%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU057+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:47:09 PM UTC 2026
% Result : Theorem 7.23s 2.15s
% Output : Refutation 8.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 30
% Syntax : Number of formulae : 289 ( 30 unt; 22 def)
% Number of atoms : 1128 ( 144 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 1456 ( 617 ~; 683 |; 107 &)
% ( 36 <=>; 12 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 17 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-3 aty)
% Number of variables : 330 ( 1 sgn 304 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f7,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f8,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f15,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f18,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f30,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> relation_image(relation_rng_restriction(X0,X2),X1) = set_intersection2(X0,relation_image(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_funct_1) ).
fof(f31,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> relation_image(relation_rng_restriction(X0,X2),X1) = set_intersection2(X0,relation_image(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f35,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f41,axiom,
! [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(f43,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f18]) ).
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(f56,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f57,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f61,plain,
! [X0,X1] :
( ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f62,plain,
! [X0,X1] :
( ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f61]) ).
fof(f67,plain,
? [X0,X1,X2] :
( relation_image(relation_rng_restriction(X0,X2),X1) != set_intersection2(X0,relation_image(X2,X1))
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f31]) ).
fof(f68,plain,
? [X0,X1,X2] :
( relation_image(relation_rng_restriction(X0,X2),X1) != set_intersection2(X0,relation_image(X2,X1))
& relation(X2)
& function(X2) ),
inference(flattening,[],[f67]) ).
fof(f72,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f79,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(f80,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,[],[f79]) ).
fof(f82,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( ! [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)) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f83,definition,
! [X1,X0,X2] :
( ( X1 = relation_rng_restriction(X0,X2)
<=> sP0(X2,X0,X1) )
| ~ sP1(X1,X0,X2) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f84,plain,
! [X0,X1] :
( ! [X2] :
( sP1(X1,X0,X2)
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(definition_folding,[],[f80,f83,f82]) ).
fof(f85,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 ) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f57]) ).
fof(f86,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,relation_dom(X0))
& in(X5,X1)
& apply(X0,X5) = X3 )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6 ) )
& ( ? [X8] :
( in(X8,relation_dom(X0))
& in(X8,X1)
& apply(X0,X8) = X6 )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f85]) ).
fof(f87,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != sK2(X0,X1,X2) )
| ~ in(sK2(X0,X1,X2),X2) )
& ( ( in(sK3(X0,X1,X2),relation_dom(X0))
& in(sK3(X0,X1,X2),X1)
& sK2(X0,X1,X2) = apply(X0,sK3(X0,X1,X2)) )
| in(sK2(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6 ) )
& ( ( in(sK4(X0,X1,X6),relation_dom(X0))
& in(sK4(X0,X1,X6),X1)
& apply(X0,sK4(X0,X1,X6)) = X6 )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X3,sK2(X0,X1,X2)),skolemize(X5,sK3(X0,X1,X2)),skolemize(X8,sK4(X0,X1,X6))],[f86]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( in(sK5(X0,X1,X2),X0)
& in(sK5(X0,X1,X2),X1) )
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f90]) ).
fof(f103,plain,
( relation_image(relation_rng_restriction(sK17,sK19),sK18) != set_intersection2(sK17,relation_image(sK19,sK18))
& relation(sK19)
& function(sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19]),skolemize(X0,sK17),skolemize(X1,sK18),skolemize(X2,sK19)],[f68]) ).
fof(f104,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f105,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK20(X0,X1),X1)
| ~ in(sK20(X0,X1),X0) )
& ( in(sK20(X0,X1),X1)
| in(sK20(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X2,sK20(X0,X1))],[f104]) ).
fof(f106,plain,
! [X1,X0,X2] :
( ( ( X1 = relation_rng_restriction(X0,X2)
| ~ sP0(X2,X0,X1) )
& ( sP0(X2,X0,X1)
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ sP1(X1,X0,X2) ),
inference(nnf_transformation,[],[f83]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ( ( relation_rng_restriction(X1,X2) = X0
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0 ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f106]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ? [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)) ) )
& ( ( ! [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)) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f82]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ? [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)) ) )
& ( ( ! [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)) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X2)) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,relation_dom(X2)) ) )
| ? [X4] :
( apply(X0,X4) != apply(X2,X4)
& in(X4,relation_dom(X2)) ) )
& ( ( ! [X5] :
( ( in(X5,relation_dom(X2))
| ~ in(X5,relation_dom(X0))
| ~ in(apply(X0,X5),X1) )
& ( ( in(X5,relation_dom(X0))
& in(apply(X0,X5),X1) )
| ~ in(X5,relation_dom(X2)) ) )
& ! [X6] :
( apply(X0,X6) = apply(X2,X6)
| ~ in(X6,relation_dom(X2)) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f109]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ~ in(sK21(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK21(X0,X1,X2)),X1)
| ~ in(sK21(X0,X1,X2),relation_dom(X2)) )
& ( ( in(sK21(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK21(X0,X1,X2)),X1) )
| in(sK21(X0,X1,X2),relation_dom(X2)) ) )
| ( apply(X0,sK22(X0,X2)) != apply(X2,sK22(X0,X2))
& in(sK22(X0,X2),relation_dom(X2)) ) )
& ( ( ! [X5] :
( ( in(X5,relation_dom(X2))
| ~ in(X5,relation_dom(X0))
| ~ in(apply(X0,X5),X1) )
& ( ( in(X5,relation_dom(X0))
& in(apply(X0,X5),X1) )
| ~ in(X5,relation_dom(X2)) ) )
& ! [X6] :
( apply(X0,X6) = apply(X2,X6)
| ~ in(X6,relation_dom(X2)) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22]),skolemize(X3,sK21(X0,X1,X2)),skolemize(X4,sK22(X0,X2))],[f110]) ).
fof(f118,plain,
! [X2,X0,X1,X6] :
( apply(X0,sK4(X0,X1,X6)) = X6
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f119,plain,
! [X2,X0,X1,X6] :
( in(sK4(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f120,plain,
! [X2,X0,X1,X6] :
( in(sK4(X0,X1,X6),relation_dom(X0))
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f121,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f126,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f91]) ).
fof(f127,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f91]) ).
fof(f128,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f91]) ).
fof(f132,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f141,plain,
! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f142,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f146,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f43]) ).
fof(f166,plain,
function(sK19),
inference(cnf_transformation,[],[f103]) ).
fof(f167,plain,
relation(sK19),
inference(cnf_transformation,[],[f103]) ).
fof(f168,plain,
relation_image(relation_rng_restriction(sK17,sK19),sK18) != set_intersection2(sK17,relation_image(sK19,sK18)),
inference(cnf_transformation,[],[f103]) ).
fof(f172,plain,
! [X0,X1] :
( in(sK20(X0,X1),X1)
| in(sK20(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f105]) ).
fof(f173,plain,
! [X0,X1] :
( ~ in(sK20(X0,X1),X1)
| X0 = X1
| ~ in(sK20(X0,X1),X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f179,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f107]) ).
fof(f181,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| ~ in(X6,relation_dom(X2))
| apply(X0,X6) = apply(X2,X6) ),
inference(cnf_transformation,[],[f111]) ).
fof(f182,plain,
! [X2,X0,X1,X5] :
( ~ sP0(X0,X1,X2)
| ~ in(X5,relation_dom(X2))
| in(apply(X0,X5),X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f183,plain,
! [X2,X0,X1,X5] :
( ~ sP0(X0,X1,X2)
| ~ in(X5,relation_dom(X2))
| in(X5,relation_dom(X0)) ),
inference(cnf_transformation,[],[f111]) ).
fof(f184,plain,
! [X2,X0,X1,X5] :
( ~ in(apply(X0,X5),X1)
| ~ in(X5,relation_dom(X0))
| in(X5,relation_dom(X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f111]) ).
fof(f191,plain,
! [X2,X0,X1] :
( sP1(X1,X0,X2)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f193,plain,
! [X2,X0,X1,X7] :
( in(apply(X0,X7),X2)
| ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f121]) ).
fof(f194,plain,
! [X0,X1,X7] :
( in(apply(X0,X7),relation_image(X0,X1))
| ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f193]) ).
