TSTP Solution File: SEU214+3 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU214+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n024.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 : Wed Aug 31 18:32:33 EDT 2022
% Result : Theorem 2.05s 0.64s
% Output : Refutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 19
% Syntax : Number of formulae : 99 ( 27 unt; 0 def)
% Number of atoms : 424 ( 69 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 513 ( 188 ~; 184 |; 95 &)
% ( 16 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-4 aty)
% Number of variables : 220 ( 176 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f646,plain,
$false,
inference(subsumption_resolution,[],[f645,f221]) ).
fof(f221,plain,
sF23 != sF21,
inference(definition_folding,[],[f167,f220,f219,f218,f215]) ).
fof(f215,plain,
sF19 = relation_composition(sK9,sK8),
introduced(function_definition,[]) ).
fof(f218,plain,
apply(sF19,sK7) = sF21,
introduced(function_definition,[]) ).
fof(f219,plain,
apply(sK9,sK7) = sF22,
introduced(function_definition,[]) ).
fof(f220,plain,
sF23 = apply(sK8,sF22),
introduced(function_definition,[]) ).
fof(f167,plain,
apply(relation_composition(sK9,sK8),sK7) != apply(sK8,apply(sK9,sK7)),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
( function(sK8)
& in(sK7,relation_dom(relation_composition(sK9,sK8)))
& apply(relation_composition(sK9,sK8),sK7) != apply(sK8,apply(sK9,sK7))
& function(sK9)
& relation(sK9)
& relation(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f110,f112,f111]) ).
fof(f111,plain,
( ? [X0,X1] :
( function(X1)
& ? [X2] :
( in(X0,relation_dom(relation_composition(X2,X1)))
& apply(relation_composition(X2,X1),X0) != apply(X1,apply(X2,X0))
& function(X2)
& relation(X2) )
& relation(X1) )
=> ( function(sK8)
& ? [X2] :
( in(sK7,relation_dom(relation_composition(X2,sK8)))
& apply(relation_composition(X2,sK8),sK7) != apply(sK8,apply(X2,sK7))
& function(X2)
& relation(X2) )
& relation(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
( ? [X2] :
( in(sK7,relation_dom(relation_composition(X2,sK8)))
& apply(relation_composition(X2,sK8),sK7) != apply(sK8,apply(X2,sK7))
& function(X2)
& relation(X2) )
=> ( in(sK7,relation_dom(relation_composition(sK9,sK8)))
& apply(relation_composition(sK9,sK8),sK7) != apply(sK8,apply(sK9,sK7))
& function(sK9)
& relation(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
? [X0,X1] :
( function(X1)
& ? [X2] :
( in(X0,relation_dom(relation_composition(X2,X1)))
& apply(relation_composition(X2,X1),X0) != apply(X1,apply(X2,X0))
& function(X2)
& relation(X2) )
& relation(X1) ),
inference(rectify,[],[f66]) ).
fof(f66,plain,
? [X1,X0] :
( function(X0)
& ? [X2] :
( in(X1,relation_dom(relation_composition(X2,X0)))
& apply(X0,apply(X2,X1)) != apply(relation_composition(X2,X0),X1)
& function(X2)
& relation(X2) )
& relation(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
? [X0,X1] :
( ? [X2] :
( apply(X0,apply(X2,X1)) != apply(relation_composition(X2,X0),X1)
& in(X1,relation_dom(relation_composition(X2,X0)))
& function(X2)
& relation(X2) )
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,plain,
~ ! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_composition(X2,X0)))
=> apply(X0,apply(X2,X1)) = apply(relation_composition(X2,X0),X1) ) ) ),
inference(rectify,[],[f34]) ).
fof(f34,negated_conjecture,
~ ! [X1,X0] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
inference(negated_conjecture,[],[f33]) ).
fof(f33,conjecture,
! [X1,X0] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f645,plain,
sF23 = sF21,
inference(backward_demodulation,[],[f220,f639]) ).
fof(f639,plain,
apply(sK8,sF22) = sF21,
inference(backward_demodulation,[],[f566,f634]) ).
fof(f634,plain,
sF22 = sK14(sK9,sK8,sK7,sF21),
inference(forward_demodulation,[],[f633,f219]) ).
fof(f633,plain,
apply(sK9,sK7) = sK14(sK9,sK8,sK7,sF21),
inference(subsumption_resolution,[],[f632,f166]) ).
fof(f166,plain,
function(sK9),
inference(cnf_transformation,[],[f113]) ).
