TSTP Solution File: SYN036+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SYN036+1 : TPTP v8.1.0. Released v2.0.0.
% 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 : n003.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 19:36:36 EDT 2022
% Result : Theorem 0.22s 0.49s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 53
% Syntax : Number of formulae : 187 ( 1 unt; 0 def)
% Number of atoms : 821 ( 0 equ)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 1010 ( 376 ~; 464 |; 83 &)
% ( 61 <=>; 24 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 31 ( 30 usr; 29 prp; 0-1 aty)
% Number of functors : 24 ( 24 usr; 20 con; 0-1 aty)
% Number of variables : 284 ( 192 !; 92 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f319,plain,
$false,
inference(avatar_sat_refutation,[],[f103,f118,f138,f146,f163,f164,f168,f173,f186,f188,f198,f203,f211,f212,f213,f214,f215,f217,f218,f219,f224,f225,f227,f228,f229,f230,f232,f234,f236,f238,f242,f244,f246,f250,f253,f256,f262,f266,f277,f280,f282,f288,f294,f299,f301,f318]) ).
fof(f318,plain,
( ~ spl26_5
| ~ spl26_10 ),
inference(avatar_contradiction_clause,[],[f317]) ).
fof(f317,plain,
( $false
| ~ spl26_5
| ~ spl26_10 ),
inference(subsumption_resolution,[],[f302,f109]) ).
fof(f109,plain,
( ! [X19] : ~ big_p(X19)
| ~ spl26_10 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f108,plain,
( spl26_10
<=> ! [X19] : ~ big_p(X19) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_10])]) ).
fof(f302,plain,
( ! [X0] : big_p(X0)
| ~ spl26_5
| ~ spl26_10 ),
inference(resolution,[],[f109,f91]) ).
fof(f91,plain,
( ! [X0] :
( big_p(sK2(X0))
| big_p(X0) )
| ~ spl26_5 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f90,plain,
( spl26_5
<=> ! [X0] :
( big_p(sK2(X0))
| big_p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_5])]) ).
fof(f301,plain,
( ~ spl26_10
| ~ spl26_30 ),
inference(avatar_contradiction_clause,[],[f300]) ).
fof(f300,plain,
( $false
| ~ spl26_10
| ~ spl26_30 ),
inference(subsumption_resolution,[],[f197,f109]) ).
fof(f197,plain,
( big_p(sK22)
| ~ spl26_30 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f195,plain,
( spl26_30
<=> big_p(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_30])]) ).
fof(f299,plain,
( ~ spl26_2
| ~ spl26_6 ),
inference(avatar_contradiction_clause,[],[f298]) ).
fof(f298,plain,
( $false
| ~ spl26_2
| ~ spl26_6 ),
inference(subsumption_resolution,[],[f296,f94]) ).
fof(f94,plain,
( ! [X5] : big_q(X5)
| ~ spl26_6 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f93,plain,
( spl26_6
<=> ! [X5] : big_q(X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_6])]) ).
fof(f296,plain,
( ! [X0] : ~ big_q(X0)
| ~ spl26_2
| ~ spl26_6 ),
inference(resolution,[],[f94,f79]) ).
fof(f79,plain,
( ! [X22] :
( ~ big_q(sK25(X22))
| ~ big_q(X22) )
| ~ spl26_2 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f78,plain,
( spl26_2
<=> ! [X22] :
( ~ big_q(sK25(X22))
| ~ big_q(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_2])]) ).
fof(f294,plain,
( ~ spl26_9
| ~ spl26_16 ),
inference(avatar_contradiction_clause,[],[f293]) ).
fof(f293,plain,
( $false
| ~ spl26_9
| ~ spl26_16 ),
inference(subsumption_resolution,[],[f292,f106]) ).
fof(f106,plain,
( ! [X20] : ~ big_q(X20)
| ~ spl26_9 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f105,plain,
( spl26_9
<=> ! [X20] : ~ big_q(X20) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_9])]) ).
fof(f292,plain,
( ! [X1] : big_q(X1)
| ~ spl26_9
| ~ spl26_16 ),
inference(resolution,[],[f134,f106]) ).
fof(f134,plain,
( ! [X22] :
( big_q(sK25(X22))
| big_q(X22) )
| ~ spl26_16 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f133,plain,
( spl26_16
<=> ! [X22] :
( big_q(sK25(X22))
| big_q(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_16])]) ).
fof(f288,plain,
( ~ spl26_6
| spl26_25 ),
inference(avatar_contradiction_clause,[],[f287]) ).
fof(f287,plain,
( $false
| ~ spl26_6
| spl26_25 ),
inference(resolution,[],[f172,f94]) ).
fof(f172,plain,
( ~ big_q(sK3)
| spl26_25 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f170,plain,
( spl26_25
<=> big_q(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_25])]) ).
fof(f282,plain,
( ~ spl26_17
| spl26_34 ),
inference(avatar_contradiction_clause,[],[f281]) ).
fof(f281,plain,
( $false
| ~ spl26_17
| spl26_34 ),
inference(subsumption_resolution,[],[f223,f137]) ).