fof(f195,plain,
! [X0,X1,X6] :
( in(sK4(X0,X1,X6),relation_dom(X0))
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f120]) ).
fof(f196,plain,
! [X0,X1,X6] :
( in(sK4(X0,X1,X6),X1)
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f119]) ).
fof(f197,plain,
! [X0,X1,X6] :
( ~ in(X6,relation_image(X0,X1))
| apply(X0,sK4(X0,X1,X6)) = X6
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f118]) ).
fof(f198,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f128]) ).
fof(f199,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f127]) ).
fof(f200,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f126]) ).
fof(f201,plain,
! [X2,X1] :
( ~ sP1(relation_rng_restriction(X1,X2),X1,X2)
| sP0(X2,X1,relation_rng_restriction(X1,X2)) ),
inference(equality_resolution,[],[f179]) ).
fof(f202,definition,
sF23 = relation_rng_restriction(sK17,sK19),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f203,plain,
relation_rng_restriction(sK17,sK19) = sF23,
inference(reorient_equations,[],[f202]) ).
fof(f204,definition,
sF24 = relation_image(sF23,sK18),
introduced(definition,[new_symbols(definition,[sF24])],[function_definition]) ).
fof(f205,plain,
relation_image(sF23,sK18) = sF24,
inference(reorient_equations,[],[f204]) ).
fof(f206,definition,
sF25 = relation_image(sK19,sK18),
introduced(definition,[new_symbols(definition,[sF25])],[function_definition]) ).
fof(f207,plain,
relation_image(sK19,sK18) = sF25,
inference(reorient_equations,[],[f206]) ).
fof(f208,definition,
sF26 = set_intersection2(sK17,sF25),
introduced(definition,[new_symbols(definition,[sF26])],[function_definition]) ).
fof(f209,plain,
set_intersection2(sK17,sF25) = sF26,
inference(reorient_equations,[],[f208]) ).
fof(f210,plain,
sF24 != sF26,
inference(definition_folding,[],[f168,f209,f207,f205,f203]) ).
fof(f211,plain,
! [X0] :
( ~ in(X0,sF25)
| apply(sK19,sK4(sK19,sK18,X0)) = X0
| ~ relation(sK19)
| ~ function(sK19) ),
inference(superposition,[],[f197,f207]) ).
fof(f212,plain,
! [X0] :
( ~ in(X0,sF24)
| apply(sF23,sK4(sF23,sK18,X0)) = X0
| ~ relation(sF23)
| ~ function(sF23) ),
inference(superposition,[],[f197,f205]) ).
fof(f214,definition,
( spl27_1
<=> function(sF23) ),
introduced(definition,[new_symbols(definition,[spl27_1])],[avatar_definition]) ).
fof(f215,plain,
( function(sF23)
| ~ spl27_1 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f216,plain,
( ~ function(sF23)
| spl27_1 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f218,definition,
( spl27_2
<=> relation(sF23) ),
introduced(definition,[new_symbols(definition,[spl27_2])],[avatar_definition]) ).
fof(f219,plain,
( relation(sF23)
| ~ spl27_2 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f220,plain,
( ~ relation(sF23)
| spl27_2 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f222,definition,
( spl27_3
<=> ! [X0] :
( ~ in(X0,sF24)
| apply(sF23,sK4(sF23,sK18,X0)) = X0 ) ),
introduced(definition,[new_symbols(definition,[spl27_3])],[avatar_definition]) ).
fof(f223,plain,
( ! [X0] :
( ~ in(X0,sF24)
| apply(sF23,sK4(sF23,sK18,X0)) = X0 )
| ~ spl27_3 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f224,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_3 ),
inference(avatar_split_clause,[],[f212,f222,f218,f214]) ).
fof(f225,plain,
! [X0] :
( ~ in(X0,sF25)
| apply(sK19,sK4(sK19,sK18,X0)) = X0
| ~ function(sK19) ),
inference(forward_subsumption_resolution,[],[f211,f167]) ).
fof(f226,plain,
! [X0] :
( ~ in(X0,sF25)
| apply(sK19,sK4(sK19,sK18,X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f225,f166]) ).
fof(f227,plain,
! [X0,X1] :
( sP0(X0,X1,relation_rng_restriction(X1,X0))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(relation_rng_restriction(X1,X0)) ),
inference(resolution,[],[f201,f191]) ).
fof(f230,definition,
( spl27_4
<=> sP0(sK19,sK17,sF23) ),
introduced(definition,[new_symbols(definition,[spl27_4])],[avatar_definition]) ).
fof(f232,plain,
( sP0(sK19,sK17,sF23)
| ~ spl27_4 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f238,plain,
! [X0,X1] :
( sP0(X0,X1,relation_rng_restriction(X1,X0))
| ~ relation(X0)
| ~ function(X0)
| ~ function(relation_rng_restriction(X1,X0)) ),
inference(forward_subsumption_resolution,[],[f227,f132]) ).
fof(f239,plain,
! [X0,X1] :
( sP0(X0,X1,relation_rng_restriction(X1,X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f238,f141]) ).
fof(f240,plain,
( sP0(sK19,sK17,sF23)
| ~ relation(sK19)
| ~ function(sK19) ),
inference(superposition,[],[f239,f203]) ).
fof(f241,plain,
( sP0(sK19,sK17,sF23)
| ~ function(sK19) ),
inference(forward_subsumption_resolution,[],[f240,f167]) ).
fof(f242,plain,
sP0(sK19,sK17,sF23),
inference(forward_subsumption_resolution,[],[f241,f166]) ).
fof(f243,plain,
spl27_4,
inference(avatar_split_clause,[],[f242,f230]) ).
fof(f244,plain,
! [X0] :
( ~ in(X0,sF26)
| in(X0,sK17) ),
inference(superposition,[],[f199,f209]) ).
fof(f245,plain,
! [X0] :
( ~ in(X0,sF26)
| in(X0,sF25) ),
inference(superposition,[],[f200,f209]) ).
fof(f246,plain,
( function(sF23)
| ~ relation(sK19)
| ~ function(sK19) ),
inference(superposition,[],[f141,f203]) ).
fof(f247,plain,
( ~ relation(sK19)
| ~ function(sK19)
| spl27_1 ),
inference(forward_subsumption_resolution,[],[f246,f216]) ).
fof(f248,plain,
( ~ function(sK19)
| spl27_1 ),
inference(forward_subsumption_resolution,[],[f247,f167]) ).
fof(f249,plain,
( $false
| spl27_1 ),
inference(forward_subsumption_resolution,[],[f248,f166]) ).
fof(f250,plain,
spl27_1,
inference(avatar_contradiction_clause,[],[f249]) ).
fof(f253,plain,
! [X0] :
( ~ in(X0,sF25)
| ~ in(X0,sK17)
| in(X0,sF26) ),
inference(superposition,[],[f198,f209]) ).
fof(f254,plain,
( relation(sF23)
| ~ relation(sK19)
| ~ function(sK19) ),
inference(superposition,[],[f142,f203]) ).
fof(f255,plain,
( ~ relation(sK19)
| ~ function(sK19)
| spl27_2 ),
inference(forward_subsumption_resolution,[],[f254,f220]) ).
fof(f256,plain,
( ~ function(sK19)
| spl27_2 ),
inference(forward_subsumption_resolution,[],[f255,f167]) ).
fof(f257,plain,
( $false
| spl27_2 ),
inference(forward_subsumption_resolution,[],[f256,f166]) ).
fof(f258,plain,
spl27_2,
inference(avatar_contradiction_clause,[],[f257]) ).
fof(f262,plain,
! [X0] :
( in(apply(sF23,X0),sF24)
| ~ in(X0,relation_dom(sF23))
| ~ in(X0,sK18)
| ~ relation(sF23)
| ~ function(sF23) ),
inference(superposition,[],[f194,f205]) ).
fof(f264,plain,
( ! [X0] :
( in(apply(sF23,X0),sF24)
| ~ in(X0,relation_dom(sF23))
| ~ in(X0,sK18)
| ~ function(sF23) )
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f262,f219]) ).
