%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU074+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 : n008.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 8.39s 2.19s
% Output : Refutation 9.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 20
% Syntax : Number of formulae : 232 ( 23 unt; 13 def)
% Number of atoms : 1162 ( 207 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 1646 ( 716 ~; 738 |; 144 &)
% ( 33 <=>; 14 =>; 0 <=; 1 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 10 prp; 0-4 aty)
% Number of functors : 21 ( 21 usr; 5 con; 0-3 aty)
% Number of variables : 332 ( 0 sgn 299 !; 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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f29,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> relation_inverse_image(X1,X0) = relation_image(function_inverse(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_funct_1) ).
fof(f30,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> relation_inverse_image(X1,X0) = relation_image(function_inverse(X1),X0) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f36,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/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f50,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(f51,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,[],[f50]) ).
fof(f52,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(f53,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,[],[f52]) ).
fof(f54,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(f55,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,[],[f54]) ).
fof(f56,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f57,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f56]) ).
fof(f65,plain,
? [X0,X1] :
( relation_inverse_image(X1,X0) != relation_image(function_inverse(X1),X0)
& one_to_one(X1)
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f66,plain,
? [X0,X1] :
( relation_inverse_image(X1,X0) != relation_image(function_inverse(X1),X0)
& one_to_one(X1)
& relation(X1)
& function(X1) ),
inference(flattening,[],[f65]) ).
fof(f70,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f74,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,[],[f36]) ).
fof(f75,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,[],[f74]) ).
fof(f80,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(f81,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,[],[f75,f80]) ).
fof(f82,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,[],[f51]) ).
fof(f83,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,[],[f82]) ).
fof(f84,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))],[f83]) ).
fof(f85,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,[],[f53]) ).
fof(f86,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,[],[f85]) ).
fof(f87,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,[],[f86]) ).
fof(f88,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))],[f87]) ).
fof(f89,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,[],[f55]) ).
fof(f90,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,[],[f89]) ).
fof(f91,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))],[f90]) ).
fof(f103,plain,
( relation_inverse_image(sK20,sK19) != relation_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)],[f66]) ).
fof(f104,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f105,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))],[f104]) ).
fof(f106,plain,
! [X0,X2,X3,X1] :
( ( sP0(X0,X2,X3,X1)
| ( ( ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& in(X3,relation_dom(X0))
& apply(X0,X3) = X2 ) )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2
| ~ sP0(X0,X2,X3,X1) ) ),
inference(nnf_transformation,[],[f80]) ).
fof(f107,plain,
! [X0,X2,X3,X1] :
( ( sP0(X0,X2,X3,X1)
| ( ( ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& in(X3,relation_dom(X0))
& apply(X0,X3) = X2 ) )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2
| ~ sP0(X0,X2,X3,X1) ) ),
inference(flattening,[],[f106]) ).
fof(f108,plain,
! [X0,X1,X2,X3] :
( ( sP0(X0,X1,X2,X3)
| ( ( ~ in(X1,relation_rng(X0))
| apply(X3,X1) != X2 )
& in(X2,relation_dom(X0))
& apply(X0,X2) = X1 ) )
& ( ( in(X1,relation_rng(X0))
& apply(X3,X1) = X2 )
| ~ in(X2,relation_dom(X0))
| apply(X0,X2) != X1
| ~ sP0(X0,X1,X2,X3) ) ),
inference(rectify,[],[f107]) ).
fof(f109,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,[],[f81]) ).
fof(f110,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,[],[f109]) ).
fof(f111,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,[],[f110]) ).
fof(f112,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))],[f111]) ).
fof(f119,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,[],[f84]) ).
fof(f120,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,[],[f84]) ).
fof(f121,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,[],[f84]) ).
fof(f122,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,[],[f84]) ).
fof(f127,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,[],[f88]) ).
fof(f128,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,[],[f88]) ).
fof(f129,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,[],[f88]) ).
fof(f135,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,[],[f91]) ).
fof(f139,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f140,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f174,plain,
function(sK20),
inference(cnf_transformation,[],[f103]) ).
fof(f175,plain,
relation(sK20),
inference(cnf_transformation,[],[f103]) ).
fof(f176,plain,
one_to_one(sK20),
inference(cnf_transformation,[],[f103]) ).
fof(f177,plain,
relation_inverse_image(sK20,sK19) != relation_image(function_inverse(sK20),sK19),
inference(cnf_transformation,[],[f103]) ).
fof(f180,plain,
! [X0,X1] :
( in(sK21(X0,X1),X1)
| in(sK21(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f105]) ).
fof(f181,plain,
! [X0,X1] :
( ~ in(sK21(X0,X1),X1)
| X0 = X1
| ~ in(sK21(X0,X1),X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f184,plain,
! [X2,X3,X0,X1] :
( apply(X3,X1) = X2
| ~ in(X2,relation_dom(X0))
| apply(X0,X2) != X1
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f108]) ).
fof(f189,plain,
! [X0,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(cnf_transformation,[],[f112]) ).
fof(f190,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,[],[f112]) ).
fof(f191,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,[],[f112]) ).
fof(f192,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,[],[f112]) ).
fof(f200,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,[],[f122]) ).
fof(f201,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,[],[f200]) ).
fof(f202,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,[],[f121]) ).
fof(f203,plain,
! [X0,X1,X6] :
( in(sK3(X0,X1,X6),X1)
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f120]) ).
