%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU073+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 12:47:11 PM UTC 2026
% Result : Theorem 4.60s 1.81s
% Output : Refutation 8.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 23
% Syntax : Number of formulae : 247 ( 24 unt; 15 def)
% Number of atoms : 1190 ( 214 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 1661 ( 718 ~; 754 |; 137 &)
% ( 35 <=>; 16 =>; 0 <=; 1 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 12 prp; 0-4 aty)
% Number of functors : 22 ( 22 usr; 5 con; 0-3 aty)
% Number of variables : 303 ( 0 sgn 270 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f6,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f7,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f8,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( relation(function_inverse(X0))
& function(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f33,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> relation_image(X1,X0) = relation_inverse_image(function_inverse(X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t154_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> relation_image(X1,X0) = relation_inverse_image(function_inverse(X1),X0) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f37,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f40,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
=> ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) )
& ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
=> ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f41,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X1)
& in(X0,relation_dom(X1)) )
=> ( X0 = apply(function_inverse(X1),apply(X1,X0))
& X0 = apply(relation_composition(X1,function_inverse(X1)),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funct_1) ).
fof(f55,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,[],[f5]) ).
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(flattening,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f58,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f62,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f61]) ).
fof(f78,plain,
? [X0,X1] :
( relation_image(X1,X0) != relation_inverse_image(function_inverse(X1),X0)
& one_to_one(X1)
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f79,plain,
? [X0,X1] :
( relation_image(X1,X0) != relation_inverse_image(function_inverse(X1),X0)
& one_to_one(X1)
& relation(X1)
& function(X1) ),
inference(flattening,[],[f78]) ).
fof(f83,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f88,plain,
! [X0] :
( ! [X1] :
( ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( ( X0 = apply(function_inverse(X1),apply(X1,X0))
& X0 = apply(relation_composition(X1,function_inverse(X1)),X0) )
| ~ one_to_one(X1)
| ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f90,plain,
! [X0,X1] :
( ( X0 = apply(function_inverse(X1),apply(X1,X0))
& X0 = apply(relation_composition(X1,function_inverse(X1)),X0) )
| ~ one_to_one(X1)
| ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f89]) ).
fof(f95,definition,
! [X0,X2,X3,X1] :
( sP0(X0,X2,X3,X1)
<=> ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f96,plain,
! [X0] :
( ! [X1] :
( ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& sP0(X0,X2,X3,X1) ) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(definition_folding,[],[f88,f95]) ).
fof(f97,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,[],[f56]) ).
fof(f98,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,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != sK1(X0,X1,X2) )
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( in(sK2(X0,X1,X2),relation_dom(X0))
& in(sK2(X0,X1,X2),X1)
& sK1(X0,X1,X2) = apply(X0,sK2(X0,X1,X2)) )
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6 ) )
& ( ( in(sK3(X0,X1,X6),relation_dom(X0))
& in(sK3(X0,X1,X6),X1)
& apply(X0,sK3(X0,X1,X6)) = X6 )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X3,sK1(X0,X1,X2)),skolemize(X5,sK2(X0,X1,X2)),skolemize(X8,sK3(X0,X1,X6))],[f98]) ).
fof(f100,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f58]) ).
fof(f101,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f101]) ).
fof(f103,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ~ in(sK4(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK4(X0,X1,X2)),X1)
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( in(sK4(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK4(X0,X1,X2)),X1) )
| in(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f102]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f60]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& apply(X0,X4) = X2 )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ? [X7] :
( in(X7,relation_dom(X0))
& apply(X0,X7) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f104]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK5(X0,X1) )
| ~ in(sK5(X0,X1),X1) )
& ( ( in(sK6(X0,X1),relation_dom(X0))
& sK5(X0,X1) = apply(X0,sK6(X0,X1)) )
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK7(X0,X5),relation_dom(X0))
& apply(X0,sK7(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X2,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X7,sK7(X0,X5))],[f105]) ).
fof(f118,plain,
( relation_image(sK20,sK19) != relation_inverse_image(function_inverse(sK20),sK19)
& one_to_one(sK20)
& relation(sK20)
& function(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20]),skolemize(X0,sK19),skolemize(X1,sK20)],[f79]) ).
fof(f119,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f83]) ).
fof(f120,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK21(X0,X1),X1)
| ~ in(sK21(X0,X1),X0) )
& ( in(sK21(X0,X1),X1)
| in(sK21(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X2,sK21(X0,X1))],[f119]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = function_inverse(X0)
| relation_rng(X0) != relation_dom(X1)
| ? [X2,X3] :
( ( ( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
& in(X2,relation_rng(X0))
& apply(X1,X2) = X3 )
| ~ sP0(X0,X2,X3,X1) ) )
& ( ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& sP0(X0,X2,X3,X1) ) )
| function_inverse(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f96]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = function_inverse(X0)
| relation_rng(X0) != relation_dom(X1)
| ? [X2,X3] :
( ( ( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
& in(X2,relation_rng(X0))
& apply(X1,X2) = X3 )
| ~ sP0(X0,X2,X3,X1) ) )
& ( ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& sP0(X0,X2,X3,X1) ) )
| function_inverse(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f124]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = function_inverse(X0)
| relation_rng(X0) != relation_dom(X1)
| ? [X2,X3] :
( ( ( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
& in(X2,relation_rng(X0))
& apply(X1,X2) = X3 )
| ~ sP0(X0,X2,X3,X1) ) )
& ( ( relation_dom(X1) = relation_rng(X0)
& ! [X4,X5] :
( ( ( in(X5,relation_dom(X0))
& apply(X0,X5) = X4 )
| ~ in(X4,relation_rng(X0))
| apply(X1,X4) != X5 )
& sP0(X0,X4,X5,X1) ) )
| function_inverse(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f125]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = function_inverse(X0)
| relation_rng(X0) != relation_dom(X1)
| ( ( ~ in(sK23(X0,X1),relation_dom(X0))
| sK22(X0,X1) != apply(X0,sK23(X0,X1)) )
& in(sK22(X0,X1),relation_rng(X0))
& sK23(X0,X1) = apply(X1,sK22(X0,X1)) )
| ~ sP0(X0,sK22(X0,X1),sK23(X0,X1),X1) )
& ( ( relation_dom(X1) = relation_rng(X0)
& ! [X4,X5] :
( ( ( in(X5,relation_dom(X0))
& apply(X0,X5) = X4 )
| ~ in(X4,relation_rng(X0))
| apply(X1,X4) != X5 )
& sP0(X0,X4,X5,X1) ) )
| function_inverse(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23]),skolemize(X2,sK22(X0,X1)),skolemize(X3,sK23(X0,X1))],[f126]) ).
fof(f134,plain,
! [X2,X0,X1,X6] :
( apply(X0,sK3(X0,X1,X6)) = X6
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f135,plain,
! [X2,X0,X1,X6] :
( in(sK3(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f136,plain,
! [X2,X0,X1,X6] :
( in(sK3(X0,X1,X6),relation_dom(X0))
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f137,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,[],[f99]) ).