fof(f266,plain,
( ! [X0] :
( in(apply(sF23,X0),sF24)
| ~ in(X0,relation_dom(sF23))
| ~ in(X0,sK18) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f264,f215]) ).
fof(f299,plain,
! [X0] :
( in(sK20(X0,sF26),sF25)
| in(sK20(X0,sF26),X0)
| sF26 = X0 ),
inference(resolution,[],[f172,f245]) ).
fof(f300,plain,
! [X0] :
( in(sK20(X0,sF26),sK17)
| in(sK20(X0,sF26),X0)
| sF26 = X0 ),
inference(resolution,[],[f172,f244]) ).
fof(f327,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF23))
| apply(sK19,X0) = apply(sF23,X0) )
| ~ spl27_4 ),
inference(resolution,[],[f181,f232]) ).
fof(f328,plain,
( ! [X0,X1] :
( apply(sK19,sK4(sF23,X0,X1)) = apply(sF23,sK4(sF23,X0,X1))
| ~ in(X1,relation_image(sF23,X0))
| ~ relation(sF23)
| ~ function(sF23) )
| ~ spl27_4 ),
inference(resolution,[],[f327,f195]) ).
fof(f332,plain,
( ! [X0,X1] :
( apply(sK19,sK4(sF23,X0,X1)) = apply(sF23,sK4(sF23,X0,X1))
| ~ in(X1,relation_image(sF23,X0))
| ~ function(sF23) )
| ~ spl27_2
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f328,f219]) ).
fof(f333,plain,
( ! [X0,X1] :
( ~ in(X1,relation_image(sF23,X0))
| apply(sK19,sK4(sF23,X0,X1)) = apply(sF23,sK4(sF23,X0,X1)) )
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f332,f215]) ).
fof(f345,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF23))
| in(X0,relation_dom(sK19)) )
| ~ spl27_4 ),
inference(resolution,[],[f183,f232]) ).
fof(f346,plain,
( ! [X0,X1] :
( in(sK4(sF23,X0,X1),relation_dom(sK19))
| ~ in(X1,relation_image(sF23,X0))
| ~ relation(sF23)
| ~ function(sF23) )
| ~ spl27_4 ),
inference(resolution,[],[f345,f195]) ).
fof(f350,plain,
( ! [X0,X1] :
( in(sK4(sF23,X0,X1),relation_dom(sK19))
| ~ in(X1,relation_image(sF23,X0))
| ~ function(sF23) )
| ~ spl27_2
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f346,f219]) ).
fof(f351,plain,
( ! [X0,X1] :
( in(sK4(sF23,X0,X1),relation_dom(sK19))
| ~ in(X1,relation_image(sF23,X0)) )
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f350,f215]) ).
fof(f356,plain,
( ! [X0] :
( ~ in(X0,sF24)
| apply(sF23,sK4(sF23,sK18,X0)) = apply(sK19,sK4(sF23,sK18,X0)) )
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4 ),
inference(superposition,[],[f333,f205]) ).
fof(f367,plain,
( in(sK20(sF24,sF26),sK17)
| sF24 = sF26
| sK20(sF24,sF26) = apply(sF23,sK4(sF23,sK18,sK20(sF24,sF26)))
| ~ spl27_3 ),
inference(resolution,[],[f300,f223]) ).
fof(f382,plain,
( in(sK20(sF24,sF26),sK17)
| sK20(sF24,sF26) = apply(sF23,sK4(sF23,sK18,sK20(sF24,sF26)))
| ~ spl27_3 ),
inference(forward_subsumption_resolution,[],[f367,f210]) ).
fof(f402,definition,
( spl27_15
<=> sK20(sF24,sF26) = apply(sF23,sK4(sF23,sK18,sK20(sF24,sF26))) ),
introduced(definition,[new_symbols(definition,[spl27_15])],[avatar_definition]) ).
fof(f403,plain,
( sK20(sF24,sF26) != apply(sF23,sK4(sF23,sK18,sK20(sF24,sF26)))
| spl27_15 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f404,plain,
( sK20(sF24,sF26) = apply(sF23,sK4(sF23,sK18,sK20(sF24,sF26)))
| ~ spl27_15 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f406,definition,
( spl27_16
<=> in(sK20(sF24,sF26),sK17) ),
introduced(definition,[new_symbols(definition,[spl27_16])],[avatar_definition]) ).
fof(f407,plain,
( ~ in(sK20(sF24,sF26),sK17)
| spl27_16 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f408,plain,
( in(sK20(sF24,sF26),sK17)
| ~ spl27_16 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f409,plain,
( spl27_15
| spl27_16
| ~ spl27_3 ),
inference(avatar_split_clause,[],[f382,f222,f406,f402]) ).
fof(f502,definition,
( spl27_26
<=> in(sK20(sF24,sF26),sF24) ),
introduced(definition,[new_symbols(definition,[spl27_26])],[avatar_definition]) ).
fof(f503,plain,
( ~ in(sK20(sF24,sF26),sF24)
| spl27_26 ),
inference(avatar_component_clause,[],[f502]) ).
fof(f504,plain,
( in(sK20(sF24,sF26),sF24)
| ~ spl27_26 ),
inference(avatar_component_clause,[],[f502]) ).
fof(f521,plain,
! [X0] :
( in(sK20(X0,sF26),X0)
| sF26 = X0
| sK20(X0,sF26) = apply(sK19,sK4(sK19,sK18,sK20(X0,sF26))) ),
inference(resolution,[],[f299,f226]) ).
fof(f530,plain,
( in(sK20(sF24,sF26),sF25)
| sF24 = sF26
| sK20(sF24,sF26) = apply(sF23,sK4(sF23,sK18,sK20(sF24,sF26)))
| ~ spl27_3 ),
inference(resolution,[],[f299,f223]) ).
fof(f546,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_rng_restriction(X1,X2)))
| in(apply(X2,X0),X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(resolution,[],[f182,f239]) ).
fof(f550,plain,
! [X2,X3,X0,X1] :
( in(apply(X0,sK4(relation_rng_restriction(X1,X0),X2,X3)),X1)
| ~ relation(X0)
| ~ function(X0)
| ~ in(X3,relation_image(relation_rng_restriction(X1,X0),X2))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(relation_rng_restriction(X1,X0)) ),
inference(resolution,[],[f546,f195]) ).
fof(f562,plain,
! [X2,X3,X0,X1] :
( in(apply(X0,sK4(relation_rng_restriction(X1,X0),X2,X3)),X1)
| ~ relation(X0)
| ~ function(X0)
| ~ in(X3,relation_image(relation_rng_restriction(X1,X0),X2))
| ~ function(relation_rng_restriction(X1,X0)) ),
inference(forward_subsumption_resolution,[],[f550,f132]) ).
fof(f567,plain,
! [X2,X3,X0,X1] :
( in(apply(X0,sK4(relation_rng_restriction(X1,X0),X2,X3)),X1)
| ~ relation(X0)
| ~ function(X0)
| ~ in(X3,relation_image(relation_rng_restriction(X1,X0),X2)) ),
inference(forward_subsumption_resolution,[],[f562,f141]) ).
fof(f744,plain,
( apply(sF23,sK4(sF23,sK18,sK20(sF24,sF26))) = apply(sK19,sK4(sF23,sK18,sK20(sF24,sF26)))
| in(sK20(sF24,sF26),sF25)
| sF24 = sF26
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4 ),
inference(resolution,[],[f356,f299]) ).
fof(f745,plain,
( apply(sF23,sK4(sF23,sK18,sK20(sF24,sF26))) = apply(sK19,sK4(sF23,sK18,sK20(sF24,sF26)))
| in(sK20(sF24,sF26),sK17)
| sF24 = sF26
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4 ),
inference(resolution,[],[f356,f300]) ).
fof(f753,plain,
( apply(sF23,sK4(sF23,sK18,sK20(sF24,sF26))) = apply(sK19,sK4(sF23,sK18,sK20(sF24,sF26)))
| in(sK20(sF24,sF26),sK17)
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f745,f210]) ).