fof(f204,plain,
! [X0,X1,X6] :
( ~ in(X6,relation_image(X0,X1))
| apply(X0,sK3(X0,X1,X6)) = X6
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f119]) ).
fof(f205,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,[],[f129]) ).
fof(f206,plain,
! [X0,X1,X4] :
( ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f128]) ).
fof(f207,plain,
! [X0,X1,X4] :
( ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f127]) ).
fof(f208,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,[],[f135]) ).
fof(f209,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f208]) ).
fof(f214,plain,
! [X2,X3,X0] :
( ~ sP0(X0,apply(X0,X2),X2,X3)
| ~ in(X2,relation_dom(X0))
| apply(X3,apply(X0,X2)) = X2 ),
inference(equality_resolution,[],[f184]) ).
fof(f215,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,[],[f192]) ).
fof(f216,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,[],[f191]) ).
fof(f217,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,[],[f216]) ).
fof(f218,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,[],[f190]) ).
fof(f219,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,[],[f218]) ).
fof(f220,plain,
! [X0,X4,X5] :
( sP0(X0,X4,X5,function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ function(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f189]) ).
fof(f221,definition,
sF24 = relation_inverse_image(sK20,sK19),
introduced(definition,[new_symbols(definition,[sF24])],[function_definition]) ).
fof(f222,plain,
relation_inverse_image(sK20,sK19) = sF24,
inference(reorient_equations,[],[f221]) ).
fof(f223,definition,
sF25 = function_inverse(sK20),
introduced(definition,[new_symbols(definition,[sF25])],[function_definition]) ).
fof(f224,plain,
function_inverse(sK20) = sF25,
inference(reorient_equations,[],[f223]) ).
fof(f225,definition,
sF26 = relation_image(sF25,sK19),
introduced(definition,[new_symbols(definition,[sF26])],[function_definition]) ).
fof(f226,plain,
relation_image(sF25,sK19) = sF26,
inference(reorient_equations,[],[f225]) ).
fof(f227,plain,
sF24 != sF26,
inference(definition_folding,[],[f177,f226,f224,f222]) ).
fof(f228,plain,
! [X0] :
( ~ in(X0,sF26)
| apply(sF25,sK3(sF25,sK19,X0)) = X0
| ~ relation(sF25)
| ~ function(sF25) ),
inference(superposition,[],[f204,f226]) ).
fof(f230,definition,
( spl27_1
<=> function(sF25) ),
introduced(definition,[new_symbols(definition,[spl27_1])],[avatar_definition]) ).
fof(f231,plain,
( function(sF25)
| ~ spl27_1 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f232,plain,
( ~ function(sF25)
| spl27_1 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f234,definition,
( spl27_2
<=> relation(sF25) ),
introduced(definition,[new_symbols(definition,[spl27_2])],[avatar_definition]) ).
fof(f235,plain,
( relation(sF25)
| ~ spl27_2 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f236,plain,
( ~ relation(sF25)
| spl27_2 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f238,definition,
( spl27_3
<=> ! [X0] :
( ~ in(X0,sF26)
| apply(sF25,sK3(sF25,sK19,X0)) = X0 ) ),
introduced(definition,[new_symbols(definition,[spl27_3])],[avatar_definition]) ).
fof(f239,plain,
( ! [X0] :
( ~ in(X0,sF26)
| apply(sF25,sK3(sF25,sK19,X0)) = X0 )
| ~ spl27_3 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f240,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_3 ),
inference(avatar_split_clause,[],[f228,f238,f234,f230]) ).
fof(f241,plain,
! [X0] :
( ~ in(X0,sF24)
| in(apply(sK20,X0),sK19)
| ~ relation(sK20)
| ~ function(sK20) ),
inference(superposition,[],[f207,f222]) ).
fof(f242,plain,
! [X0] :
( ~ in(X0,sF24)
| in(apply(sK20,X0),sK19)
| ~ function(sK20) ),
inference(forward_subsumption_resolution,[],[f241,f175]) ).
fof(f243,plain,
! [X0] :
( in(apply(sK20,X0),sK19)
| ~ in(X0,sF24) ),
inference(forward_subsumption_resolution,[],[f242,f174]) ).
fof(f244,plain,
! [X0,X1] :
( sP0(sK20,X0,X1,sF25)
| ~ relation(sF25)
| ~ function(sF25)
| ~ one_to_one(sK20)
| ~ relation(sK20)
| ~ function(sK20) ),
inference(superposition,[],[f220,f224]) ).
fof(f245,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,[],[f217,f224]) ).
fof(f246,plain,
( function(sF25)
| ~ relation(sK20)
| ~ function(sK20) ),
inference(superposition,[],[f139,f224]) ).
fof(f247,plain,
( ~ relation(sK20)
| ~ function(sK20)
| spl27_1 ),
inference(forward_subsumption_resolution,[],[f246,f232]) ).
fof(f248,plain,
( ~ function(sK20)
| spl27_1 ),
inference(forward_subsumption_resolution,[],[f247,f175]) ).
fof(f249,plain,
( $false
| spl27_1 ),
inference(forward_subsumption_resolution,[],[f248,f174]) ).
fof(f250,plain,
spl27_1,
inference(avatar_contradiction_clause,[],[f249]) ).
