%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU027+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:47:05 PM UTC 2026
% Result : Theorem 3.06s 1.43s
% Output : Refutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 10
% Syntax : Number of formulae : 153 ( 17 unt; 7 def)
% Number of atoms : 784 ( 215 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 1081 ( 450 ~; 476 |; 121 &)
% ( 20 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 6 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 203 ( 0 sgn 182 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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(f31,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(f33,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X0)
& relation_dom(X0) = relation_rng(X1)
& relation_rng(X0) = relation_dom(X1)
& ! [X2,X3] :
( ( in(X2,relation_dom(X0))
& in(X3,relation_dom(X1)) )
=> ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 ) ) )
=> X1 = function_inverse(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X0)
& relation_dom(X0) = relation_rng(X1)
& relation_rng(X0) = relation_dom(X1)
& ! [X2,X3] :
( ( in(X2,relation_dom(X0))
& in(X3,relation_dom(X1)) )
=> ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 ) ) )
=> X1 = function_inverse(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f39,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& one_to_one(X0)
& relation_dom(X0) = relation_rng(X1)
& relation_rng(X0) = relation_dom(X1)
& ! [X2,X3] :
( ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 )
| ~ in(X2,relation_dom(X0))
| ~ in(X3,relation_dom(X1)) )
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f40,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& one_to_one(X0)
& relation_dom(X0) = relation_rng(X1)
& relation_rng(X0) = relation_dom(X1)
& ! [X2,X3] :
( ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 )
| ~ in(X2,relation_dom(X0))
| ~ in(X3,relation_dom(X1)) )
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(flattening,[],[f39]) ).
fof(f52,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,[],[f5]) ).
fof(f53,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,[],[f52]) ).
fof(f55,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,[],[f31]) ).
fof(f56,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,[],[f55]) ).
fof(f62,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(f63,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,[],[f56,f62]) ).
fof(f64,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& one_to_one(X0)
& relation_dom(X0) = relation_rng(X1)
& relation_rng(X0) = relation_dom(X1)
& ! [X2,X3] :
( ( ( apply(X0,X2) = X3
| apply(X1,X3) != X2 )
& ( apply(X1,X3) = X2
| apply(X0,X2) != X3 ) )
| ~ in(X2,relation_dom(X0))
| ~ in(X3,relation_dom(X1)) )
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(nnf_transformation,[],[f40]) ).
fof(f65,plain,
( sK2 != function_inverse(sK1)
& one_to_one(sK1)
& relation_dom(sK1) = relation_rng(sK2)
& relation_rng(sK1) = relation_dom(sK2)
& ! [X2,X3] :
( ( ( apply(sK1,X2) = X3
| apply(sK2,X3) != X2 )
& ( apply(sK2,X3) = X2
| apply(sK1,X2) != X3 ) )
| ~ in(X2,relation_dom(sK1))
| ~ in(X3,relation_dom(sK2)) )
& relation(sK2)
& function(sK2)
& relation(sK1)
& function(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f64]) ).
fof(f67,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,[],[f53]) ).
fof(f68,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,[],[f67]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK4(X0,X1) )
| ~ in(sK4(X0,X1),X1) )
& ( ( in(sK5(X0,X1),relation_dom(X0))
& sK4(X0,X1) = apply(X0,sK5(X0,X1)) )
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK6(X0,X5),relation_dom(X0))
& apply(X0,sK6(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X2,sK4(X0,X1)),skolemize(X4,sK5(X0,X1)),skolemize(X7,sK6(X0,X5))],[f68]) ).
fof(f72,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,[],[f62]) ).
fof(f73,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,[],[f72]) ).
fof(f74,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,[],[f73]) ).
fof(f75,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,[],[f63]) ).
fof(f76,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,[],[f75]) ).
fof(f77,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,[],[f76]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = function_inverse(X0)
| relation_rng(X0) != relation_dom(X1)
| ( ( ~ in(sK10(X0,X1),relation_dom(X0))
| sK9(X0,X1) != apply(X0,sK10(X0,X1)) )
& in(sK9(X0,X1),relation_rng(X0))
& sK10(X0,X1) = apply(X1,sK9(X0,X1)) )
| ~ sP0(X0,sK9(X0,X1),sK10(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,[sK9,sK10]),skolemize(X2,sK9(X0,X1)),skolemize(X3,sK10(X0,X1))],[f77]) ).
fof(f82,plain,
function(sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f83,plain,
relation(sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f84,plain,
function(sK2),
inference(cnf_transformation,[],[f65]) ).
fof(f85,plain,
relation(sK2),
inference(cnf_transformation,[],[f65]) ).