fof(f1049,plain,
( sF24 = sF26
| sK20(sF24,sF26) = apply(sK19,sK4(sK19,sK18,sK20(sF24,sF26)))
| sK20(sF24,sF26) = apply(sF23,sK4(sF23,sK18,sK20(sF24,sF26)))
| ~ spl27_3 ),
inference(resolution,[],[f521,f223]) ).
fof(f1376,plain,
! [X0,X1] :
( in(apply(sK19,sK4(sF23,X0,X1)),sK17)
| ~ relation(sK19)
| ~ function(sK19)
| ~ in(X1,relation_image(sF23,X0)) ),
inference(superposition,[],[f567,f203]) ).
fof(f1377,plain,
! [X0,X1] :
( in(apply(sK19,sK4(sF23,X0,X1)),sK17)
| ~ function(sK19)
| ~ in(X1,relation_image(sF23,X0)) ),
inference(forward_subsumption_resolution,[],[f1376,f167]) ).
fof(f1386,plain,
! [X0,X1] :
( in(apply(sK19,sK4(sF23,X0,X1)),sK17)
| ~ in(X1,relation_image(sF23,X0)) ),
inference(forward_subsumption_resolution,[],[f1377,f166]) ).
fof(f1615,plain,
( apply(sF23,sK4(sF23,sK18,sK20(sF24,sF26))) = apply(sK19,sK4(sF23,sK18,sK20(sF24,sF26)))
| in(sK20(sF24,sF26),sF25)
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f744,f210]) ).
fof(f1776,plain,
( sK20(sF24,sF26) = apply(sK19,sK4(sF23,sK18,sK20(sF24,sF26)))
| in(sK20(sF24,sF26),sK17)
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| ~ spl27_15 ),
inference(forward_demodulation,[],[f753,f404]) ).
fof(f1795,plain,
( sK20(sF24,sF26) = apply(sK19,sK4(sF23,sK18,sK20(sF24,sF26)))
| in(sK20(sF24,sF26),sF25)
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| ~ spl27_15 ),
inference(forward_demodulation,[],[f1615,f404]) ).
fof(f1810,definition,
( spl27_110
<=> sK20(sF24,sF26) = apply(sK19,sK4(sF23,sK18,sK20(sF24,sF26))) ),
introduced(definition,[new_symbols(definition,[spl27_110])],[avatar_definition]) ).
fof(f1812,plain,
( sK20(sF24,sF26) = apply(sK19,sK4(sF23,sK18,sK20(sF24,sF26)))
| ~ spl27_110 ),
inference(avatar_component_clause,[],[f1810]) ).
fof(f1813,plain,
( spl27_16
| spl27_110
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| ~ spl27_15 ),
inference(avatar_split_clause,[],[f1776,f402,f230,f218,f214,f1810,f406]) ).
fof(f1816,definition,
( spl27_111
<=> sK20(sF24,sF26) = apply(sK19,sK4(sK19,sK18,sK20(sF24,sF26))) ),
introduced(definition,[new_symbols(definition,[spl27_111])],[avatar_definition]) ).
fof(f1817,plain,
( sK20(sF24,sF26) != apply(sK19,sK4(sK19,sK18,sK20(sF24,sF26)))
| spl27_111 ),
inference(avatar_component_clause,[],[f1816]) ).
fof(f1818,plain,
( sK20(sF24,sF26) = apply(sK19,sK4(sK19,sK18,sK20(sF24,sF26)))
| ~ spl27_111 ),
inference(avatar_component_clause,[],[f1816]) ).
fof(f1831,definition,
( spl27_114
<=> in(sK20(sF24,sF26),sF25) ),
introduced(definition,[new_symbols(definition,[spl27_114])],[avatar_definition]) ).
fof(f1832,plain,
( ~ in(sK20(sF24,sF26),sF25)
| spl27_114 ),
inference(avatar_component_clause,[],[f1831]) ).
fof(f1833,plain,
( in(sK20(sF24,sF26),sF25)
| ~ spl27_114 ),
inference(avatar_component_clause,[],[f1831]) ).
fof(f1834,plain,
( spl27_114
| spl27_110
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| ~ spl27_15 ),
inference(avatar_split_clause,[],[f1795,f402,f230,f218,f214,f1810,f1831]) ).
fof(f1840,plain,
( in(sK20(sF24,sF26),sF25)
| sK20(sF24,sF26) = apply(sF23,sK4(sF23,sK18,sK20(sF24,sF26)))
| ~ spl27_3 ),
inference(forward_subsumption_resolution,[],[f530,f210]) ).
fof(f1844,plain,
( sK20(sF24,sF26) = apply(sK19,sK4(sK19,sK18,sK20(sF24,sF26)))
| sK20(sF24,sF26) = apply(sF23,sK4(sF23,sK18,sK20(sF24,sF26)))
| ~ spl27_3 ),
inference(forward_subsumption_resolution,[],[f1049,f210]) ).
fof(f1852,plain,
( in(sK20(sF24,sF26),sF25)
| ~ spl27_3
| spl27_15 ),
inference(forward_subsumption_resolution,[],[f1840,f403]) ).
fof(f1856,plain,
( sK20(sF24,sF26) = apply(sK19,sK4(sK19,sK18,sK20(sF24,sF26)))
| ~ spl27_3
| spl27_15 ),
inference(forward_subsumption_resolution,[],[f1844,f403]) ).
fof(f1866,plain,
( spl27_114
| ~ spl27_3
| spl27_15 ),
inference(avatar_split_clause,[],[f1852,f402,f222,f1831]) ).
fof(f1867,plain,
( spl27_111
| ~ spl27_3
| spl27_15 ),
inference(avatar_split_clause,[],[f1856,f402,f222,f1816]) ).
fof(f1868,plain,
( ~ in(sK20(sF24,sF26),sK17)
| in(sK20(sF24,sF26),sF26)
| ~ spl27_114 ),
inference(resolution,[],[f1833,f253]) ).
fof(f1871,plain,
( in(sK20(sF24,sF26),sF26)
| ~ spl27_16
| ~ spl27_114 ),
inference(forward_subsumption_resolution,[],[f1868,f408]) ).
fof(f1872,plain,
( sF24 = sF26
| ~ in(sK20(sF24,sF26),sF24)
| ~ spl27_16
| ~ spl27_114 ),
inference(resolution,[],[f1871,f173]) ).
fof(f1876,plain,
( ~ in(sK20(sF24,sF26),sF24)
| ~ spl27_16
| ~ spl27_114 ),
inference(forward_subsumption_resolution,[],[f1872,f210]) ).
fof(f1877,plain,
( ~ spl27_26
| ~ spl27_16
| ~ spl27_114 ),
inference(avatar_split_clause,[],[f1876,f1831,f406,f502]) ).
fof(f1910,plain,
( in(sK20(sF24,sF26),sF25)
| sF24 = sF26
| spl27_26 ),
inference(resolution,[],[f503,f299]) ).
fof(f1917,plain,
( ! [X0,X1] :
( ~ in(sK20(sF24,sF26),X0)
| ~ in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(sK19))
| in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(X1))
| ~ sP0(sK19,X0,X1) )
| ~ spl27_111 ),
inference(superposition,[],[f184,f1818]) ).
fof(f1921,definition,
( spl27_122
<=> in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(sK19)) ),
introduced(definition,[new_symbols(definition,[spl27_122])],[avatar_definition]) ).
fof(f1923,plain,
( ~ in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(sK19))
| spl27_122 ),
inference(avatar_component_clause,[],[f1921]) ).
fof(f1925,definition,
( spl27_123
<=> ! [X0,X1] :
( ~ in(sK20(sF24,sF26),X0)
| ~ sP0(sK19,X0,X1)
| in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(X1)) ) ),
introduced(definition,[new_symbols(definition,[spl27_123])],[avatar_definition]) ).
fof(f1926,plain,
( ! [X0,X1] :
( ~ in(sK20(sF24,sF26),X0)
| ~ sP0(sK19,X0,X1)
| in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(X1)) )
| ~ spl27_123 ),
inference(avatar_component_clause,[],[f1925]) ).