fof(f142,plain,
! [X2,X0,X1,X4] :
( in(apply(X0,X4),X1)
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f143,plain,
! [X2,X0,X1,X4] :
( in(X4,relation_dom(X0))
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f144,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f150,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f154,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f155,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f196,plain,
function(sK20),
inference(cnf_transformation,[],[f118]) ).
fof(f197,plain,
relation(sK20),
inference(cnf_transformation,[],[f118]) ).
fof(f198,plain,
one_to_one(sK20),
inference(cnf_transformation,[],[f118]) ).
fof(f199,plain,
relation_image(sK20,sK19) != relation_inverse_image(function_inverse(sK20),sK19),
inference(cnf_transformation,[],[f118]) ).
fof(f202,plain,
! [X0,X1] :
( in(sK21(X0,X1),X1)
| in(sK21(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f120]) ).
fof(f203,plain,
! [X0,X1] :
( ~ in(sK21(X0,X1),X1)
| X0 = X1
| ~ in(sK21(X0,X1),X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f212,plain,
! [X0,X1,X4,X5] :
( apply(X0,X5) = X4
| ~ in(X4,relation_rng(X0))
| apply(X1,X4) != X5
| function_inverse(X0) != X1
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f213,plain,
! [X0,X1,X4,X5] :
( in(X5,relation_dom(X0))
| ~ in(X4,relation_rng(X0))
| apply(X1,X4) != X5
| function_inverse(X0) != X1
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f214,plain,
! [X0,X1] :
( relation_rng(X0) = relation_dom(X1)
| function_inverse(X0) != X1
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f219,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ one_to_one(X1)
| apply(function_inverse(X1),apply(X1,X0)) = X0
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f224,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,[],[f137]) ).
fof(f225,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,[],[f224]) ).
fof(f226,plain,
! [X0,X1,X6] :
( in(sK3(X0,X1,X6),relation_dom(X0))
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f136]) ).
fof(f227,plain,
! [X0,X1,X6] :
( in(sK3(X0,X1,X6),X1)
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f135]) ).
fof(f228,plain,
! [X0,X1,X6] :
( ~ in(X6,relation_image(X0,X1))
| apply(X0,sK3(X0,X1,X6)) = X6
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f134]) ).
fof(f229,plain,
! [X0,X1,X4] :
( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,relation_inverse_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f144]) ).
fof(f230,plain,
! [X0,X1,X4] :
( ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f143]) ).
fof(f231,plain,
! [X0,X1,X4] :
( ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f142]) ).
fof(f232,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f150]) ).
fof(f233,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f232]) ).
fof(f239,plain,
! [X0] :
( ~ relation(function_inverse(X0))
| relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ function(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f214]) ).
fof(f240,plain,
! [X0,X1,X4] :
( in(apply(X1,X4),relation_dom(X0))
| ~ in(X4,relation_rng(X0))
| function_inverse(X0) != X1
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f213]) ).
fof(f241,plain,
! [X0,X4] :
( in(apply(function_inverse(X0),X4),relation_dom(X0))
| ~ in(X4,relation_rng(X0))
| ~ relation(function_inverse(X0))
| ~ function(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f240]) ).
fof(f242,plain,
! [X0,X1,X4] :
( apply(X0,apply(X1,X4)) = X4
| ~ in(X4,relation_rng(X0))
| function_inverse(X0) != X1
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f212]) ).
fof(f243,plain,
! [X0,X4] :
( ~ in(X4,relation_rng(X0))
| apply(X0,apply(function_inverse(X0),X4)) = X4
| ~ relation(function_inverse(X0))
| ~ function(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f242]) ).
fof(f245,definition,
sF24 = relation_image(sK20,sK19),
introduced(definition,[new_symbols(definition,[sF24])],[function_definition]) ).
fof(f246,plain,
relation_image(sK20,sK19) = sF24,
inference(reorient_equations,[],[f245]) ).
fof(f247,definition,
sF25 = function_inverse(sK20),
introduced(definition,[new_symbols(definition,[sF25])],[function_definition]) ).
fof(f248,plain,
function_inverse(sK20) = sF25,
inference(reorient_equations,[],[f247]) ).
fof(f249,definition,
sF26 = relation_inverse_image(sF25,sK19),
introduced(definition,[new_symbols(definition,[sF26])],[function_definition]) ).
fof(f250,plain,
relation_inverse_image(sF25,sK19) = sF26,
inference(reorient_equations,[],[f249]) ).
fof(f251,plain,
sF24 != sF26,
inference(definition_folding,[],[f199,f250,f248,f246]) ).
fof(f252,plain,
! [X0] :
( ~ in(X0,sF24)
| apply(sK20,sK3(sK20,sK19,X0)) = X0
| ~ relation(sK20)
| ~ function(sK20) ),
inference(superposition,[],[f228,f246]) ).
fof(f253,plain,
! [X0] :
( ~ in(X0,sF24)
| apply(sK20,sK3(sK20,sK19,X0)) = X0
| ~ function(sK20) ),
inference(forward_subsumption_resolution,[],[f252,f197]) ).
fof(f254,plain,
! [X0] :
( ~ in(X0,sF24)
| apply(sK20,sK3(sK20,sK19,X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f253,f196]) ).
fof(f255,plain,
! [X0] :
( ~ in(X0,sF26)
| in(apply(sF25,X0),sK19)
| ~ relation(sF25)
| ~ function(sF25) ),
inference(superposition,[],[f231,f250]) ).
fof(f257,definition,
( spl27_1
<=> function(sF25) ),
introduced(definition,[new_symbols(definition,[spl27_1])],[avatar_definition]) ).
fof(f258,plain,
( function(sF25)
| ~ spl27_1 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f259,plain,
( ~ function(sF25)
| spl27_1 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f261,definition,
( spl27_2
<=> relation(sF25) ),
introduced(definition,[new_symbols(definition,[spl27_2])],[avatar_definition]) ).
fof(f262,plain,
( relation(sF25)
| ~ spl27_2 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f263,plain,
( ~ relation(sF25)
| spl27_2 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f265,definition,
( spl27_3
<=> ! [X0] :
( ~ in(X0,sF26)
| in(apply(sF25,X0),sK19) ) ),
introduced(definition,[new_symbols(definition,[spl27_3])],[avatar_definition]) ).
fof(f266,plain,
( ! [X0] :
( in(apply(sF25,X0),sK19)
| ~ in(X0,sF26) )
| ~ spl27_3 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f267,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_3 ),
inference(avatar_split_clause,[],[f255,f265,f261,f257]) ).
fof(f269,plain,
( function(sF25)
| ~ relation(sK20)
| ~ function(sK20) ),
inference(superposition,[],[f154,f248]) ).
fof(f270,plain,
( ~ relation(sK20)
| ~ function(sK20)
| spl27_1 ),
inference(forward_subsumption_resolution,[],[f269,f259]) ).
