TSTP Solution File: SYN067+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYN067+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.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 18:02:03 EDT 2024
% Result : Theorem 0.16s 0.39s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 34
% Syntax : Number of formulae : 159 ( 1 unt; 0 def)
% Number of atoms : 753 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 964 ( 370 ~; 402 |; 147 &)
% ( 29 <=>; 13 =>; 0 <=; 3 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 29 ( 28 usr; 25 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-1 aty)
% Number of variables : 232 ( 155 !; 77 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f452,plain,
$false,
inference(avatar_sat_refutation,[],[f69,f74,f79,f83,f87,f91,f95,f104,f113,f118,f119,f123,f127,f128,f132,f136,f140,f141,f142,f144,f158,f161,f182,f187,f255,f279,f349,f451]) ).
fof(f451,plain,
( spl14_6
| ~ spl14_15 ),
inference(avatar_split_clause,[],[f450,f121,f81]) ).
fof(f81,plain,
( spl14_6
<=> ! [X3] : sP1(X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_6])]) ).
fof(f121,plain,
( spl14_15
<=> ! [X2,X3] :
( sP0(X2)
| ~ big_p(X3)
| ~ big_r(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_15])]) ).
fof(f450,plain,
( ! [X0] : sP1(X0)
| ~ spl14_15 ),
inference(subsumption_resolution,[],[f449,f422]) ).
fof(f422,plain,
( ! [X0] :
( sP1(X0)
| sP0(X0) )
| ~ spl14_15 ),
inference(duplicate_literal_removal,[],[f421]) ).
fof(f421,plain,
( ! [X0] :
( sP0(X0)
| sP1(X0)
| sP1(X0) )
| ~ spl14_15 ),
inference(resolution,[],[f372,f50]) ).
fof(f50,plain,
! [X0] :
( big_r(X0,sK9(X0))
| sP1(X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0] :
( ( sP1(X0)
| ( ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1) )
& big_r(X0,sK9(X0))
& big_p(sK9(X0))
& big_p(a) ) )
& ( ( big_r(sK11(X0),sK10(X0))
& big_r(X0,sK11(X0))
& big_p(sK10(X0)) )
| ! [X6] :
( ~ big_r(X0,X6)
| ~ big_p(X6) )
| ~ big_p(a)
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f23,f25,f24]) ).
fof(f24,plain,
! [X0] :
( ? [X3] :
( big_r(X0,X3)
& big_p(X3) )
=> ( big_r(X0,sK9(X0))
& big_p(sK9(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0] :
( ? [X4,X5] :
( big_r(X5,X4)
& big_r(X0,X5)
& big_p(X4) )
=> ( big_r(sK11(X0),sK10(X0))
& big_r(X0,sK11(X0))
& big_p(sK10(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0] :
( ( sP1(X0)
| ( ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1) )
& ? [X3] :
( big_r(X0,X3)
& big_p(X3) )
& big_p(a) ) )
& ( ? [X4,X5] :
( big_r(X5,X4)
& big_r(X0,X5)
& big_p(X4) )
| ! [X6] :
( ~ big_r(X0,X6)
| ~ big_p(X6) )
| ~ big_p(a)
| ~ sP1(X0) ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X4] :
( ( sP1(X4)
| ( ! [X5,X6] :
( ~ big_r(X6,X5)
| ~ big_r(X4,X6)
| ~ big_p(X5) )
& ? [X7] :
( big_r(X4,X7)
& big_p(X7) )
& big_p(a) ) )
& ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| ! [X7] :
( ~ big_r(X4,X7)
| ~ big_p(X7) )
| ~ big_p(a)
| ~ sP1(X4) ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X4] :
( ( sP1(X4)
| ( ! [X5,X6] :
( ~ big_r(X6,X5)
| ~ big_r(X4,X6)
| ~ big_p(X5) )
& ? [X7] :
( big_r(X4,X7)
& big_p(X7) )
& big_p(a) ) )
& ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| ! [X7] :
( ~ big_r(X4,X7)
| ~ big_p(X7) )
| ~ big_p(a)
| ~ sP1(X4) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,plain,
! [X4] :
( sP1(X4)
<=> ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| ! [X7] :
( ~ big_r(X4,X7)
| ~ big_p(X7) )
| ~ big_p(a) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f372,plain,
( ! [X0,X1] :
( ~ big_r(X0,sK9(X1))
| sP0(X0)
| sP1(X1) )
| ~ spl14_15 ),
inference(resolution,[],[f122,f49]) ).