fof(f1927,plain,
( ~ spl27_122
| spl27_123
| ~ spl27_111 ),
inference(avatar_split_clause,[],[f1917,f1816,f1925,f1921]) ).
fof(f1937,plain,
( ~ in(sK20(sF24,sF26),relation_image(sK19,sK18))
| ~ relation(sK19)
| ~ function(sK19)
| spl27_122 ),
inference(resolution,[],[f1923,f195]) ).
fof(f1939,plain,
( ~ in(sK20(sF24,sF26),relation_image(sK19,sK18))
| ~ function(sK19)
| spl27_122 ),
inference(forward_subsumption_resolution,[],[f1937,f167]) ).
fof(f1940,plain,
( ~ in(sK20(sF24,sF26),relation_image(sK19,sK18))
| spl27_122 ),
inference(forward_subsumption_resolution,[],[f1939,f166]) ).
fof(f1941,plain,
( ~ in(sK20(sF24,sF26),sF25)
| spl27_122 ),
inference(forward_demodulation,[],[f1940,f207]) ).
fof(f1942,plain,
( $false
| ~ spl27_114
| spl27_122 ),
inference(forward_subsumption_resolution,[],[f1941,f1833]) ).
fof(f1943,plain,
( ~ spl27_114
| spl27_122 ),
inference(avatar_contradiction_clause,[],[f1942]) ).
fof(f1945,plain,
( sF24 = sF26
| spl27_26
| spl27_114 ),
inference(forward_subsumption_resolution,[],[f1910,f1832]) ).
fof(f1946,plain,
( $false
| spl27_26
| spl27_114 ),
inference(forward_subsumption_resolution,[],[f1945,f210]) ).
fof(f1947,plain,
( spl27_26
| spl27_114 ),
inference(avatar_contradiction_clause,[],[f1946]) ).
fof(f1957,plain,
( in(sK20(sF24,sF26),sK17)
| ~ in(sK20(sF24,sF26),relation_image(sF23,sK18))
| ~ spl27_110 ),
inference(superposition,[],[f1386,f1812]) ).
fof(f1965,plain,
( ! [X0] :
( in(sK20(sF24,sF26),relation_image(sK19,X0))
| ~ in(sK4(sF23,sK18,sK20(sF24,sF26)),relation_dom(sK19))
| ~ in(sK4(sF23,sK18,sK20(sF24,sF26)),X0)
| ~ relation(sK19)
| ~ function(sK19) )
| ~ spl27_110 ),
inference(superposition,[],[f194,f1812]) ).
fof(f1966,plain,
( ! [X0] :
( in(sK20(sF24,sF26),relation_image(sK19,X0))
| ~ in(sK4(sF23,sK18,sK20(sF24,sF26)),relation_dom(sK19))
| ~ in(sK4(sF23,sK18,sK20(sF24,sF26)),X0)
| ~ function(sK19) )
| ~ spl27_110 ),
inference(forward_subsumption_resolution,[],[f1965,f167]) ).
fof(f1968,definition,
( spl27_125
<=> in(sK4(sF23,sK18,sK20(sF24,sF26)),relation_dom(sK19)) ),
introduced(definition,[new_symbols(definition,[spl27_125])],[avatar_definition]) ).
fof(f1970,plain,
( ~ in(sK4(sF23,sK18,sK20(sF24,sF26)),relation_dom(sK19))
| spl27_125 ),
inference(avatar_component_clause,[],[f1968]) ).
fof(f1977,plain,
( ! [X0] :
( in(sK20(sF24,sF26),relation_image(sK19,X0))
| ~ in(sK4(sF23,sK18,sK20(sF24,sF26)),relation_dom(sK19))
| ~ in(sK4(sF23,sK18,sK20(sF24,sF26)),X0) )
| ~ spl27_110 ),
inference(forward_subsumption_resolution,[],[f1966,f166]) ).
fof(f1980,definition,
( spl27_127
<=> in(sK20(sF24,sF26),sF26) ),
introduced(definition,[new_symbols(definition,[spl27_127])],[avatar_definition]) ).
fof(f1981,plain,
( ~ in(sK20(sF24,sF26),sF26)
| spl27_127 ),
inference(avatar_component_clause,[],[f1980]) ).
fof(f1982,plain,
( in(sK20(sF24,sF26),sF26)
| ~ spl27_127 ),
inference(avatar_component_clause,[],[f1980]) ).
fof(f1985,definition,
( spl27_128
<=> ! [X0] :
( in(sK20(sF24,sF26),relation_image(sK19,X0))
| ~ in(sK4(sF23,sK18,sK20(sF24,sF26)),X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_128])],[avatar_definition]) ).
fof(f1986,plain,
( ! [X0] :
( ~ in(sK4(sF23,sK18,sK20(sF24,sF26)),X0)
| in(sK20(sF24,sF26),relation_image(sK19,X0)) )
| ~ spl27_128 ),
inference(avatar_component_clause,[],[f1985]) ).
fof(f1987,plain,
( ~ spl27_125
| spl27_128
| ~ spl27_110 ),
inference(avatar_split_clause,[],[f1977,f1810,f1985,f1968]) ).
fof(f1992,plain,
( ~ in(sK20(sF24,sF26),relation_image(sF23,sK18))
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| spl27_125 ),
inference(resolution,[],[f1970,f351]) ).
fof(f2706,plain,
( sK20(sF24,sF26) = apply(sK19,sK4(sK19,sK18,sK20(sF24,sF26)))
| ~ spl27_114 ),
inference(resolution,[],[f1833,f226]) ).
fof(f2708,plain,
( $false
| spl27_111
| ~ spl27_114 ),
inference(forward_subsumption_resolution,[],[f2706,f1817]) ).
fof(f2709,plain,
( spl27_111
| ~ spl27_114 ),
inference(avatar_contradiction_clause,[],[f2708]) ).
fof(f2774,plain,
( ! [X2,X0,X1] :
( ~ sP0(sK19,set_intersection2(X0,X1),X2)
| in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(X2))
| ~ in(sK20(sF24,sF26),X0)
| ~ in(sK20(sF24,sF26),X1) )
| ~ spl27_123 ),
inference(resolution,[],[f1926,f198]) ).
fof(f2811,definition,
( spl27_177
<=> in(sK4(sK19,sK18,sK20(sF24,sF26)),sK18) ),
introduced(definition,[new_symbols(definition,[spl27_177])],[avatar_definition]) ).
fof(f2812,plain,
( in(sK4(sK19,sK18,sK20(sF24,sF26)),sK18)
| ~ spl27_177 ),
inference(avatar_component_clause,[],[f2811]) ).
fof(f2813,plain,
( ~ in(sK4(sK19,sK18,sK20(sF24,sF26)),sK18)
| spl27_177 ),
inference(avatar_component_clause,[],[f2811]) ).
fof(f2818,plain,
( in(sK20(sF24,sF26),sK17)
| ~ spl27_127 ),
inference(resolution,[],[f1982,f244]) ).
fof(f2820,plain,
( ! [X0] :
( in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(X0))
| ~ sP0(sK19,sK17,X0) )
| ~ spl27_16
| ~ spl27_123 ),
inference(resolution,[],[f408,f1926]) ).
fof(f2825,plain,
( ! [X0,X1] :
( in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(relation_rng_restriction(set_intersection2(X0,X1),sK19)))
| ~ in(sK20(sF24,sF26),X0)
| ~ in(sK20(sF24,sF26),X1)
| ~ relation(sK19)
| ~ function(sK19) )
| ~ spl27_123 ),
inference(resolution,[],[f2774,f239]) ).
fof(f2832,plain,
( ! [X0,X1] :
( in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(relation_rng_restriction(set_intersection2(X0,X1),sK19)))
| ~ in(sK20(sF24,sF26),X0)
| ~ in(sK20(sF24,sF26),X1)
| ~ function(sK19) )
| ~ spl27_123 ),
inference(forward_subsumption_resolution,[],[f2825,f167]) ).