fof(f271,plain,
( ~ function(sK20)
| spl27_1 ),
inference(forward_subsumption_resolution,[],[f270,f197]) ).
fof(f272,plain,
( $false
| spl27_1 ),
inference(forward_subsumption_resolution,[],[f271,f196]) ).
fof(f273,plain,
spl27_1,
inference(avatar_contradiction_clause,[],[f272]) ).
fof(f275,plain,
! [X0] :
( in(apply(sF25,X0),relation_dom(sK20))
| ~ in(X0,relation_rng(sK20))
| ~ relation(sF25)
| ~ function(sF25)
| ~ one_to_one(sK20)
| ~ relation(sK20)
| ~ function(sK20) ),
inference(superposition,[],[f241,f248]) ).
fof(f279,plain,
! [X0] :
( ~ in(X0,sF26)
| in(X0,relation_dom(sF25))
| ~ relation(sF25)
| ~ function(sF25) ),
inference(superposition,[],[f230,f250]) ).
fof(f284,plain,
( ~ relation(sF25)
| relation_rng(sK20) = relation_dom(sF25)
| ~ function(sF25)
| ~ one_to_one(sK20)
| ~ relation(sK20)
| ~ function(sK20) ),
inference(superposition,[],[f239,f248]) ).
fof(f286,plain,
( relation(sF25)
| ~ relation(sK20)
| ~ function(sK20) ),
inference(superposition,[],[f155,f248]) ).
fof(f288,plain,
( ~ relation(sK20)
| ~ function(sK20)
| spl27_2 ),
inference(forward_subsumption_resolution,[],[f286,f263]) ).
fof(f290,plain,
( ~ function(sK20)
| spl27_2 ),
inference(forward_subsumption_resolution,[],[f288,f197]) ).
fof(f291,plain,
( $false
| spl27_2 ),
inference(forward_subsumption_resolution,[],[f290,f196]) ).
fof(f292,plain,
spl27_2,
inference(avatar_contradiction_clause,[],[f291]) ).
fof(f294,plain,
( ! [X0] :
( in(apply(sF25,X0),relation_dom(sK20))
| ~ in(X0,relation_rng(sK20))
| ~ function(sF25)
| ~ one_to_one(sK20)
| ~ relation(sK20)
| ~ function(sK20) )
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f275,f262]) ).
fof(f295,plain,
( ! [X0] :
( ~ in(X0,sF26)
| in(X0,relation_dom(sF25))
| ~ function(sF25) )
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f279,f262]) ).
fof(f296,plain,
( relation_rng(sK20) = relation_dom(sF25)
| ~ function(sF25)
| ~ one_to_one(sK20)
| ~ relation(sK20)
| ~ function(sK20)
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f284,f262]) ).
fof(f298,plain,
( ! [X0] :
( in(apply(sF25,X0),relation_dom(sK20))
| ~ in(X0,relation_rng(sK20))
| ~ one_to_one(sK20)
| ~ relation(sK20)
| ~ function(sK20) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f294,f258]) ).
fof(f299,plain,
( ! [X0] :
( in(X0,relation_dom(sF25))
| ~ in(X0,sF26) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f295,f258]) ).
fof(f300,plain,
( relation_rng(sK20) = relation_dom(sF25)
| ~ one_to_one(sK20)
| ~ relation(sK20)
| ~ function(sK20)
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f296,f258]) ).
fof(f302,plain,
( ! [X0] :
( in(apply(sF25,X0),relation_dom(sK20))
| ~ in(X0,relation_rng(sK20))
| ~ relation(sK20)
| ~ function(sK20) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f298,f198]) ).
fof(f303,plain,
( relation_rng(sK20) = relation_dom(sF25)
| ~ relation(sK20)
| ~ function(sK20)
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f300,f198]) ).
fof(f305,plain,
( ! [X0] :
( in(apply(sF25,X0),relation_dom(sK20))
| ~ in(X0,relation_rng(sK20))
| ~ function(sK20) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f302,f197]) ).
fof(f306,plain,
( relation_rng(sK20) = relation_dom(sF25)
| ~ function(sK20)
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f303,f197]) ).
fof(f308,plain,
( ! [X0] :
( in(apply(sF25,X0),relation_dom(sK20))
| ~ in(X0,relation_rng(sK20)) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f305,f196]) ).
fof(f309,plain,
( relation_rng(sK20) = relation_dom(sF25)
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f306,f196]) ).
fof(f315,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF25))
| apply(sK20,apply(function_inverse(sK20),X0)) = X0
| ~ relation(function_inverse(sK20))
| ~ function(function_inverse(sK20))
| ~ one_to_one(sK20)
| ~ relation(sK20)
| ~ function(sK20) )
| ~ spl27_1
| ~ spl27_2 ),
inference(superposition,[],[f243,f309]) ).
fof(f316,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF25))
| apply(sK20,apply(function_inverse(sK20),X0)) = X0
| ~ function(function_inverse(sK20))
| ~ one_to_one(sK20)
| ~ relation(sK20)
| ~ function(sK20) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f315,f155]) ).
fof(f317,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF25))
| apply(sK20,apply(function_inverse(sK20),X0)) = X0
| ~ one_to_one(sK20)
| ~ relation(sK20)
| ~ function(sK20) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f316,f154]) ).
fof(f318,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF25))
| apply(sK20,apply(function_inverse(sK20),X0)) = X0
| ~ relation(sK20)
| ~ function(sK20) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f317,f198]) ).
fof(f319,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF25))
| apply(sK20,apply(function_inverse(sK20),X0)) = X0
| ~ function(sK20) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f318,f197]) ).
fof(f320,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF25))
| apply(sK20,apply(function_inverse(sK20),X0)) = X0 )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f319,f196]) ).
fof(f321,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF25))
| apply(sK20,apply(sF25,X0)) = X0 )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_demodulation,[],[f320,f248]) ).
fof(f335,plain,
( ! [X0] :
( ~ in(X0,relation_rng(sK20))
| ~ in(X0,relation_dom(sF25))
| in(X0,relation_inverse_image(sF25,relation_dom(sK20)))
| ~ relation(sF25)
| ~ function(sF25) )
| ~ spl27_1
| ~ spl27_2 ),
inference(resolution,[],[f308,f229]) ).
fof(f338,plain,
( ! [X0] :
( ~ in(X0,relation_rng(sK20))
| ~ in(X0,relation_dom(sF25))
| in(X0,relation_inverse_image(sF25,relation_dom(sK20)))
| ~ function(sF25) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f335,f262]) ).
fof(f340,plain,
( ! [X0] :
( ~ in(X0,relation_rng(sK20))
| ~ in(X0,relation_dom(sF25))
| in(X0,relation_inverse_image(sF25,relation_dom(sK20))) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f338,f258]) ).
fof(f342,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF25))
| ~ in(X0,relation_dom(sF25))
| in(X0,relation_inverse_image(sF25,relation_dom(sK20))) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_demodulation,[],[f340,f309]) ).
