TSTP Solution File: SYN917+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYN917+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n029.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 : Sun May 5 12:18:23 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 122
% Syntax : Number of formulae : 466 ( 1 unt; 0 def)
% Number of atoms : 2191 ( 0 equ)
% Maximal formula atoms : 94 ( 4 avg)
% Number of connectives : 2661 ( 936 ~;1054 |; 404 &)
% ( 100 <=>; 137 =>; 0 <=; 30 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 100 ( 99 usr; 93 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 29 con; 0-1 aty)
% Number of variables : 674 ( 436 !; 238 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f704,plain,
$false,
inference(avatar_sat_refutation,[],[f236,f240,f249,f250,f259,f260,f274,f275,f283,f288,f293,f302,f307,f311,f316,f317,f321,f330,f341,f342,f355,f358,f359,f364,f367,f376,f381,f384,f393,f398,f399,f410,f415,f426,f427,f432,f435,f452,f473,f474,f477,f485,f489,f496,f501,f510,f515,f519,f523,f528,f529,f530,f535,f544,f549,f554,f559,f564,f572,f577,f578,f579,f581,f583,f585,f587,f589,f591,f593,f603,f606,f608,f610,f623,f625,f627,f629,f631,f633,f637,f639,f641,f646,f647,f653,f655,f667,f669,f671,f673,f675,f677,f687,f689,f697,f699,f701,f703]) ).
fof(f703,plain,
( ~ spl52_2
| ~ spl52_32 ),
inference(avatar_contradiction_clause,[],[f702]) ).
fof(f702,plain,
( $false
| ~ spl52_2
| ~ spl52_32 ),
inference(subsumption_resolution,[],[f388,f235]) ).
fof(f235,plain,
( ! [X0] : ~ p(X0)
| ~ spl52_2 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f234,plain,
( spl52_2
<=> ! [X0] : ~ p(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_2])]) ).
fof(f388,plain,
( p(sK36)
| ~ spl52_32 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f386,plain,
( spl52_32
<=> p(sK36) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_32])]) ).
fof(f701,plain,
( ~ spl52_2
| ~ spl52_33 ),
inference(avatar_contradiction_clause,[],[f700]) ).
fof(f700,plain,
( $false
| ~ spl52_2
| ~ spl52_33 ),
inference(subsumption_resolution,[],[f392,f235]) ).
fof(f392,plain,
( p(sK35)
| ~ spl52_33 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f390,plain,
( spl52_33
<=> p(sK35) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_33])]) ).
fof(f699,plain,
( ~ spl52_2
| ~ spl52_36 ),
inference(avatar_contradiction_clause,[],[f698]) ).
fof(f698,plain,
( $false
| ~ spl52_2
| ~ spl52_36 ),
inference(subsumption_resolution,[],[f408,f235]) ).
fof(f408,plain,
( p(sK37)
| ~ spl52_36 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f406,plain,
( spl52_36
<=> p(sK37) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_36])]) ).
fof(f697,plain,
( ~ spl52_2
| ~ spl52_35 ),
inference(avatar_contradiction_clause,[],[f696]) ).
fof(f696,plain,
( $false
| ~ spl52_2
| ~ spl52_35 ),
inference(subsumption_resolution,[],[f403,f235]) ).
fof(f403,plain,
( p(sK38)
| ~ spl52_35 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f401,plain,
( spl52_35
<=> p(sK38) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_35])]) ).
fof(f689,plain,
( ~ spl52_3
| spl52_26 ),
inference(avatar_contradiction_clause,[],[f688]) ).
fof(f688,plain,
( $false
| ~ spl52_3
| spl52_26 ),
inference(subsumption_resolution,[],[f350,f239]) ).
fof(f239,plain,
( ! [X1] : p(X1)
| ~ spl52_3 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f238,plain,
( spl52_3
<=> ! [X1] : p(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_3])]) ).
fof(f350,plain,
( ~ p(sK32)
| spl52_26 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f348,plain,
( spl52_26
<=> p(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_26])]) ).
fof(f687,plain,
( ~ spl52_3
| spl52_27 ),
inference(avatar_contradiction_clause,[],[f686]) ).
fof(f686,plain,
( $false
| ~ spl52_3
| spl52_27 ),
inference(subsumption_resolution,[],[f354,f239]) ).
fof(f354,plain,
( ~ p(sK31)
| spl52_27 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f352,plain,
( spl52_27
<=> p(sK31) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_27])]) ).
fof(f677,plain,
( ~ spl52_2
| ~ spl52_24 ),
inference(avatar_contradiction_clause,[],[f676]) ).
fof(f676,plain,
( $false
| ~ spl52_2
| ~ spl52_24 ),
inference(subsumption_resolution,[],[f339,f235]) ).