fof(f137,plain,
( ! [X18] : big_p(X18)
| ~ spl26_17 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f136,plain,
( spl26_17
<=> ! [X18] : big_p(X18) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_17])]) ).
fof(f223,plain,
( ~ big_p(sK21)
| spl26_34 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f221,plain,
( spl26_34
<=> big_p(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_34])]) ).
fof(f280,plain,
( ~ spl26_17
| ~ spl26_24 ),
inference(avatar_contradiction_clause,[],[f279]) ).
fof(f279,plain,
( $false
| ~ spl26_17
| ~ spl26_24 ),
inference(subsumption_resolution,[],[f278,f137]) ).
fof(f278,plain,
( ! [X0] : ~ big_p(sK2(X0))
| ~ spl26_17
| ~ spl26_24 ),
inference(subsumption_resolution,[],[f167,f137]) ).
fof(f167,plain,
( ! [X0] :
( ~ big_p(sK2(X0))
| ~ big_p(X0) )
| ~ spl26_24 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f166,plain,
( spl26_24
<=> ! [X0] :
( ~ big_p(sK2(X0))
| ~ big_p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_24])]) ).
fof(f277,plain,
( ~ spl26_17
| ~ spl26_23 ),
inference(avatar_contradiction_clause,[],[f276]) ).
fof(f276,plain,
( $false
| ~ spl26_17
| ~ spl26_23 ),
inference(subsumption_resolution,[],[f275,f137]) ).
fof(f275,plain,
( ! [X0] : ~ big_p(X0)
| ~ spl26_17
| ~ spl26_23 ),
inference(resolution,[],[f162,f137]) ).
fof(f162,plain,
( ! [X16] :
( ~ big_p(sK10(X16))
| ~ big_p(X16) )
| ~ spl26_23 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f161,plain,
( spl26_23
<=> ! [X16] :
( ~ big_p(sK10(X16))
| ~ big_p(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_23])]) ).
fof(f266,plain,
( ~ spl26_9
| ~ spl26_33 ),
inference(avatar_contradiction_clause,[],[f265]) ).
fof(f265,plain,
( $false
| ~ spl26_9
| ~ spl26_33 ),
inference(subsumption_resolution,[],[f264,f106]) ).
fof(f264,plain,
( ! [X1] : big_q(X1)
| ~ spl26_9
| ~ spl26_33 ),
inference(resolution,[],[f210,f106]) ).
fof(f210,plain,
( ! [X4] :
( big_q(sK16(X4))
| big_q(X4) )
| ~ spl26_33 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f209,plain,
( spl26_33
<=> ! [X4] :
( big_q(sK16(X4))
| big_q(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_33])]) ).
fof(f262,plain,
( ~ spl26_9
| ~ spl26_29 ),
inference(avatar_contradiction_clause,[],[f261]) ).
fof(f261,plain,
( $false
| ~ spl26_9
| ~ spl26_29 ),
inference(resolution,[],[f192,f106]) ).
fof(f192,plain,
( big_q(sK20)
| ~ spl26_29 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f191,plain,
( spl26_29
<=> big_q(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_29])]) ).
fof(f256,plain,
( ~ spl26_10
| ~ spl26_26 ),
inference(avatar_contradiction_clause,[],[f255]) ).
fof(f255,plain,
( $false
| ~ spl26_10
| ~ spl26_26 ),
inference(subsumption_resolution,[],[f254,f109]) ).
fof(f254,plain,
( ! [X16] : big_p(X16)
| ~ spl26_10
| ~ spl26_26 ),
inference(subsumption_resolution,[],[f176,f109]) ).
fof(f176,plain,
( ! [X16] :
( big_p(X16)
| big_p(sK10(X16)) )
| ~ spl26_26 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f175,plain,
( spl26_26
<=> ! [X16] :
( big_p(sK10(X16))
| big_p(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_26])]) ).
fof(f253,plain,
( ~ spl26_6
| ~ spl26_19 ),
inference(avatar_contradiction_clause,[],[f252]) ).
fof(f252,plain,
( $false
| ~ spl26_6
| ~ spl26_19 ),
inference(subsumption_resolution,[],[f251,f94]) ).
fof(f251,plain,
( ! [X4] : ~ big_q(X4)
| ~ spl26_6
| ~ spl26_19 ),
inference(subsumption_resolution,[],[f145,f94]) ).
fof(f145,plain,
( ! [X4] :
( ~ big_q(sK16(X4))
| ~ big_q(X4) )
| ~ spl26_19 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f144,plain,
( spl26_19
<=> ! [X4] :
( ~ big_q(X4)
| ~ big_q(sK16(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_19])]) ).
fof(f250,plain,
( ~ spl26_6
| spl26_12 ),
inference(avatar_contradiction_clause,[],[f249]) ).
fof(f249,plain,
( $false
| ~ spl26_6
| spl26_12 ),
inference(resolution,[],[f117,f94]) ).
fof(f117,plain,
( ~ big_q(sK12)
| spl26_12 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f115,plain,
( spl26_12
<=> big_q(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_12])]) ).