fof(f343,plain,
( ! [X0] :
( in(X0,relation_inverse_image(sF25,relation_dom(sK20)))
| ~ in(X0,relation_dom(sF25)) )
| ~ spl27_1
| ~ spl27_2 ),
inference(duplicate_literal_removal,[],[f342]) ).
fof(f367,plain,
( ! [X0] :
( ~ in(X0,sF26)
| apply(sK20,apply(sF25,X0)) = X0 )
| ~ spl27_1
| ~ spl27_2 ),
inference(resolution,[],[f299,f321]) ).
fof(f417,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF25))
| in(apply(sF25,X0),relation_dom(sK20))
| ~ relation(sF25)
| ~ function(sF25) )
| ~ spl27_1
| ~ spl27_2 ),
inference(resolution,[],[f343,f231]) ).
fof(f419,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF25))
| in(apply(sF25,X0),relation_dom(sK20))
| ~ function(sF25) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f417,f262]) ).
fof(f420,plain,
( ! [X0] :
( in(apply(sF25,X0),relation_dom(sK20))
| ~ in(X0,relation_dom(sF25)) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f419,f258]) ).
fof(f438,plain,
! [X0] :
( in(sK21(X0,sF24),X0)
| sF24 = X0
| sK21(X0,sF24) = apply(sK20,sK3(sK20,sK19,sK21(X0,sF24))) ),
inference(resolution,[],[f202,f254]) ).
fof(f453,plain,
( ! [X0] :
( in(sK21(sF26,X0),X0)
| sF26 = X0
| sK21(sF26,X0) = apply(sK20,apply(sF25,sK21(sF26,X0))) )
| ~ spl27_1
| ~ spl27_2 ),
inference(resolution,[],[f202,f367]) ).
fof(f471,plain,
( sF24 = sF26
| sK21(sF26,sF24) = apply(sK20,sK3(sK20,sK19,sK21(sF26,sF24)))
| sK21(sF26,sF24) = apply(sK20,apply(sF25,sK21(sF26,sF24)))
| ~ spl27_1
| ~ spl27_2 ),
inference(resolution,[],[f438,f367]) ).
fof(f473,plain,
( sK21(sF26,sF24) = apply(sK20,sK3(sK20,sK19,sK21(sF26,sF24)))
| sK21(sF26,sF24) = apply(sK20,apply(sF25,sK21(sF26,sF24)))
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f471,f251]) ).
fof(f500,definition,
( spl27_11
<=> sK21(sF26,sF24) = apply(sK20,apply(sF25,sK21(sF26,sF24))) ),
introduced(definition,[new_symbols(definition,[spl27_11])],[avatar_definition]) ).
fof(f501,plain,
( sK21(sF26,sF24) != apply(sK20,apply(sF25,sK21(sF26,sF24)))
| spl27_11 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f502,plain,
( sK21(sF26,sF24) = apply(sK20,apply(sF25,sK21(sF26,sF24)))
| ~ spl27_11 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f504,definition,
( spl27_12
<=> sK21(sF26,sF24) = apply(sK20,sK3(sK20,sK19,sK21(sF26,sF24))) ),
introduced(definition,[new_symbols(definition,[spl27_12])],[avatar_definition]) ).
fof(f506,plain,
( sK21(sF26,sF24) = apply(sK20,sK3(sK20,sK19,sK21(sF26,sF24)))
| ~ spl27_12 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f507,plain,
( spl27_11
| spl27_12
| ~ spl27_1
| ~ spl27_2 ),
inference(avatar_split_clause,[],[f473,f261,f257,f504,f500]) ).
fof(f514,plain,
( in(sK21(sF26,sF24),relation_rng(sK20))
| ~ in(sK3(sK20,sK19,sK21(sF26,sF24)),relation_dom(sK20))
| ~ relation(sK20)
| ~ function(sK20)
| ~ spl27_12 ),
inference(superposition,[],[f233,f506]) ).
fof(f524,definition,
( spl27_15
<=> in(sK3(sK20,sK19,sK21(sF26,sF24)),relation_dom(sK20)) ),
introduced(definition,[new_symbols(definition,[spl27_15])],[avatar_definition]) ).
fof(f525,plain,
( in(sK3(sK20,sK19,sK21(sF26,sF24)),relation_dom(sK20))
| ~ spl27_15 ),
inference(avatar_component_clause,[],[f524]) ).
fof(f526,plain,
( ~ in(sK3(sK20,sK19,sK21(sF26,sF24)),relation_dom(sK20))
| spl27_15 ),
inference(avatar_component_clause,[],[f524]) ).
fof(f528,definition,
( spl27_16
<=> in(sK21(sF26,sF24),sF24) ),
introduced(definition,[new_symbols(definition,[spl27_16])],[avatar_definition]) ).
fof(f529,plain,
( ~ in(sK21(sF26,sF24),sF24)
| spl27_16 ),
inference(avatar_component_clause,[],[f528]) ).
fof(f530,plain,
( in(sK21(sF26,sF24),sF24)
| ~ spl27_16 ),
inference(avatar_component_clause,[],[f528]) ).
fof(f533,definition,
( spl27_17
<=> in(sK21(sF26,sF24),relation_dom(sF25)) ),
introduced(definition,[new_symbols(definition,[spl27_17])],[avatar_definition]) ).
fof(f534,plain,
( ~ in(sK21(sF26,sF24),relation_dom(sF25))
| spl27_17 ),
inference(avatar_component_clause,[],[f533]) ).
fof(f535,plain,
( in(sK21(sF26,sF24),relation_dom(sF25))
| ~ spl27_17 ),
inference(avatar_component_clause,[],[f533]) ).
fof(f539,plain,
( in(sK21(sF26,sF24),relation_rng(sK20))
| ~ in(sK3(sK20,sK19,sK21(sF26,sF24)),relation_dom(sK20))
| ~ function(sK20)
| ~ spl27_12 ),
inference(forward_subsumption_resolution,[],[f514,f197]) ).
fof(f542,plain,
( in(sK21(sF26,sF24),relation_rng(sK20))
| ~ in(sK3(sK20,sK19,sK21(sF26,sF24)),relation_dom(sK20))
| ~ spl27_12 ),
inference(forward_subsumption_resolution,[],[f539,f196]) ).
fof(f551,plain,
( in(sK21(sF26,sF24),relation_dom(sF25))
| ~ in(sK3(sK20,sK19,sK21(sF26,sF24)),relation_dom(sK20))
| ~ spl27_1
| ~ spl27_2
| ~ spl27_12 ),
inference(forward_demodulation,[],[f542,f309]) ).
fof(f552,plain,
( ~ spl27_15
| spl27_17
| ~ spl27_1
| ~ spl27_2
| ~ spl27_12 ),
inference(avatar_split_clause,[],[f551,f504,f261,f257,f533,f524]) ).
fof(f553,plain,
( ~ in(sK21(sF26,sF24),relation_image(sK20,sK19))
| ~ relation(sK20)
| ~ function(sK20)
| spl27_15 ),
inference(resolution,[],[f526,f226]) ).