fof(f251,plain,
( ~ relation(sF25)
| relation_rng(sK20) = relation_dom(sF25)
| ~ function(sF25)
| ~ one_to_one(sK20)
| ~ relation(sK20)
| ~ function(sK20) ),
inference(superposition,[],[f215,f224]) ).
fof(f252,plain,
! [X0] :
( ~ in(X0,sF24)
| in(X0,relation_dom(sK20))
| ~ relation(sK20)
| ~ function(sK20) ),
inference(superposition,[],[f206,f222]) ).
fof(f253,plain,
! [X0] :
( ~ in(X0,sF24)
| in(X0,relation_dom(sK20))
| ~ function(sK20) ),
inference(forward_subsumption_resolution,[],[f252,f175]) ).
fof(f254,plain,
! [X0] :
( in(X0,relation_dom(sK20))
| ~ in(X0,sF24) ),
inference(forward_subsumption_resolution,[],[f253,f174]) ).
fof(f266,plain,
( relation(sF25)
| ~ relation(sK20)
| ~ function(sK20) ),
inference(superposition,[],[f140,f224]) ).
fof(f268,plain,
( ~ relation(sK20)
| ~ function(sK20)
| spl27_2 ),
inference(forward_subsumption_resolution,[],[f266,f236]) ).
fof(f270,plain,
( ~ function(sK20)
| spl27_2 ),
inference(forward_subsumption_resolution,[],[f268,f175]) ).
fof(f271,plain,
( $false
| spl27_2 ),
inference(forward_subsumption_resolution,[],[f270,f174]) ).
fof(f272,plain,
spl27_2,
inference(avatar_contradiction_clause,[],[f271]) ).
fof(f273,plain,
( ! [X0,X1] :
( sP0(sK20,X0,X1,sF25)
| ~ function(sF25)
| ~ one_to_one(sK20)
| ~ relation(sK20)
| ~ function(sK20) )
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f244,f235]) ).
fof(f274,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,[],[f245,f235]) ).
fof(f275,plain,
( relation_rng(sK20) = relation_dom(sF25)
| ~ function(sF25)
| ~ one_to_one(sK20)
| ~ relation(sK20)
| ~ function(sK20)
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f251,f235]) ).
fof(f276,plain,
( ! [X0,X1] :
( sP0(sK20,X0,X1,sF25)
| ~ one_to_one(sK20)
| ~ relation(sK20)
| ~ function(sK20) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f273,f231]) ).
fof(f277,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,[],[f274,f231]) ).
fof(f278,plain,
( relation_rng(sK20) = relation_dom(sF25)
| ~ one_to_one(sK20)
| ~ relation(sK20)
| ~ function(sK20)
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f275,f231]) ).
fof(f279,plain,
( ! [X0,X1] :
( sP0(sK20,X0,X1,sF25)
| ~ relation(sK20)
| ~ function(sK20) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f276,f176]) ).
fof(f280,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,[],[f277,f176]) ).
fof(f281,plain,
( relation_rng(sK20) = relation_dom(sF25)
| ~ relation(sK20)
| ~ function(sK20)
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f278,f176]) ).
fof(f282,plain,
( ! [X0,X1] :
( sP0(sK20,X0,X1,sF25)
| ~ function(sK20) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f279,f175]) ).
fof(f283,plain,
( ! [X0] :
( in(apply(sF25,X0),relation_dom(sK20))
| ~ in(X0,relation_rng(sK20))
| ~ function(sK20) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f280,f175]) ).
fof(f284,plain,
( relation_rng(sK20) = relation_dom(sF25)
| ~ function(sK20)
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f281,f175]) ).
fof(f285,plain,
( ! [X0,X1] : sP0(sK20,X0,X1,sF25)
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f282,f174]) ).
fof(f286,plain,
( ! [X0] :
( in(apply(sF25,X0),relation_dom(sK20))
| ~ in(X0,relation_rng(sK20)) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f283,f174]) ).
fof(f287,plain,
( relation_rng(sK20) = relation_dom(sF25)
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f284,f174]) ).
fof(f288,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,[],[f219,f287]) ).
fof(f289,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,[],[f288,f140]) ).
fof(f290,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,[],[f289,f139]) ).
fof(f291,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,[],[f290,f176]) ).
fof(f292,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,[],[f291,f175]) ).
fof(f293,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF25))
| apply(sK20,apply(function_inverse(sK20),X0)) = X0 )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f292,f174]) ).
fof(f294,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF25))
| apply(sK20,apply(sF25,X0)) = X0 )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_demodulation,[],[f293,f224]) ).
fof(f315,plain,
! [X0] :
( in(apply(sF25,X0),sF26)
| ~ in(X0,relation_dom(sF25))
| ~ in(X0,sK19)
| ~ relation(sF25)
| ~ function(sF25) ),
inference(superposition,[],[f201,f226]) ).
fof(f318,plain,
( ! [X0] :
( in(apply(sF25,X0),sF26)
| ~ in(X0,relation_dom(sF25))
| ~ in(X0,sK19)
| ~ function(sF25) )
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f315,f235]) ).
fof(f319,plain,
( ! [X0] :
( in(apply(sF25,X0),sF26)
| ~ in(X0,relation_dom(sF25))
| ~ in(X0,sK19) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f318,f231]) ).