fof(f632,plain,
( apply(sK9,sK7) = sK14(sK9,sK8,sK7,sF21)
| ~ function(sK9) ),
inference(subsumption_resolution,[],[f626,f165]) ).
fof(f165,plain,
relation(sK9),
inference(cnf_transformation,[],[f113]) ).
fof(f626,plain,
( apply(sK9,sK7) = sK14(sK9,sK8,sK7,sF21)
| ~ relation(sK9)
| ~ function(sK9) ),
inference(resolution,[],[f466,f225]) ).
fof(f225,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(X1,X2),X0)
| ~ relation(X0)
| ~ function(X0)
| apply(X0,X1) = X2 ),
inference(subsumption_resolution,[],[f203,f208]) ).
fof(f208,plain,
! [X0,X7,X5] :
( ~ in(ordered_pair(X5,X7),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f149]) ).
fof(f149,plain,
! [X0,X1,X7,X5] :
( ~ relation(X0)
| in(X5,X1)
| ~ in(ordered_pair(X5,X7),X0)
| relation_dom(X0) != X1 ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ~ in(sK3(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK3(X0,X1),X3),X0) )
& ( in(sK3(X0,X1),X1)
| in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0) ) ) )
& ( ! [X5] :
( ( in(ordered_pair(X5,sK5(X0,X5)),X0)
| ~ in(X5,X1) )
& ( in(X5,X1)
| ! [X7] : ~ in(ordered_pair(X5,X7),X0) ) )
| relation_dom(X0) != X1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f101,f104,f103,f102]) ).
fof(f102,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( in(X2,X1)
| ? [X4] : in(ordered_pair(X2,X4),X0) ) )
=> ( ( ~ in(sK3(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK3(X0,X1),X3),X0) )
& ( in(sK3(X0,X1),X1)
| ? [X4] : in(ordered_pair(sK3(X0,X1),X4),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK3(X0,X1),X4),X0)
=> in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
! [X0,X5] :
( ? [X6] : in(ordered_pair(X5,X6),X0)
=> in(ordered_pair(X5,sK5(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( in(X2,X1)
| ? [X4] : in(ordered_pair(X2,X4),X0) ) ) )
& ( ! [X5] :
( ( ? [X6] : in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1) )
& ( in(X5,X1)
| ! [X7] : ~ in(ordered_pair(X5,X7),X0) ) )
| relation_dom(X0) != X1 ) ) ),
inference(rectify,[],[f100]) ).
fof(f100,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) ) ) )
& ( ! [X2] :
( ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| relation_dom(X0) != X1 ) ) ),
inference(nnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( ? [X3] : in(ordered_pair(X2,X3),X0)
<=> in(X2,X1) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( ? [X3] : in(ordered_pair(X2,X3),X0)
<=> in(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f203,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ function(X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( ( ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 )
& ( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0) ) )
| ~ in(X1,relation_dom(X0)) )
& ( ( ( empty_set = X2
| apply(X0,X1) != X2 )
& ( apply(X0,X1) = X2
| empty_set != X2 ) )
| in(X1,relation_dom(X0)) ) )
| ~ function(X0) ),
inference(nnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( ( in(ordered_pair(X1,X2),X0)
<=> apply(X0,X1) = X2 )
| ~ in(X1,relation_dom(X0)) )
& ( ( empty_set = X2
<=> apply(X0,X1) = X2 )
| in(X1,relation_dom(X0)) ) )
| ~ function(X0) ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ! [X1,X2] :
( ( ( in(ordered_pair(X1,X2),X0)
<=> apply(X0,X1) = X2 )
| ~ in(X1,relation_dom(X0)) )
& ( ( empty_set = X2
<=> apply(X0,X1) = X2 )
| in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( empty_set = X2
<=> apply(X0,X1) = X2 ) )
& ( in(X1,relation_dom(X0))
=> ( in(ordered_pair(X1,X2),X0)
<=> apply(X0,X1) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f466,plain,
in(ordered_pair(sK7,sK14(sK9,sK8,sK7,sF21)),sK9),
inference(resolution,[],[f354,f439]) ).
fof(f439,plain,
in(ordered_pair(sK7,sF21),sF19),
inference(backward_demodulation,[],[f428,f438]) ).
fof(f438,plain,
sK5(sF19,sK7) = sF21,
inference(forward_demodulation,[],[f437,f218]) ).
fof(f437,plain,
sK5(sF19,sK7) = apply(sF19,sK7),
inference(subsumption_resolution,[],[f436,f253]) ).