fof(f554,plain,
( ~ in(sK21(sF26,sF24),relation_image(sK20,sK19))
| ~ function(sK20)
| spl27_15 ),
inference(forward_subsumption_resolution,[],[f553,f197]) ).
fof(f555,plain,
( ~ in(sK21(sF26,sF24),relation_image(sK20,sK19))
| spl27_15 ),
inference(forward_subsumption_resolution,[],[f554,f196]) ).
fof(f556,plain,
( ~ in(sK21(sF26,sF24),sF24)
| spl27_15 ),
inference(forward_demodulation,[],[f555,f246]) ).
fof(f557,plain,
( ~ spl27_16
| spl27_15 ),
inference(avatar_split_clause,[],[f556,f524,f528]) ).
fof(f1000,plain,
( sF24 = sF26
| sK21(sF26,sF24) = apply(sK20,apply(sF25,sK21(sF26,sF24)))
| ~ spl27_1
| ~ spl27_2
| spl27_16 ),
inference(resolution,[],[f453,f529]) ).
fof(f1068,plain,
( sK21(sF26,sF24) = apply(sK20,apply(sF25,sK21(sF26,sF24)))
| ~ spl27_1
| ~ spl27_2
| spl27_16 ),
inference(forward_subsumption_resolution,[],[f1000,f251]) ).
fof(f1076,plain,
( spl27_11
| ~ spl27_1
| ~ spl27_2
| spl27_16 ),
inference(avatar_split_clause,[],[f1068,f528,f261,f257,f500]) ).
fof(f1087,plain,
( ! [X0] :
( in(sK21(sF26,sF24),relation_image(sK20,X0))
| ~ in(apply(sF25,sK21(sF26,sF24)),relation_dom(sK20))
| ~ in(apply(sF25,sK21(sF26,sF24)),X0)
| ~ relation(sK20)
| ~ function(sK20) )
| ~ spl27_11 ),
inference(superposition,[],[f225,f502]) ).
fof(f1090,plain,
( ! [X0] :
( in(sK21(sF26,sF24),relation_image(sK20,X0))
| ~ in(apply(sF25,sK21(sF26,sF24)),relation_dom(sK20))
| ~ in(apply(sF25,sK21(sF26,sF24)),X0)
| ~ function(sK20) )
| ~ spl27_11 ),
inference(forward_subsumption_resolution,[],[f1087,f197]) ).
fof(f1094,definition,
( spl27_67
<=> in(apply(sF25,sK21(sF26,sF24)),relation_dom(sK20)) ),
introduced(definition,[new_symbols(definition,[spl27_67])],[avatar_definition]) ).
fof(f1096,plain,
( ~ in(apply(sF25,sK21(sF26,sF24)),relation_dom(sK20))
| spl27_67 ),
inference(avatar_component_clause,[],[f1094]) ).
fof(f1099,plain,
( ! [X0] :
( in(sK21(sF26,sF24),relation_image(sK20,X0))
| ~ in(apply(sF25,sK21(sF26,sF24)),relation_dom(sK20))
| ~ in(apply(sF25,sK21(sF26,sF24)),X0) )
| ~ spl27_11 ),
inference(forward_subsumption_resolution,[],[f1090,f196]) ).
fof(f1102,definition,
( spl27_68
<=> in(apply(sF25,sK21(sF26,sF24)),sK19) ),
introduced(definition,[new_symbols(definition,[spl27_68])],[avatar_definition]) ).
fof(f1103,plain,
( in(apply(sF25,sK21(sF26,sF24)),sK19)
| ~ spl27_68 ),
inference(avatar_component_clause,[],[f1102]) ).
fof(f1104,plain,
( ~ in(apply(sF25,sK21(sF26,sF24)),sK19)
| spl27_68 ),
inference(avatar_component_clause,[],[f1102]) ).
fof(f1111,definition,
( spl27_70
<=> ! [X0] :
( in(sK21(sF26,sF24),relation_image(sK20,X0))
| ~ in(apply(sF25,sK21(sF26,sF24)),X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_70])],[avatar_definition]) ).
fof(f1112,plain,
( ! [X0] :
( ~ in(apply(sF25,sK21(sF26,sF24)),X0)
| in(sK21(sF26,sF24),relation_image(sK20,X0)) )
| ~ spl27_70 ),
inference(avatar_component_clause,[],[f1111]) ).
fof(f1113,plain,
( ~ spl27_67
| spl27_70
| ~ spl27_11 ),
inference(avatar_split_clause,[],[f1099,f500,f1111,f1094]) ).
fof(f1116,plain,
( ~ in(sK21(sF26,sF24),relation_dom(sF25))
| ~ spl27_1
| ~ spl27_2
| spl27_67 ),
inference(resolution,[],[f1096,f420]) ).
fof(f1119,plain,
( ~ spl27_17
| ~ spl27_1
| ~ spl27_2
| spl27_67 ),
inference(avatar_split_clause,[],[f1116,f1094,f261,f257,f533]) ).
fof(f1120,plain,
( ~ in(sK21(sF26,sF24),sF26)
| ~ spl27_1
| ~ spl27_2
| spl27_17 ),
inference(resolution,[],[f534,f299]) ).
fof(f1122,plain,
( in(sK21(sF26,sF24),sF24)
| sF24 = sF26
| ~ spl27_1
| ~ spl27_2
| spl27_17 ),
inference(resolution,[],[f1120,f202]) ).
fof(f1123,plain,
( sF24 = sF26
| ~ spl27_1
| ~ spl27_2
| spl27_16
| spl27_17 ),
inference(forward_subsumption_resolution,[],[f1122,f529]) ).
fof(f1124,plain,
( $false
| ~ spl27_1
| ~ spl27_2
| spl27_16
| spl27_17 ),
inference(forward_subsumption_resolution,[],[f1123,f251]) ).
fof(f1125,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_16
| spl27_17 ),
inference(avatar_contradiction_clause,[],[f1124]) ).
fof(f1131,plain,
( sF24 = sF26
| ~ in(sK21(sF26,sF24),sF26)
| ~ spl27_16 ),
inference(resolution,[],[f530,f203]) ).
fof(f1133,plain,
( sK21(sF26,sF24) = apply(sK20,sK3(sK20,sK19,sK21(sF26,sF24)))
| ~ spl27_16 ),
inference(resolution,[],[f530,f254]) ).
fof(f1134,plain,
( spl27_12
| ~ spl27_16 ),
inference(avatar_split_clause,[],[f1133,f528,f504]) ).
fof(f1136,plain,
( ~ in(sK21(sF26,sF24),sF26)
| ~ spl27_16 ),
inference(forward_subsumption_resolution,[],[f1131,f251]) ).
fof(f1156,plain,
( in(sK21(sF26,sF24),relation_image(sK20,sK19))
| ~ in(sK21(sF26,sF24),sF26)
| ~ spl27_3
| ~ spl27_70 ),
inference(resolution,[],[f1112,f266]) ).