fof(f86,plain,
! [X2,X3] :
( apply(sK2,X3) = X2
| apply(sK1,X2) != X3
| ~ in(X2,relation_dom(sK1))
| ~ in(X3,relation_dom(sK2)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f87,plain,
! [X2,X3] :
( apply(sK1,X2) = X3
| apply(sK2,X3) != X2
| ~ in(X2,relation_dom(sK1))
| ~ in(X3,relation_dom(sK2)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f88,plain,
relation_rng(sK1) = relation_dom(sK2),
inference(cnf_transformation,[],[f65]) ).
fof(f89,plain,
relation_dom(sK1) = relation_rng(sK2),
inference(cnf_transformation,[],[f65]) ).
fof(f90,plain,
one_to_one(sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f91,plain,
sK2 != function_inverse(sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f103,plain,
! [X0,X1,X5] :
( apply(X0,sK6(X0,X5)) = X5
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f104,plain,
! [X0,X1,X5] :
( in(sK6(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f105,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,[],[f69]) ).
fof(f115,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,[],[f74]) ).
fof(f117,plain,
! [X2,X3,X0,X1] :
( sP0(X0,X1,X2,X3)
| apply(X0,X2) = X1 ),
inference(cnf_transformation,[],[f74]) ).
fof(f118,plain,
! [X2,X3,X0,X1] :
( sP0(X0,X1,X2,X3)
| in(X2,relation_dom(X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f119,plain,
! [X2,X3,X0,X1] :
( sP0(X0,X1,X2,X3)
| ~ in(X1,relation_rng(X0))
| apply(X3,X1) != X2 ),
inference(cnf_transformation,[],[f74]) ).
fof(f124,plain,
! [X0,X1] :
( relation_rng(X0) != relation_dom(X1)
| function_inverse(X0) = X1
| sK10(X0,X1) = apply(X1,sK9(X0,X1))
| ~ sP0(X0,sK9(X0,X1),sK10(X0,X1),X1)
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f125,plain,
! [X0,X1] :
( relation_rng(X0) != relation_dom(X1)
| function_inverse(X0) = X1
| in(sK9(X0,X1),relation_rng(X0))
| ~ sP0(X0,sK9(X0,X1),sK10(X0,X1),X1)
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f126,plain,
! [X0,X1] :
( sK9(X0,X1) != apply(X0,sK10(X0,X1))
| relation_rng(X0) != relation_dom(X1)
| ~ in(sK10(X0,X1),relation_dom(X0))
| function_inverse(X0) = X1
| ~ sP0(X0,sK9(X0,X1),sK10(X0,X1),X1)
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f140,definition,
~ sP14(sK2),
introduced(definition,[new_symbols(definition,[sP14])],[inequality_splitting_name_introduction]) ).
fof(f141,plain,
sP14(function_inverse(sK1)),
inference(inequality_splitting,[],[f91,f140]) ).
fof(f142,plain,
! [X3] :
( apply(sK1,apply(sK2,X3)) = X3
| ~ in(apply(sK2,X3),relation_dom(sK1))
| ~ in(X3,relation_dom(sK2)) ),
inference(equality_resolution,[],[f87]) ).
fof(f143,plain,
! [X2] :
( apply(sK2,apply(sK1,X2)) = X2
| ~ in(X2,relation_dom(sK1))
| ~ in(apply(sK1,X2),relation_dom(sK2)) ),
inference(equality_resolution,[],[f86]) ).
fof(f144,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,[],[f105]) ).
fof(f145,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f144]) ).
fof(f146,plain,
! [X0,X5] :
( in(sK6(X0,X5),relation_dom(X0))
| ~ in(X5,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f104]) ).
fof(f147,plain,
! [X0,X5] :
( apply(X0,sK6(X0,X5)) = X5
| ~ in(X5,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f103]) ).
fof(f148,plain,
! [X3,X0,X1] :
( sP0(X0,X1,apply(X3,X1),X3)
| ~ in(X1,relation_rng(X0)) ),
inference(equality_resolution,[],[f119]) ).
fof(f150,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,[],[f115]) ).
fof(f175,plain,
! [X0] :
( relation_rng(X0) != relation_rng(sK1)
| function_inverse(X0) = sK2
| sK10(X0,sK2) = apply(sK2,sK9(X0,sK2))
| ~ sP0(X0,sK9(X0,sK2),sK10(X0,sK2),sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[],[f124,f88]) ).
fof(f176,plain,
! [X0] :
( relation_rng(X0) != relation_rng(sK1)
| function_inverse(X0) = sK2
| in(sK9(X0,sK2),relation_rng(X0))
| ~ sP0(X0,sK9(X0,sK2),sK10(X0,sK2),sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[],[f125,f88]) ).