fof(f333,plain,
( ! [X0,X1] :
( ~ in(X0,relation_image(sF25,X1))
| ~ relation(sF25)
| ~ function(sF25)
| sK3(sF25,X1,X0) = apply(sK20,apply(sF25,sK3(sF25,X1,X0))) )
| ~ spl27_1
| ~ spl27_2 ),
inference(resolution,[],[f202,f294]) ).
fof(f334,plain,
( ! [X0,X1] :
( ~ in(X0,relation_image(sF25,X1))
| ~ function(sF25)
| sK3(sF25,X1,X0) = apply(sK20,apply(sF25,sK3(sF25,X1,X0))) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f333,f235]) ).
fof(f335,plain,
( ! [X0,X1] :
( ~ in(X0,relation_image(sF25,X1))
| sK3(sF25,X1,X0) = apply(sK20,apply(sF25,sK3(sF25,X1,X0))) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f334,f231]) ).
fof(f348,plain,
( ! [X0] :
( in(apply(sK20,X0),relation_dom(sF25))
| ~ in(X0,relation_dom(sK20))
| ~ relation(sK20)
| ~ function(sK20) )
| ~ spl27_1
| ~ spl27_2 ),
inference(superposition,[],[f209,f287]) ).
fof(f352,plain,
( ! [X0] :
( in(apply(sK20,X0),relation_dom(sF25))
| ~ in(X0,relation_dom(sK20))
| ~ function(sK20) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f348,f175]) ).
fof(f354,plain,
( ! [X0] :
( in(apply(sK20,X0),relation_dom(sF25))
| ~ in(X0,relation_dom(sK20)) )
| ~ spl27_1
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f352,f174]) ).
fof(f364,plain,
( ! [X0] :
( ~ in(X0,sF26)
| sK3(sF25,sK19,X0) = apply(sK20,apply(sF25,sK3(sF25,sK19,X0))) )
| ~ spl27_1
| ~ spl27_2 ),
inference(superposition,[],[f335,f226]) ).
fof(f911,definition,
( spl27_47
<=> in(sK3(sF25,sK19,sK21(sF26,sF24)),relation_dom(sF25)) ),
introduced(definition,[new_symbols(definition,[spl27_47])],[avatar_definition]) ).
fof(f912,plain,
( in(sK3(sF25,sK19,sK21(sF26,sF24)),relation_dom(sF25))
| ~ spl27_47 ),
inference(avatar_component_clause,[],[f911]) ).
fof(f913,plain,
( ~ in(sK3(sF25,sK19,sK21(sF26,sF24)),relation_dom(sF25))
| spl27_47 ),
inference(avatar_component_clause,[],[f911]) ).
fof(f915,definition,
( spl27_48
<=> in(sK21(sF26,sF24),sF26) ),
introduced(definition,[new_symbols(definition,[spl27_48])],[avatar_definition]) ).
fof(f916,plain,
( ~ in(sK21(sF26,sF24),sF26)
| spl27_48 ),
inference(avatar_component_clause,[],[f915]) ).
fof(f917,plain,
( in(sK21(sF26,sF24),sF26)
| ~ spl27_48 ),
inference(avatar_component_clause,[],[f915]) ).
fof(f937,plain,
( ~ in(sK21(sF26,sF24),relation_image(sF25,sK19))
| ~ relation(sF25)
| ~ function(sF25)
| spl27_47 ),
inference(resolution,[],[f913,f202]) ).
fof(f938,plain,
( ~ in(sK21(sF26,sF24),relation_image(sF25,sK19))
| ~ function(sF25)
| ~ spl27_2
| spl27_47 ),
inference(forward_subsumption_resolution,[],[f937,f235]) ).
fof(f939,plain,
( ~ in(sK21(sF26,sF24),relation_image(sF25,sK19))
| ~ spl27_1
| ~ spl27_2
| spl27_47 ),
inference(forward_subsumption_resolution,[],[f938,f231]) ).
fof(f940,plain,
( ~ in(sK21(sF26,sF24),sF26)
| ~ spl27_1
| ~ spl27_2
| spl27_47 ),
inference(forward_demodulation,[],[f939,f226]) ).
fof(f941,plain,
( ~ spl27_48
| ~ spl27_1
| ~ spl27_2
| spl27_47 ),
inference(avatar_split_clause,[],[f940,f911,f234,f230,f915]) ).
fof(f942,plain,
( in(sK21(sF26,sF24),sF24)
| sF24 = sF26
| spl27_48 ),
inference(resolution,[],[f916,f180]) ).
fof(f943,plain,
( in(sK21(sF26,sF24),sF24)
| spl27_48 ),
inference(forward_subsumption_resolution,[],[f942,f227]) ).
fof(f1010,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK20))
| apply(sF25,apply(sK20,X0)) = X0 )
| ~ spl27_1
| ~ spl27_2 ),
inference(resolution,[],[f214,f285]) ).
fof(f1015,plain,
( ! [X0] :
( ~ in(X0,sF24)
| apply(sF25,apply(sK20,X0)) = X0 )
| ~ spl27_1
| ~ spl27_2 ),
inference(resolution,[],[f1010,f254]) ).
fof(f1045,plain,
( sK21(sF26,sF24) = apply(sF25,apply(sK20,sK21(sF26,sF24)))
| ~ spl27_1
| ~ spl27_2
| spl27_48 ),
inference(resolution,[],[f1015,f943]) ).
