_seed=3190837379: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)
% 3.28/1.32 % (2012723)First to succeed.
% 3.28/1.32 % (2012723)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2012712"
% 3.28/1.32 % (2012721)Instruction limit reached!
% 3.28/1.32 % (2012721)------------------------------
% 3.28/1.32 % (2012721)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.28/1.32 % (2012721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.28/1.32 % (2012721)CaDiCaL version: 2.1.3
% 3.28/1.32 % (2012721)Termination reason: Instruction limit
% 3.28/1.32 % (2012721)Termination phase: Saturation
% 3.28/1.32 % (2012721)Time elapsed: 0.068 s
% 3.28/1.32 % (2012721)Peak memory usage: 88 MB
% 3.28/1.32 % (2012721)Instructions burned: 120 (million)
% 3.28/1.32 % (2012731)lrs+10_1_sil=8000:sp=occurrence:random_seed=3631377191:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.28/1.32 % (2012731)Instruction limit reached!
% 3.28/1.32 % (2012731)------------------------------
% 3.28/1.32 % (2012731)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.28/1.32 % (2012731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.28/1.32 % (2012731)CaDiCaL version: 2.1.3
% 3.28/1.32 % (2012731)Termination reason: Instruction limit
% 3.28/1.32 % (2012731)Termination phase: Saturation
% 3.28/1.32 % (2012731)Time elapsed: 0.085 s
% 3.28/1.32 % (2012731)Peak memory usage: 90 MB
% 3.28/1.32 % (2012731)Instructions burned: 287 (million)
% 3.28/1.32 % (2012720)------------------------------
% 3.28/1.32 % (2012720)------------------------------
% 3.28/1.32 % (2012732)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2146655367:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.28/1.32 % (2012723)Refutation found. Thanks to Tanya!
% 3.28/1.32 % SZS status Theorem for theBenchmark
% 3.28/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.91/1.51 % (2012723)------------------------------
% 3.91/1.51 % (2012723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.51 % (2012723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.51 % (2012723)CaDiCaL version: 2.1.3
% 3.91/1.51 % (2012723)Termination reason: Refutation
% 3.91/1.51 % (2012723)Time elapsed: 0.026 s
% 3.91/1.51 % (2012723)Peak memory usage: 90 MB
% 3.91/1.51 % (2012723)Instructions burned: 41 (million)
% 3.91/1.51 % (2012723)------------------------------
% 3.91/1.51 % (2012723)------------------------------
% 3.91/1.51 % (2012712)Success in time 0.462 s
% 3.91/1.51 % Vampire exiting
%------------------------------------------------------------------------------