fof(f49,plain,
! [X0] :
( big_p(sK9(X0))
| sP1(X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f122,plain,
( ! [X2,X3] :
( ~ big_p(X3)
| sP0(X2)
| ~ big_r(X2,X3) )
| ~ spl14_15 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f449,plain,
( ! [X0] :
( sP1(X0)
| ~ sP0(X0) )
| ~ spl14_15 ),
inference(resolution,[],[f447,f52]) ).
fof(f52,plain,
! [X0] :
( big_p(sK12(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( ( sP0(X0)
| ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1) ) )
& ( ( big_r(sK13(X0),sK12(X0))
& big_r(X0,sK13(X0))
& big_p(sK12(X0)) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f28,f29]) ).
fof(f29,plain,
! [X0] :
( ? [X3,X4] :
( big_r(X4,X3)
& big_r(X0,X4)
& big_p(X3) )
=> ( big_r(sK13(X0),sK12(X0))
& big_r(X0,sK13(X0))
& big_p(sK12(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X0] :
( ( sP0(X0)
| ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1) ) )
& ( ? [X3,X4] :
( big_r(X4,X3)
& big_r(X0,X4)
& big_p(X3) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
! [X0] :
( ( sP0(X0)
| ! [X2,X3] :
( ~ big_r(X3,X2)
| ~ big_r(X0,X3)
| ~ big_p(X2) ) )
& ( ? [X2,X3] :
( big_r(X3,X2)
& big_r(X0,X3)
& big_p(X2) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,plain,
! [X0] :
( sP0(X0)
<=> ? [X2,X3] :
( big_r(X3,X2)
& big_r(X0,X3)
& big_p(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f447,plain,
( ! [X0] :
( ~ big_p(sK12(X0))
| sP1(X0) )
| ~ spl14_15 ),
inference(subsumption_resolution,[],[f443,f422]) ).
fof(f443,plain,
( ! [X0] :
( sP1(X0)
| ~ big_p(sK12(X0))
| ~ sP0(X0) )
| ~ spl14_15 ),
inference(resolution,[],[f439,f54]) ).
fof(f54,plain,
! [X0] :
( big_r(sK13(X0),sK12(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f439,plain,
( ! [X0,X1] :
( ~ big_r(sK13(X0),X1)
| sP1(X0)
| ~ big_p(X1) )
| ~ spl14_15 ),
inference(subsumption_resolution,[],[f376,f422]) ).
fof(f376,plain,
! [X0,X1] :
( ~ big_r(sK13(X0),X1)
| sP1(X0)
| ~ big_p(X1)
| ~ sP0(X0) ),
inference(resolution,[],[f51,f53]) ).
fof(f53,plain,
! [X0] :
( big_r(X0,sK13(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ big_r(X0,X2)
| ~ big_r(X2,X1)
| sP1(X0)
| ~ big_p(X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f349,plain,
( spl14_16
| ~ spl14_7
| ~ spl14_8
| ~ spl14_9 ),
inference(avatar_split_clause,[],[f348,f93,f89,f85,f125]) ).
fof(f125,plain,
( spl14_16
<=> ! [X2] :
( sP0(X2)
| big_p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_16])]) ).
fof(f85,plain,
( spl14_7
<=> ! [X3] :
( big_r(sK6(X3),sK5(X3))
| big_p(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_7])]) ).
fof(f89,plain,
( spl14_8
<=> ! [X3] :
( big_r(X3,sK6(X3))
| big_p(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_8])]) ).
fof(f93,plain,
( spl14_9
<=> ! [X3] :
( big_p(sK5(X3))
| big_p(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_9])]) ).
fof(f348,plain,
( ! [X0] :
( sP0(X0)
| big_p(X0) )
| ~ spl14_7
| ~ spl14_8
| ~ spl14_9 ),
inference(subsumption_resolution,[],[f347,f94]) ).
fof(f94,plain,
( ! [X3] :
( big_p(sK5(X3))
| big_p(X3) )
| ~ spl14_9 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f347,plain,
( ! [X0] :
( sP0(X0)
| ~ big_p(sK5(X0))
| big_p(X0) )
| ~ spl14_7
| ~ spl14_8 ),
inference(duplicate_literal_removal,[],[f342]) ).
