%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU246+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:47:59 PM UTC 2026
% Result : Theorem 3.12s 1.33s
% Output : Refutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 144 ( 17 unt; 8 def)
% Number of atoms : 534 ( 40 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 671 ( 281 ~; 305 |; 57 &)
% ( 19 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 272 ( 0 sgn 258 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,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/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f7,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/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
fof(f9,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f14,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f19,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f32,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f33,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f34,conjecture,
! [X0,X1] :
( relation(X1)
=> relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_wellord1) ).
fof(f35,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f49,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,[],[f6]) ).
fof(f50,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,[],[f7]) ).
fof(f53,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f55,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f61,plain,
? [X0,X1] :
( relation_restriction(X1,X0) != relation_dom_restriction(relation_rng_restriction(X0,X1),X0)
& relation(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f68,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,[],[f49]) ).
fof(f69,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,[],[f68]) ).
fof(f70,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,[],[f69]) ).
fof(f71,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))],[f70]) ).
fof(f72,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,[],[f50]) ).
fof(f73,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,[],[f72]) ).
fof(f74,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,[],[f73]) ).
fof(f75,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))],[f74]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,cartesian_product2(X1,X1)) )
& ( ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f60]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,cartesian_product2(X1,X1)) )
& ( ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
( relation_restriction(sK13,sK12) != relation_dom_restriction(relation_rng_restriction(sK12,sK13),sK12)
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X1,sK13)],[f61]) ).
fof(f99,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0)
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f100,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| in(sK0(X0,X1,X2),X1)
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f101,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = 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)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f102,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,[],[f75]) ).
fof(f103,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,[],[f75]) ).
fof(f104,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,[],[f75]) ).
fof(f112,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f114,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f116,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f135,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f86]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_restriction(X2,X1))
| in(X0,cartesian_product2(X1,X1)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_restriction(X2,X1))
| in(X0,X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,X2)
| ~ in(X0,cartesian_product2(X1,X1))
| in(X0,relation_restriction(X2,X1)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f140,plain,
relation(sK13),
inference(cnf_transformation,[],[f89]) ).
fof(f141,plain,
relation_restriction(sK13,sK12) != relation_dom_restriction(relation_rng_restriction(sK12,sK13),sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f148,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(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(X0) ),
inference(definition_unfolding,[],[f101,f112,f112]) ).
fof(f149,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| in(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(X0) ),
inference(definition_unfolding,[],[f100,f112]) ).
fof(f150,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(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(X0) ),
inference(definition_unfolding,[],[f99,f112,f112]) ).
fof(f157,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,[],[f104,f112,f112]) ).
fof(f158,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,[],[f103,f112]) ).
fof(f159,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,[],[f102,f112,f112]) ).
fof(f165,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f136,f112]) ).
fof(f166,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f135,f112]) ).
fof(f167,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f134,f112]) ).
fof(f171,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,[],[f157]) ).
fof(f172,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,[],[f158]) ).
fof(f173,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,[],[f159]) ).
fof(f176,definition,
! [X0,X1] :
( sQ14_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ14_eqProxy])],[equality_proxy_definition]) ).
fof(f179,plain,
! [X2,X0,X1] :
( sQ14_eqProxy(relation_dom_restriction(X0,X1),X2)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(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(X0) ),
inference(equality_proxy_replacement,[],[f148,f176]) ).
fof(f180,plain,
! [X2,X0,X1] :
( sQ14_eqProxy(relation_dom_restriction(X0,X1),X2)
| in(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(X0) ),
inference(equality_proxy_replacement,[],[f149,f176]) ).
fof(f181,plain,
! [X2,X0,X1] :
( sQ14_eqProxy(relation_dom_restriction(X0,X1),X2)
| in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(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(X0) ),
inference(equality_proxy_replacement,[],[f150,f176]) ).
fof(f189,plain,
~ sQ14_eqProxy(relation_restriction(sK13,sK12),relation_dom_restriction(relation_rng_restriction(sK12,sK13),sK12)),
inference(equality_proxy_replacement,[],[f141,f176]) ).
fof(f194,plain,
! [X0,X1] :
( sQ14_eqProxy(X1,X0)
| ~ sQ14_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f176]) ).
fof(f201,plain,
~ sQ14_eqProxy(relation_dom_restriction(relation_rng_restriction(sK12,sK13),sK12),relation_restriction(sK13,sK12)),
inference(resolution,[],[f194,f189]) ).
fof(f221,plain,
! [X0,X1] :
( ~ in(X0,relation_restriction(sK13,X1))
| in(X0,sK13) ),
inference(resolution,[],[f138,f140]) ).