fof(f177,plain,
! [X0] :
( in(sK6(sK2,X0),relation_rng(sK1))
| ~ in(X0,relation_rng(sK2))
| ~ relation(sK2)
| ~ function(sK2) ),
inference(superposition,[],[f146,f88]) ).
fof(f180,plain,
! [X0] :
( in(sK6(sK2,X0),relation_rng(sK1))
| ~ in(X0,relation_rng(sK2))
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f177,f85]) ).
fof(f181,plain,
! [X0] :
( relation_rng(X0) != relation_rng(sK1)
| function_inverse(X0) = sK2
| in(sK9(X0,sK2),relation_rng(X0))
| ~ sP0(X0,sK9(X0,sK2),sK10(X0,sK2),sK2)
| ~ function(sK2)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f176,f85]) ).
fof(f182,plain,
! [X0] :
( relation_rng(X0) != relation_rng(sK1)
| function_inverse(X0) = sK2
| sK10(X0,sK2) = apply(sK2,sK9(X0,sK2))
| ~ sP0(X0,sK9(X0,sK2),sK10(X0,sK2),sK2)
| ~ function(sK2)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f175,f85]) ).
fof(f188,plain,
! [X0] :
( in(sK6(sK2,X0),relation_rng(sK1))
| ~ in(X0,relation_rng(sK2)) ),
inference(forward_subsumption_resolution,[],[f180,f84]) ).
fof(f189,plain,
! [X0] :
( relation_rng(X0) != relation_rng(sK1)
| function_inverse(X0) = sK2
| in(sK9(X0,sK2),relation_rng(X0))
| ~ sP0(X0,sK9(X0,sK2),sK10(X0,sK2),sK2)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f181,f84]) ).
fof(f190,plain,
! [X0] :
( relation_rng(X0) != relation_rng(sK1)
| function_inverse(X0) = sK2
| sK10(X0,sK2) = apply(sK2,sK9(X0,sK2))
| ~ sP0(X0,sK9(X0,sK2),sK10(X0,sK2),sK2)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f182,f84]) ).
fof(f196,plain,
! [X0] :
( in(sK6(sK2,X0),relation_rng(sK1))
| ~ in(X0,relation_dom(sK1)) ),
inference(forward_demodulation,[],[f188,f89]) ).
fof(f206,plain,
! [X0] :
( in(apply(sK2,X0),relation_dom(sK1))
| ~ in(X0,relation_dom(sK2))
| ~ relation(sK2)
| ~ function(sK2) ),
inference(superposition,[],[f145,f89]) ).
fof(f211,plain,
! [X0] :
( in(apply(sK2,X0),relation_dom(sK1))
| ~ in(X0,relation_dom(sK2))
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f206,f85]) ).
fof(f213,plain,
! [X0] :
( in(apply(sK2,X0),relation_dom(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[],[f211,f84]) ).
fof(f214,plain,
! [X0] :
( in(apply(sK2,X0),relation_dom(sK1))
| ~ in(X0,relation_rng(sK1)) ),
inference(forward_demodulation,[],[f213,f88]) ).
fof(f216,plain,
! [X0] :
( sK6(sK2,X0) = apply(sK1,X0)
| ~ in(X0,relation_dom(sK1))
| ~ in(sK6(sK2,X0),relation_dom(sK2))
| ~ in(X0,relation_rng(sK2))
| ~ relation(sK2)
| ~ function(sK2) ),
inference(superposition,[],[f142,f147]) ).
fof(f220,plain,
! [X0,X1] :
( sP0(X1,apply(sK2,X0),X0,sK1)
| ~ in(apply(sK2,X0),relation_rng(X1))
| ~ in(apply(sK2,X0),relation_dom(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[],[f148,f142]) ).
fof(f229,plain,
! [X0,X1] :
( ~ in(X0,relation_rng(sK1))
| sP0(X1,apply(sK2,X0),X0,sK1)
| ~ in(apply(sK2,X0),relation_rng(X1))
| ~ in(apply(sK2,X0),relation_dom(sK1)) ),
inference(forward_demodulation,[],[f220,f88]) ).
fof(f232,plain,
! [X0] :
( sK6(sK2,X0) = apply(sK1,X0)
| ~ in(X0,relation_dom(sK1))
| ~ in(X0,relation_rng(sK2))
| ~ relation(sK2)
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f216,f146]) ).
fof(f236,plain,
! [X0,X1] :
( sP0(X1,apply(sK2,X0),X0,sK1)
| ~ in(X0,relation_rng(sK1))
| ~ in(apply(sK2,X0),relation_rng(X1)) ),
inference(forward_subsumption_resolution,[],[f229,f214]) ).
