TSTP Solution File: SEU027+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU027+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:21:54 EDT 2024
% Result : Theorem 8.66s 1.81s
% Output : Refutation 8.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 105 ( 24 unt; 0 def)
% Number of atoms : 553 ( 186 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 696 ( 248 ~; 241 |; 161 &)
% ( 21 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 225 ( 194 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f67568,plain,
$false,
inference(subsumption_resolution,[],[f67567,f25666]) ).
fof(f25666,plain,
apply(function_inverse(sK8),sK13(function_inverse(sK8),sK9)) != apply(sK9,sK13(function_inverse(sK8),sK9)),
inference(unit_resulting_resolution,[],[f694,f756,f146,f5692,f13497]) ).
fof(f13497,plain,
! [X0] :
( ~ relation(X0)
| apply(sK9,sK13(X0,sK9)) != apply(X0,sK13(X0,sK9))
| sK9 = X0
| ~ function(X0)
| relation_dom(X0) != relation_rng(sK8) ),
inference(forward_demodulation,[],[f13496,f143]) ).
fof(f143,plain,
relation_rng(sK8) = relation_dom(sK9),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
( function_inverse(sK8) != sK9
& ! [X2,X3] :
( ( ( apply(sK8,X2) = X3
| apply(sK9,X3) != X2 )
& ( apply(sK9,X3) = X2
| apply(sK8,X2) != X3 ) )
| ~ in(X3,relation_dom(sK9))
| ~ in(X2,relation_dom(sK8)) )
& relation_rng(sK8) = relation_dom(sK9)
& relation_dom(sK8) = relation_rng(sK9)
& one_to_one(sK8)
& function(sK9)
& relation(sK9)
& function(sK8)
& relation(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f86,f88,f87]) ).
fof(f87,plain,
( ? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& ! [X2,X3] :
( ( ( apply(X0,X2) = X3
| apply(X1,X3) != X2 )
& ( apply(X1,X3) = X2
| apply(X0,X2) != X3 ) )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X0)) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0)
& function(X1)
& relation(X1) )
& function(X0)
& relation(X0) )
=> ( ? [X1] :
( function_inverse(sK8) != X1
& ! [X3,X2] :
( ( ( apply(sK8,X2) = X3
| apply(X1,X3) != X2 )
& ( apply(X1,X3) = X2
| apply(sK8,X2) != X3 ) )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(sK8)) )
& relation_dom(X1) = relation_rng(sK8)
& relation_rng(X1) = relation_dom(sK8)
& one_to_one(sK8)
& function(X1)
& relation(X1) )
& function(sK8)
& relation(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
( ? [X1] :
( function_inverse(sK8) != X1
& ! [X3,X2] :
( ( ( apply(sK8,X2) = X3
| apply(X1,X3) != X2 )
& ( apply(X1,X3) = X2
| apply(sK8,X2) != X3 ) )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(sK8)) )
& relation_dom(X1) = relation_rng(sK8)
& relation_rng(X1) = relation_dom(sK8)
& one_to_one(sK8)
& function(X1)
& relation(X1) )
=> ( function_inverse(sK8) != sK9
& ! [X3,X2] :
( ( ( apply(sK8,X2) = X3
| apply(sK9,X3) != X2 )
& ( apply(sK9,X3) = X2
| apply(sK8,X2) != X3 ) )
| ~ in(X3,relation_dom(sK9))
| ~ in(X2,relation_dom(sK8)) )
& relation_rng(sK8) = relation_dom(sK9)
& relation_dom(sK8) = relation_rng(sK9)
& one_to_one(sK8)
& function(sK9)
& relation(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& ! [X2,X3] :
( ( ( apply(X0,X2) = X3
| apply(X1,X3) != X2 )
& ( apply(X1,X3) = X2
| apply(X0,X2) != X3 ) )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X0)) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0)
& function(X1)
& relation(X1) )
& function(X0)
& relation(X0) ),
inference(nnf_transformation,[],[f44]) ).