fof(f1363,plain,
( ~ one_to_one(sK20)
| sK3(sK20,sK19,sK21(sF26,sF24)) = apply(function_inverse(sK20),apply(sK20,sK3(sK20,sK19,sK21(sF26,sF24))))
| ~ relation(sK20)
| ~ function(sK20)
| ~ spl27_15 ),
inference(resolution,[],[f525,f219]) ).
fof(f1364,plain,
( sK3(sK20,sK19,sK21(sF26,sF24)) = apply(function_inverse(sK20),apply(sK20,sK3(sK20,sK19,sK21(sF26,sF24))))
| ~ relation(sK20)
| ~ function(sK20)
| ~ spl27_15 ),
inference(forward_subsumption_resolution,[],[f1363,f198]) ).
fof(f1366,plain,
( sK3(sK20,sK19,sK21(sF26,sF24)) = apply(function_inverse(sK20),apply(sK20,sK3(sK20,sK19,sK21(sF26,sF24))))
| ~ function(sK20)
| ~ spl27_15 ),
inference(forward_subsumption_resolution,[],[f1364,f197]) ).
fof(f1368,plain,
( sK3(sK20,sK19,sK21(sF26,sF24)) = apply(function_inverse(sK20),apply(sK20,sK3(sK20,sK19,sK21(sF26,sF24))))
| ~ spl27_15 ),
inference(forward_subsumption_resolution,[],[f1366,f196]) ).
fof(f1370,plain,
( sK3(sK20,sK19,sK21(sF26,sF24)) = apply(function_inverse(sK20),sK21(sF26,sF24))
| ~ spl27_12
| ~ spl27_15 ),
inference(forward_demodulation,[],[f1368,f506]) ).
fof(f1372,plain,
( sK3(sK20,sK19,sK21(sF26,sF24)) = apply(sF25,sK21(sF26,sF24))
| ~ spl27_12
| ~ spl27_15 ),
inference(forward_demodulation,[],[f1370,f248]) ).
fof(f1375,plain,
( sK21(sF26,sF24) = apply(sK20,apply(sF25,sK21(sF26,sF24)))
| ~ spl27_12
| ~ spl27_15 ),
inference(superposition,[],[f506,f1372]) ).
fof(f1379,plain,
( in(apply(sF25,sK21(sF26,sF24)),sK19)
| ~ in(sK21(sF26,sF24),relation_image(sK20,sK19))
| ~ relation(sK20)
| ~ function(sK20)
| ~ spl27_12
| ~ spl27_15 ),
inference(superposition,[],[f227,f1372]) ).
fof(f1380,plain,
( ~ in(sK21(sF26,sF24),relation_image(sK20,sK19))
| ~ relation(sK20)
| ~ function(sK20)
| ~ spl27_12
| ~ spl27_15
| spl27_68 ),
inference(forward_subsumption_resolution,[],[f1379,f1104]) ).
fof(f1381,plain,
( ~ in(sK21(sF26,sF24),relation_image(sK20,sK19))
| ~ function(sK20)
| ~ spl27_12
| ~ spl27_15
| spl27_68 ),
inference(forward_subsumption_resolution,[],[f1380,f197]) ).
fof(f1382,plain,
( ~ in(sK21(sF26,sF24),relation_image(sK20,sK19))
| ~ spl27_12
| ~ spl27_15
| spl27_68 ),
inference(forward_subsumption_resolution,[],[f1381,f196]) ).
fof(f1383,plain,
( ~ in(sK21(sF26,sF24),sF24)
| ~ spl27_12
| ~ spl27_15
| spl27_68 ),
inference(forward_demodulation,[],[f1382,f246]) ).
fof(f1384,plain,
( $false
| ~ spl27_12
| ~ spl27_15
| ~ spl27_16
| spl27_68 ),
inference(forward_subsumption_resolution,[],[f1383,f530]) ).
fof(f1385,plain,
( ~ spl27_12
| ~ spl27_15
| ~ spl27_16
| spl27_68 ),
inference(avatar_contradiction_clause,[],[f1384]) ).
fof(f1397,plain,
( $false
| spl27_11
| ~ spl27_12
| ~ spl27_15 ),
inference(forward_subsumption_resolution,[],[f1375,f501]) ).
fof(f1398,plain,
( spl27_11
| ~ spl27_12
| ~ spl27_15 ),
inference(avatar_contradiction_clause,[],[f1397]) ).
fof(f1424,plain,
( ~ in(sK21(sF26,sF24),relation_dom(sF25))
| in(sK21(sF26,sF24),relation_inverse_image(sF25,sK19))
| ~ relation(sF25)
| ~ function(sF25)
| ~ spl27_68 ),
inference(resolution,[],[f1103,f229]) ).
fof(f1425,plain,
( in(sK21(sF26,sF24),relation_inverse_image(sF25,sK19))
| ~ relation(sF25)
| ~ function(sF25)
| ~ spl27_17
| ~ spl27_68 ),
inference(forward_subsumption_resolution,[],[f1424,f535]) ).
fof(f1427,plain,
( in(sK21(sF26,sF24),relation_inverse_image(sF25,sK19))
| ~ function(sF25)
| ~ spl27_2
| ~ spl27_17
| ~ spl27_68 ),
inference(forward_subsumption_resolution,[],[f1425,f262]) ).
fof(f1428,plain,
( in(sK21(sF26,sF24),relation_inverse_image(sF25,sK19))
| ~ spl27_1
| ~ spl27_2
| ~ spl27_17
| ~ spl27_68 ),
inference(forward_subsumption_resolution,[],[f1427,f258]) ).
fof(f1429,plain,
( in(sK21(sF26,sF24),sF26)
| ~ spl27_1
| ~ spl27_2
| ~ spl27_17
| ~ spl27_68 ),
inference(forward_demodulation,[],[f1428,f250]) ).
fof(f1430,plain,
( $false
| ~ spl27_1
| ~ spl27_2
| ~ spl27_16
| ~ spl27_17
| ~ spl27_68 ),
inference(forward_subsumption_resolution,[],[f1429,f1136]) ).
fof(f1431,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_16
| ~ spl27_17
| ~ spl27_68 ),
inference(avatar_contradiction_clause,[],[f1430]) ).
fof(f1434,plain,
( in(sK21(sF26,sF24),sF24)
| ~ in(sK21(sF26,sF24),sF26)
| ~ spl27_3
| ~ spl27_70 ),
inference(forward_demodulation,[],[f1156,f246]) ).
fof(f1438,plain,
( ~ in(sK21(sF26,sF24),sF26)
| ~ spl27_3
| spl27_16
| ~ spl27_70 ),
inference(forward_subsumption_resolution,[],[f1434,f529]) ).
fof(f1444,plain,
( in(sK21(sF26,sF24),sF24)
| sF24 = sF26
| ~ spl27_3
| spl27_16
| ~ spl27_70 ),
inference(resolution,[],[f1438,f202]) ).