fof(f253,plain,
relation(sF19),
inference(subsumption_resolution,[],[f252,f164]) ).
fof(f164,plain,
relation(sK8),
inference(cnf_transformation,[],[f113]) ).
fof(f252,plain,
( ~ relation(sK8)
| relation(sF19) ),
inference(subsumption_resolution,[],[f251,f165]) ).
fof(f251,plain,
( relation(sF19)
| ~ relation(sK9)
| ~ relation(sK8) ),
inference(superposition,[],[f142,f215]) ).
fof(f142,plain,
! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_composition(X1,X0))
| ~ relation(X0) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X1,X0)) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X1,X0] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f436,plain,
( ~ relation(sF19)
| sK5(sF19,sK7) = apply(sF19,sK7) ),
inference(subsumption_resolution,[],[f430,f302]) ).
fof(f302,plain,
function(sF19),
inference(subsumption_resolution,[],[f301,f165]) ).
fof(f301,plain,
( function(sF19)
| ~ relation(sK9) ),
inference(subsumption_resolution,[],[f300,f169]) ).
fof(f169,plain,
function(sK8),
inference(cnf_transformation,[],[f113]) ).
fof(f300,plain,
( function(sF19)
| ~ function(sK8)
| ~ relation(sK9) ),
inference(subsumption_resolution,[],[f299,f164]) ).
fof(f299,plain,
( ~ relation(sK8)
| ~ relation(sK9)
| function(sF19)
| ~ function(sK8) ),
inference(subsumption_resolution,[],[f298,f166]) ).
fof(f298,plain,
( function(sF19)
| ~ function(sK9)
| ~ relation(sK8)
| ~ relation(sK9)
| ~ function(sK8) ),
inference(superposition,[],[f199,f215]) ).
fof(f199,plain,
! [X0,X1] :
( function(relation_composition(X1,X0))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| ~ function(X0)
| ~ function(X1)
| ( relation(relation_composition(X1,X0))
& function(relation_composition(X1,X0)) ) ),
inference(rectify,[],[f88]) ).
fof(f88,plain,
! [X1,X0] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(X1)
| ~ function(X0)
| ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( ( function(X0)
& relation(X1)
& function(X1)
& relation(X0) )
=> ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f430,plain,
( sK5(sF19,sK7) = apply(sF19,sK7)
| ~ function(sF19)
| ~ relation(sF19) ),
inference(resolution,[],[f428,f225]) ).
fof(f428,plain,
in(ordered_pair(sK7,sK5(sF19,sK7)),sF19),
inference(resolution,[],[f305,f217]) ).
fof(f217,plain,
in(sK7,sF20),
inference(definition_folding,[],[f168,f216,f215]) ).
fof(f216,plain,
sF20 = relation_dom(sF19),
introduced(function_definition,[]) ).
fof(f168,plain,
in(sK7,relation_dom(relation_composition(sK9,sK8))),
inference(cnf_transformation,[],[f113]) ).
fof(f305,plain,
! [X0] :
( ~ in(X0,sF20)
| in(ordered_pair(X0,sK5(sF19,X0)),sF19) ),
inference(subsumption_resolution,[],[f303,f253]) ).
fof(f303,plain,
! [X0] :
( ~ relation(sF19)
| ~ in(X0,sF20)
| in(ordered_pair(X0,sK5(sF19,X0)),sF19) ),
inference(superposition,[],[f207,f216]) ).
fof(f207,plain,
! [X0,X5] :
( ~ in(X5,relation_dom(X0))
| ~ relation(X0)
| in(ordered_pair(X5,sK5(X0,X5)),X0) ),
inference(equality_resolution,[],[f150]) ).
fof(f150,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| in(ordered_pair(X5,sK5(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1 ),
inference(cnf_transformation,[],[f105]) ).
fof(f354,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sF19)
| in(ordered_pair(X0,sK14(sK9,sK8,X0,X1)),sK9) ),
inference(subsumption_resolution,[],[f353,f164]) ).
fof(f353,plain,
! [X0,X1] :
( in(ordered_pair(X0,sK14(sK9,sK8,X0,X1)),sK9)
| ~ relation(sK8)
| ~ in(ordered_pair(X0,X1),sF19) ),
inference(subsumption_resolution,[],[f351,f165]) ).