fof(f246,plain,
( ~ spl26_6
| spl26_29 ),
inference(avatar_contradiction_clause,[],[f245]) ).
fof(f245,plain,
( $false
| ~ spl26_6
| spl26_29 ),
inference(resolution,[],[f94,f193]) ).
fof(f193,plain,
( ~ big_q(sK20)
| spl26_29 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f244,plain,
( ~ spl26_10
| ~ spl26_32 ),
inference(avatar_contradiction_clause,[],[f243]) ).
fof(f243,plain,
( $false
| ~ spl26_10
| ~ spl26_32 ),
inference(resolution,[],[f207,f109]) ).
fof(f207,plain,
( big_p(sK15)
| ~ spl26_32 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f205,plain,
( spl26_32
<=> big_p(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_32])]) ).
fof(f242,plain,
( ~ spl26_9
| ~ spl26_31 ),
inference(avatar_contradiction_clause,[],[f241]) ).
fof(f241,plain,
( $false
| ~ spl26_9
| ~ spl26_31 ),
inference(subsumption_resolution,[],[f202,f106]) ).
fof(f202,plain,
( big_q(sK13)
| ~ spl26_31 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f200,plain,
( spl26_31
<=> big_q(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_31])]) ).
fof(f238,plain,
( ~ spl26_17
| spl26_18 ),
inference(avatar_contradiction_clause,[],[f237]) ).
fof(f237,plain,
( $false
| ~ spl26_17
| spl26_18 ),
inference(subsumption_resolution,[],[f142,f137]) ).
fof(f142,plain,
( ~ big_p(sK14)
| spl26_18 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f140,plain,
( spl26_18
<=> big_p(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_18])]) ).
fof(f236,plain,
( ~ spl26_10
| ~ spl26_17 ),
inference(avatar_contradiction_clause,[],[f235]) ).
fof(f235,plain,
( $false
| ~ spl26_10
| ~ spl26_17 ),
inference(subsumption_resolution,[],[f137,f109]) ).
fof(f234,plain,
( ~ spl26_7
| ~ spl26_9 ),
inference(avatar_contradiction_clause,[],[f233]) ).
fof(f233,plain,
( $false
| ~ spl26_7
| ~ spl26_9 ),
inference(resolution,[],[f106,f98]) ).
fof(f98,plain,
( big_q(sK4)
| ~ spl26_7 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f96,plain,
( spl26_7
<=> big_q(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_7])]) ).
fof(f232,plain,
( ~ spl26_6
| ~ spl26_9 ),
inference(avatar_contradiction_clause,[],[f231]) ).
fof(f231,plain,
( $false
| ~ spl26_6
| ~ spl26_9 ),
inference(subsumption_resolution,[],[f106,f94]) ).
fof(f230,plain,
( spl26_4
| spl26_8 ),
inference(avatar_split_clause,[],[f71,f100,f85]) ).
fof(f85,plain,
( spl26_4
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl26_4])]) ).
fof(f100,plain,
( spl26_8
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl26_8])]) ).
fof(f71,plain,
( sP1
| sP0 ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
( ( ~ sP1
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,plain,
( sP0
<~> sP1 ),
inference(definition_folding,[],[f4,f6,f5]) ).
fof(f5,plain,
( sP0
<=> ( ? [X0] :
! [X1] :
( big_q(X1)
<=> big_q(X0) )
<=> ( ! [X3] : big_p(X3)
<=> ? [X2] : big_p(X2) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f6,plain,
( sP1
<=> ( ( ! [X7] : big_q(X7)
<=> ? [X6] : big_q(X6) )
<=> ? [X4] :
! [X5] :
( big_p(X4)
<=> big_p(X5) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f4,plain,
( ( ? [X0] :
! [X1] :
( big_q(X1)
<=> big_q(X0) )
<=> ( ! [X3] : big_p(X3)
<=> ? [X2] : big_p(X2) ) )
<~> ( ( ! [X7] : big_q(X7)
<=> ? [X6] : big_q(X6) )
<=> ? [X4] :
! [X5] :
( big_p(X4)
<=> big_p(X5) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,plain,
~ ( ( ( ! [X7] : big_q(X7)
<=> ? [X6] : big_q(X6) )
<=> ? [X4] :
! [X5] :
( big_p(X4)
<=> big_p(X5) ) )
<=> ( ? [X0] :
! [X1] :
( big_q(X1)
<=> big_q(X0) )
<=> ( ! [X3] : big_p(X3)
<=> ? [X2] : big_p(X2) ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,negated_conjecture,
~ ( ( ? [X4] :
! [X5] :
( big_q(X5)
<=> big_q(X4) )
<=> ( ? [X6] : big_p(X6)
<=> ! [X7] : big_p(X7) ) )
<=> ( ? [X0] :
! [X1] :
( big_p(X1)
<=> big_p(X0) )
<=> ( ? [X2] : big_q(X2)
<=> ! [X3] : big_q(X3) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
( ( ? [X4] :
! [X5] :
( big_q(X5)
<=> big_q(X4) )
<=> ( ? [X6] : big_p(X6)
<=> ! [X7] : big_p(X7) ) )
<=> ( ? [X0] :
! [X1] :
( big_p(X1)
<=> big_p(X0) )
<=> ( ? [X2] : big_q(X2)
<=> ! [X3] : big_q(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel34) ).