fof(f44,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& ! [X2,X3] :
( ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X0)) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0)
& function(X1)
& relation(X1) )
& function(X0)
& relation(X0) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& ! [X2,X3] :
( ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X0)) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0)
& function(X1)
& relation(X1) )
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( ! [X2,X3] :
( ( in(X3,relation_dom(X1))
& in(X2,relation_dom(X0)) )
=> ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 ) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0) )
=> function_inverse(X0) = X1 ) ) ),
inference(negated_conjecture,[],[f33]) ).
fof(f33,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( ! [X2,X3] :
( ( in(X3,relation_dom(X1))
& in(X2,relation_dom(X0)) )
=> ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 ) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0) )
=> function_inverse(X0) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_1) ).
fof(f13496,plain,
! [X0] :
( apply(sK9,sK13(X0,sK9)) != apply(X0,sK13(X0,sK9))
| relation_dom(X0) != relation_dom(sK9)
| sK9 = X0
| ~ function(X0)
| ~ relation(X0) ),
inference(subsumption_resolution,[],[f13346,f140]) ).
fof(f140,plain,
function(sK9),
inference(cnf_transformation,[],[f89]) ).
fof(f13346,plain,
! [X0] :
( apply(sK9,sK13(X0,sK9)) != apply(X0,sK13(X0,sK9))
| relation_dom(X0) != relation_dom(sK9)
| ~ function(sK9)
| sK9 = X0
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[],[f184,f139]) ).
fof(f139,plain,
relation(sK9),
inference(cnf_transformation,[],[f89]) ).
fof(f184,plain,
! [X0,X1] :
( ~ relation(X1)
| apply(X1,sK13(X0,X1)) != apply(X0,sK13(X0,X1))
| relation_dom(X0) != relation_dom(X1)
| ~ function(X1)
| X0 = X1
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ( apply(X1,sK13(X0,X1)) != apply(X0,sK13(X0,X1))
& in(sK13(X0,X1),relation_dom(X0)) )
| relation_dom(X0) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f60,f105]) ).
fof(f105,plain,
! [X0,X1] :
( ? [X2] :
( apply(X1,X2) != apply(X0,X2)
& in(X2,relation_dom(X0)) )
=> ( apply(X1,sK13(X0,X1)) != apply(X0,sK13(X0,X1))
& in(sK13(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( apply(X1,X2) != apply(X0,X2)
& in(X2,relation_dom(X0)) )
| relation_dom(X0) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( apply(X1,X2) != apply(X0,X2)
& in(X2,relation_dom(X0)) )
| relation_dom(X0) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( ! [X2] :
( in(X2,relation_dom(X0))
=> apply(X1,X2) = apply(X0,X2) )
& relation_dom(X0) = relation_dom(X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
fof(f5692,plain,
relation_rng(sK8) = relation_dom(function_inverse(sK8)),
inference(unit_resulting_resolution,[],[f5679,f168]) ).
fof(f168,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| relation_rng(X0) = relation_dom(X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ~ sP1(sK12(X0,X1),sK11(X0,X1),X1,X0)
| ~ sP0(sK11(X0,X1),sK12(X0,X1),X0,X1)
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X4,X5] :
( sP1(X5,X4,X1,X0)
& sP0(X4,X5,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| ~ sP2(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f96,f97]) ).