fof(f1237,plain,
( in(sK21(sF26,sF24),sF26)
| ~ in(apply(sK20,sK21(sF26,sF24)),relation_dom(sF25))
| ~ in(apply(sK20,sK21(sF26,sF24)),sK19)
| ~ spl27_1
| ~ spl27_2
| spl27_48 ),
inference(superposition,[],[f319,f1045]) ).
fof(f1252,definition,
( spl27_72
<=> in(apply(sK20,sK21(sF26,sF24)),relation_dom(sF25)) ),
introduced(definition,[new_symbols(definition,[spl27_72])],[avatar_definition]) ).
fof(f1254,plain,
( ~ in(apply(sK20,sK21(sF26,sF24)),relation_dom(sF25))
| spl27_72 ),
inference(avatar_component_clause,[],[f1252]) ).
fof(f1264,plain,
( ~ in(apply(sK20,sK21(sF26,sF24)),relation_dom(sF25))
| ~ in(apply(sK20,sK21(sF26,sF24)),sK19)
| ~ spl27_1
| ~ spl27_2
| spl27_48 ),
inference(forward_subsumption_resolution,[],[f1237,f916]) ).
fof(f1266,definition,
( spl27_75
<=> in(sK21(sF26,sF24),relation_dom(sK20)) ),
introduced(definition,[new_symbols(definition,[spl27_75])],[avatar_definition]) ).
fof(f1267,plain,
( ~ in(sK21(sF26,sF24),relation_dom(sK20))
| spl27_75 ),
inference(avatar_component_clause,[],[f1266]) ).
fof(f1268,plain,
( in(sK21(sF26,sF24),relation_dom(sK20))
| ~ spl27_75 ),
inference(avatar_component_clause,[],[f1266]) ).
fof(f1275,definition,
( spl27_76
<=> in(apply(sK20,sK21(sF26,sF24)),sK19) ),
introduced(definition,[new_symbols(definition,[spl27_76])],[avatar_definition]) ).
fof(f1276,plain,
( in(apply(sK20,sK21(sF26,sF24)),sK19)
| ~ spl27_76 ),
inference(avatar_component_clause,[],[f1275]) ).
fof(f1277,plain,
( ~ in(apply(sK20,sK21(sF26,sF24)),sK19)
| spl27_76 ),
inference(avatar_component_clause,[],[f1275]) ).
fof(f1278,plain,
( ~ spl27_76
| ~ spl27_72
| ~ spl27_1
| ~ spl27_2
| spl27_48 ),
inference(avatar_split_clause,[],[f1264,f915,f234,f230,f1252,f1275]) ).
fof(f1288,plain,
( ~ in(sK21(sF26,sF24),relation_dom(sK20))
| ~ spl27_1
| ~ spl27_2
| spl27_72 ),
inference(resolution,[],[f1254,f354]) ).
fof(f1289,plain,
( ~ spl27_75
| ~ spl27_1
| ~ spl27_2
| spl27_72 ),
inference(avatar_split_clause,[],[f1288,f1252,f234,f230,f1266]) ).
fof(f1290,plain,
( ~ in(sK21(sF26,sF24),sF24)
| spl27_75 ),
inference(resolution,[],[f1267,f254]) ).
fof(f1291,plain,
( $false
| spl27_48
| spl27_75 ),
inference(forward_subsumption_resolution,[],[f1290,f943]) ).
fof(f1292,plain,
( spl27_48
| spl27_75 ),
inference(avatar_contradiction_clause,[],[f1291]) ).
fof(f1294,definition,
( spl27_79
<=> sK21(sF26,sF24) = apply(sF25,sK3(sF25,sK19,sK21(sF26,sF24))) ),
introduced(definition,[new_symbols(definition,[spl27_79])],[avatar_definition]) ).
fof(f1295,plain,
( sK21(sF26,sF24) != apply(sF25,sK3(sF25,sK19,sK21(sF26,sF24)))
| spl27_79 ),
inference(avatar_component_clause,[],[f1294]) ).
fof(f1296,plain,
( sK21(sF26,sF24) = apply(sF25,sK3(sF25,sK19,sK21(sF26,sF24)))
| ~ spl27_79 ),
inference(avatar_component_clause,[],[f1294]) ).
fof(f1303,plain,
( sK3(sF25,sK19,sK21(sF26,sF24)) = apply(sK20,apply(sF25,sK3(sF25,sK19,sK21(sF26,sF24))))
| ~ spl27_1
| ~ spl27_2
| ~ spl27_48 ),
inference(resolution,[],[f917,f364]) ).
fof(f1305,plain,
( sK3(sF25,sK19,sK21(sF26,sF24)) = apply(sK20,sK21(sF26,sF24))
| ~ spl27_1
| ~ spl27_2
| ~ spl27_48
| ~ spl27_79 ),
inference(forward_demodulation,[],[f1303,f1296]) ).
fof(f1308,plain,
( in(sK21(sF26,sF24),relation_dom(sK20))
| ~ in(sK3(sF25,sK19,sK21(sF26,sF24)),relation_rng(sK20))
| ~ spl27_1
| ~ spl27_2
| ~ spl27_79 ),
inference(superposition,[],[f286,f1296]) ).
fof(f1319,plain,
( ~ in(sK3(sF25,sK19,sK21(sF26,sF24)),relation_rng(sK20))
| ~ spl27_1
| ~ spl27_2
| spl27_75
| ~ spl27_79 ),
inference(forward_subsumption_resolution,[],[f1308,f1267]) ).