fof(f1445,plain,
( sF24 = sF26
| ~ spl27_3
| spl27_16
| ~ spl27_70 ),
inference(forward_subsumption_resolution,[],[f1444,f529]) ).
fof(f1446,plain,
( $false
| ~ spl27_3
| spl27_16
| ~ spl27_70 ),
inference(forward_subsumption_resolution,[],[f1445,f251]) ).
fof(f1447,plain,
( ~ spl27_3
| spl27_16
| ~ spl27_70 ),
inference(avatar_contradiction_clause,[],[f1446]) ).
cnf(s1,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_3 ),
inference(sat_conversion,[],[f267]) ).
cnf(s2,plain,
spl27_1,
inference(sat_conversion,[],[f273]) ).
cnf(s3,plain,
spl27_2,
inference(sat_conversion,[],[f292]) ).
cnf(s8,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_11
| spl27_12 ),
inference(sat_conversion,[],[f507]) ).
cnf(s14,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_12
| ~ spl27_15
| spl27_17 ),
inference(sat_conversion,[],[f552]) ).
cnf(s15,plain,
( spl27_15
| ~ spl27_16 ),
inference(sat_conversion,[],[f557]) ).
cnf(s50,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_11
| spl27_16 ),
inference(sat_conversion,[],[f1076]) ).
cnf(s55,plain,
( ~ spl27_11
| ~ spl27_67
| spl27_70 ),
inference(sat_conversion,[],[f1113]) ).
cnf(s57,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_17
| spl27_67 ),
inference(sat_conversion,[],[f1119]) ).
cnf(s59,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_16
| spl27_17 ),
inference(sat_conversion,[],[f1125]) ).
cnf(s61,plain,
( spl27_12
| ~ spl27_16 ),
inference(sat_conversion,[],[f1134]) ).
cnf(s76,plain,
( ~ spl27_12
| ~ spl27_15
| ~ spl27_16
| spl27_68 ),
inference(sat_conversion,[],[f1385]) ).
cnf(s81,plain,
( spl27_11
| ~ spl27_12
| ~ spl27_15 ),
inference(sat_conversion,[],[f1398]) ).
cnf(s83,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_16
| ~ spl27_17
| ~ spl27_68 ),
inference(sat_conversion,[],[f1431]) ).
cnf(s84,plain,
( ~ spl27_3
| spl27_16
| ~ spl27_70 ),
inference(sat_conversion,[],[f1447]) ).
cnf(s85,plain,
spl27_3,
inference(rat,[],[s1,s3,s2]) ).
cnf(s86,plain,
spl27_11,
inference(rat,[],[s15,s81,s8,s50,s3,s2]) ).
cnf(s87,plain,
spl27_16,
inference(rat,[],[s57,s55,s59,s84,s3,s2,s86,s85]) ).
cnf(s88,plain,
spl27_12,
inference(rat,[],[s61,s87]) ).
cnf(s89,plain,
spl27_15,
inference(rat,[],[s15,s87]) ).
cnf(s92,plain,
spl27_17,
inference(rat,[],[s14,s88,s2,s3,s89]) ).
cnf(s93,plain,
spl27_68,
inference(rat,[],[s76,s87,s88,s89]) ).
cnf(s97,plain,
$false,
inference(rat,[],[s83,s87,s2,s3,s92,s93]) ).
fof(f1448,plain,
$false,
inference(avatar_sat_refutation,[],[s97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU073+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % 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 03:33:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 4.60/1.81 % (2230770)Detected formulas, will run a generic FOF schedule.
% 4.60/1.81 % (2230777)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=3998470244:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.60/1.81 % (2230778)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2907261841:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.60/1.81 % (2230779)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1239460092:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.60/1.81 % (2230775)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=1683759984:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.60/1.81 % (2230776)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=2893847941:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.60/1.81 % (2230781)dis-21_1_sil=8000:lcm=predicate:random_seed=4039018713: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)
% 4.60/1.81 % (2230778)Refutation not found, incomplete strategy
% 4.60/1.81 % (2230778)------------------------------
% 4.60/1.81 % (2230778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.81 % (2230778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.81 % (2230778)CaDiCaL version: 2.1.3
% 4.60/1.81 % (2230778)Termination reason: Refutation not found, incomplete strategy
% 4.60/1.81 % (2230778)Time elapsed: 0.004 s
% 4.60/1.81 % (2230778)Peak memory usage: 88 MB
% 4.60/1.81 % (2230778)Instructions burned: 5 (million)
% 4.60/1.81 % (2230780)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2748735366:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.60/1.81 % (2230780)Instruction limit reached!
% 4.60/1.81 % (2230780)------------------------------
% 4.60/1.81 % (2230780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.81 % (2230780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.81 % (2230780)CaDiCaL version: 2.1.3
% 4.60/1.81 % (2230780)Termination reason: Instruction limit
% 4.60/1.81 % (2230780)Termination phase: Saturation
% 4.60/1.81 % (2230780)Time elapsed: 0.049 s
% 4.60/1.81 % (2230780)Peak memory usage: 90 MB
% 4.60/1.81 % (2230780)Instructions burned: 142 (million)
% 4.60/1.81 % (2230779)Instruction limit reached!
% 4.60/1.81 % (2230779)------------------------------
% 4.60/1.81 % (2230779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.81 % (2230779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.81 % (2230779)CaDiCaL version: 2.1.3
% 4.60/1.81 % (2230779)Termination reason: Instruction limit
% 4.60/1.81 % (2230779)Termination phase: Saturation
% 4.60/1.81 % (2230779)Time elapsed: 0.071 s
% 4.60/1.81 % (2230779)Peak memory usage: 88 MB
% 4.60/1.81 % (2230779)Instructions burned: 120 (million)
% 4.60/1.81 % (2230781)Instruction limit reached!
% 4.60/1.81 % (2230781)------------------------------
% 4.60/1.81 % (2230781)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.81 % (2230781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.81 % (2230781)CaDiCaL version: 2.1.3
% 4.60/1.81 % (2230781)Termination reason: Instruction limit
% 4.60/1.81 % (2230781)Termination phase: Saturation
% 4.60/1.81 % (2230781)Time elapsed: 0.072 s
% 4.60/1.81 % (2230781)Peak memory usage: 91 MB
% 4.60/1.81 % (2230781)Instructions burned: 130 (million)
% 4.60/1.81 % (2230789)lrs+10_1_sil=8000:sp=occurrence:random_seed=921901574:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.60/1.81 % (2230791)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1555100798:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.60/1.81 % (2230790)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2069565930:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.60/1.81 % (2230778)------------------------------
% 4.60/1.81 % (2230778)------------------------------
% 4.60/1.81 % (2230789)Instruction limit reached!