fof(f237,plain,
! [X0,X1] :
( in(X0,cartesian_product2(X1,X1))
| ~ in(X0,relation_restriction(sK13,X1)) ),
inference(resolution,[],[f137,f140]) ).
fof(f241,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),relation_restriction(sK13,X1))
| in(X0,X1) ),
inference(resolution,[],[f166,f237]) ).
fof(f242,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),relation_restriction(sK13,X1))
| in(X0,X1) ),
inference(resolution,[],[f167,f237]) ).
fof(f251,plain,
! [X0,X1] :
( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,sK13)
| in(X0,relation_restriction(sK13,X1)) ),
inference(resolution,[],[f139,f140]) ).
fof(f257,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_restriction(sK13,X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK13)
| ~ in(X0,X2)
| ~ in(X1,X2) ),
inference(resolution,[],[f251,f165]) ).
fof(f260,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,[],[f172,f116]) ).
fof(f261,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,[],[f260]) ).
fof(f265,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,[],[f173,f116]) ).
fof(f266,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,[],[f265]) ).
fof(f275,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,[],[f171,f116]) ).
fof(f276,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,[],[f275]) ).
fof(f277,plain,
( in(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12)
| in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_restriction(sK13,sK12))
| ~ relation(relation_restriction(sK13,sK12))
| ~ relation(relation_rng_restriction(sK12,sK13)) ),
inference(resolution,[],[f180,f201]) ).
fof(f279,definition,
( spl15_3
<=> relation(relation_rng_restriction(sK12,sK13)) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f280,plain,
( ~ relation(relation_rng_restriction(sK12,sK13))
| spl15_3 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f282,definition,
( spl15_4
<=> relation(relation_restriction(sK13,sK12)) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
fof(f283,plain,
( ~ relation(relation_restriction(sK13,sK12))
| spl15_4 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f285,definition,
( spl15_5
<=> in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_restriction(sK13,sK12)) ),
introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).
fof(f286,plain,
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_restriction(sK13,sK12))
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f288,definition,
( spl15_6
<=> in(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12) ),
introduced(definition,[new_symbols(definition,[spl15_6])],[avatar_definition]) ).
fof(f290,plain,
( ~ spl15_3
| ~ spl15_4
| spl15_5
| spl15_6 ),
inference(avatar_split_clause,[],[f277,f288,f285,f282,f279]) ).
fof(f291,plain,
( ~ relation(sK13)
| spl15_3 ),
inference(resolution,[],[f280,f116]) ).
fof(f292,plain,
( $false
| spl15_3 ),
inference(resolution,[],[f291,f140]) ).
fof(f293,plain,
spl15_3,
inference(avatar_contradiction_clause,[],[f292]) ).
fof(f294,plain,
( ~ relation(sK13)
| spl15_4 ),
inference(resolution,[],[f283,f114]) ).
fof(f295,plain,
( $false
| spl15_4 ),
inference(resolution,[],[f294,f140]) ).
fof(f296,plain,
spl15_4,
inference(avatar_contradiction_clause,[],[f295]) ).
fof(f297,plain,
( in(sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12)
| ~ spl15_5 ),
inference(resolution,[],[f286,f242]) ).
fof(f298,plain,
( in(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12)
| ~ spl15_5 ),
inference(resolution,[],[f286,f241]) ).
fof(f300,plain,
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),sK13)
| ~ spl15_5 ),
inference(resolution,[],[f286,f221]) ).
fof(f303,plain,
( spl15_6
| ~ spl15_5 ),
inference(avatar_split_clause,[],[f298,f285,f288]) ).
fof(f365,plain,
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_rng_restriction(sK12,sK13))
| in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_restriction(sK13,sK12))
| ~ relation(relation_restriction(sK13,sK12))
| ~ relation(relation_rng_restriction(sK12,sK13)) ),
inference(resolution,[],[f181,f201]) ).
fof(f376,plain,
( ~ in(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12)
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_rng_restriction(sK12,sK13))
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_restriction(sK13,sK12))
| ~ relation(relation_restriction(sK13,sK12))
| ~ relation(relation_rng_restriction(sK12,sK13)) ),
inference(resolution,[],[f179,f201]) ).
fof(f377,plain,
( ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_restriction(sK13,sK12))
| spl15_5 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f379,definition,
( spl15_12
<=> in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_rng_restriction(sK12,sK13)) ),
introduced(definition,[new_symbols(definition,[spl15_12])],[avatar_definition]) ).
fof(f380,plain,
( ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_rng_restriction(sK12,sK13))
| spl15_12 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f382,plain,
( ~ spl15_3
| ~ spl15_4
| ~ spl15_5
| ~ spl15_12
| ~ spl15_6 ),
inference(avatar_split_clause,[],[f376,f288,f379,f285,f282,f279]) ).