fof(f351,plain,
! [X0,X1] :
( in(ordered_pair(X0,sK14(sK9,sK8,X0,X1)),sK9)
| ~ relation(sK9)
| ~ in(ordered_pair(X0,X1),sF19)
| ~ relation(sK8) ),
inference(superposition,[],[f223,f215]) ).
fof(f223,plain,
! [X0,X1,X8,X7] :
( ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(X7,sK14(X0,X1,X7,X8)),X0) ),
inference(subsumption_resolution,[],[f210,f142]) ).
fof(f210,plain,
! [X0,X1,X8,X7] :
( ~ relation(relation_composition(X0,X1))
| in(ordered_pair(X7,sK14(X0,X1,X7,X8)),X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1)) ),
inference(equality_resolution,[],[f176]) ).
fof(f176,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X2)
| in(ordered_pair(X7,sK14(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) = X2
| ( ( ! [X5] :
( ~ in(ordered_pair(sK11(X0,X1,X2),X5),X0)
| ~ in(ordered_pair(X5,sK12(X0,X1,X2)),X1) )
| ~ in(ordered_pair(sK11(X0,X1,X2),sK12(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK11(X0,X1,X2),sK13(X0,X1,X2)),X0)
& in(ordered_pair(sK13(X0,X1,X2),sK12(X0,X1,X2)),X1) )
| in(ordered_pair(sK11(X0,X1,X2),sK12(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ( in(ordered_pair(X7,sK14(X0,X1,X7,X8)),X0)
& in(ordered_pair(sK14(X0,X1,X7,X8),X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14])],[f118,f121,f120,f119]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X3,X6),X0)
& in(ordered_pair(X6,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) )
=> ( ( ! [X5] :
( ~ in(ordered_pair(sK11(X0,X1,X2),X5),X0)
| ~ in(ordered_pair(X5,sK12(X0,X1,X2)),X1) )
| ~ in(ordered_pair(sK11(X0,X1,X2),sK12(X0,X1,X2)),X2) )
& ( ? [X6] :
( in(ordered_pair(sK11(X0,X1,X2),X6),X0)
& in(ordered_pair(X6,sK12(X0,X1,X2)),X1) )
| in(ordered_pair(sK11(X0,X1,X2),sK12(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ? [X6] :
( in(ordered_pair(sK11(X0,X1,X2),X6),X0)
& in(ordered_pair(X6,sK12(X0,X1,X2)),X1) )
=> ( in(ordered_pair(sK11(X0,X1,X2),sK13(X0,X1,X2)),X0)
& in(ordered_pair(sK13(X0,X1,X2),sK12(X0,X1,X2)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f121,plain,
! [X0,X1,X7,X8] :
( ? [X10] :
( in(ordered_pair(X7,X10),X0)
& in(ordered_pair(X10,X8),X1) )
=> ( in(ordered_pair(X7,sK14(X0,X1,X7,X8)),X0)
& in(ordered_pair(sK14(X0,X1,X7,X8),X8),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) = X2
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X3,X6),X0)
& in(ordered_pair(X6,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ? [X10] :
( in(ordered_pair(X7,X10),X0)
& in(ordered_pair(X10,X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f117]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) = X2
| ? [X4,X3] :
( ( ! [X5] :
( ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X5,X3),X1) )
| ~ in(ordered_pair(X4,X3),X2) )
& ( ? [X5] :
( in(ordered_pair(X4,X5),X0)
& in(ordered_pair(X5,X3),X1) )
| in(ordered_pair(X4,X3),X2) ) ) )
& ( ! [X4,X3] :
( ( in(ordered_pair(X4,X3),X2)
| ! [X5] :
( ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X5,X3),X1) ) )
& ( ? [X5] :
( in(ordered_pair(X4,X5),X0)
& in(ordered_pair(X5,X3),X1) )
| ~ in(ordered_pair(X4,X3),X2) ) )
| relation_composition(X0,X1) != X2 ) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ relation(X2)
| ( relation_composition(X0,X1) = X2
<=> ! [X4,X3] :
( in(ordered_pair(X4,X3),X2)
<=> ? [X5] :
( in(ordered_pair(X4,X5),X0)
& in(ordered_pair(X5,X3),X1) ) ) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( relation_composition(X0,X1) = X2
<=> ! [X4,X3] :
( in(ordered_pair(X4,X3),X2)
<=> ? [X5] :
( in(ordered_pair(X4,X5),X0)
& in(ordered_pair(X5,X3),X1) ) ) ) ) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( ! [X4,X3] :
( ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) )
<=> in(ordered_pair(X3,X4),X2) )
<=> relation_composition(X0,X1) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f566,plain,
apply(sK8,sK14(sK9,sK8,sK7,sF21)) = sF21,
inference(subsumption_resolution,[],[f565,f169]) ).