fof(f339,plain,
( p(sK29)
| ~ spl52_24 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f337,plain,
( spl52_24
<=> p(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_24])]) ).
fof(f675,plain,
( ~ spl52_2
| ~ spl52_23 ),
inference(avatar_contradiction_clause,[],[f674]) ).
fof(f674,plain,
( $false
| ~ spl52_2
| ~ spl52_23 ),
inference(subsumption_resolution,[],[f334,f235]) ).
fof(f334,plain,
( p(sK30)
| ~ spl52_23 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f332,plain,
( spl52_23
<=> p(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_23])]) ).
fof(f673,plain,
( ~ spl52_2
| ~ spl52_43 ),
inference(avatar_contradiction_clause,[],[f672]) ).
fof(f672,plain,
( $false
| ~ spl52_2
| ~ spl52_43 ),
inference(subsumption_resolution,[],[f447,f235]) ).
fof(f447,plain,
( p(sK42)
| ~ spl52_43 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f445,plain,
( spl52_43
<=> p(sK42) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_43])]) ).
fof(f671,plain,
( ~ spl52_12
| ~ spl52_44 ),
inference(avatar_contradiction_clause,[],[f670]) ).
fof(f670,plain,
( $false
| ~ spl52_12
| ~ spl52_44 ),
inference(subsumption_resolution,[],[f451,f282]) ).
fof(f282,plain,
( ! [X0] : ~ q(X0)
| ~ spl52_12 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f281,plain,
( spl52_12
<=> ! [X0] : ~ q(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_12])]) ).
fof(f451,plain,
( q(sK41)
| ~ spl52_44 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f449,plain,
( spl52_44
<=> q(sK41) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_44])]) ).
fof(f669,plain,
( ~ spl52_2
| ~ spl52_41 ),
inference(avatar_contradiction_clause,[],[f668]) ).
fof(f668,plain,
( $false
| ~ spl52_2
| ~ spl52_41 ),
inference(subsumption_resolution,[],[f439,f235]) ).
fof(f439,plain,
( p(sK43)
| ~ spl52_41 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f437,plain,
( spl52_41
<=> p(sK43) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_41])]) ).
fof(f667,plain,
( ~ spl52_12
| ~ spl52_42 ),
inference(avatar_contradiction_clause,[],[f666]) ).
fof(f666,plain,
( $false
| ~ spl52_12
| ~ spl52_42 ),
inference(subsumption_resolution,[],[f443,f282]) ).
fof(f443,plain,
( q(sK43)
| ~ spl52_42 ),
inference(avatar_component_clause,[],[f441]) ).
fof(f441,plain,
( spl52_42
<=> q(sK43) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_42])]) ).
fof(f655,plain,
( ~ spl52_2
| ~ spl52_14 ),
inference(avatar_contradiction_clause,[],[f654]) ).
fof(f654,plain,
( $false
| ~ spl52_2
| ~ spl52_14 ),
inference(subsumption_resolution,[],[f292,f235]) ).
fof(f292,plain,
( p(sK26)
| ~ spl52_14 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f290,plain,
( spl52_14
<=> p(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_14])]) ).
fof(f653,plain,
( ~ spl52_2
| ~ spl52_10 ),
inference(avatar_contradiction_clause,[],[f652]) ).
fof(f652,plain,
( $false
| ~ spl52_2
| ~ spl52_10 ),
inference(subsumption_resolution,[],[f273,f235]) ).
fof(f273,plain,
( p(sK25)
| ~ spl52_10 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f271,plain,
( spl52_10
<=> p(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_10])]) ).
fof(f647,plain,
( ~ spl52_65
| ~ spl52_53
| spl52_64 ),
inference(avatar_split_clause,[],[f642,f541,f491,f546]) ).
fof(f546,plain,
( spl52_65
<=> f(sK49) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_65])]) ).
fof(f491,plain,
( spl52_53
<=> ! [X3] :
( g(X3)
| ~ f(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_53])]) ).
fof(f541,plain,
( spl52_64
<=> g(sK49) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_64])]) ).
fof(f642,plain,
( ~ f(sK49)
| ~ spl52_53
| spl52_64 ),
inference(resolution,[],[f492,f543]) ).
fof(f543,plain,
( ~ g(sK49)
| spl52_64 ),
inference(avatar_component_clause,[],[f541]) ).
fof(f492,plain,
( ! [X3] :
( g(X3)
| ~ f(X3) )
| ~ spl52_53 ),
inference(avatar_component_clause,[],[f491]) ).
fof(f646,plain,
( spl52_18
| ~ spl52_3
| ~ spl52_20 ),
inference(avatar_split_clause,[],[f645,f319,f238,f309]) ).