fof(f97,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ sP1(X3,X2,X1,X0)
| ~ sP0(X2,X3,X0,X1) )
=> ( ~ sP1(sK12(X0,X1),sK11(X0,X1),X1,X0)
| ~ sP0(sK11(X0,X1),sK12(X0,X1),X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2,X3] :
( ~ sP1(X3,X2,X1,X0)
| ~ sP0(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X4,X5] :
( sP1(X5,X4,X1,X0)
& sP0(X4,X5,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2,X3] :
( ~ sP1(X3,X2,X1,X0)
| ~ sP0(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( sP1(X3,X2,X1,X0)
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| ~ sP2(X0,X1) ) ),
inference(flattening,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2,X3] :
( ~ sP1(X3,X2,X1,X0)
| ~ sP0(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( sP1(X3,X2,X1,X0)
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| ~ sP2(X0,X1) ) ),
inference(nnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( sP2(X0,X1)
<=> ( ! [X2,X3] :
( sP1(X3,X2,X1,X0)
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f5679,plain,
sP2(sK8,function_inverse(sK8)),
inference(unit_resulting_resolution,[],[f5169,f228]) ).
fof(f228,plain,
! [X1] :
( ~ sP3(function_inverse(X1),X1)
| sP2(X1,function_inverse(X1)) ),
inference(equality_resolution,[],[f166]) ).
fof(f166,plain,
! [X0,X1] :
( sP2(X1,X0)
| function_inverse(X1) != X0
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( ( ( function_inverse(X1) = X0
| ~ sP2(X1,X0) )
& ( sP2(X1,X0)
| function_inverse(X1) != X0 ) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f92]) ).
fof(f92,plain,
! [X1,X0] :
( ( ( function_inverse(X0) = X1
| ~ sP2(X0,X1) )
& ( sP2(X0,X1)
| function_inverse(X0) != X1 ) )
| ~ sP3(X1,X0) ),
inference(nnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X1,X0] :
( ( function_inverse(X0) = X1
<=> sP2(X0,X1) )
| ~ sP3(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f5169,plain,
sP3(function_inverse(sK8),sK8),
inference(unit_resulting_resolution,[],[f756,f694,f137,f138,f141,f182]) ).
fof(f182,plain,
! [X0,X1] :
( ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| sP3(X1,X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( sP3(X1,X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f58,f78,f77,f76,f75]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( sP0(X2,X3,X0,X1)
<=> ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f76,plain,
! [X3,X2,X1,X0] :
( sP1(X3,X2,X1,X0)
<=> ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
=> ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
=> ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
& relation_rng(X0) = relation_dom(X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f141,plain,
one_to_one(sK8),
inference(cnf_transformation,[],[f89]) ).
fof(f138,plain,
function(sK8),
inference(cnf_transformation,[],[f89]) ).
fof(f137,plain,
relation(sK8),
inference(cnf_transformation,[],[f89]) ).
fof(f146,plain,
function_inverse(sK8) != sK9,
inference(cnf_transformation,[],[f89]) ).
fof(f756,plain,
function(function_inverse(sK8)),
inference(unit_resulting_resolution,[],[f137,f138,f165]) ).
fof(f165,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f694,plain,
relation(function_inverse(sK8)),
inference(unit_resulting_resolution,[],[f137,f138,f164]) ).
fof(f164,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f67567,plain,
apply(function_inverse(sK8),sK13(function_inverse(sK8),sK9)) = apply(sK9,sK13(function_inverse(sK8),sK9)),
inference(forward_demodulation,[],[f67405,f27409]) ).
fof(f27409,plain,
sK13(function_inverse(sK8),sK9) = apply(sK8,apply(sK9,sK13(function_inverse(sK8),sK9))),
inference(unit_resulting_resolution,[],[f19543,f24575,f7340]) ).
fof(f7340,plain,
! [X0] :
( ~ in(apply(sK9,X0),relation_rng(sK9))
| ~ in(X0,relation_rng(sK8))
| apply(sK8,apply(sK9,X0)) = X0 ),
inference(forward_demodulation,[],[f7339,f143]) ).
fof(f7339,plain,
! [X0] :
( ~ in(apply(sK9,X0),relation_rng(sK9))
| ~ in(X0,relation_dom(sK9))
| apply(sK8,apply(sK9,X0)) = X0 ),
inference(superposition,[],[f226,f142]) ).
fof(f142,plain,
relation_dom(sK8) = relation_rng(sK9),
inference(cnf_transformation,[],[f89]) ).