fof(f342,plain,
( ! [X0] :
( sP0(X0)
| ~ big_p(sK5(X0))
| big_p(X0)
| big_p(X0) )
| ~ spl14_7
| ~ spl14_8 ),
inference(resolution,[],[f208,f86]) ).
fof(f86,plain,
( ! [X3] :
( big_r(sK6(X3),sK5(X3))
| big_p(X3) )
| ~ spl14_7 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f208,plain,
( ! [X0,X1] :
( ~ big_r(sK6(X0),X1)
| sP0(X0)
| ~ big_p(X1)
| big_p(X0) )
| ~ spl14_8 ),
inference(resolution,[],[f55,f90]) ).
fof(f90,plain,
( ! [X3] :
( big_r(X3,sK6(X3))
| big_p(X3) )
| ~ spl14_8 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ big_r(X0,X2)
| ~ big_r(X2,X1)
| sP0(X0)
| ~ big_p(X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f279,plain,
( ~ spl14_6
| spl14_10
| ~ spl14_13
| ~ spl14_14
| ~ spl14_17
| ~ spl14_18
| ~ spl14_27 ),
inference(avatar_contradiction_clause,[],[f278]) ).
fof(f278,plain,
( $false
| ~ spl14_6
| spl14_10
| ~ spl14_13
| ~ spl14_14
| ~ spl14_17
| ~ spl14_18
| ~ spl14_27 ),
inference(subsumption_resolution,[],[f275,f241]) ).
fof(f241,plain,
( big_p(sK10(sK7))
| ~ spl14_27 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f240,plain,
( spl14_27
<=> big_p(sK10(sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_27])]) ).
fof(f275,plain,
( ~ big_p(sK10(sK7))
| ~ spl14_6
| spl14_10
| ~ spl14_13
| ~ spl14_14
| ~ spl14_17
| ~ spl14_18 ),
inference(resolution,[],[f273,f230]) ).
fof(f230,plain,
( big_r(sK11(sK7),sK10(sK7))
| ~ spl14_6
| ~ spl14_13
| ~ spl14_14
| ~ spl14_17 ),
inference(subsumption_resolution,[],[f227,f117]) ).
fof(f117,plain,
( big_p(sK8)
| ~ spl14_14 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f115,plain,
( spl14_14
<=> big_p(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_14])]) ).
fof(f227,plain,
( ~ big_p(sK8)
| big_r(sK11(sK7),sK10(sK7))
| ~ spl14_6
| ~ spl14_13
| ~ spl14_17 ),
inference(resolution,[],[f147,f112]) ).
fof(f112,plain,
( big_r(sK7,sK8)
| ~ spl14_13 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f110,plain,
( spl14_13
<=> big_r(sK7,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_13])]) ).
fof(f147,plain,
( ! [X0,X6] :
( ~ big_r(X0,X6)
| ~ big_p(X6)
| big_r(sK11(X0),sK10(X0)) )
| ~ spl14_6
| ~ spl14_17 ),
inference(subsumption_resolution,[],[f131,f82]) ).
fof(f82,plain,
( ! [X3] : sP1(X3)
| ~ spl14_6 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f131,plain,
( ! [X0,X6] :
( ~ sP1(X0)
| big_r(sK11(X0),sK10(X0))
| ~ big_p(X6)
| ~ big_r(X0,X6) )
| ~ spl14_17 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f130,plain,
( spl14_17
<=> ! [X6,X0] :
( big_r(sK11(X0),sK10(X0))
| ~ sP1(X0)
| ~ big_p(X6)
| ~ big_r(X0,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_17])]) ).
fof(f273,plain,
( ! [X0] :
( ~ big_r(sK11(sK7),X0)
| ~ big_p(X0) )
| ~ spl14_6
| spl14_10
| ~ spl14_13
| ~ spl14_14
| ~ spl14_18 ),
inference(subsumption_resolution,[],[f272,f99]) ).
fof(f99,plain,
( ~ sP0(sK7)
| spl14_10 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f97,plain,
( spl14_10
<=> sP0(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_10])]) ).
fof(f272,plain,
( ! [X0] :
( ~ big_r(sK11(sK7),X0)
| sP0(sK7)
| ~ big_p(X0) )
| ~ spl14_6
| ~ spl14_13
| ~ spl14_14
| ~ spl14_18 ),
inference(resolution,[],[f270,f55]) ).