fof(f238,plain,
! [X0] :
( sK6(sK2,X0) = apply(sK1,X0)
| ~ in(X0,relation_dom(sK1))
| ~ in(X0,relation_rng(sK2))
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f232,f85]) ).
fof(f242,plain,
! [X0] :
( sK6(sK2,X0) = apply(sK1,X0)
| ~ in(X0,relation_dom(sK1))
| ~ in(X0,relation_rng(sK2)) ),
inference(forward_subsumption_resolution,[],[f238,f84]) ).
fof(f245,plain,
! [X0] :
( ~ in(X0,relation_dom(sK1))
| sK6(sK2,X0) = apply(sK1,X0)
| ~ in(X0,relation_dom(sK1)) ),
inference(forward_demodulation,[],[f242,f89]) ).
fof(f246,plain,
! [X0] :
( sK6(sK2,X0) = apply(sK1,X0)
| ~ in(X0,relation_dom(sK1)) ),
inference(duplicate_literal_removal,[],[f245]) ).
fof(f254,plain,
! [X0,X1] :
( sP0(X1,apply(sK1,X0),X0,sK2)
| ~ in(apply(sK1,X0),relation_rng(X1))
| ~ in(X0,relation_dom(sK1))
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[],[f148,f143]) ).
fof(f263,plain,
! [X0,X1] :
( sP0(X1,apply(sK1,X0),X0,sK2)
| ~ in(apply(sK1,X0),relation_rng(sK1))
| ~ in(apply(sK1,X0),relation_rng(X1))
| ~ in(X0,relation_dom(sK1)) ),
inference(forward_demodulation,[],[f254,f88]) ).
fof(f310,plain,
! [X0] :
( in(apply(sK1,X0),relation_rng(sK1))
| ~ in(X0,relation_dom(sK1))
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[],[f196,f246]) ).
fof(f333,plain,
! [X0] :
( in(apply(sK1,X0),relation_rng(sK1))
| ~ in(X0,relation_dom(sK1)) ),
inference(duplicate_literal_removal,[],[f310]) ).
fof(f558,plain,
! [X0] :
( ~ in(X0,relation_rng(sK1))
| ~ in(apply(sK2,X0),relation_rng(sK2))
| ~ in(X0,relation_dom(sK2))
| apply(sK1,apply(sK2,X0)) = X0 ),
inference(resolution,[],[f236,f150]) ).
fof(f570,plain,
! [X0] :
( ~ in(apply(sK2,X0),relation_dom(sK1))
| ~ in(X0,relation_rng(sK1))
| ~ in(X0,relation_dom(sK2))
| apply(sK1,apply(sK2,X0)) = X0 ),
inference(forward_demodulation,[],[f558,f89]) ).
fof(f573,plain,
! [X0] :
( ~ in(X0,relation_rng(sK1))
| ~ in(X0,relation_dom(sK2))
| apply(sK1,apply(sK2,X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f570,f214]) ).
fof(f576,plain,
! [X0] :
( ~ in(X0,relation_rng(sK1))
| ~ in(X0,relation_rng(sK1))
| apply(sK1,apply(sK2,X0)) = X0 ),
inference(forward_demodulation,[],[f573,f88]) ).
fof(f577,plain,
! [X0] :
( apply(sK1,apply(sK2,X0)) = X0
| ~ in(X0,relation_rng(sK1)) ),
inference(duplicate_literal_removal,[],[f576]) ).
fof(f907,plain,
( sK2 = function_inverse(sK1)
| in(sK9(sK1,sK2),relation_rng(sK1))
| ~ sP0(sK1,sK9(sK1,sK2),sK10(sK1,sK2),sK2)
| ~ one_to_one(sK1)
| ~ relation(sK1)
| ~ function(sK1) ),
inference(equality_resolution,[],[f189]) ).
fof(f908,plain,
( sK2 = function_inverse(sK1)
| in(sK9(sK1,sK2),relation_rng(sK1))
| ~ sP0(sK1,sK9(sK1,sK2),sK10(sK1,sK2),sK2)
| ~ relation(sK1)
| ~ function(sK1) ),
inference(forward_subsumption_resolution,[],[f907,f90]) ).
fof(f909,plain,
( sK2 = function_inverse(sK1)
| in(sK9(sK1,sK2),relation_rng(sK1))
| ~ sP0(sK1,sK9(sK1,sK2),sK10(sK1,sK2),sK2)
| ~ function(sK1) ),
inference(forward_subsumption_resolution,[],[f908,f83]) ).