fof(f536,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),relation_rng_restriction(X1,sK13))
| in(X0,X1) ),
inference(resolution,[],[f261,f140]) ).
fof(f608,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,[],[f266,f140]) ).
fof(f631,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,[],[f276,f140]) ).
fof(f805,plain,
( ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),sK13)
| ~ in(sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12)
| spl15_12 ),
inference(resolution,[],[f631,f380]) ).
fof(f809,definition,
( spl15_29
<=> in(sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12) ),
introduced(definition,[new_symbols(definition,[spl15_29])],[avatar_definition]) ).
fof(f810,plain,
( ~ in(sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12)
| spl15_29 ),
inference(avatar_component_clause,[],[f809]) ).
fof(f812,definition,
( spl15_30
<=> in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),sK13) ),
introduced(definition,[new_symbols(definition,[spl15_30])],[avatar_definition]) ).
fof(f813,plain,
( ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),sK13)
| spl15_30 ),
inference(avatar_component_clause,[],[f812]) ).
fof(f814,plain,
( ~ spl15_29
| ~ spl15_30
| spl15_12 ),
inference(avatar_split_clause,[],[f805,f379,f812,f809]) ).
fof(f815,plain,
( $false
| ~ spl15_5
| spl15_29 ),
inference(resolution,[],[f810,f297]) ).
fof(f816,plain,
( ~ spl15_5
| spl15_29 ),
inference(avatar_contradiction_clause,[],[f815]) ).
fof(f817,plain,
( $false
| ~ spl15_5
| spl15_30 ),
inference(resolution,[],[f813,f300]) ).
fof(f818,plain,
( ~ spl15_5
| spl15_30 ),
inference(avatar_contradiction_clause,[],[f817]) ).
fof(f819,plain,
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_rng_restriction(sK12,sK13))
| ~ spl15_12 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f820,plain,
( ~ spl15_3
| ~ spl15_4
| spl15_5
| spl15_12 ),
inference(avatar_split_clause,[],[f365,f379,f285,f282,f279]) ).
fof(f821,plain,
( ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),sK13)
| ~ in(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12)
| ~ in(sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12)
| spl15_5 ),
inference(resolution,[],[f377,f257]) ).
fof(f827,plain,
( ~ spl15_29
| ~ spl15_6
| ~ spl15_30
| spl15_5 ),
inference(avatar_split_clause,[],[f821,f285,f812,f288,f809]) ).
fof(f828,plain,
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),sK13)
| ~ spl15_12 ),
inference(resolution,[],[f819,f608]) ).
fof(f829,plain,
( in(sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12)
| ~ spl15_12 ),
inference(resolution,[],[f819,f536]) ).
fof(f834,plain,
( $false
| ~ spl15_12
| spl15_30 ),
inference(resolution,[],[f828,f813]) ).
fof(f837,plain,
( ~ spl15_12
| spl15_30 ),
inference(avatar_contradiction_clause,[],[f834]) ).
fof(f838,plain,
( $false
| ~ spl15_12
| spl15_29 ),
inference(resolution,[],[f810,f829]) ).
fof(f839,plain,
( ~ spl15_12
| spl15_29 ),
inference(avatar_contradiction_clause,[],[f838]) ).
cnf(s3,plain,
( ~ spl15_3
| ~ spl15_4
| spl15_5
| spl15_6 ),
inference(sat_conversion,[],[f290]) ).
cnf(s4,plain,
spl15_3,
inference(sat_conversion,[],[f293]) ).
cnf(s5,plain,
spl15_4,
inference(sat_conversion,[],[f296]) ).
cnf(s6,plain,
( ~ spl15_5
| spl15_6 ),
inference(sat_conversion,[],[f303]) ).
cnf(s12,plain,
( ~ spl15_3
| ~ spl15_4
| ~ spl15_5
| ~ spl15_6
| ~ spl15_12 ),
inference(sat_conversion,[],[f382]) ).
cnf(s21,plain,
( spl15_12
| ~ spl15_29
| ~ spl15_30 ),
inference(sat_conversion,[],[f814]) ).
cnf(s22,plain,
( ~ spl15_5
| spl15_29 ),
inference(sat_conversion,[],[f816]) ).
cnf(s23,plain,
( ~ spl15_5
| spl15_30 ),
inference(sat_conversion,[],[f818]) ).
cnf(s24,plain,
( ~ spl15_3
| ~ spl15_4
| spl15_5
| spl15_12 ),
inference(sat_conversion,[],[f820]) ).