fof(f229,plain,
( spl26_10
| spl26_33
| spl26_4
| ~ spl26_18 ),
inference(avatar_split_clause,[],[f69,f140,f85,f209,f108]) ).
fof(f69,plain,
! [X0,X4] :
( ~ big_p(sK14)
| sP0
| big_q(X4)
| big_q(sK16(X4))
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
( ( sP0
| ( ( ( ( ! [X0] : ~ big_p(X0)
| ~ big_p(sK14) )
& ( big_p(sK15)
| ! [X3] : big_p(X3) ) )
| ! [X4] :
( ( ~ big_q(X4)
| ~ big_q(sK16(X4)) )
& ( big_q(X4)
| big_q(sK16(X4)) ) ) )
& ( ( ( ! [X6] : big_p(X6)
| ! [X7] : ~ big_p(X7) )
& ( big_p(sK17)
| ~ big_p(sK18) ) )
| ! [X11] :
( ( big_q(X11)
| ~ big_q(sK19) )
& ( big_q(sK19)
| ~ big_q(X11) ) ) ) ) )
& ( ( ( ! [X13] :
( ( big_q(X13)
| ~ big_q(sK20) )
& ( big_q(sK20)
| ~ big_q(X13) ) )
| ( ( ! [X14] : ~ big_p(X14)
| ~ big_p(sK21) )
& ( big_p(sK22)
| ! [X17] : big_p(X17) ) ) )
& ( ( ( ! [X18] : big_p(X18)
| ! [X19] : ~ big_p(X19) )
& ( big_p(sK23)
| ~ big_p(sK24) ) )
| ! [X22] :
( ( ~ big_q(X22)
| ~ big_q(sK25(X22)) )
& ( big_q(X22)
| big_q(sK25(X22)) ) ) ) )
| ~ sP0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17,sK18,sK19,sK20,sK21,sK22,sK23,sK24,sK25])],[f24,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25]) ).
fof(f25,plain,
( ? [X1] : ~ big_p(X1)
=> ~ big_p(sK14) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
( ? [X2] : big_p(X2)
=> big_p(sK15) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X4] :
( ? [X5] :
( ( ~ big_q(X4)
| ~ big_q(X5) )
& ( big_q(X4)
| big_q(X5) ) )
=> ( ( ~ big_q(X4)
| ~ big_q(sK16(X4)) )
& ( big_q(X4)
| big_q(sK16(X4)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
( ? [X8] : big_p(X8)
=> big_p(sK17) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
( ? [X9] : ~ big_p(X9)
=> ~ big_p(sK18) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
( ? [X10] :
! [X11] :
( ( big_q(X11)
| ~ big_q(X10) )
& ( big_q(X10)
| ~ big_q(X11) ) )
=> ! [X11] :
( ( big_q(X11)
| ~ big_q(sK19) )
& ( big_q(sK19)
| ~ big_q(X11) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
( ? [X12] :
! [X13] :
( ( big_q(X13)
| ~ big_q(X12) )
& ( big_q(X12)
| ~ big_q(X13) ) )
=> ! [X13] :
( ( big_q(X13)
| ~ big_q(sK20) )
& ( big_q(sK20)
| ~ big_q(X13) ) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
( ? [X15] : ~ big_p(X15)
=> ~ big_p(sK21) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
( ? [X16] : big_p(X16)
=> big_p(sK22) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
( ? [X20] : big_p(X20)
=> big_p(sK23) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
( ? [X21] : ~ big_p(X21)
=> ~ big_p(sK24) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
! [X22] :
( ? [X23] :
( ( ~ big_q(X22)
| ~ big_q(X23) )
& ( big_q(X22)
| big_q(X23) ) )
=> ( ( ~ big_q(X22)
| ~ big_q(sK25(X22)) )
& ( big_q(X22)
| big_q(sK25(X22)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
( ( sP0
| ( ( ( ( ! [X0] : ~ big_p(X0)
| ? [X1] : ~ big_p(X1) )
& ( ? [X2] : big_p(X2)
| ! [X3] : big_p(X3) ) )
| ! [X4] :
? [X5] :
( ( ~ big_q(X4)
| ~ big_q(X5) )
& ( big_q(X4)
| big_q(X5) ) ) )
& ( ( ( ! [X6] : big_p(X6)
| ! [X7] : ~ big_p(X7) )
& ( ? [X8] : big_p(X8)
| ? [X9] : ~ big_p(X9) ) )
| ? [X10] :
! [X11] :
( ( big_q(X11)
| ~ big_q(X10) )
& ( big_q(X10)
| ~ big_q(X11) ) ) ) ) )
& ( ( ( ? [X12] :
! [X13] :
( ( big_q(X13)
| ~ big_q(X12) )
& ( big_q(X12)
| ~ big_q(X13) ) )
| ( ( ! [X14] : ~ big_p(X14)
| ? [X15] : ~ big_p(X15) )
& ( ? [X16] : big_p(X16)
| ! [X17] : big_p(X17) ) ) )
& ( ( ( ! [X18] : big_p(X18)
| ! [X19] : ~ big_p(X19) )
& ( ? [X20] : big_p(X20)
| ? [X21] : ~ big_p(X21) ) )
| ! [X22] :
? [X23] :
( ( ~ big_q(X22)
| ~ big_q(X23) )
& ( big_q(X22)
| big_q(X23) ) ) ) )
| ~ sP0 ) ),
inference(rectify,[],[f23]) ).