fof(f910,plain,
( sK2 = function_inverse(sK1)
| in(sK9(sK1,sK2),relation_rng(sK1))
| ~ sP0(sK1,sK9(sK1,sK2),sK10(sK1,sK2),sK2) ),
inference(forward_subsumption_resolution,[],[f909,f82]) ).
fof(f912,definition,
( spl15_10
<=> sP0(sK1,sK9(sK1,sK2),sK10(sK1,sK2),sK2) ),
introduced(definition,[new_symbols(definition,[spl15_10])],[avatar_definition]) ).
fof(f913,plain,
( sP0(sK1,sK9(sK1,sK2),sK10(sK1,sK2),sK2)
| ~ spl15_10 ),
inference(avatar_component_clause,[],[f912]) ).
fof(f914,plain,
( ~ sP0(sK1,sK9(sK1,sK2),sK10(sK1,sK2),sK2)
| spl15_10 ),
inference(avatar_component_clause,[],[f912]) ).
fof(f916,definition,
( spl15_11
<=> in(sK9(sK1,sK2),relation_rng(sK1)) ),
introduced(definition,[new_symbols(definition,[spl15_11])],[avatar_definition]) ).
fof(f918,plain,
( in(sK9(sK1,sK2),relation_rng(sK1))
| ~ spl15_11 ),
inference(avatar_component_clause,[],[f916]) ).
fof(f920,definition,
( spl15_12
<=> sK2 = function_inverse(sK1) ),
introduced(definition,[new_symbols(definition,[spl15_12])],[avatar_definition]) ).
fof(f922,plain,
( sK2 = function_inverse(sK1)
| ~ spl15_12 ),
inference(avatar_component_clause,[],[f920]) ).
fof(f923,plain,
( ~ spl15_10
| spl15_11
| spl15_12 ),
inference(avatar_split_clause,[],[f910,f920,f916,f912]) ).
fof(f925,plain,
( sK2 = function_inverse(sK1)
| sK10(sK1,sK2) = apply(sK2,sK9(sK1,sK2))
| ~ sP0(sK1,sK9(sK1,sK2),sK10(sK1,sK2),sK2)
| ~ one_to_one(sK1)
| ~ relation(sK1)
| ~ function(sK1) ),
inference(equality_resolution,[],[f190]) ).
fof(f930,plain,
( sK9(sK1,sK2) = apply(sK1,sK10(sK1,sK2))
| spl15_10 ),
inference(resolution,[],[f914,f117]) ).
fof(f931,plain,
( in(sK10(sK1,sK2),relation_dom(sK1))
| spl15_10 ),
inference(resolution,[],[f914,f118]) ).
fof(f1082,plain,
( ! [X0] :
( sP0(X0,sK9(sK1,sK2),sK10(sK1,sK2),sK2)
| ~ in(sK9(sK1,sK2),relation_rng(sK1))
| ~ in(sK9(sK1,sK2),relation_rng(X0))
| ~ in(sK10(sK1,sK2),relation_dom(sK1)) )
| spl15_10 ),
inference(superposition,[],[f263,f930]) ).
fof(f1084,plain,
( in(sK9(sK1,sK2),relation_rng(sK1))
| ~ in(sK10(sK1,sK2),relation_dom(sK1))
| spl15_10 ),
inference(superposition,[],[f333,f930]) ).
fof(f1104,plain,
( in(sK9(sK1,sK2),relation_rng(sK1))
| spl15_10 ),
inference(forward_subsumption_resolution,[],[f1084,f931]) ).
fof(f1106,plain,
( ! [X0] :
( sP0(X0,sK9(sK1,sK2),sK10(sK1,sK2),sK2)
| ~ in(sK9(sK1,sK2),relation_rng(sK1))
| ~ in(sK9(sK1,sK2),relation_rng(X0)) )
| spl15_10 ),
inference(forward_subsumption_resolution,[],[f1082,f931]) ).
fof(f1116,plain,
( spl15_11
| spl15_10 ),
inference(avatar_split_clause,[],[f1104,f912,f916]) ).
fof(f1122,definition,
( spl15_15
<=> ! [X0] :
( sP0(X0,sK9(sK1,sK2),sK10(sK1,sK2),sK2)
| ~ in(sK9(sK1,sK2),relation_rng(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl15_15])],[avatar_definition]) ).
fof(f1123,plain,
( ! [X0] :
( sP0(X0,sK9(sK1,sK2),sK10(sK1,sK2),sK2)
| ~ in(sK9(sK1,sK2),relation_rng(X0)) )
| ~ spl15_15 ),
inference(avatar_component_clause,[],[f1122]) ).