fof(f2833,plain,
( ! [X0,X1] :
( in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(relation_rng_restriction(set_intersection2(X0,X1),sK19)))
| ~ in(sK20(sF24,sF26),X0)
| ~ in(sK20(sF24,sF26),X1) )
| ~ spl27_123 ),
inference(forward_subsumption_resolution,[],[f2832,f166]) ).
fof(f2844,plain,
( ! [X0] :
( in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(relation_rng_restriction(X0,sK19)))
| ~ in(sK20(sF24,sF26),X0)
| ~ in(sK20(sF24,sF26),X0) )
| ~ spl27_123 ),
inference(superposition,[],[f2833,f146]) ).
fof(f2846,plain,
( ! [X0] :
( in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(relation_rng_restriction(X0,sK19)))
| ~ in(sK20(sF24,sF26),X0) )
| ~ spl27_123 ),
inference(duplicate_literal_removal,[],[f2844]) ).
fof(f2895,plain,
( in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(sF23))
| ~ in(sK20(sF24,sF26),sK17)
| ~ spl27_123 ),
inference(superposition,[],[f2846,f203]) ).
fof(f2896,plain,
( in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(sF23))
| ~ spl27_16
| ~ spl27_123 ),
inference(forward_subsumption_resolution,[],[f2895,f408]) ).
fof(f2973,plain,
( in(sK20(sF24,sF26),sF24)
| sF24 = sF26
| spl27_127 ),
inference(resolution,[],[f1981,f172]) ).
fof(f2981,plain,
( ~ in(sK20(sF24,sF26),relation_image(sK19,sK18))
| ~ relation(sK19)
| ~ function(sK19)
| spl27_177 ),
inference(resolution,[],[f2813,f196]) ).
fof(f2982,plain,
( ~ in(sK20(sF24,sF26),relation_image(sK19,sK18))
| ~ function(sK19)
| spl27_177 ),
inference(forward_subsumption_resolution,[],[f2981,f167]) ).
fof(f2983,plain,
( ~ in(sK20(sF24,sF26),relation_image(sK19,sK18))
| spl27_177 ),
inference(forward_subsumption_resolution,[],[f2982,f166]) ).
fof(f2984,plain,
( ~ in(sK20(sF24,sF26),sF25)
| spl27_177 ),
inference(forward_demodulation,[],[f2983,f207]) ).
fof(f3090,plain,
( ~ sP0(sK19,sK17,sF23)
| apply(sK19,sK4(sK19,sK18,sK20(sF24,sF26))) = apply(sF23,sK4(sK19,sK18,sK20(sF24,sF26)))
| ~ spl27_4
| ~ spl27_16
| ~ spl27_123 ),
inference(resolution,[],[f2820,f327]) ).
fof(f3095,plain,
( apply(sK19,sK4(sK19,sK18,sK20(sF24,sF26))) = apply(sF23,sK4(sK19,sK18,sK20(sF24,sF26)))
| ~ spl27_4
| ~ spl27_16
| ~ spl27_123 ),
inference(forward_subsumption_resolution,[],[f3090,f232]) ).
fof(f3097,plain,
( sK20(sF24,sF26) = apply(sF23,sK4(sK19,sK18,sK20(sF24,sF26)))
| ~ spl27_4
| ~ spl27_16
| ~ spl27_111
| ~ spl27_123 ),
inference(forward_demodulation,[],[f3095,f1818]) ).
fof(f3269,plain,
( ~ in(sK20(sF24,sF26),sF24)
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| spl27_125 ),
inference(forward_demodulation,[],[f1992,f205]) ).
fof(f3302,plain,
( $false
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| ~ spl27_26
| spl27_125 ),
inference(forward_subsumption_resolution,[],[f3269,f504]) ).
fof(f3303,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| ~ spl27_26
| spl27_125 ),
inference(avatar_contradiction_clause,[],[f3302]) ).
fof(f3353,plain,
( in(sK20(sF24,sF26),relation_image(sK19,sK18))
| ~ in(sK20(sF24,sF26),relation_image(sF23,sK18))
| ~ relation(sF23)
| ~ function(sF23)
| ~ spl27_128 ),
inference(resolution,[],[f1986,f196]) ).
fof(f3357,plain,
( in(sK20(sF24,sF26),relation_image(sK19,sK18))
| ~ in(sK20(sF24,sF26),relation_image(sF23,sK18))
| ~ function(sF23)
| ~ spl27_2
| ~ spl27_128 ),
inference(forward_subsumption_resolution,[],[f3353,f219]) ).
fof(f3360,plain,
( in(sK20(sF24,sF26),relation_image(sK19,sK18))
| ~ in(sK20(sF24,sF26),relation_image(sF23,sK18))
| ~ spl27_1
| ~ spl27_2
| ~ spl27_128 ),
inference(forward_subsumption_resolution,[],[f3357,f215]) ).
fof(f3362,plain,
( in(sK20(sF24,sF26),sF25)
| ~ in(sK20(sF24,sF26),relation_image(sF23,sK18))
| ~ spl27_1
| ~ spl27_2
| ~ spl27_128 ),
inference(forward_demodulation,[],[f3360,f207]) ).
fof(f3363,plain,
( ~ in(sK20(sF24,sF26),relation_image(sF23,sK18))
| ~ spl27_1
| ~ spl27_2
| spl27_114
| ~ spl27_128 ),
inference(forward_subsumption_resolution,[],[f3362,f1832]) ).
fof(f3364,plain,
( ~ in(sK20(sF24,sF26),sF24)
| ~ spl27_1
| ~ spl27_2
| spl27_114
| ~ spl27_128 ),
inference(forward_demodulation,[],[f3363,f205]) ).
fof(f3365,plain,
( $false
| ~ spl27_1
| ~ spl27_2
| ~ spl27_26
| spl27_114
| ~ spl27_128 ),
inference(forward_subsumption_resolution,[],[f3364,f504]) ).
fof(f3366,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_26
| spl27_114
| ~ spl27_128 ),
inference(avatar_contradiction_clause,[],[f3365]) ).
fof(f3371,plain,
( $false
| ~ spl27_114
| spl27_177 ),
inference(forward_subsumption_resolution,[],[f2984,f1833]) ).
fof(f3372,plain,
( ~ spl27_114
| spl27_177 ),
inference(avatar_contradiction_clause,[],[f3371]) ).
fof(f3377,plain,
( ~ in(sK20(sF24,sF26),relation_image(sF23,sK18))
| spl27_16
| ~ spl27_110 ),
inference(forward_subsumption_resolution,[],[f1957,f407]) ).
fof(f3401,plain,
( ~ in(sK20(sF24,sF26),sF24)
| spl27_16
| ~ spl27_110 ),
inference(forward_demodulation,[],[f3377,f205]) ).
fof(f3412,plain,
( $false
| spl27_16
| ~ spl27_26
| ~ spl27_110 ),
inference(forward_subsumption_resolution,[],[f3401,f504]) ).
fof(f3413,plain,
( spl27_16
| ~ spl27_26
| ~ spl27_110 ),
inference(avatar_contradiction_clause,[],[f3412]) ).
fof(f3416,plain,
( sF24 = sF26
| spl27_26
| spl27_127 ),
inference(forward_subsumption_resolution,[],[f2973,f503]) ).
fof(f3421,plain,
( $false
| spl27_26
| spl27_127 ),
inference(forward_subsumption_resolution,[],[f3416,f210]) ).
fof(f3422,plain,
( spl27_26
| spl27_127 ),
inference(avatar_contradiction_clause,[],[f3421]) ).
fof(f3425,plain,
( $false
| spl27_16
| ~ spl27_127 ),
inference(forward_subsumption_resolution,[],[f2818,f407]) ).
fof(f3426,plain,
( spl27_16
| ~ spl27_127 ),
inference(avatar_contradiction_clause,[],[f3425]) ).
fof(f3493,plain,
( in(sK20(sF24,sF26),sF24)
| ~ in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(sF23))
| ~ in(sK4(sK19,sK18,sK20(sF24,sF26)),sK18)
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| ~ spl27_16
| ~ spl27_111
| ~ spl27_123 ),
inference(superposition,[],[f266,f3097]) ).