fof(f565,plain,
( ~ function(sK8)
| apply(sK8,sK14(sK9,sK8,sK7,sF21)) = sF21 ),
inference(subsumption_resolution,[],[f559,f164]) ).
fof(f559,plain,
( ~ relation(sK8)
| apply(sK8,sK14(sK9,sK8,sK7,sF21)) = sF21
| ~ function(sK8) ),
inference(resolution,[],[f459,f225]) ).
fof(f459,plain,
in(ordered_pair(sK14(sK9,sK8,sK7,sF21),sF21),sK8),
inference(resolution,[],[f348,f439]) ).
fof(f348,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sF19)
| in(ordered_pair(sK14(sK9,sK8,X0,X1),X1),sK8) ),
inference(subsumption_resolution,[],[f347,f165]) ).
fof(f347,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sF19)
| ~ relation(sK9)
| in(ordered_pair(sK14(sK9,sK8,X0,X1),X1),sK8) ),
inference(subsumption_resolution,[],[f346,f164]) ).
fof(f346,plain,
! [X0,X1] :
( ~ relation(sK8)
| ~ in(ordered_pair(X0,X1),sF19)
| ~ relation(sK9)
| in(ordered_pair(sK14(sK9,sK8,X0,X1),X1),sK8) ),
inference(superposition,[],[f222,f215]) ).
fof(f222,plain,
! [X0,X1,X8,X7] :
( ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK14(X0,X1,X7,X8),X8),X1) ),
inference(subsumption_resolution,[],[f211,f142]) ).
fof(f211,plain,
! [X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(relation_composition(X0,X1))
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| in(ordered_pair(sK14(X0,X1,X7,X8),X8),X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f175]) ).
fof(f175,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X2)
| in(ordered_pair(sK14(X0,X1,X7,X8),X8),X1)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU214+3 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 14:52:04 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.50 % (20593)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.21/0.51 % (20585)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51 % (20590)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.51 % (20587)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.52 % (20601)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.21/0.52 % (20598)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.52 % (20587)Instruction limit reached!
% 0.21/0.52 % (20587)------------------------------
% 0.21/0.52 % (20587)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52 % (20587)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52 % (20587)Termination reason: Unknown
% 0.21/0.52 % (20587)Termination phase: Preprocessing 3
% 0.21/0.52
% 0.21/0.52 % (20587)Memory used [KB]: 895
% 0.21/0.52 % (20587)Time elapsed: 0.004 s
% 0.21/0.52 % (20587)Instructions burned: 2 (million)
% 0.21/0.52 % (20587)------------------------------
% 0.21/0.52 % (20587)------------------------------
% 0.21/0.52 % (20606)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.21/0.53 % (20603)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.36/0.53 % (20595)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.36/0.53 % (20607)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.36/0.53 TRYING [1]
% 1.36/0.53 % (20581)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.36/0.53 % (20599)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.36/0.53 % (20579)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 1.36/0.54 % (20588)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.36/0.54 TRYING [2]
% 1.36/0.54 % (20589)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.36/0.54 % (20583)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.36/0.55 % (20608)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.36/0.55 % (20580)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.36/0.55 % (20597)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.36/0.55 % (20591)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.47/0.55 % (20582)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.47/0.55 % (20600)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.47/0.55 % (20580)Refutation not found, incomplete strategy% (20580)------------------------------
% 1.47/0.55 % (20580)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.47/0.55 % (20580)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.47/0.55 % (20580)Termination reason: Refutation not found, incomplete strategy
% 1.47/0.55
% 1.47/0.55 % (20580)Memory used [KB]: 5628
% 1.47/0.55 % (20580)Time elapsed: 0.144 s
% 1.47/0.55 % (20580)Instructions burned: 10 (million)
% 1.47/0.55 % (20580)------------------------------
% 1.47/0.55 % (20580)------------------------------
% 1.47/0.55 % (20596)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.47/0.55 % (20592)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.47/0.55 % (20602)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.47/0.55 % (20594)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.47/0.56 % (20605)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.47/0.56 % (20584)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.47/0.56 TRYING [3]
% 1.47/0.56 TRYING [1]
% 1.47/0.56 % (20586)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.47/0.57 % (20604)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.47/0.57 % (20586)Instruction limit reached!