fof(f1124,plain,
( ~ spl15_11
| spl15_15
| spl15_10 ),
inference(avatar_split_clause,[],[f1106,f912,f1122,f916]) ).
fof(f1127,plain,
( sK2 = function_inverse(sK1)
| sK10(sK1,sK2) = apply(sK2,sK9(sK1,sK2))
| ~ one_to_one(sK1)
| ~ relation(sK1)
| ~ function(sK1)
| ~ spl15_10 ),
inference(forward_subsumption_resolution,[],[f925,f913]) ).
fof(f1128,plain,
( sK2 = function_inverse(sK1)
| sK10(sK1,sK2) = apply(sK2,sK9(sK1,sK2))
| ~ relation(sK1)
| ~ function(sK1)
| ~ spl15_10 ),
inference(forward_subsumption_resolution,[],[f1127,f90]) ).
fof(f1129,plain,
( sK2 = function_inverse(sK1)
| sK10(sK1,sK2) = apply(sK2,sK9(sK1,sK2))
| ~ function(sK1)
| ~ spl15_10 ),
inference(forward_subsumption_resolution,[],[f1128,f83]) ).
fof(f1130,plain,
( sK2 = function_inverse(sK1)
| sK10(sK1,sK2) = apply(sK2,sK9(sK1,sK2))
| ~ spl15_10 ),
inference(forward_subsumption_resolution,[],[f1129,f82]) ).
fof(f1132,definition,
( spl15_16
<=> sK10(sK1,sK2) = apply(sK2,sK9(sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl15_16])],[avatar_definition]) ).
fof(f1134,plain,
( sK10(sK1,sK2) = apply(sK2,sK9(sK1,sK2))
| ~ spl15_16 ),
inference(avatar_component_clause,[],[f1132]) ).
fof(f1135,plain,
( spl15_16
| spl15_12
| ~ spl15_10 ),
inference(avatar_split_clause,[],[f1130,f912,f920,f1132]) ).
fof(f1141,plain,
( in(sK10(sK1,sK2),relation_dom(sK1))
| ~ in(sK9(sK1,sK2),relation_rng(sK1))
| ~ spl15_16 ),
inference(superposition,[],[f214,f1134]) ).
fof(f1148,plain,
( sK9(sK1,sK2) = apply(sK1,sK10(sK1,sK2))
| ~ in(sK9(sK1,sK2),relation_rng(sK1))
| ~ spl15_16 ),
inference(superposition,[],[f577,f1134]) ).
fof(f1159,plain,
( sK9(sK1,sK2) = apply(sK1,sK10(sK1,sK2))
| ~ spl15_11
| ~ spl15_16 ),
inference(forward_subsumption_resolution,[],[f1148,f918]) ).
fof(f1166,plain,
( in(sK10(sK1,sK2),relation_dom(sK1))
| ~ spl15_11
| ~ spl15_16 ),
inference(forward_subsumption_resolution,[],[f1141,f918]) ).
fof(f1219,plain,
( sK9(sK1,sK2) != sK9(sK1,sK2)
| relation_rng(sK1) != relation_dom(sK2)
| ~ in(sK10(sK1,sK2),relation_dom(sK1))
| sK2 = function_inverse(sK1)
| ~ sP0(sK1,sK9(sK1,sK2),sK10(sK1,sK2),sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ one_to_one(sK1)
| ~ relation(sK1)
| ~ function(sK1)
| ~ spl15_11
| ~ spl15_16 ),
inference(superposition,[],[f126,f1159]) ).
fof(f1225,plain,
( relation_rng(sK1) != relation_dom(sK2)
| ~ in(sK10(sK1,sK2),relation_dom(sK1))
| sK2 = function_inverse(sK1)
| ~ sP0(sK1,sK9(sK1,sK2),sK10(sK1,sK2),sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ one_to_one(sK1)
| ~ relation(sK1)
| ~ function(sK1)
| ~ spl15_11
| ~ spl15_16 ),
inference(trivial_inequality_removal,[],[f1219]) ).
fof(f1227,plain,
( ~ in(sK10(sK1,sK2),relation_dom(sK1))
| sK2 = function_inverse(sK1)
| ~ sP0(sK1,sK9(sK1,sK2),sK10(sK1,sK2),sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ one_to_one(sK1)
| ~ relation(sK1)
| ~ function(sK1)
| ~ spl15_11
| ~ spl15_16 ),
inference(forward_subsumption_resolution,[],[f1225,f88]) ).