fof(f226,plain,
! [X3] :
( ~ in(apply(sK9,X3),relation_dom(sK8))
| ~ in(X3,relation_dom(sK9))
| apply(sK8,apply(sK9,X3)) = X3 ),
inference(equality_resolution,[],[f145]) ).
fof(f145,plain,
! [X2,X3] :
( apply(sK8,X2) = X3
| apply(sK9,X3) != X2
| ~ in(X3,relation_dom(sK9))
| ~ in(X2,relation_dom(sK8)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f24575,plain,
in(apply(sK9,sK13(function_inverse(sK8),sK9)),relation_rng(sK9)),
inference(unit_resulting_resolution,[],[f615,f19790,f188]) ).
fof(f188,plain,
! [X3,X0,X1] :
( ~ sP5(X0,X1)
| ~ sP4(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ( ( ~ sP4(sK14(X0,X1),X0)
| ~ in(sK14(X0,X1),X1) )
& ( sP4(sK14(X0,X1),X0)
| in(sK14(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ sP4(X3,X0) )
& ( sP4(X3,X0)
| ~ in(X3,X1) ) )
| ~ sP5(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f109,f110]) ).
fof(f110,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ sP4(X2,X0)
| ~ in(X2,X1) )
& ( sP4(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ sP4(sK14(X0,X1),X0)
| ~ in(sK14(X0,X1),X1) )
& ( sP4(sK14(X0,X1),X0)
| in(sK14(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ? [X2] :
( ( ~ sP4(X2,X0)
| ~ in(X2,X1) )
& ( sP4(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ sP4(X3,X0) )
& ( sP4(X3,X0)
| ~ in(X3,X1) ) )
| ~ sP5(X0,X1) ) ),
inference(rectify,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ? [X2] :
( ( ~ sP4(X2,X0)
| ~ in(X2,X1) )
& ( sP4(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ sP4(X2,X0) )
& ( sP4(X2,X0)
| ~ in(X2,X1) ) )
| ~ sP5(X0,X1) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( sP5(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> sP4(X2,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f19790,plain,
sP4(apply(sK9,sK13(function_inverse(sK8),sK9)),sK9),
inference(unit_resulting_resolution,[],[f19543,f3064]) ).
fof(f3064,plain,
! [X0] :
( ~ in(X0,relation_rng(sK8))
| sP4(apply(sK9,X0),sK9) ),
inference(superposition,[],[f236,f143]) ).
fof(f236,plain,
! [X2,X1] :
( ~ in(X2,relation_dom(X1))
| sP4(apply(X1,X2),X1) ),
inference(equality_resolution,[],[f193]) ).
fof(f193,plain,
! [X2,X0,X1] :
( sP4(X0,X1)
| apply(X1,X2) != X0
| ~ in(X2,relation_dom(X1)) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ! [X2] :
( apply(X1,X2) != X0
| ~ in(X2,relation_dom(X1)) ) )
& ( ( apply(X1,sK15(X0,X1)) = X0
& in(sK15(X0,X1),relation_dom(X1)) )
| ~ sP4(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f113,f114]) ).
fof(f114,plain,
! [X0,X1] :
( ? [X3] :
( apply(X1,X3) = X0
& in(X3,relation_dom(X1)) )
=> ( apply(X1,sK15(X0,X1)) = X0
& in(sK15(X0,X1),relation_dom(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f113,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ! [X2] :
( apply(X1,X2) != X0
| ~ in(X2,relation_dom(X1)) ) )
& ( ? [X3] :
( apply(X1,X3) = X0
& in(X3,relation_dom(X1)) )
| ~ sP4(X0,X1) ) ),
inference(rectify,[],[f112]) ).
fof(f112,plain,
! [X2,X0] :
( ( sP4(X2,X0)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP4(X2,X0) ) ),
inference(nnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X2,X0] :
( sP4(X2,X0)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f615,plain,
sP5(sK9,relation_rng(sK9)),
inference(unit_resulting_resolution,[],[f574,f235]) ).