fof(f23,plain,
( ( sP0
| ( ( ( ( ! [X2] : ~ big_p(X2)
| ? [X3] : ~ big_p(X3) )
& ( ? [X2] : big_p(X2)
| ! [X3] : big_p(X3) ) )
| ! [X0] :
? [X1] :
( ( ~ big_q(X0)
| ~ big_q(X1) )
& ( big_q(X0)
| big_q(X1) ) ) )
& ( ( ( ! [X3] : big_p(X3)
| ! [X2] : ~ big_p(X2) )
& ( ? [X2] : big_p(X2)
| ? [X3] : ~ big_p(X3) ) )
| ? [X0] :
! [X1] :
( ( big_q(X1)
| ~ big_q(X0) )
& ( big_q(X0)
| ~ big_q(X1) ) ) ) ) )
& ( ( ( ? [X0] :
! [X1] :
( ( big_q(X1)
| ~ big_q(X0) )
& ( big_q(X0)
| ~ big_q(X1) ) )
| ( ( ! [X2] : ~ big_p(X2)
| ? [X3] : ~ big_p(X3) )
& ( ? [X2] : big_p(X2)
| ! [X3] : big_p(X3) ) ) )
& ( ( ( ! [X3] : big_p(X3)
| ! [X2] : ~ big_p(X2) )
& ( ? [X2] : big_p(X2)
| ? [X3] : ~ big_p(X3) ) )
| ! [X0] :
? [X1] :
( ( ~ big_q(X0)
| ~ big_q(X1) )
& ( big_q(X0)
| big_q(X1) ) ) ) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f228,plain,
( spl26_9
| spl26_10
| spl26_6
| spl26_21
| spl26_8 ),
inference(avatar_split_clause,[],[f50,f100,f152,f93,f108,f105]) ).
fof(f152,plain,
( spl26_21
<=> big_p(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_21])]) ).
fof(f50,plain,
! [X8,X9,X7] :
( sP1
| big_p(sK5)
| big_q(X8)
| ~ big_p(X7)
| ~ big_q(X9) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
( ( sP1
| ( ( ! [X0] :
( ( ~ big_p(sK2(X0))
| ~ big_p(X0) )
& ( big_p(sK2(X0))
| big_p(X0) ) )
| ( ( ! [X2] : ~ big_q(X2)
| ~ big_q(sK3) )
& ( big_q(sK4)
| ! [X5] : big_q(X5) ) ) )
& ( ! [X7] :
( ( big_p(sK5)
| ~ big_p(X7) )
& ( big_p(X7)
| ~ big_p(sK5) ) )
| ( ( ! [X8] : big_q(X8)
| ! [X9] : ~ big_q(X9) )
& ( big_q(sK6)
| ~ big_q(sK7) ) ) ) ) )
& ( ( ( ( ( ! [X12] : big_q(X12)
| ! [X13] : ~ big_q(X13) )
& ( big_q(sK8)
| ~ big_q(sK9) ) )
| ! [X16] :
( ( ~ big_p(sK10(X16))
| ~ big_p(X16) )
& ( big_p(sK10(X16))
| big_p(X16) ) ) )
& ( ! [X19] :
( ( big_p(sK11)
| ~ big_p(X19) )
& ( big_p(X19)
| ~ big_p(sK11) ) )
| ( ( ! [X20] : ~ big_q(X20)
| ~ big_q(sK12) )
& ( big_q(sK13)
| ! [X23] : big_q(X23) ) ) ) )
| ~ sP1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13])],[f9,f21,f20,f19,f18,f17,f16,f15,f14,f13,f12,f11,f10]) ).
fof(f10,plain,
! [X0] :
( ? [X1] :
( ( ~ big_p(X1)
| ~ big_p(X0) )
& ( big_p(X1)
| big_p(X0) ) )
=> ( ( ~ big_p(sK2(X0))
| ~ big_p(X0) )
& ( big_p(sK2(X0))
| big_p(X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
( ? [X3] : ~ big_q(X3)
=> ~ big_q(sK3) ),
introduced(choice_axiom,[]) ).