fof(f3500,plain,
( ~ in(sK4(sK19,sK18,sK20(sF24,sF26)),relation_dom(sF23))
| ~ in(sK4(sK19,sK18,sK20(sF24,sF26)),sK18)
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| ~ spl27_16
| spl27_26
| ~ spl27_111
| ~ spl27_123 ),
inference(forward_subsumption_resolution,[],[f3493,f503]) ).
fof(f3503,plain,
( ~ in(sK4(sK19,sK18,sK20(sF24,sF26)),sK18)
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| ~ spl27_16
| spl27_26
| ~ spl27_111
| ~ spl27_123 ),
inference(forward_subsumption_resolution,[],[f3500,f2896]) ).
fof(f3506,plain,
( $false
| ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| ~ spl27_16
| spl27_26
| ~ spl27_111
| ~ spl27_123
| ~ spl27_177 ),
inference(forward_subsumption_resolution,[],[f3503,f2812]) ).
fof(f3507,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| ~ spl27_16
| spl27_26
| ~ spl27_111
| ~ spl27_123
| ~ spl27_177 ),
inference(avatar_contradiction_clause,[],[f3506]) ).
cnf(s1,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_3 ),
inference(sat_conversion,[],[f224]) ).
cnf(s3,plain,
spl27_4,
inference(sat_conversion,[],[f243]) ).
cnf(s4,plain,
spl27_1,
inference(sat_conversion,[],[f250]) ).
cnf(s5,plain,
spl27_2,
inference(sat_conversion,[],[f258]) ).
cnf(s10,plain,
( ~ spl27_3
| spl27_15
| spl27_16 ),
inference(sat_conversion,[],[f409]) ).
cnf(s86,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| ~ spl27_15
| spl27_16
| spl27_110 ),
inference(sat_conversion,[],[f1813]) ).
cnf(s90,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| ~ spl27_15
| spl27_110
| spl27_114 ),
inference(sat_conversion,[],[f1834]) ).
cnf(s94,plain,
( ~ spl27_3
| spl27_15
| spl27_114 ),
inference(sat_conversion,[],[f1866]) ).
cnf(s96,plain,
( ~ spl27_3
| spl27_15
| spl27_111 ),
inference(sat_conversion,[],[f1867]) ).
cnf(s97,plain,
( ~ spl27_16
| ~ spl27_26
| ~ spl27_114 ),
inference(sat_conversion,[],[f1877]) ).
cnf(s102,plain,
( ~ spl27_111
| ~ spl27_122
| spl27_123 ),
inference(sat_conversion,[],[f1927]) ).
cnf(s104,plain,
( ~ spl27_114
| spl27_122 ),
inference(sat_conversion,[],[f1943]) ).
cnf(s105,plain,
( spl27_26
| spl27_114 ),
inference(sat_conversion,[],[f1947]) ).
cnf(s109,plain,
( ~ spl27_110
| ~ spl27_125
| spl27_128 ),
inference(sat_conversion,[],[f1987]) ).
cnf(s171,plain,
( spl27_111
| ~ spl27_114 ),
inference(sat_conversion,[],[f2709]) ).
cnf(s214,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| ~ spl27_26
| spl27_125 ),
inference(sat_conversion,[],[f3303]) ).
cnf(s223,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_26
| spl27_114
| ~ spl27_128 ),
inference(sat_conversion,[],[f3366]) ).
cnf(s225,plain,
( ~ spl27_114
| spl27_177 ),
inference(sat_conversion,[],[f3372]) ).
cnf(s232,plain,
( spl27_16
| ~ spl27_26
| ~ spl27_110 ),
inference(sat_conversion,[],[f3413]) ).
cnf(s233,plain,
( spl27_26
| spl27_127 ),
inference(sat_conversion,[],[f3422]) ).
cnf(s234,plain,
( spl27_16
| ~ spl27_127 ),
inference(sat_conversion,[],[f3426]) ).
cnf(s235,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_4
| ~ spl27_16
| spl27_26
| ~ spl27_111
| ~ spl27_123
| ~ spl27_177 ),
inference(sat_conversion,[],[f3507]) ).
cnf(s237,plain,
spl27_3,
inference(rat,[],[s1,s5,s4]) ).
cnf(s238,plain,
spl27_15,
inference(rat,[],[s235,s102,s97,s104,s225,s10,s94,s96,s5,s4,s3,s237]) ).
cnf(s239,plain,
( spl27_26
| ~ spl27_16 ),
inference(rat,[],[s102,s235,s104,s171,s225,s105,s5,s4,s3]) ).
cnf(s240,plain,
~ spl27_16,
inference(rat,[],[s109,s90,s223,s97,s214,s239,s5,s4,s3,s238]) ).
cnf(s241,plain,
~ spl27_127,
inference(rat,[],[s234,s240]) ).
cnf(s242,plain,
spl27_110,
inference(rat,[],[s86,s238,s3,s4,s5,s240]) ).
cnf(s243,plain,
spl27_26,
inference(rat,[],[s233,s241]) ).
cnf(s245,plain,
$false,
inference(rat,[],[s232,s240,s243,s242]) ).
fof(f3508,plain,
$false,
inference(avatar_sat_refutation,[],[s245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU057+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:33:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 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
% 7.23/2.15 % (4182364)Detected formulas, will run a generic FOF schedule.
% 7.23/2.15 % (4182381)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=3911304074:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.23/2.15 % (4182386)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=74633500:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.23/2.15 % (4182387)dis-21_1_sil=8000:lcm=predicate:random_seed=3305958594: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)
% 7.23/2.15 % (4182385)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3710528087:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.23/2.15 % (4182384)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2968277241:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.23/2.15 % (4182383)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=4234439730:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.23/2.15 % (4182382)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=3963606835:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.23/2.15 % (4182384)Refutation not found, incomplete strategy
% 7.23/2.15 % (4182384)------------------------------
% 7.23/2.15 % (4182384)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.23/2.15 % (4182384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.23/2.15 % (4182384)CaDiCaL version: 2.1.3
% 7.23/2.15 % (4182384)Termination reason: Refutation not found, incomplete strategy
% 7.23/2.15 % (4182384)Time elapsed: 0.002 s
% 7.23/2.15 % (4182384)Peak memory usage: 88 MB
% 7.23/2.15 % (4182384)Instructions burned: 2 (million)
% 7.23/2.15 % (4182385)Instruction limit reached!
% 7.23/2.15 % (4182385)------------------------------
% 7.23/2.15 % (4182385)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.23/2.15 % (4182385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.23/2.15 % (4182385)CaDiCaL version: 2.1.3
% 7.23/2.15 % (4182385)Termination reason: Instruction limit
% 7.23/2.15 % (4182385)Termination phase: Saturation
% 7.23/2.15 % (4182385)Time elapsed: 0.071 s
% 7.23/2.15 % (4182385)Peak memory usage: 88 MB
% 7.23/2.15 % (4182385)Instructions burned: 119 (million)
% 7.23/2.15 % (4182387)Instruction limit reached!
% 7.23/2.15 % (4182387)------------------------------
% 7.23/2.15 % (4182387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.23/2.15 % (4182387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.23/2.15 % (4182387)CaDiCaL version: 2.1.3
% 7.23/2.15 % (4182387)Termination reason: Instruction limit
% 7.23/2.15 % (4182387)Termination phase: Saturation
% 7.23/2.15 % (4182387)Time elapsed: 0.071 s
% 7.23/2.15 % (4182387)Peak memory usage: 91 MB
% 7.23/2.15 % (4182387)Instructions burned: 131 (million)
% 7.23/2.15 % (4182386)Instruction limit reached!