fof(f1326,plain,
( ~ in(sK3(sF25,sK19,sK21(sF26,sF24)),relation_dom(sF25))
| ~ spl27_1
| ~ spl27_2
| spl27_75
| ~ spl27_79 ),
inference(forward_demodulation,[],[f1319,f287]) ).
fof(f1334,plain,
( $false
| ~ spl27_1
| ~ spl27_2
| ~ spl27_47
| spl27_75
| ~ spl27_79 ),
inference(forward_subsumption_resolution,[],[f1326,f912]) ).
fof(f1335,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_47
| spl27_75
| ~ spl27_79 ),
inference(avatar_contradiction_clause,[],[f1334]) ).
fof(f1350,plain,
( ~ in(sK21(sF26,sF24),sF24)
| spl27_76 ),
inference(resolution,[],[f1277,f243]) ).
fof(f1351,plain,
( $false
| spl27_48
| spl27_76 ),
inference(forward_subsumption_resolution,[],[f1350,f943]) ).
fof(f1352,plain,
( spl27_48
| spl27_76 ),
inference(avatar_contradiction_clause,[],[f1351]) ).
fof(f1365,plain,
( sK21(sF26,sF24) = apply(sF25,sK3(sF25,sK19,sK21(sF26,sF24)))
| ~ spl27_3
| ~ spl27_48 ),
inference(resolution,[],[f917,f239]) ).
fof(f1528,plain,
( in(apply(sK20,sK21(sF26,sF24)),sK19)
| ~ in(sK21(sF26,sF24),relation_image(sF25,sK19))
| ~ relation(sF25)
| ~ function(sF25)
| ~ spl27_1
| ~ spl27_2
| ~ spl27_48
| ~ spl27_79 ),
inference(superposition,[],[f203,f1305]) ).
fof(f1529,plain,
( in(apply(sK20,sK21(sF26,sF24)),sK19)
| ~ in(sK21(sF26,sF24),relation_image(sF25,sK19))
| ~ function(sF25)
| ~ spl27_1
| ~ spl27_2
| ~ spl27_48
| ~ spl27_79 ),
inference(forward_subsumption_resolution,[],[f1528,f235]) ).
fof(f1530,plain,
( in(apply(sK20,sK21(sF26,sF24)),sK19)
| ~ in(sK21(sF26,sF24),relation_image(sF25,sK19))
| ~ spl27_1
| ~ spl27_2
| ~ spl27_48
| ~ spl27_79 ),
inference(forward_subsumption_resolution,[],[f1529,f231]) ).
fof(f1531,plain,
( ~ in(sK21(sF26,sF24),sF26)
| in(apply(sK20,sK21(sF26,sF24)),sK19)
| ~ spl27_1
| ~ spl27_2
| ~ spl27_48
| ~ spl27_79 ),
inference(forward_demodulation,[],[f1530,f226]) ).
fof(f1532,plain,
( in(apply(sK20,sK21(sF26,sF24)),sK19)
| ~ spl27_1
| ~ spl27_2
| ~ spl27_48
| ~ spl27_79 ),
inference(forward_subsumption_resolution,[],[f1531,f917]) ).
fof(f1533,plain,
( spl27_76
| ~ spl27_1
| ~ spl27_2
| ~ spl27_48
| ~ spl27_79 ),
inference(avatar_split_clause,[],[f1532,f1294,f915,f234,f230,f1275]) ).
fof(f1534,plain,
( ~ in(sK21(sF26,sF24),relation_dom(sK20))
| in(sK21(sF26,sF24),relation_inverse_image(sK20,sK19))
| ~ relation(sK20)
| ~ function(sK20)
| ~ spl27_76 ),
inference(resolution,[],[f1276,f205]) ).
fof(f1537,plain,
( in(sK21(sF26,sF24),relation_inverse_image(sK20,sK19))
| ~ relation(sK20)
| ~ function(sK20)
| ~ spl27_75
| ~ spl27_76 ),
inference(forward_subsumption_resolution,[],[f1534,f1268]) ).
fof(f1538,plain,
( in(sK21(sF26,sF24),relation_inverse_image(sK20,sK19))
| ~ function(sK20)
| ~ spl27_75
| ~ spl27_76 ),
inference(forward_subsumption_resolution,[],[f1537,f175]) ).
fof(f1539,plain,
( in(sK21(sF26,sF24),relation_inverse_image(sK20,sK19))
| ~ spl27_75
| ~ spl27_76 ),
inference(forward_subsumption_resolution,[],[f1538,f174]) ).
fof(f1540,plain,
( in(sK21(sF26,sF24),sF24)
| ~ spl27_75
| ~ spl27_76 ),
inference(forward_demodulation,[],[f1539,f222]) ).
fof(f1541,plain,
( sF24 = sF26
| ~ in(sK21(sF26,sF24),sF26)
| ~ spl27_75
| ~ spl27_76 ),
inference(resolution,[],[f1540,f181]) ).
fof(f1543,plain,
( ~ in(sK21(sF26,sF24),sF26)
| ~ spl27_75
| ~ spl27_76 ),
inference(forward_subsumption_resolution,[],[f1541,f227]) ).
fof(f1544,plain,
( $false
| ~ spl27_48
| ~ spl27_75
| ~ spl27_76 ),
inference(forward_subsumption_resolution,[],[f1543,f917]) ).