fof(f235,plain,
! [X0] :
( ~ sP6(X0)
| sP5(X0,relation_rng(X0)) ),
inference(equality_resolution,[],[f185]) ).
fof(f185,plain,
! [X0,X1] :
( sP5(X0,X1)
| relation_rng(X0) != X1
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ~ sP5(X0,X1) )
& ( sP5(X0,X1)
| relation_rng(X0) != X1 ) )
| ~ sP6(X0) ),
inference(nnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> sP5(X0,X1) )
| ~ sP6(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f574,plain,
sP6(sK9),
inference(unit_resulting_resolution,[],[f140,f139,f194]) ).
fof(f194,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| sP6(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0] :
( sP6(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f62,f82,f81,f80]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f19543,plain,
in(sK13(function_inverse(sK8),sK9),relation_rng(sK8)),
inference(unit_resulting_resolution,[],[f694,f756,f146,f5692,f12288]) ).
fof(f12288,plain,
! [X0] :
( ~ relation(X0)
| in(sK13(X0,sK9),relation_rng(sK8))
| sK9 = X0
| ~ function(X0)
| relation_dom(X0) != relation_rng(sK8) ),
inference(inner_rewriting,[],[f12287]) ).
fof(f12287,plain,
! [X0] :
( relation_dom(X0) != relation_rng(sK8)
| in(sK13(X0,sK9),relation_dom(X0))
| sK9 = X0
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f12286,f143]) ).
fof(f12286,plain,
! [X0] :
( in(sK13(X0,sK9),relation_dom(X0))
| relation_dom(X0) != relation_dom(sK9)
| sK9 = X0
| ~ function(X0)
| ~ relation(X0) ),
inference(subsumption_resolution,[],[f12131,f140]) ).
fof(f12131,plain,
! [X0] :
( in(sK13(X0,sK9),relation_dom(X0))
| relation_dom(X0) != relation_dom(sK9)
| ~ function(sK9)
| sK9 = X0
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[],[f183,f139]) ).
fof(f183,plain,
! [X0,X1] :
( ~ relation(X1)
| in(sK13(X0,X1),relation_dom(X0))
| relation_dom(X0) != relation_dom(X1)
| ~ function(X1)
| X0 = X1
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f67405,plain,
apply(sK9,sK13(function_inverse(sK8),sK9)) = apply(function_inverse(sK8),apply(sK8,apply(sK9,sK13(function_inverse(sK8),sK9)))),
inference(unit_resulting_resolution,[],[f24575,f10293]) ).
fof(f10293,plain,
! [X0] :
( ~ in(X0,relation_rng(sK9))
| apply(function_inverse(sK8),apply(sK8,X0)) = X0 ),
inference(forward_demodulation,[],[f10283,f142]) ).
fof(f10283,plain,
! [X0] :
( ~ in(X0,relation_dom(sK8))
| apply(function_inverse(sK8),apply(sK8,X0)) = X0 ),
inference(resolution,[],[f230,f5690]) ).
fof(f5690,plain,
! [X0,X1] : sP1(X0,X1,function_inverse(sK8),sK8),
inference(unit_resulting_resolution,[],[f5679,f170]) ).
fof(f170,plain,
! [X0,X1,X4,X5] :
( ~ sP2(X0,X1)
| sP1(X5,X4,X1,X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f230,plain,
! [X2,X3,X0] :
( ~ sP1(X0,apply(X3,X0),X2,X3)
| ~ in(X0,relation_dom(X3))
| apply(X2,apply(X3,X0)) = X0 ),
inference(equality_resolution,[],[f173]) ).