fof(f270,plain,
( big_r(sK7,sK11(sK7))
| ~ spl14_6
| ~ spl14_13
| ~ spl14_14
| ~ spl14_18 ),
inference(resolution,[],[f191,f112]) ).
fof(f191,plain,
( ! [X0] :
( ~ big_r(X0,sK8)
| big_r(X0,sK11(X0)) )
| ~ spl14_6
| ~ spl14_14
| ~ spl14_18 ),
inference(resolution,[],[f117,f146]) ).
fof(f146,plain,
( ! [X0,X6] :
( ~ big_p(X6)
| big_r(X0,sK11(X0))
| ~ big_r(X0,X6) )
| ~ spl14_6
| ~ spl14_18 ),
inference(subsumption_resolution,[],[f135,f82]) ).
fof(f135,plain,
( ! [X0,X6] :
( ~ sP1(X0)
| big_r(X0,sK11(X0))
| ~ big_p(X6)
| ~ big_r(X0,X6) )
| ~ spl14_18 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f134,plain,
( spl14_18
<=> ! [X6,X0] :
( big_r(X0,sK11(X0))
| ~ sP1(X0)
| ~ big_p(X6)
| ~ big_r(X0,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_18])]) ).
fof(f255,plain,
( spl14_27
| ~ spl14_6
| ~ spl14_13
| ~ spl14_14
| ~ spl14_19 ),
inference(avatar_split_clause,[],[f252,f138,f115,f110,f81,f240]) ).
fof(f138,plain,
( spl14_19
<=> ! [X6,X0] :
( big_p(sK10(X0))
| ~ sP1(X0)
| ~ big_p(X6)
| ~ big_r(X0,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_19])]) ).
fof(f252,plain,
( big_p(sK10(sK7))
| ~ spl14_6
| ~ spl14_13
| ~ spl14_14
| ~ spl14_19 ),
inference(resolution,[],[f192,f112]) ).
fof(f192,plain,
( ! [X0] :
( ~ big_r(X0,sK8)
| big_p(sK10(X0)) )
| ~ spl14_6
| ~ spl14_14
| ~ spl14_19 ),
inference(resolution,[],[f117,f145]) ).
fof(f145,plain,
( ! [X0,X6] :
( ~ big_p(X6)
| big_p(sK10(X0))
| ~ big_r(X0,X6) )
| ~ spl14_6
| ~ spl14_19 ),
inference(subsumption_resolution,[],[f139,f82]) ).
fof(f139,plain,
( ! [X0,X6] :
( ~ sP1(X0)
| big_p(sK10(X0))
| ~ big_p(X6)
| ~ big_r(X0,X6) )
| ~ spl14_19 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f187,plain,
( spl14_12
| spl14_10
| ~ spl14_16 ),
inference(avatar_split_clause,[],[f186,f125,f97,f106]) ).
fof(f106,plain,
( spl14_12
<=> big_p(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_12])]) ).
fof(f186,plain,
( big_p(sK7)
| spl14_10
| ~ spl14_16 ),
inference(resolution,[],[f99,f126]) ).
fof(f126,plain,
( ! [X2] :
( sP0(X2)
| big_p(X2) )
| ~ spl14_16 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f182,plain,
( ~ spl14_20
| ~ spl14_21 ),
inference(avatar_split_clause,[],[f181,f156,f152]) ).
fof(f152,plain,
( spl14_20
<=> sP0(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_20])]) ).
fof(f156,plain,
( spl14_21
<=> ! [X0] :
( ~ big_p(X0)
| ~ big_r(sK13(sK4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_21])]) ).
fof(f181,plain,
( ~ sP0(sK4)
| ~ spl14_21 ),
inference(subsumption_resolution,[],[f166,f52]) ).
fof(f166,plain,
( ~ big_p(sK12(sK4))
| ~ sP0(sK4)
| ~ spl14_21 ),
inference(resolution,[],[f157,f54]) ).
fof(f157,plain,
( ! [X0] :
( ~ big_r(sK13(sK4),X0)
| ~ big_p(X0) )
| ~ spl14_21 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f161,plain,
( spl14_4
| ~ spl14_16
| spl14_20 ),
inference(avatar_contradiction_clause,[],[f160]) ).