fof(f309,plain,
( spl52_18
<=> ! [X1] : q(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_18])]) ).
fof(f319,plain,
( spl52_20
<=> ! [X0] :
( q(X0)
| ~ p(sK28(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_20])]) ).
fof(f645,plain,
( ! [X0] : q(X0)
| ~ spl52_3
| ~ spl52_20 ),
inference(subsumption_resolution,[],[f320,f239]) ).
fof(f320,plain,
( ! [X0] :
( q(X0)
| ~ p(sK28(X0)) )
| ~ spl52_20 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f641,plain,
( ~ spl52_67
| ~ spl52_68
| ~ spl52_51
| spl52_66 ),
inference(avatar_split_clause,[],[f640,f551,f483,f561,f556]) ).
fof(f556,plain,
( spl52_67
<=> g(sK50) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_67])]) ).
fof(f561,plain,
( spl52_68
<=> f(sK50) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_68])]) ).
fof(f483,plain,
( spl52_51
<=> ! [X0] :
( h(X0)
| ~ f(X0)
| ~ g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_51])]) ).
fof(f551,plain,
( spl52_66
<=> h(sK50) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_66])]) ).
fof(f640,plain,
( ~ f(sK50)
| ~ g(sK50)
| ~ spl52_51
| spl52_66 ),
inference(resolution,[],[f553,f484]) ).
fof(f484,plain,
( ! [X0] :
( h(X0)
| ~ f(X0)
| ~ g(X0) )
| ~ spl52_51 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f553,plain,
( ~ h(sK50)
| spl52_66 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f639,plain,
( ~ spl52_3
| spl52_30 ),
inference(avatar_contradiction_clause,[],[f638]) ).
fof(f638,plain,
( $false
| ~ spl52_3
| spl52_30 ),
inference(subsumption_resolution,[],[f375,f239]) ).
fof(f375,plain,
( ~ p(sK33)
| spl52_30 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f373,plain,
( spl52_30
<=> p(sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_30])]) ).
fof(f637,plain,
( ~ spl52_12
| ~ spl52_18 ),
inference(avatar_contradiction_clause,[],[f636]) ).
fof(f636,plain,
( $false
| ~ spl52_12
| ~ spl52_18 ),
inference(subsumption_resolution,[],[f282,f310]) ).
fof(f310,plain,
( ! [X1] : q(X1)
| ~ spl52_18 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f633,plain,
( ~ spl52_18
| spl52_47 ),
inference(avatar_contradiction_clause,[],[f632]) ).
fof(f632,plain,
( $false
| ~ spl52_18
| spl52_47 ),
inference(subsumption_resolution,[],[f464,f310]) ).
fof(f464,plain,
( ~ q(sK46)
| spl52_47 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f462,plain,
( spl52_47
<=> q(sK46) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_47])]) ).
fof(f631,plain,
( ~ spl52_3
| spl52_48 ),
inference(avatar_contradiction_clause,[],[f630]) ).
fof(f630,plain,
( $false
| ~ spl52_3
| spl52_48 ),
inference(subsumption_resolution,[],[f468,f239]) ).
fof(f468,plain,
( ~ p(sK45)
| spl52_48 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f466,plain,
( spl52_48
<=> p(sK45) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_48])]) ).
fof(f629,plain,
( ~ spl52_3
| spl52_46 ),
inference(avatar_contradiction_clause,[],[f628]) ).
fof(f628,plain,
( $false
| ~ spl52_3
| spl52_46 ),
inference(subsumption_resolution,[],[f460,f239]) ).
fof(f460,plain,
( ~ p(sK46)
| spl52_46 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f458,plain,
( spl52_46
<=> p(sK46) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_46])]) ).
fof(f627,plain,
( ~ spl52_18
| spl52_49 ),
inference(avatar_contradiction_clause,[],[f626]) ).
fof(f626,plain,
( $false
| ~ spl52_18
| spl52_49 ),
inference(subsumption_resolution,[],[f472,f310]) ).
fof(f472,plain,
( ~ q(sK44)
| spl52_49 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f470,plain,
( spl52_49
<=> q(sK44) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_49])]) ).
fof(f625,plain,
( spl52_16
| ~ spl52_18 ),
inference(avatar_contradiction_clause,[],[f624]) ).
fof(f624,plain,
( $false
| spl52_16
| ~ spl52_18 ),
inference(resolution,[],[f310,f301]) ).
fof(f301,plain,
( ~ q(sK27)
| spl52_16 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f299,plain,
( spl52_16
<=> q(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_16])]) ).