fof(f1229,plain,
( sK2 = function_inverse(sK1)
| ~ sP0(sK1,sK9(sK1,sK2),sK10(sK1,sK2),sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ one_to_one(sK1)
| ~ relation(sK1)
| ~ function(sK1)
| ~ spl15_11
| ~ spl15_16 ),
inference(forward_subsumption_resolution,[],[f1227,f1166]) ).
fof(f1231,plain,
( sK2 = function_inverse(sK1)
| ~ relation(sK2)
| ~ function(sK2)
| ~ one_to_one(sK1)
| ~ relation(sK1)
| ~ function(sK1)
| ~ spl15_10
| ~ spl15_11
| ~ spl15_16 ),
inference(forward_subsumption_resolution,[],[f1229,f913]) ).
fof(f1232,plain,
( sK2 = function_inverse(sK1)
| ~ function(sK2)
| ~ one_to_one(sK1)
| ~ relation(sK1)
| ~ function(sK1)
| ~ spl15_10
| ~ spl15_11
| ~ spl15_16 ),
inference(forward_subsumption_resolution,[],[f1231,f85]) ).
fof(f1233,plain,
( sK2 = function_inverse(sK1)
| ~ one_to_one(sK1)
| ~ relation(sK1)
| ~ function(sK1)
| ~ spl15_10
| ~ spl15_11
| ~ spl15_16 ),
inference(forward_subsumption_resolution,[],[f1232,f84]) ).
fof(f1234,plain,
( sK2 = function_inverse(sK1)
| ~ relation(sK1)
| ~ function(sK1)
| ~ spl15_10
| ~ spl15_11
| ~ spl15_16 ),
inference(forward_subsumption_resolution,[],[f1233,f90]) ).
fof(f1235,plain,
( sK2 = function_inverse(sK1)
| ~ function(sK1)
| ~ spl15_10
| ~ spl15_11
| ~ spl15_16 ),
inference(forward_subsumption_resolution,[],[f1234,f83]) ).
fof(f1236,plain,
( sK2 = function_inverse(sK1)
| ~ spl15_10
| ~ spl15_11
| ~ spl15_16 ),
inference(forward_subsumption_resolution,[],[f1235,f82]) ).
fof(f1237,plain,
( spl15_12
| ~ spl15_10
| ~ spl15_11
| ~ spl15_16 ),
inference(avatar_split_clause,[],[f1236,f1132,f916,f912,f920]) ).
fof(f1242,plain,
( ~ sP14(function_inverse(sK1))
| ~ spl15_12 ),
inference(superposition,[],[f140,f922]) ).
fof(f1281,plain,
( $false
| ~ spl15_12 ),
inference(forward_subsumption_resolution,[],[f1242,f141]) ).
fof(f1282,plain,
~ spl15_12,
inference(avatar_contradiction_clause,[],[f1281]) ).
fof(f1498,plain,
( ~ in(sK9(sK1,sK2),relation_rng(sK1))
| spl15_10
| ~ spl15_15 ),
inference(resolution,[],[f1123,f914]) ).
fof(f1499,plain,
( $false
| spl15_10
| ~ spl15_11
| ~ spl15_15 ),
inference(forward_subsumption_resolution,[],[f1498,f918]) ).
fof(f1500,plain,
( spl15_10
| ~ spl15_11
| ~ spl15_15 ),
inference(avatar_contradiction_clause,[],[f1499]) ).
cnf(s7,plain,
( ~ spl15_10
| spl15_11
| spl15_12 ),
inference(sat_conversion,[],[f923]) ).
cnf(s10,plain,
( spl15_10
| spl15_11 ),
inference(sat_conversion,[],[f1116]) ).
cnf(s12,plain,
( spl15_10
| ~ spl15_11
| spl15_15 ),
inference(sat_conversion,[],[f1124]) ).
cnf(s14,plain,
( ~ spl15_10
| spl15_12
| spl15_16 ),
inference(sat_conversion,[],[f1135]) ).
cnf(s17,plain,
( ~ spl15_10
| ~ spl15_11
| spl15_12
| ~ spl15_16 ),
inference(sat_conversion,[],[f1237]) ).
cnf(s18,plain,
~ spl15_12,
inference(sat_conversion,[],[f1282]) ).
cnf(s24,plain,
( spl15_10
| ~ spl15_11
| ~ spl15_15 ),
inference(sat_conversion,[],[f1500]) ).
cnf(s25,plain,
( ~ spl15_10
| ~ spl15_11
| ~ spl15_16 ),
inference(rat,[],[s17,s18]) ).
cnf(s26,plain,
( ~ spl15_10
| spl15_16 ),
inference(rat,[],[s14,s18]) ).
cnf(s27,plain,
( ~ spl15_10
| spl15_11 ),
inference(rat,[],[s7,s18]) ).