% 7.23/2.15 % (4182386)------------------------------
% 7.23/2.15 % (4182386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.23/2.15 % (4182386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.23/2.15 % (4182386)CaDiCaL version: 2.1.3
% 7.23/2.15 % (4182386)Termination reason: Instruction limit
% 7.23/2.15 % (4182386)Termination phase: Saturation
% 7.23/2.15 % (4182386)Time elapsed: 0.091 s
% 7.23/2.15 % (4182386)Peak memory usage: 89 MB
% 7.23/2.15 % (4182386)Instructions burned: 139 (million)
% 7.23/2.15 % (4182441)lrs+10_1_sil=8000:sp=occurrence:random_seed=375119169:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 7.23/2.15 % (4182443)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4081610145:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 7.23/2.15 % (4182452)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1073683627:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 7.23/2.15 % (4182384)------------------------------
% 7.23/2.15 % (4182384)------------------------------
% 7.23/2.15 % (4182443)Instruction limit reached!
% 7.23/2.15 % (4182443)------------------------------
% 7.23/2.15 % (4182443)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.23/2.15 % (4182443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.23/2.15 % (4182443)CaDiCaL version: 2.1.3
% 7.23/2.15 % (4182443)Termination reason: Instruction limit
% 7.23/2.15 % (4182443)Termination phase: Saturation
% 7.23/2.15 % (4182443)Time elapsed: 0.081 s
% 7.23/2.15 % (4182443)Peak memory usage: 90 MB
% 7.23/2.15 % (4182443)Instructions burned: 157 (million)
% 7.23/2.15 % (4182441)Instruction limit reached!
% 7.23/2.15 % (4182441)------------------------------
% 7.23/2.15 % (4182441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.23/2.15 % (4182441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.23/2.15 % (4182441)CaDiCaL version: 2.1.3
% 7.23/2.15 % (4182441)Termination reason: Instruction limit
% 7.23/2.15 % (4182441)Termination phase: Saturation
% 7.23/2.15 % (4182441)Time elapsed: 0.168 s
% 7.23/2.15 % (4182441)Peak memory usage: 91 MB
% 7.23/2.15 % (4182441)Instructions burned: 285 (million)
% 7.23/2.15 % (4182497)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=1730953043:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 7.23/2.15 % (4182452)Instruction limit reached!
% 7.23/2.15 % (4182452)------------------------------
% 7.23/2.15 % (4182452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.23/2.15 % (4182452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.23/2.15 % (4182452)CaDiCaL version: 2.1.3
% 7.23/2.15 % (4182452)Termination reason: Instruction limit
% 7.23/2.15 % (4182452)Termination phase: Saturation
% 7.23/2.15 % (4182452)Time elapsed: 0.207 s
% 7.23/2.15 % (4182452)Peak memory usage: 91 MB
% 7.23/2.15 % (4182452)Instructions burned: 326 (million)
% 7.23/2.15 % (4182507)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1589343183:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 7.23/2.15 % (4182507)Refutation not found, incomplete strategy
% 7.23/2.15 % (4182507)------------------------------
% 7.23/2.15 % (4182507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.23/2.15 % (4182507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.23/2.15 % (4182507)CaDiCaL version: 2.1.3
% 7.23/2.15 % (4182507)Termination reason: Refutation not found, incomplete strategy
% 7.23/2.15 % (4182507)Time elapsed: 0.003 s
% 7.23/2.15 % (4182507)Peak memory usage: 88 MB
% 7.23/2.15 % (4182507)Instructions burned: 3 (million)
% 7.23/2.15 % (4182508)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1737735090:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 7.23/2.15 % (4182497)Instruction limit reached!
% 7.23/2.15 % (4182497)------------------------------
% 7.23/2.15 % (4182497)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.23/2.15 % (4182497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.23/2.15 % (4182497)CaDiCaL version: 2.1.3
% 7.23/2.15 % (4182497)Termination reason: Instruction limit
% 7.23/2.15 % (4182497)Termination phase: Saturation
% 7.23/2.15 % (4182497)Time elapsed: 0.135 s
% 7.23/2.15 % (4182497)Peak memory usage: 95 MB
% 7.23/2.15 % (4182497)Instructions burned: 249 (million)
% 7.23/2.15 % (4182520)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3286282004:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 7.23/2.15 % (4182520)Instruction limit reached!
% 7.23/2.15 % (4182520)------------------------------
% 7.23/2.15 % (4182520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.23/2.15 % (4182520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.23/2.15 % (4182520)CaDiCaL version: 2.1.3
% 7.23/2.15 % (4182520)Termination reason: Instruction limit
% 7.23/2.15 % (4182520)Termination phase: Saturation
% 7.23/2.15 % (4182520)Time elapsed: 0.077 s
% 7.23/2.15 % (4182520)Peak memory usage: 90 MB
% 7.23/2.15 % (4182520)Instructions burned: 113 (million)
% 7.23/2.15 % (4182560)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2456361407:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 7.23/2.15 % (4182507)------------------------------
% 7.23/2.15 % (4182507)------------------------------
% 7.23/2.15 % (4182381)First to succeed.
% 7.23/2.15 % (4182383)Also succeeded, but the first one will report.
% 7.23/2.15 % (4182560)Instruction limit reached!
% 7.23/2.15 % (4182560)------------------------------
% 7.23/2.15 % (4182560)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.23/2.15 % (4182560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.23/2.15 % (4182560)CaDiCaL version: 2.1.3
% 7.23/2.15 % (4182560)Termination reason: Instruction limit
% 7.23/2.15 % (4182560)Termination phase: Saturation
% 7.23/2.15 % (4182560)Time elapsed: 0.067 s
% 7.23/2.15 % (4182560)Peak memory usage: 89 MB
% 7.23/2.15 % (4182560)Instructions burned: 128 (million)
% 7.23/2.15 % (4182381)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4182364"
% 7.23/2.15 % (4182562)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3320571226:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 7.23/2.15 % (4182564)lrs+10_1_sil=8000:sp=occurrence:random_seed=360211:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 7.23/2.15 % (4182562)Instruction limit reached!
% 7.23/2.15 % (4182562)------------------------------
% 7.23/2.15 % (4182562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.23/2.15 % (4182562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.23/2.15 % (4182562)CaDiCaL version: 2.1.3
% 7.23/2.15 % (4182562)Termination reason: Instruction limit
% 7.23/2.15 % (4182562)Termination phase: Saturation
% 7.23/2.15 % (4182562)Time elapsed: 0.069 s
% 7.23/2.15 % (4182562)Peak memory usage: 89 MB
% 7.23/2.15 % (4182562)Instructions burned: 114 (million)
% 7.23/2.15 % (4182565)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=442424658:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 7.23/2.15 % (4182565)Refutation not found, incomplete strategy
% 7.23/2.15 % (4182565)------------------------------
% 7.23/2.15 % (4182565)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.23/2.15 % (4182565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.23/2.15 % (4182565)CaDiCaL version: 2.1.3
% 7.23/2.15 % (4182565)Termination reason: Refutation not found, incomplete strategy
% 7.23/2.15 % (4182565)Time elapsed: 0.003 s
% 7.23/2.15 % (4182565)Peak memory usage: 88 MB
% 7.23/2.15 % (4182565)Instructions burned: 4 (million)
% 7.23/2.15 % (4182570)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=4227261720:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 7.23/2.15 % (4182568)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3176885990:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 7.23/2.15 % (4182381)Refutation found. Thanks to Tanya!
% 7.23/2.15 % SZS status Theorem for theBenchmark
% 7.23/2.15 % SZS output start Proof for theBenchmark
% See solution above
% 8.66/2.24 % (4182381)------------------------------
% 8.66/2.24 % (4182381)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.66/2.24 % (4182381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.66/2.24 % (4182381)CaDiCaL version: 2.1.3
% 8.66/2.24 % (4182381)Termination reason: Refutation
% 8.66/2.24 % (4182381)Time elapsed: 0.761 s
% 8.66/2.24 % (4182381)Peak memory usage: 134 MB
% 8.66/2.24 % (4182381)Instructions burned: 1486 (million)
% 8.66/2.24 % (4182381)------------------------------
% 8.66/2.24 % (4182381)------------------------------
% 8.66/2.24 % (4182364)Success in time 1.123 s
% 8.66/2.24 % Vampire exiting
%------------------------------------------------------------------------------