% 4.60/1.81 % (2230789)------------------------------
% 4.60/1.81 % (2230789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.81 % (2230789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.81 % (2230789)CaDiCaL version: 2.1.3
% 4.60/1.81 % (2230789)Termination reason: Instruction limit
% 4.60/1.81 % (2230789)Termination phase: Saturation
% 4.60/1.81 % (2230789)Time elapsed: 0.086 s
% 4.60/1.81 % (2230789)Peak memory usage: 91 MB
% 4.60/1.81 % (2230789)Instructions burned: 286 (million)
% 4.60/1.81 % (2230790)Instruction limit reached!
% 4.60/1.81 % (2230790)------------------------------
% 4.60/1.81 % (2230790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.81 % (2230790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.81 % (2230790)CaDiCaL version: 2.1.3
% 4.60/1.81 % (2230790)Termination reason: Instruction limit
% 4.60/1.81 % (2230790)Termination phase: Saturation
% 4.60/1.81 % (2230790)Time elapsed: 0.081 s
% 4.60/1.81 % (2230790)Peak memory usage: 89 MB
% 4.60/1.81 % (2230790)Instructions burned: 159 (million)
% 4.60/1.81 % (2230795)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=1105419153:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.60/1.81 % (2230796)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2898849664:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.60/1.81 % (2230796)Refutation not found, incomplete strategy
% 4.60/1.81 % (2230796)------------------------------
% 4.60/1.81 % (2230796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.81 % (2230796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.81 % (2230796)CaDiCaL version: 2.1.3
% 4.60/1.81 % (2230796)Termination reason: Refutation not found, incomplete strategy
% 4.60/1.81 % (2230796)Time elapsed: 0.003 s
% 4.60/1.81 % (2230796)Peak memory usage: 88 MB
% 4.60/1.81 % (2230796)Instructions burned: 4 (million)
% 4.60/1.81 % (2230791)Instruction limit reached!
% 4.60/1.81 % (2230791)------------------------------
% 4.60/1.81 % (2230791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.81 % (2230791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.81 % (2230791)CaDiCaL version: 2.1.3
% 4.60/1.81 % (2230791)Termination reason: Instruction limit
% 4.60/1.81 % (2230791)Termination phase: Saturation
% 4.60/1.81 % (2230791)Time elapsed: 0.220 s
% 4.60/1.81 % (2230791)Peak memory usage: 92 MB
% 4.60/1.81 % (2230791)Instructions burned: 326 (million)
% 4.60/1.81 % (2230795)Instruction limit reached!
% 4.60/1.81 % (2230795)------------------------------
% 4.60/1.81 % (2230795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.81 % (2230795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.81 % (2230795)CaDiCaL version: 2.1.3
% 4.60/1.81 % (2230795)Termination reason: Instruction limit
% 4.60/1.81 % (2230795)Termination phase: Saturation
% 4.60/1.81 % (2230795)Time elapsed: 0.074 s
% 4.60/1.81 % (2230795)Peak memory usage: 92 MB
% 4.60/1.81 % (2230795)Instructions burned: 249 (million)
% 4.60/1.81 % (2230797)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=572700084:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.60/1.81 % (2230801)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3440731995:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 4.60/1.81 % (2230801)Instruction limit reached!
% 4.60/1.81 % (2230801)------------------------------
% 4.60/1.81 % (2230801)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.81 % (2230801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.81 % (2230801)CaDiCaL version: 2.1.3
% 4.60/1.81 % (2230801)Termination reason: Instruction limit
% 4.60/1.81 % (2230801)Termination phase: Saturation
% 4.60/1.81 % (2230801)Time elapsed: 0.035 s
% 4.60/1.81 % (2230801)Peak memory usage: 89 MB
% 4.60/1.81 % (2230801)Instructions burned: 127 (million)
% 4.60/1.81 % (2230800)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=745179213:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 4.60/1.81 % (2230796)------------------------------
% 4.60/1.81 % (2230796)------------------------------
% 4.60/1.81 % (2230800)Instruction limit reached!
% 4.60/1.81 % (2230800)------------------------------
% 4.60/1.81 % (2230800)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.81 % (2230800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.81 % (2230800)CaDiCaL version: 2.1.3
% 4.60/1.81 % (2230800)Termination reason: Instruction limit
% 4.60/1.81 % (2230800)Termination phase: Saturation
% 4.60/1.81 % (2230800)Time elapsed: 0.075 s
% 4.60/1.81 % (2230800)Peak memory usage: 90 MB
% 4.60/1.81 % (2230800)Instructions burned: 113 (million)
% 4.60/1.81 % (2230805)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2455006938:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 4.60/1.81 % (2230775)First to succeed.
% 4.60/1.81 % (2230775)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2230770"
% 4.60/1.81 % (2230805)Instruction limit reached!
% 4.60/1.81 % (2230805)------------------------------
% 4.60/1.81 % (2230805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.81 % (2230805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.81 % (2230805)CaDiCaL version: 2.1.3
% 4.60/1.81 % (2230805)Termination reason: Instruction limit
% 4.60/1.81 % (2230805)Termination phase: Saturation
% 4.60/1.81 % (2230805)Time elapsed: 0.035 s
% 4.60/1.81 % (2230805)Peak memory usage: 89 MB
% 4.60/1.81 % (2230805)Instructions burned: 116 (million)
% 4.60/1.81 % (2230806)lrs+10_1_sil=8000:sp=occurrence:random_seed=1812593994:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 4.60/1.81 % (2230807)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1314556874:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 4.60/1.81 % (2230807)Refutation not found, incomplete strategy
% 4.60/1.81 % (2230807)------------------------------
% 4.60/1.81 % (2230807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.60/1.81 % (2230807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.60/1.81 % (2230807)CaDiCaL version: 2.1.3
% 4.60/1.81 % (2230807)Termination reason: Refutation not found, incomplete strategy
% 4.60/1.81 % (2230807)Time elapsed: 0.004 s
% 4.60/1.81 % (2230807)Peak memory usage: 88 MB
% 4.60/1.81 % (2230807)Instructions burned: 4 (million)
% 4.60/1.81 % (2230777)Also succeeded, but the first one will report.
% 4.60/1.81 % (2230809)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2019571844:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 4.60/1.81 % (2230775)Refutation found. Thanks to Tanya!
% 4.60/1.81 % SZS status Theorem for theBenchmark
% 4.60/1.81 % SZS output start Proof for theBenchmark
% See solution above
% 8.85/2.01 % (2230775)------------------------------
% 8.85/2.01 % (2230775)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.85/2.01 % (2230775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.85/2.01 % (2230775)CaDiCaL version: 2.1.3
% 8.85/2.01 % (2230775)Termination reason: Refutation
% 8.85/2.01 % (2230775)Time elapsed: 0.779 s
% 8.85/2.01 % (2230775)Peak memory usage: 130 MB
% 8.85/2.01 % (2230775)Instructions burned: 1151 (million)
% 8.85/2.01 % (2230775)------------------------------
% 8.85/2.01 % (2230775)------------------------------
% 8.85/2.01 % (2230770)Success in time 1.213 s
% 8.85/2.01 % Vampire exiting
%------------------------------------------------------------------------------