cnf(s31,plain,
( ~ spl15_11
| spl15_10 ),
inference(rat,[],[s12,s24]) ).
cnf(s32,plain,
spl15_10,
inference(rat,[],[s31,s10]) ).
cnf(s33,plain,
spl15_16,
inference(rat,[],[s26,s32]) ).
cnf(s34,plain,
spl15_11,
inference(rat,[],[s27,s32]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s25,s33,s32,s34]) ).
fof(f1501,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU027+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.46 % Computer : n005.cluster.edu
% 0.11/0.46 % Model : x86_64 x86_64
% 0.11/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.46 % Memory : 8046.5625MB
% 0.11/0.46 % OS : Linux 6.8.0-71-generic
% 0.11/0.46 % CPULimit : 300
% 0.11/0.46 % WCLimit : 300
% 0.11/0.46 % DateTime : Mon Sep 28 03:22:47 UTC 2026
% 0.11/0.46 % CPUTime :
% 0.11/0.46 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.50 Running first-order theorem proving
% 0.11/0.50 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.06/1.43 % (404490)Detected formulas, will run a generic FOF schedule.
% 3.06/1.43 % (404495)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=1944680366:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.06/1.43 % (404496)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=2571035123:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.06/1.43 % (404499)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1827301751:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.06/1.43 % (404497)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=645147926:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.06/1.43 % (404498)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=945652513:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.06/1.43 % (404501)dis-21_1_sil=8000:lcm=predicate:random_seed=1363375877:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.06/1.43 % (404500)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4265174278:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.06/1.43 % (404498)First to succeed.
% 3.06/1.43 % (404498)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-404490"
% 3.06/1.43 % (404499)Instruction limit reached!
% 3.06/1.43 % (404499)------------------------------
% 3.06/1.43 % (404499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.43 % (404499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.43 % (404499)CaDiCaL version: 2.1.3
% 3.06/1.43 % (404499)Termination reason: Instruction limit
% 3.06/1.43 % (404499)Termination phase: Saturation
% 3.06/1.43 % (404499)Time elapsed: 0.068 s
% 3.06/1.43 % (404499)Peak memory usage: 88 MB
% 3.06/1.43 % (404499)Instructions burned: 119 (million)
% 3.06/1.43 % (404501)Instruction limit reached!
% 3.06/1.43 % (404501)------------------------------
% 3.06/1.43 % (404501)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.43 % (404501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.43 % (404501)CaDiCaL version: 2.1.3
% 3.06/1.43 % (404501)Termination reason: Instruction limit
% 3.06/1.43 % (404501)Termination phase: Saturation
% 3.06/1.43 % (404501)Time elapsed: 0.079 s
% 3.06/1.43 % (404501)Peak memory usage: 90 MB
% 3.06/1.43 % (404501)Instructions burned: 130 (million)
% 3.06/1.43 % (404500)Instruction limit reached!
% 3.06/1.43 % (404500)------------------------------
% 3.06/1.43 % (404500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.43 % (404500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.43 % (404500)CaDiCaL version: 2.1.3
% 3.06/1.43 % (404500)Termination reason: Instruction limit
% 3.06/1.43 % (404500)Termination phase: Saturation
% 3.06/1.43 % (404500)Time elapsed: 0.092 s
% 3.06/1.43 % (404500)Peak memory usage: 90 MB
% 3.06/1.43 % (404500)Instructions burned: 139 (million)
% 3.06/1.43 % (404509)lrs+10_1_sil=8000:sp=occurrence:random_seed=787365782:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.06/1.43 % (404510)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4172071744:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.06/1.43 % (404510)Also succeeded, but the first one will report.
% 3.06/1.43 % (404511)lrs+1011_1_sil=32000:sp=occurrence:random_seed=234354969:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.06/1.43 % (404498)Refutation found. Thanks to Tanya!
% 3.06/1.43 % SZS status Theorem for theBenchmark
% 3.06/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 4.03/1.63 % (404498)------------------------------
% 4.03/1.63 % (404498)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.63 % (404498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.63 % (404498)CaDiCaL version: 2.1.3
% 4.03/1.63 % (404498)Termination reason: Refutation
% 4.03/1.63 % (404498)Time elapsed: 0.039 s
% 4.03/1.63 % (404498)Peak memory usage: 89 MB
% 4.03/1.63 % (404498)Instructions burned: 62 (million)
% 4.03/1.63 % (404498)------------------------------
% 4.03/1.63 % (404498)------------------------------
% 4.03/1.63 % (404490)Success in time 0.483 s
% 4.03/1.63 % Vampire exiting
%------------------------------------------------------------------------------