fof(f160,plain,
( $false
| spl14_4
| ~ spl14_16
| spl14_20 ),
inference(subsumption_resolution,[],[f159,f73]) ).
fof(f73,plain,
( ~ big_p(sK4)
| spl14_4 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f71,plain,
( spl14_4
<=> big_p(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_4])]) ).
fof(f159,plain,
( big_p(sK4)
| ~ spl14_16
| spl14_20 ),
inference(resolution,[],[f154,f126]) ).
fof(f154,plain,
( ~ sP0(sK4)
| spl14_20 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f158,plain,
( ~ spl14_20
| spl14_21
| ~ spl14_1 ),
inference(avatar_split_clause,[],[f150,f59,f156,f152]) ).
fof(f59,plain,
( spl14_1
<=> ! [X2,X1] :
( ~ big_r(X2,X1)
| ~ big_p(X1)
| ~ big_r(sK4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_1])]) ).
fof(f150,plain,
( ! [X0] :
( ~ big_p(X0)
| ~ big_r(sK13(sK4),X0)
| ~ sP0(sK4) )
| ~ spl14_1 ),
inference(resolution,[],[f60,f53]) ).
fof(f60,plain,
( ! [X2,X1] :
( ~ big_r(sK4,X2)
| ~ big_p(X1)
| ~ big_r(X2,X1) )
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f144,plain,
( spl14_2
| ~ spl14_6 ),
inference(avatar_contradiction_clause,[],[f143]) ).
fof(f143,plain,
( $false
| spl14_2
| ~ spl14_6 ),
inference(resolution,[],[f82,f64]) ).
fof(f64,plain,
( ~ sP1(sK4)
| spl14_2 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f62,plain,
( spl14_2
<=> sP1(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_2])]) ).
fof(f142,plain,
( spl14_11
| spl14_3 ),
inference(avatar_split_clause,[],[f56,f66,f101]) ).
fof(f101,plain,
( spl14_11
<=> sP2 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_11])]) ).
fof(f66,plain,
( spl14_3
<=> sP3 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_3])]) ).
fof(f56,plain,
( sP3
| sP2 ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
( ( ~ sP3
| ~ sP2 )
& ( sP3
| sP2 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,plain,
( sP2
<~> sP3 ),
inference(definition_folding,[],[f5,f9,f8,f7,f6]) ).
fof(f8,plain,
( sP2
<=> ! [X0] :
( sP0(X0)
| ( ! [X1] :
( ~ big_r(X0,X1)
| ~ big_p(X1) )
& big_p(X0) )
| ~ big_p(a) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f9,plain,
( sP3
<=> ! [X4] :
( sP1(X4)
& ( ? [X8,X9] :
( big_r(X9,X8)
& big_r(X4,X9)
& big_p(X8) )
| big_p(X4)
| ~ big_p(a) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f5,plain,
( ! [X0] :
( ? [X2,X3] :
( big_r(X3,X2)
& big_r(X0,X3)
& big_p(X2) )
| ( ! [X1] :
( ~ big_r(X0,X1)
| ~ big_p(X1) )
& big_p(X0) )
| ~ big_p(a) )
<~> ! [X4] :
( ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| ! [X7] :
( ~ big_r(X4,X7)
| ~ big_p(X7) )
| ~ big_p(a) )
& ( ? [X8,X9] :
( big_r(X9,X8)
& big_r(X4,X9)
& big_p(X8) )
| big_p(X4)
| ~ big_p(a) ) ) ),
inference(flattening,[],[f4]) ).