fof(f12,plain,
( ? [X4] : big_q(X4)
=> big_q(sK4) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
( ? [X6] :
! [X7] :
( ( big_p(X6)
| ~ big_p(X7) )
& ( big_p(X7)
| ~ big_p(X6) ) )
=> ! [X7] :
( ( big_p(sK5)
| ~ big_p(X7) )
& ( big_p(X7)
| ~ big_p(sK5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
( ? [X10] : big_q(X10)
=> big_q(sK6) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
( ? [X11] : ~ big_q(X11)
=> ~ big_q(sK7) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
( ? [X14] : big_q(X14)
=> big_q(sK8) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
( ? [X15] : ~ big_q(X15)
=> ~ big_q(sK9) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X16] :
( ? [X17] :
( ( ~ big_p(X17)
| ~ big_p(X16) )
& ( big_p(X17)
| big_p(X16) ) )
=> ( ( ~ big_p(sK10(X16))
| ~ big_p(X16) )
& ( big_p(sK10(X16))
| big_p(X16) ) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
( ? [X18] :
! [X19] :
( ( big_p(X18)
| ~ big_p(X19) )
& ( big_p(X19)
| ~ big_p(X18) ) )
=> ! [X19] :
( ( big_p(sK11)
| ~ big_p(X19) )
& ( big_p(X19)
| ~ big_p(sK11) ) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
( ? [X21] : ~ big_q(X21)
=> ~ big_q(sK12) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
( ? [X22] : big_q(X22)
=> big_q(sK13) ),
introduced(choice_axiom,[]) ).
fof(f9,plain,
( ( sP1
| ( ( ! [X0] :
? [X1] :
( ( ~ big_p(X1)
| ~ big_p(X0) )
& ( big_p(X1)
| big_p(X0) ) )
| ( ( ! [X2] : ~ big_q(X2)
| ? [X3] : ~ big_q(X3) )
& ( ? [X4] : big_q(X4)
| ! [X5] : big_q(X5) ) ) )
& ( ? [X6] :
! [X7] :
( ( big_p(X6)
| ~ big_p(X7) )
& ( big_p(X7)
| ~ big_p(X6) ) )
| ( ( ! [X8] : big_q(X8)
| ! [X9] : ~ big_q(X9) )
& ( ? [X10] : big_q(X10)
| ? [X11] : ~ big_q(X11) ) ) ) ) )
& ( ( ( ( ( ! [X12] : big_q(X12)
| ! [X13] : ~ big_q(X13) )
& ( ? [X14] : big_q(X14)
| ? [X15] : ~ big_q(X15) ) )
| ! [X16] :
? [X17] :
( ( ~ big_p(X17)
| ~ big_p(X16) )
& ( big_p(X17)
| big_p(X16) ) ) )
& ( ? [X18] :
! [X19] :
( ( big_p(X18)
| ~ big_p(X19) )
& ( big_p(X19)
| ~ big_p(X18) ) )
| ( ( ! [X20] : ~ big_q(X20)
| ? [X21] : ~ big_q(X21) )
& ( ? [X22] : big_q(X22)
| ! [X23] : big_q(X23) ) ) ) )
| ~ sP1 ) ),
inference(rectify,[],[f8]) ).
fof(f8,plain,
( ( sP1
| ( ( ! [X4] :
? [X5] :
( ( ~ big_p(X5)
| ~ big_p(X4) )
& ( big_p(X5)
| big_p(X4) ) )
| ( ( ! [X6] : ~ big_q(X6)
| ? [X7] : ~ big_q(X7) )
& ( ? [X6] : big_q(X6)
| ! [X7] : big_q(X7) ) ) )
& ( ? [X4] :
! [X5] :
( ( big_p(X4)
| ~ big_p(X5) )
& ( big_p(X5)
| ~ big_p(X4) ) )
| ( ( ! [X7] : big_q(X7)
| ! [X6] : ~ big_q(X6) )
& ( ? [X6] : big_q(X6)
| ? [X7] : ~ big_q(X7) ) ) ) ) )
& ( ( ( ( ( ! [X7] : big_q(X7)
| ! [X6] : ~ big_q(X6) )
& ( ? [X6] : big_q(X6)
| ? [X7] : ~ big_q(X7) ) )
| ! [X4] :
? [X5] :
( ( ~ big_p(X5)
| ~ big_p(X4) )
& ( big_p(X5)
| big_p(X4) ) ) )
& ( ? [X4] :
! [X5] :
( ( big_p(X4)
| ~ big_p(X5) )
& ( big_p(X5)
| ~ big_p(X4) ) )
| ( ( ! [X6] : ~ big_q(X6)
| ? [X7] : ~ big_q(X7) )
& ( ? [X6] : big_q(X6)
| ! [X7] : big_q(X7) ) ) ) )
| ~ sP1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f227,plain,
( spl26_4
| spl26_17
| spl26_32
| spl26_19 ),
inference(avatar_split_clause,[],[f68,f144,f205,f136,f85]) ).
fof(f68,plain,
! [X3,X4] :
( ~ big_q(sK16(X4))
| ~ big_q(X4)
| big_p(sK15)
| big_p(X3)
| sP0 ),
inference(cnf_transformation,[],[f37]) ).
fof(f225,plain,
( ~ spl26_34
| spl26_9
| spl26_10
| ~ spl26_4
| spl26_29 ),
inference(avatar_split_clause,[],[f60,f191,f85,f108,f105,f221]) ).
fof(f60,plain,
! [X14,X13] :
( big_q(sK20)
| ~ sP0
| ~ big_p(X14)
| ~ big_q(X13)
| ~ big_p(sK21) ),
inference(cnf_transformation,[],[f37]) ).