cnf(s26,plain,
( spl15_5
| ~ spl15_6
| ~ spl15_29
| ~ spl15_30 ),
inference(sat_conversion,[],[f827]) ).
cnf(s27,plain,
( ~ spl15_12
| spl15_30 ),
inference(sat_conversion,[],[f837]) ).
cnf(s28,plain,
( ~ spl15_12
| spl15_29 ),
inference(sat_conversion,[],[f839]) ).
cnf(s30,plain,
( spl15_5
| spl15_6 ),
inference(rat,[],[s3,s5,s4]) ).
cnf(s31,plain,
spl15_5,
inference(rat,[],[s26,s27,s28,s30,s24,s5,s4]) ).
cnf(s32,plain,
spl15_30,
inference(rat,[],[s23,s31]) ).
cnf(s33,plain,
spl15_29,
inference(rat,[],[s22,s31]) ).
cnf(s34,plain,
spl15_6,
inference(rat,[],[s6,s31]) ).
cnf(s35,plain,
spl15_12,
inference(rat,[],[s21,s32,s33]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s12,s31,s4,s5,s35,s34]) ).
fof(f840,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU246+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n015.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 04:20:46 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.12/1.33 % (2255189)Detected formulas, will run a generic FOF schedule.
% 3.12/1.33 % (2255195)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=573310469:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.12/1.33 % (2255200)dis-21_1_sil=8000:lcm=predicate:random_seed=3907652546: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)
% 3.12/1.33 % (2255199)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2286419136:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.12/1.33 % (2255196)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=3210372809:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.12/1.33 % (2255194)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=1621742914:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.12/1.33 % (2255197)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2480031474:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.12/1.33 % (2255198)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2628244501:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.12/1.33 % (2255197)Refutation not found, incomplete strategy
% 3.12/1.33 % (2255197)------------------------------
% 3.12/1.33 % (2255197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.33 % (2255197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.33 % (2255197)CaDiCaL version: 2.1.3
% 3.12/1.33 % (2255197)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.33 % (2255197)Time elapsed: 0.002 s
% 3.12/1.33 % (2255197)Peak memory usage: 88 MB
% 3.12/1.33 % (2255197)Instructions burned: 2 (million)
% 3.12/1.33 % (2255200)First to succeed.
% 3.12/1.33 % (2255200)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2255189"
% 3.12/1.33 % (2255198)Instruction limit reached!
% 3.12/1.33 % (2255198)------------------------------
% 3.12/1.33 % (2255198)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.33 % (2255198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.33 % (2255198)CaDiCaL version: 2.1.3
% 3.12/1.33 % (2255198)Termination reason: Instruction limit
% 3.12/1.33 % (2255198)Termination phase: Saturation
% 3.12/1.33 % (2255198)Time elapsed: 0.068 s
% 3.12/1.33 % (2255198)Peak memory usage: 88 MB
% 3.12/1.33 % (2255198)Instructions burned: 120 (million)
% 3.12/1.33 % (2255199)Instruction limit reached!
% 3.12/1.33 % (2255199)------------------------------
% 3.12/1.33 % (2255199)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.33 % (2255199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.33 % (2255199)CaDiCaL version: 2.1.3
% 3.12/1.33 % (2255199)Termination reason: Instruction limit
% 3.12/1.33 % (2255199)Termination phase: Saturation
% 3.12/1.33 % (2255199)Time elapsed: 0.098 s
% 3.12/1.33 % (2255199)Peak memory usage: 89 MB
% 3.12/1.33 % (2255199)Instructions burned: 139 (million)
% 3.12/1.33 % (2255208)lrs+10_1_sil=8000:sp=occurrence:random_seed=1154989507:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.12/1.33 % (2255197)------------------------------
% 3.12/1.33 % (2255197)------------------------------
% 3.12/1.33 % (2255209)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1451211840:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.12/1.33 % (2255200)Refutation found. Thanks to Tanya!
% 3.12/1.33 % SZS status Theorem for theBenchmark
% 3.12/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.82/1.53 % (2255200)------------------------------
% 3.82/1.53 % (2255200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.53 % (2255200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.53 % (2255200)CaDiCaL version: 2.1.3
% 3.82/1.53 % (2255200)Termination reason: Refutation
% 3.82/1.53 % (2255200)Time elapsed: 0.019 s
% 3.82/1.53 % (2255200)Peak memory usage: 89 MB
% 3.82/1.53 % (2255200)Instructions burned: 30 (million)
% 3.82/1.53 % (2255200)------------------------------
% 3.82/1.53 % (2255200)------------------------------
% 3.82/1.53 % (2255189)Success in time 0.453 s
% 3.82/1.53 % Vampire exiting
%------------------------------------------------------------------------------