fof(f1545,plain,
( ~ spl27_48
| ~ spl27_75
| ~ spl27_76 ),
inference(avatar_contradiction_clause,[],[f1544]) ).
fof(f1546,plain,
( $false
| ~ spl27_3
| ~ spl27_48
| spl27_79 ),
inference(forward_subsumption_resolution,[],[f1365,f1295]) ).
fof(f1547,plain,
( ~ spl27_3
| ~ spl27_48
| spl27_79 ),
inference(avatar_contradiction_clause,[],[f1546]) ).
cnf(s1,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_3 ),
inference(sat_conversion,[],[f240]) ).
cnf(s2,plain,
spl27_1,
inference(sat_conversion,[],[f250]) ).
cnf(s3,plain,
spl27_2,
inference(sat_conversion,[],[f272]) ).
cnf(s44,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_47
| ~ spl27_48 ),
inference(sat_conversion,[],[f941]) ).
cnf(s82,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_48
| ~ spl27_72
| ~ spl27_76 ),
inference(sat_conversion,[],[f1278]) ).
cnf(s86,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_72
| ~ spl27_75 ),
inference(sat_conversion,[],[f1289]) ).
cnf(s87,plain,
( spl27_48
| spl27_75 ),
inference(sat_conversion,[],[f1292]) ).
cnf(s91,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_47
| spl27_75
| ~ spl27_79 ),
inference(sat_conversion,[],[f1335]) ).
cnf(s98,plain,
( spl27_48
| spl27_76 ),
inference(sat_conversion,[],[f1352]) ).
cnf(s108,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_48
| spl27_76
| ~ spl27_79 ),
inference(sat_conversion,[],[f1533]) ).
cnf(s109,plain,
( ~ spl27_48
| ~ spl27_75
| ~ spl27_76 ),
inference(sat_conversion,[],[f1545]) ).
cnf(s110,plain,
( ~ spl27_3
| ~ spl27_48
| spl27_79 ),
inference(sat_conversion,[],[f1547]) ).
cnf(s116,plain,
spl27_3,
inference(rat,[],[s1,s3,s2]) ).
cnf(s119,plain,
spl27_48,
inference(rat,[],[s86,s82,s87,s98,s3,s2]) ).
cnf(s120,plain,
spl27_79,
inference(rat,[],[s110,s116,s119]) ).
cnf(s121,plain,
spl27_76,
inference(rat,[],[s108,s120,s2,s3,s119]) ).
cnf(s122,plain,
spl27_47,
inference(rat,[],[s44,s2,s3,s119]) ).
cnf(s123,plain,
~ spl27_75,
inference(rat,[],[s109,s119,s121]) ).
cnf(s128,plain,
$false,
inference(rat,[],[s91,s120,s2,s3,s123,s122]) ).
fof(f1566,plain,
$false,
inference(avatar_sat_refutation,[],[s128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU074+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 % Computer : n008.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Mon Sep 28 03:30:25 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 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
% 8.39/2.19 % (1840041)Detected formulas, will run a generic FOF schedule.
% 8.39/2.19 % (1840054)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=4244871050:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.39/2.19 % (1840060)dis-21_1_sil=8000:lcm=predicate:random_seed=697910293: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)
% 8.39/2.19 % (1840056)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=1697612668:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.39/2.19 % (1840057)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=255453639:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.39/2.19 % (1840055)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=1853826855:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.39/2.19 % (1840057)Refutation not found, incomplete strategy
% 8.39/2.19 % (1840057)------------------------------
% 8.39/2.19 % (1840057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.19 % (1840057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.19 % (1840057)CaDiCaL version: 2.1.3
% 8.39/2.19 % (1840057)Termination reason: Refutation not found, incomplete strategy
% 8.39/2.19 % (1840057)Time elapsed: 0.006 s
% 8.39/2.19 % (1840057)Peak memory usage: 88 MB
% 8.39/2.19 % (1840057)Instructions burned: 4 (million)
% 8.39/2.19 % (1840058)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=165541899:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.39/2.19 % (1840059)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3226776400:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.39/2.19 % (1840060)Instruction limit reached!
% 8.39/2.19 % (1840060)------------------------------
% 8.39/2.19 % (1840060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.19 % (1840060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.19 % (1840060)CaDiCaL version: 2.1.3
% 8.39/2.19 % (1840060)Termination reason: Instruction limit
% 8.39/2.19 % (1840060)Termination phase: Saturation
% 8.39/2.19 % (1840060)Time elapsed: 0.083 s
% 8.39/2.19 % (1840060)Peak memory usage: 91 MB
% 8.39/2.19 % (1840060)Instructions burned: 130 (million)
% 8.39/2.19 % (1840058)Instruction limit reached!
% 8.39/2.19 % (1840058)------------------------------
% 8.39/2.19 % (1840058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.19 % (1840058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.19 % (1840058)CaDiCaL version: 2.1.3
% 8.39/2.19 % (1840058)Termination reason: Instruction limit
% 8.39/2.19 % (1840058)Termination phase: Saturation
% 8.39/2.19 % (1840058)Time elapsed: 0.115 s
% 8.39/2.19 % (1840058)Peak memory usage: 88 MB
% 8.39/2.19 % (1840058)Instructions burned: 120 (million)
% 8.39/2.19 % (1840059)Instruction limit reached!