fof(f173,plain,
! [X2,X3,X0,X1] :
( apply(X2,X1) = X0
| apply(X3,X0) != X1
| ~ in(X0,relation_dom(X3))
| ~ sP1(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2,X3] :
( ( sP1(X0,X1,X2,X3)
| ( ( apply(X2,X1) != X0
| ~ in(X1,relation_rng(X3)) )
& apply(X3,X0) = X1
& in(X0,relation_dom(X3)) ) )
& ( ( apply(X2,X1) = X0
& in(X1,relation_rng(X3)) )
| apply(X3,X0) != X1
| ~ in(X0,relation_dom(X3))
| ~ sP1(X0,X1,X2,X3) ) ),
inference(rectify,[],[f100]) ).
fof(f100,plain,
! [X3,X2,X1,X0] :
( ( sP1(X3,X2,X1,X0)
| ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) )
& ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ~ sP1(X3,X2,X1,X0) ) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
! [X3,X2,X1,X0] :
( ( sP1(X3,X2,X1,X0)
| ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) )
& ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ~ sP1(X3,X2,X1,X0) ) ),
inference(nnf_transformation,[],[f76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : SEU027+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.33 % Computer : n012.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Mon Apr 29 20:57:57 EDT 2024
% 0.10/0.33 % CPUTime :
% 0.10/0.33 % (28641)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.35 % (28644)WARNING: value z3 for option sas not known
% 0.10/0.35 % (28644)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.10/0.35 % (28647)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.10/0.35 % (28648)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.10/0.35 % (28646)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.10/0.35 % (28643)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.36 % (28642)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.37 % (28645)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.37 TRYING [1]
% 0.10/0.37 TRYING [2]
% 0.10/0.38 TRYING [3]
% 0.16/0.42 TRYING [1]
% 0.16/0.42 TRYING [2]
% 0.16/0.42 TRYING [4]
% 0.16/0.49 TRYING [5]
% 0.16/0.51 TRYING [1]
% 0.16/0.51 TRYING [2]
% 0.16/0.51 TRYING [3]
% 0.16/0.52 TRYING [3]
% 0.16/0.53 TRYING [4]
% 0.16/0.56 TRYING [5]
% 1.91/0.66 TRYING [6]
% 1.91/0.69 TRYING [4]
% 2.30/0.71 TRYING [6]
% 2.63/0.83 TRYING [7]
% 4.08/1.06 TRYING [5]
% 5.08/1.20 TRYING [7]
% 5.08/1.20 TRYING [8]
% 8.66/1.80 % (28648)First to succeed.
% 8.66/1.81 % (28648)Refutation found. Thanks to Tanya!
% 8.66/1.81 % SZS status Theorem for theBenchmark
% 8.66/1.81 % SZS output start Proof for theBenchmark
% See solution above
% 8.66/1.81 % (28648)------------------------------
% 8.66/1.81 % (28648)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 8.66/1.81 % (28648)Termination reason: Refutation
% 8.66/1.81
% 8.66/1.81 % (28648)Memory used [KB]: 15416
% 8.66/1.81 % (28648)Time elapsed: 1.455 s
% 8.66/1.81 % (28648)Instructions burned: 2793 (million)
% 8.66/1.81 % (28648)------------------------------
% 8.66/1.81 % (28648)------------------------------
% 8.66/1.81 % (28641)Success in time 1.451 s
% 8.66/1.81 28645 Aborted by signal SIGHUP on /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.66/1.81 % (28645)------------------------------
% 8.66/1.81 % (28645)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 8.66/1.81 % (28645)Termination reason: Unknown
% 8.66/1.81 % (28645)Termination phase: Finite model building SAT solving
% 8.66/1.81
% 8.66/1.81 % (28645)Memory used [KB]: 5474
% 8.66/1.81 % (28645)Time elapsed: 1.158 s
% 8.66/1.81 % (28645)Instructions burned: 2126 (million)
% 8.66/1.81 % (28645)------------------------------
% 8.66/1.81 % (28645)------------------------------
% 8.66/1.81 Version : Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
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%------------------------------------------------------------------------------