fof(f4,plain,
( ! [X0] :
( ? [X2,X3] :
( big_r(X3,X2)
& big_r(X0,X3)
& big_p(X2) )
| ( ! [X1] :
( ~ big_r(X0,X1)
| ~ big_p(X1) )
& big_p(X0) )
| ~ big_p(a) )
<~> ! [X4] :
( ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| ! [X7] :
( ~ big_r(X4,X7)
| ~ big_p(X7) )
| ~ big_p(a) )
& ( ? [X8,X9] :
( big_r(X9,X8)
& big_r(X4,X9)
& big_p(X8) )
| big_p(X4)
| ~ big_p(a) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,plain,
~ ( ! [X0] :
( ( ( big_p(X0)
=> ? [X1] :
( big_r(X0,X1)
& big_p(X1) ) )
& big_p(a) )
=> ? [X2,X3] :
( big_r(X3,X2)
& big_r(X0,X3)
& big_p(X2) ) )
<=> ! [X4] :
( ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| ~ ? [X7] :
( big_r(X4,X7)
& big_p(X7) )
| ~ big_p(a) )
& ( ? [X8,X9] :
( big_r(X9,X8)
& big_r(X4,X9)
& big_p(X8) )
| big_p(X4)
| ~ big_p(a) ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( ( ( big_p(X0)
=> ? [X1] :
( big_r(X0,X1)
& big_p(X1) ) )
& big_p(a) )
=> ? [X2,X3] :
( big_r(X3,X2)
& big_r(X0,X3)
& big_p(X2) ) )
<=> ! [X4] :
( ( ? [X8,X9] :
( big_r(X9,X8)
& big_r(X4,X9)
& big_p(X8) )
| ~ ? [X7] :
( big_r(X4,X7)
& big_p(X7) )
| ~ big_p(a) )
& ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| big_p(X4)
| ~ big_p(a) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
( ! [X0] :
( ( ( big_p(X0)
=> ? [X1] :
( big_r(X0,X1)
& big_p(X1) ) )
& big_p(a) )
=> ? [X2,X3] :
( big_r(X3,X2)
& big_r(X0,X3)
& big_p(X2) ) )
<=> ! [X4] :
( ( ? [X8,X9] :
( big_r(X9,X8)
& big_r(X4,X9)
& big_p(X8) )
| ~ ? [X7] :
( big_r(X4,X7)
& big_p(X7) )
| ~ big_p(a) )
& ( ? [X5,X6] :
( big_r(X6,X5)
& big_r(X4,X6)
& big_p(X5) )
| big_p(X4)
| ~ big_p(a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38) ).
fof(f141,plain,
( ~ spl14_11
| ~ spl14_3 ),
inference(avatar_split_clause,[],[f57,f66,f101]) ).
fof(f57,plain,
( ~ sP3
| ~ sP2 ),
inference(cnf_transformation,[],[f31]) ).
fof(f140,plain,
( ~ spl14_5
| spl14_19 ),
inference(avatar_split_clause,[],[f45,f138,f76]) ).
fof(f76,plain,
( spl14_5
<=> big_p(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_5])]) ).
fof(f45,plain,
! [X0,X6] :
( big_p(sK10(X0))
| ~ big_r(X0,X6)
| ~ big_p(X6)
| ~ big_p(a)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f136,plain,
( ~ spl14_5
| spl14_18 ),
inference(avatar_split_clause,[],[f46,f134,f76]) ).
fof(f46,plain,
! [X0,X6] :
( big_r(X0,sK11(X0))
| ~ big_r(X0,X6)
| ~ big_p(X6)
| ~ big_p(a)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f132,plain,
( ~ spl14_5
| spl14_17 ),
inference(avatar_split_clause,[],[f47,f130,f76]) ).
fof(f47,plain,
! [X0,X6] :
( big_r(sK11(X0),sK10(X0))
| ~ big_r(X0,X6)
| ~ big_p(X6)
| ~ big_p(a)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f128,plain,
( spl14_5
| spl14_6 ),
inference(avatar_split_clause,[],[f48,f81,f76]) ).
fof(f48,plain,
! [X0] :
( sP1(X0)
| big_p(a) ),
inference(cnf_transformation,[],[f26]) ).
fof(f127,plain,
( ~ spl14_11
| ~ spl14_5
| spl14_16 ),
inference(avatar_split_clause,[],[f39,f125,f76,f101]) ).
fof(f39,plain,
! [X2] :
( sP0(X2)
| big_p(X2)
| ~ big_p(a)
| ~ sP2 ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
( ( sP2
| ( ~ sP0(sK7)
& ( ( big_r(sK7,sK8)
& big_p(sK8) )
| ~ big_p(sK7) )
& big_p(a) ) )
& ( ! [X2] :
( sP0(X2)
| ( ! [X3] :
( ~ big_r(X2,X3)
| ~ big_p(X3) )
& big_p(X2) )
| ~ big_p(a) )
| ~ sP2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f17,f19,f18]) ).