% 8.39/2.19 % (1840059)------------------------------
% 8.39/2.19 % (1840059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.19 % (1840059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.19 % (1840059)CaDiCaL version: 2.1.3
% 8.39/2.19 % (1840059)Termination reason: Instruction limit
% 8.39/2.19 % (1840059)Termination phase: Saturation
% 8.39/2.19 % (1840059)Time elapsed: 0.160 s
% 8.39/2.19 % (1840059)Peak memory usage: 90 MB
% 8.39/2.19 % (1840059)Instructions burned: 139 (million)
% 8.39/2.19 % (1840068)lrs+10_1_sil=8000:sp=occurrence:random_seed=553557057:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 8.39/2.19 % (1840069)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3971573821:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 8.39/2.19 % (1840057)------------------------------
% 8.39/2.19 % (1840057)------------------------------
% 8.39/2.19 % (1840070)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2989570318:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 8.39/2.19 % (1840068)Instruction limit reached!
% 8.39/2.19 % (1840068)------------------------------
% 8.39/2.19 % (1840068)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.19 % (1840068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.19 % (1840068)CaDiCaL version: 2.1.3
% 8.39/2.19 % (1840068)Termination reason: Instruction limit
% 8.39/2.19 % (1840068)Termination phase: Saturation
% 8.39/2.19 % (1840068)Time elapsed: 0.264 s
% 8.39/2.19 % (1840068)Peak memory usage: 92 MB
% 8.39/2.19 % (1840068)Instructions burned: 285 (million)
% 8.39/2.19 % (1840069)Instruction limit reached!
% 8.39/2.19 % (1840069)------------------------------
% 8.39/2.19 % (1840069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.19 % (1840069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.19 % (1840069)CaDiCaL version: 2.1.3
% 8.39/2.19 % (1840069)Termination reason: Instruction limit
% 8.39/2.19 % (1840069)Termination phase: Saturation
% 8.39/2.19 % (1840069)Time elapsed: 0.139 s
% 8.39/2.19 % (1840069)Peak memory usage: 89 MB
% 8.39/2.19 % (1840069)Instructions burned: 158 (million)
% 8.39/2.19 % (1840076)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=1019256629:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 8.39/2.19 % (1840078)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3987161036:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 8.39/2.19 % (1840077)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1418464427:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 8.39/2.19 % (1840054)First to succeed.
% 8.39/2.19 % (1840077)Refutation not found, incomplete strategy
% 8.39/2.19 % (1840077)------------------------------
% 8.39/2.19 % (1840077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.19 % (1840077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.19 % (1840077)CaDiCaL version: 2.1.3
% 8.39/2.19 % (1840077)Termination reason: Refutation not found, incomplete strategy
% 8.39/2.19 % (1840077)Time elapsed: 0.005 s
% 8.39/2.19 % (1840077)Peak memory usage: 88 MB
% 8.39/2.19 % (1840077)Instructions burned: 3 (million)
% 8.39/2.19 % (1840054)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1840041"
% 8.39/2.19 % (1840070)Instruction limit reached!
% 8.39/2.19 % (1840070)------------------------------
% 8.39/2.19 % (1840070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.19 % (1840070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.19 % (1840070)CaDiCaL version: 2.1.3
% 8.39/2.19 % (1840070)Termination reason: Instruction limit
% 8.39/2.19 % (1840070)Termination phase: Saturation
% 8.39/2.19 % (1840070)Time elapsed: 0.321 s
% 8.39/2.19 % (1840070)Peak memory usage: 92 MB
% 8.39/2.19 % (1840070)Instructions burned: 325 (million)
% 8.39/2.19 % (1840076)Instruction limit reached!
% 8.39/2.19 % (1840076)------------------------------
% 8.39/2.19 % (1840076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.19 % (1840076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.19 % (1840076)CaDiCaL version: 2.1.3
% 8.39/2.19 % (1840076)Termination reason: Instruction limit
% 8.39/2.19 % (1840076)Termination phase: Saturation
% 8.39/2.19 % (1840076)Time elapsed: 0.205 s
% 8.39/2.19 % (1840076)Peak memory usage: 91 MB
% 8.39/2.19 % (1840076)Instructions burned: 249 (million)
% 8.39/2.19 % (1840082)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=203386996:cts=off:i=113:fsr=off:ss=included:sgt=4_2990 on theBenchmark for (2990ds/113Mi)
% 8.39/2.19 % (1840054)Refutation found. Thanks to Tanya!
% 8.39/2.19 % SZS status Theorem for theBenchmark
% 8.39/2.19 % SZS output start Proof for theBenchmark
% See solution above
% 9.04/2.43 % (1840054)------------------------------
% 9.04/2.43 % (1840054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.04/2.43 % (1840054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.04/2.43 % (1840054)CaDiCaL version: 2.1.3
% 9.04/2.43 % (1840054)Termination reason: Refutation
% 9.04/2.43 % (1840054)Time elapsed: 0.742 s
% 9.04/2.43 % (1840054)Peak memory usage: 131 MB
% 9.04/2.43 % (1840054)Instructions burned: 1150 (million)
% 9.04/2.43 % (1840054)------------------------------
% 9.04/2.43 % (1840054)------------------------------
% 9.04/2.43 % (1840041)Success in time 1.165 s
% 9.04/2.43 % Vampire exiting
%------------------------------------------------------------------------------