fof(f224,plain,
( spl26_6
| ~ spl26_34
| ~ spl26_29
| spl26_10
| ~ spl26_4 ),
inference(avatar_split_clause,[],[f62,f85,f108,f191,f221,f93]) ).
fof(f62,plain,
! [X14,X13] :
( ~ sP0
| ~ big_p(X14)
| ~ big_q(sK20)
| ~ big_p(sK21)
| big_q(X13) ),
inference(cnf_transformation,[],[f37]) ).
fof(f219,plain,
( spl26_10
| ~ spl26_14
| spl26_17
| spl26_4
| spl26_6 ),
inference(avatar_split_clause,[],[f66,f93,f85,f136,f124,f108]) ).
fof(f124,plain,
( spl26_14
<=> big_q(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_14])]) ).
fof(f66,plain,
! [X11,X6,X7] :
( big_q(X11)
| sP0
| big_p(X6)
| ~ big_q(sK19)
| ~ big_p(X7) ),
inference(cnf_transformation,[],[f37]) ).
fof(f218,plain,
( spl26_10
| ~ spl26_4
| spl26_2
| spl26_17 ),
inference(avatar_split_clause,[],[f58,f136,f78,f85,f108]) ).
fof(f58,plain,
! [X18,X19,X22] :
( big_p(X18)
| ~ big_q(X22)
| ~ sP0
| ~ big_p(X19)
| ~ big_q(sK25(X22)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f217,plain,
( spl26_9
| spl26_29
| spl26_30
| spl26_17
| ~ spl26_4 ),
inference(avatar_split_clause,[],[f59,f85,f136,f195,f191,f105]) ).
fof(f59,plain,
! [X17,X13] :
( ~ sP0
| big_p(X17)
| big_p(sK22)
| big_q(sK20)
| ~ big_q(X13) ),
inference(cnf_transformation,[],[f37]) ).
fof(f215,plain,
( ~ spl26_8
| spl26_6
| spl26_26
| spl26_9 ),
inference(avatar_split_clause,[],[f45,f105,f175,f93,f100]) ).
fof(f45,plain,
! [X16,X12,X13] :
( ~ big_q(X13)
| big_p(sK10(X16))
| big_q(X12)
| big_p(X16)
| ~ sP1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f214,plain,
( spl26_17
| spl26_14
| spl26_10
| spl26_4
| spl26_9 ),
inference(avatar_split_clause,[],[f65,f105,f85,f108,f124,f136]) ).
fof(f65,plain,
! [X11,X6,X7] :
( ~ big_q(X11)
| sP0
| ~ big_p(X7)
| big_q(sK19)
| big_p(X6) ),
inference(cnf_transformation,[],[f37]) ).
fof(f213,plain,
( spl26_17
| ~ spl26_8
| spl26_31
| spl26_6
| ~ spl26_11 ),
inference(avatar_split_clause,[],[f39,f111,f93,f200,f100,f136]) ).
fof(f111,plain,
( spl26_11
<=> big_p(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_11])]) ).
fof(f39,plain,
! [X19,X23] :
( ~ big_p(sK11)
| big_q(X23)
| big_q(sK13)
| ~ sP1
| big_p(X19) ),
inference(cnf_transformation,[],[f22]) ).
fof(f212,plain,
( ~ spl26_25
| spl26_8
| spl26_9
| spl26_24 ),
inference(avatar_split_clause,[],[f54,f166,f105,f100,f170]) ).
fof(f54,plain,
! [X2,X0] :
( ~ big_p(sK2(X0))
| ~ big_q(X2)
| sP1
| ~ big_p(X0)
| ~ big_q(sK3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f211,plain,
( spl26_17
| spl26_32
| spl26_4
| spl26_33 ),
inference(avatar_split_clause,[],[f67,f209,f85,f205,f136]) ).
fof(f67,plain,
! [X3,X4] :
( big_q(sK16(X4))
| big_q(X4)
| sP0
| big_p(sK15)
| big_p(X3) ),
inference(cnf_transformation,[],[f37]) ).
fof(f203,plain,
( spl26_31
| spl26_10
| spl26_6
| ~ spl26_8
| spl26_11 ),
inference(avatar_split_clause,[],[f41,f111,f100,f93,f108,f200]) ).
fof(f41,plain,
! [X19,X23] :
( big_p(sK11)
| ~ sP1
| big_q(X23)
| ~ big_p(X19)
| big_q(sK13) ),
inference(cnf_transformation,[],[f22]) ).
fof(f198,plain,
( ~ spl26_4
| ~ spl26_29
| spl26_30
| spl26_6
| spl26_17 ),
inference(avatar_split_clause,[],[f61,f136,f93,f195,f191,f85]) ).
fof(f61,plain,
! [X17,X13] :
( big_p(X17)
| big_q(X13)
| big_p(sK22)
| ~ big_q(sK20)
| ~ sP0 ),
inference(cnf_transformation,[],[f37]) ).
fof(f188,plain,
( ~ spl26_4
| ~ spl26_8 ),
inference(avatar_split_clause,[],[f72,f100,f85]) ).