fof(f18,plain,
( ? [X0] :
( ~ sP0(X0)
& ( ? [X1] :
( big_r(X0,X1)
& big_p(X1) )
| ~ big_p(X0) )
& big_p(a) )
=> ( ~ sP0(sK7)
& ( ? [X1] :
( big_r(sK7,X1)
& big_p(X1) )
| ~ big_p(sK7) )
& big_p(a) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
( ? [X1] :
( big_r(sK7,X1)
& big_p(X1) )
=> ( big_r(sK7,sK8)
& big_p(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
( ( sP2
| ? [X0] :
( ~ sP0(X0)
& ( ? [X1] :
( big_r(X0,X1)
& big_p(X1) )
| ~ big_p(X0) )
& big_p(a) ) )
& ( ! [X2] :
( sP0(X2)
| ( ! [X3] :
( ~ big_r(X2,X3)
| ~ big_p(X3) )
& big_p(X2) )
| ~ big_p(a) )
| ~ sP2 ) ),
inference(rectify,[],[f16]) ).
fof(f16,plain,
( ( sP2
| ? [X0] :
( ~ sP0(X0)
& ( ? [X1] :
( big_r(X0,X1)
& big_p(X1) )
| ~ big_p(X0) )
& big_p(a) ) )
& ( ! [X0] :
( sP0(X0)
| ( ! [X1] :
( ~ big_r(X0,X1)
| ~ big_p(X1) )
& big_p(X0) )
| ~ big_p(a) )
| ~ sP2 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f123,plain,
( ~ spl14_11
| ~ spl14_5
| spl14_15 ),
inference(avatar_split_clause,[],[f40,f121,f76,f101]) ).
fof(f40,plain,
! [X2,X3] :
( sP0(X2)
| ~ big_r(X2,X3)
| ~ big_p(X3)
| ~ big_p(a)
| ~ sP2 ),
inference(cnf_transformation,[],[f20]) ).
fof(f119,plain,
( spl14_5
| spl14_11 ),
inference(avatar_split_clause,[],[f41,f101,f76]) ).
fof(f41,plain,
( sP2
| big_p(a) ),
inference(cnf_transformation,[],[f20]) ).
fof(f118,plain,
( ~ spl14_12
| spl14_14
| spl14_11 ),
inference(avatar_split_clause,[],[f42,f101,f115,f106]) ).
fof(f42,plain,
( sP2
| big_p(sK8)
| ~ big_p(sK7) ),
inference(cnf_transformation,[],[f20]) ).
fof(f113,plain,
( ~ spl14_12
| spl14_13
| spl14_11 ),
inference(avatar_split_clause,[],[f43,f101,f110,f106]) ).
fof(f43,plain,
( sP2
| big_r(sK7,sK8)
| ~ big_p(sK7) ),
inference(cnf_transformation,[],[f20]) ).
fof(f104,plain,
( ~ spl14_10
| spl14_11 ),
inference(avatar_split_clause,[],[f44,f101,f97]) ).
fof(f44,plain,
( sP2
| ~ sP0(sK7) ),
inference(cnf_transformation,[],[f20]) ).
fof(f95,plain,
( ~ spl14_3
| ~ spl14_5
| spl14_9 ),
inference(avatar_split_clause,[],[f32,f93,f76,f66]) ).
fof(f32,plain,
! [X3] :
( big_p(sK5(X3))
| big_p(X3)
| ~ big_p(a)
| ~ sP3 ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
( ( sP3
| ~ sP1(sK4)
| ( ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(sK4,X2)
| ~ big_p(X1) )
& ~ big_p(sK4)
& big_p(a) ) )
& ( ! [X3] :
( sP1(X3)
& ( ( big_r(sK6(X3),sK5(X3))
& big_r(X3,sK6(X3))
& big_p(sK5(X3)) )
| big_p(X3)
| ~ big_p(a) ) )
| ~ sP3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f12,f14,f13]) ).
fof(f13,plain,
( ? [X0] :
( ~ sP1(X0)
| ( ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1) )
& ~ big_p(X0)
& big_p(a) ) )
=> ( ~ sP1(sK4)
| ( ! [X2,X1] :
( ~ big_r(X2,X1)
| ~ big_r(sK4,X2)
| ~ big_p(X1) )
& ~ big_p(sK4)
& big_p(a) ) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
! [X3] :
( ? [X4,X5] :
( big_r(X5,X4)
& big_r(X3,X5)
& big_p(X4) )
=> ( big_r(sK6(X3),sK5(X3))
& big_r(X3,sK6(X3))
& big_p(sK5(X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f12,plain,
( ( sP3
| ? [X0] :
( ~ sP1(X0)
| ( ! [X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1) )
& ~ big_p(X0)
& big_p(a) ) ) )
& ( ! [X3] :
( sP1(X3)
& ( ? [X4,X5] :
( big_r(X5,X4)
& big_r(X3,X5)
& big_p(X4) )
| big_p(X3)
| ~ big_p(a) ) )
| ~ sP3 ) ),
inference(rectify,[],[f11]) ).