% 1.47/0.57 % (20586)------------------------------
% 1.47/0.57 % (20586)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.47/0.57 % (20586)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.47/0.57 % (20586)Termination reason: Unknown
% 1.47/0.57 % (20586)Termination phase: Saturation
% 1.47/0.57
% 1.47/0.57 % (20586)Memory used [KB]: 5628
% 1.47/0.57 % (20586)Time elapsed: 0.168 s
% 1.47/0.57 % (20586)Instructions burned: 8 (million)
% 1.47/0.57 % (20586)------------------------------
% 1.47/0.57 % (20586)------------------------------
% 1.47/0.57 % (20585)Instruction limit reached!
% 1.47/0.57 % (20585)------------------------------
% 1.47/0.57 % (20585)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.47/0.58 TRYING [1]
% 1.47/0.58 TRYING [2]
% 1.47/0.58 TRYING [2]
% 1.47/0.58 TRYING [3]
% 1.47/0.59 % (20585)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.47/0.59 % (20585)Termination reason: Unknown
% 1.47/0.59 % (20585)Termination phase: Finite model building constraint generation
% 1.47/0.59
% 1.47/0.59 % (20585)Memory used [KB]: 8315
% 1.47/0.59 % (20585)Time elapsed: 0.143 s
% 1.47/0.59 % (20585)Instructions burned: 51 (million)
% 1.47/0.59 % (20585)------------------------------
% 1.47/0.59 % (20585)------------------------------
% 1.47/0.60 % (20581)Instruction limit reached!
% 1.47/0.60 % (20581)------------------------------
% 1.47/0.60 % (20581)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.47/0.60 TRYING [3]
% 1.47/0.62 % (20581)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.47/0.62 % (20581)Termination reason: Unknown
% 1.47/0.62 % (20581)Termination phase: Saturation
% 1.47/0.62
% 1.47/0.62 % (20581)Memory used [KB]: 1535
% 1.47/0.62 % (20581)Time elapsed: 0.204 s
% 1.47/0.62 % (20581)Instructions burned: 37 (million)
% 1.47/0.62 % (20581)------------------------------
% 1.47/0.62 % (20581)------------------------------
% 1.47/0.62 % (20588)Instruction limit reached!
% 1.47/0.62 % (20588)------------------------------
% 1.47/0.62 % (20588)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.47/0.63 % (20594)First to succeed.
% 1.47/0.63 % (20582)Instruction limit reached!
% 1.47/0.63 % (20582)------------------------------
% 1.47/0.63 % (20582)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.47/0.63 % (20596)Instruction limit reached!
% 1.47/0.63 % (20596)------------------------------
% 1.47/0.63 % (20596)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.47/0.63 % (20596)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.47/0.63 % (20596)Termination reason: Unknown
% 1.47/0.63 % (20596)Termination phase: Finite model building constraint generation
% 1.47/0.63
% 1.47/0.63 % (20596)Memory used [KB]: 8699
% 1.47/0.63 % (20596)Time elapsed: 0.210 s
% 1.47/0.63 % (20596)Instructions burned: 59 (million)
% 1.47/0.63 % (20596)------------------------------
% 1.47/0.63 % (20596)------------------------------
% 1.47/0.63 % (20582)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.47/0.63 % (20582)Termination reason: Unknown
% 1.47/0.63 % (20582)Termination phase: Saturation
% 1.47/0.63
% 1.47/0.63 % (20582)Memory used [KB]: 5884
% 1.47/0.63 % (20582)Time elapsed: 0.222 s
% 1.47/0.63 % (20582)Instructions burned: 52 (million)
% 1.47/0.63 % (20582)------------------------------
% 1.47/0.63 % (20582)------------------------------
% 2.05/0.64 % (20594)Refutation found. Thanks to Tanya!
% 2.05/0.64 % SZS status Theorem for theBenchmark
% 2.05/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 2.05/0.64 % (20594)------------------------------
% 2.05/0.64 % (20594)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.05/0.64 % (20594)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.05/0.64 % (20594)Termination reason: Refutation
% 2.05/0.64
% 2.05/0.64 % (20594)Memory used [KB]: 1535
% 2.05/0.64 % (20594)Time elapsed: 0.214 s
% 2.05/0.64 % (20594)Instructions burned: 32 (million)
% 2.05/0.64 % (20594)------------------------------
% 2.05/0.64 % (20594)------------------------------
% 2.05/0.64 % (20578)Success in time 0.272 s
%------------------------------------------------------------------------------