fof(f72,plain,
( ~ sP1
| ~ sP0 ),
inference(cnf_transformation,[],[f38]) ).
fof(f186,plain,
( ~ spl26_12
| ~ spl26_8
| spl26_17
| ~ spl26_11
| spl26_9 ),
inference(avatar_split_clause,[],[f40,f105,f111,f136,f100,f115]) ).
fof(f40,plain,
! [X19,X20] :
( ~ big_q(X20)
| ~ big_p(sK11)
| big_p(X19)
| ~ sP1
| ~ big_q(sK12) ),
inference(cnf_transformation,[],[f22]) ).
fof(f173,plain,
( spl26_9
| spl26_8
| spl26_5
| ~ spl26_25 ),
inference(avatar_split_clause,[],[f52,f170,f90,f100,f105]) ).
fof(f52,plain,
! [X2,X0] :
( ~ big_q(sK3)
| big_p(X0)
| sP1
| ~ big_q(X2)
| big_p(sK2(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f168,plain,
( spl26_6
| spl26_7
| spl26_8
| spl26_24 ),
inference(avatar_split_clause,[],[f53,f166,f100,f96,f93]) ).
fof(f53,plain,
! [X0,X5] :
( ~ big_p(sK2(X0))
| ~ big_p(X0)
| sP1
| big_q(sK4)
| big_q(X5) ),
inference(cnf_transformation,[],[f22]) ).
fof(f164,plain,
( spl26_6
| spl26_9
| spl26_8
| spl26_17
| ~ spl26_21 ),
inference(avatar_split_clause,[],[f48,f152,f136,f100,f105,f93]) ).
fof(f48,plain,
! [X8,X9,X7] :
( ~ big_p(sK5)
| big_p(X7)
| sP1
| ~ big_q(X9)
| big_q(X8) ),
inference(cnf_transformation,[],[f22]) ).
fof(f163,plain,
( ~ spl26_8
| spl26_6
| spl26_23
| spl26_9 ),
inference(avatar_split_clause,[],[f46,f105,f161,f93,f100]) ).
fof(f46,plain,
! [X16,X12,X13] :
( ~ big_q(X13)
| ~ big_p(sK10(X16))
| ~ big_p(X16)
| big_q(X12)
| ~ sP1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f146,plain,
( ~ spl26_18
| spl26_4
| spl26_19
| spl26_10 ),
inference(avatar_split_clause,[],[f70,f108,f144,f85,f140]) ).
fof(f70,plain,
! [X0,X4] :
( ~ big_p(X0)
| ~ big_q(X4)
| ~ big_q(sK16(X4))
| sP0
| ~ big_p(sK14) ),
inference(cnf_transformation,[],[f37]) ).
fof(f138,plain,
( spl26_10
| ~ spl26_4
| spl26_16
| spl26_17 ),
inference(avatar_split_clause,[],[f57,f136,f133,f85,f108]) ).
fof(f57,plain,
! [X18,X19,X22] :
( big_p(X18)
| big_q(sK25(X22))
| ~ sP0
| big_q(X22)
| ~ big_p(X19) ),
inference(cnf_transformation,[],[f37]) ).
fof(f118,plain,
( spl26_9
| spl26_10
| spl26_11
| ~ spl26_8
| ~ spl26_12 ),
inference(avatar_split_clause,[],[f42,f115,f100,f111,f108,f105]) ).
fof(f42,plain,
! [X19,X20] :
( ~ big_q(sK12)
| ~ sP1
| big_p(sK11)
| ~ big_p(X19)
| ~ big_q(X20) ),
inference(cnf_transformation,[],[f22]) ).
fof(f103,plain,
( spl26_5
| spl26_6
| spl26_7
| spl26_8 ),
inference(avatar_split_clause,[],[f51,f100,f96,f93,f90]) ).
fof(f51,plain,
! [X0,X5] :
( sP1
| big_q(sK4)
| big_q(X5)
| big_p(sK2(X0))
| big_p(X0) ),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN036+1 : TPTP v8.1.0. Released v2.0.0.
% 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 : n003.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 21:22:37 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.22/0.46 % (30023)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 (3000ds/75Mi)
% 0.22/0.47 % (30031)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 (3000ds/467Mi)
% 0.22/0.47 % (30031)First to succeed.
% 0.22/0.49 % (30031)Refutation found. Thanks to Tanya!
% 0.22/0.49 % SZS status Theorem for theBenchmark
% 0.22/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.49 % (30031)------------------------------
% 0.22/0.49 % (30031)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.49 % (30031)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.49 % (30031)Termination reason: Refutation
% 0.22/0.49
% 0.22/0.49 % (30031)Memory used [KB]: 5628
% 0.22/0.49 % (30031)Time elapsed: 0.067 s
% 0.22/0.49 % (30031)Instructions burned: 5 (million)
% 0.22/0.49 % (30031)------------------------------
% 0.22/0.49 % (30031)------------------------------
% 0.22/0.49 % (30007)Success in time 0.126 s
%------------------------------------------------------------------------------