fof(f11,plain,
( ( sP3
| ? [X4] :
( ~ sP1(X4)
| ( ! [X8,X9] :
( ~ big_r(X9,X8)
| ~ big_r(X4,X9)
| ~ big_p(X8) )
& ~ big_p(X4)
& big_p(a) ) ) )
& ( ! [X4] :
( sP1(X4)
& ( ? [X8,X9] :
( big_r(X9,X8)
& big_r(X4,X9)
& big_p(X8) )
| big_p(X4)
| ~ big_p(a) ) )
| ~ sP3 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f91,plain,
( ~ spl14_3
| ~ spl14_5
| spl14_8 ),
inference(avatar_split_clause,[],[f33,f89,f76,f66]) ).
fof(f33,plain,
! [X3] :
( big_r(X3,sK6(X3))
| big_p(X3)
| ~ big_p(a)
| ~ sP3 ),
inference(cnf_transformation,[],[f15]) ).
fof(f87,plain,
( ~ spl14_3
| ~ spl14_5
| spl14_7 ),
inference(avatar_split_clause,[],[f34,f85,f76,f66]) ).
fof(f34,plain,
! [X3] :
( big_r(sK6(X3),sK5(X3))
| big_p(X3)
| ~ big_p(a)
| ~ sP3 ),
inference(cnf_transformation,[],[f15]) ).
fof(f83,plain,
( ~ spl14_3
| spl14_6 ),
inference(avatar_split_clause,[],[f35,f81,f66]) ).
fof(f35,plain,
! [X3] :
( sP1(X3)
| ~ sP3 ),
inference(cnf_transformation,[],[f15]) ).
fof(f79,plain,
( spl14_5
| ~ spl14_2
| spl14_3 ),
inference(avatar_split_clause,[],[f36,f66,f62,f76]) ).
fof(f36,plain,
( sP3
| ~ sP1(sK4)
| big_p(a) ),
inference(cnf_transformation,[],[f15]) ).
fof(f74,plain,
( ~ spl14_4
| ~ spl14_2
| spl14_3 ),
inference(avatar_split_clause,[],[f37,f66,f62,f71]) ).
fof(f37,plain,
( sP3
| ~ sP1(sK4)
| ~ big_p(sK4) ),
inference(cnf_transformation,[],[f15]) ).
fof(f69,plain,
( spl14_1
| ~ spl14_2
| spl14_3 ),
inference(avatar_split_clause,[],[f38,f66,f62,f59]) ).
fof(f38,plain,
! [X2,X1] :
( sP3
| ~ sP1(sK4)
| ~ big_r(X2,X1)
| ~ big_r(sK4,X2)
| ~ big_p(X1) ),
inference(cnf_transformation,[],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SYN067+1 : TPTP v8.1.2. Released v2.0.0.
% 0.08/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.37 % Computer : n027.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Tue Apr 30 02:14:32 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.16/0.38 % (29830)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.39 % (29836)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.16/0.39 % (29836)First to succeed.
% 0.16/0.39 % (29831)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.16/0.39 % (29832)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.39 % (29834)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.16/0.39 % (29835)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.16/0.39 % (29833)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.16/0.39 % (29837)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.16/0.39 % (29836)Refutation found. Thanks to Tanya!
% 0.16/0.39 % SZS status Theorem for theBenchmark
% 0.16/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.40 % (29836)------------------------------
% 0.16/0.40 % (29836)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.40 % (29836)Termination reason: Refutation
% 0.16/0.40
% 0.16/0.40 % (29836)Memory used [KB]: 979
% 0.16/0.40 % (29836)Time elapsed: 0.007 s
% 0.16/0.40 % (29836)Instructions burned: 15 (million)
% 0.16/0.40 % (29836)------------------------------
% 0.16/0.40 % (29836)------------------------------
% 0.16/0.40 % (29830)Success in time 0.017 s
%------------------------------------------------------------------------------