fof(f623,plain,
( spl52_57
| ~ spl52_58
| ~ spl52_59
| ~ spl52_60 ),
inference(avatar_contradiction_clause,[],[f622]) ).
fof(f622,plain,
( $false
| spl52_57
| ~ spl52_58
| ~ spl52_59
| ~ spl52_60 ),
inference(subsumption_resolution,[],[f620,f509]) ).
fof(f509,plain,
( ~ r(sK47,sK47)
| spl52_57 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f507,plain,
( spl52_57
<=> r(sK47,sK47) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_57])]) ).
fof(f620,plain,
( r(sK47,sK47)
| ~ spl52_58
| ~ spl52_59
| ~ spl52_60 ),
inference(resolution,[],[f615,f514]) ).
fof(f514,plain,
( r(sK47,sK48)
| ~ spl52_58 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f512,plain,
( spl52_58
<=> r(sK47,sK48) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_58])]) ).
fof(f615,plain,
( ! [X0] :
( ~ r(X0,sK48)
| r(X0,sK47) )
| ~ spl52_58
| ~ spl52_59
| ~ spl52_60 ),
inference(resolution,[],[f613,f518]) ).
fof(f518,plain,
( ! [X2,X3,X4] :
( ~ r(X3,X4)
| ~ r(X2,X3)
| r(X2,X4) )
| ~ spl52_59 ),
inference(avatar_component_clause,[],[f517]) ).
fof(f517,plain,
( spl52_59
<=> ! [X4,X2,X3] :
( r(X2,X4)
| ~ r(X2,X3)
| ~ r(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_59])]) ).
fof(f613,plain,
( r(sK48,sK47)
| ~ spl52_58
| ~ spl52_60 ),
inference(resolution,[],[f522,f514]) ).
fof(f522,plain,
( ! [X6,X5] :
( ~ r(X5,X6)
| r(X6,X5) )
| ~ spl52_60 ),
inference(avatar_component_clause,[],[f521]) ).
fof(f521,plain,
( spl52_60
<=> ! [X6,X5] :
( r(X6,X5)
| ~ r(X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_60])]) ).
fof(f610,plain,
( ~ spl52_3
| spl52_17 ),
inference(avatar_contradiction_clause,[],[f609]) ).
fof(f609,plain,
( $false
| ~ spl52_3
| spl52_17 ),
inference(subsumption_resolution,[],[f306,f239]) ).
fof(f306,plain,
( ~ p(sK27)
| spl52_17 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f304,plain,
( spl52_17
<=> p(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_17])]) ).
fof(f608,plain,
( spl52_53
| ~ spl52_52
| ~ spl52_54 ),
inference(avatar_split_clause,[],[f607,f494,f487,f491]) ).
fof(f487,plain,
( spl52_52
<=> ! [X1] :
( g(X1)
| ~ f(X1)
| ~ h(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_52])]) ).
fof(f494,plain,
( spl52_54
<=> ! [X2] :
( h(X2)
| ~ f(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_54])]) ).
fof(f607,plain,
( ! [X1] :
( g(X1)
| ~ f(X1) )
| ~ spl52_52
| ~ spl52_54 ),
inference(subsumption_resolution,[],[f488,f495]) ).
fof(f495,plain,
( ! [X2] :
( h(X2)
| ~ f(X2) )
| ~ spl52_54 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f488,plain,
( ! [X1] :
( ~ h(X1)
| ~ f(X1)
| g(X1) )
| ~ spl52_52 ),
inference(avatar_component_clause,[],[f487]) ).
fof(f606,plain,
( ~ spl52_53
| spl52_70
| ~ spl52_71 ),
inference(avatar_contradiction_clause,[],[f605]) ).
fof(f605,plain,
( $false
| ~ spl52_53
| spl52_70
| ~ spl52_71 ),
inference(subsumption_resolution,[],[f604,f576]) ).
fof(f576,plain,
( f(sK51)
| ~ spl52_71 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f574,plain,
( spl52_71
<=> f(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_71])]) ).
fof(f604,plain,
( ~ f(sK51)
| ~ spl52_53
| spl52_70 ),
inference(resolution,[],[f492,f571]) ).
fof(f571,plain,
( ~ g(sK51)
| spl52_70 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f569,plain,
( spl52_70
<=> g(sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_70])]) ).
fof(f603,plain,
( ~ spl52_51
| ~ spl52_69 ),
inference(avatar_contradiction_clause,[],[f602]) ).
fof(f602,plain,
( $false
| ~ spl52_51
| ~ spl52_69 ),
inference(subsumption_resolution,[],[f601,f595]) ).
fof(f595,plain,
( ! [X0] : g(X0)
| ~ spl52_69 ),
inference(subsumption_resolution,[],[f207,f567]) ).
fof(f567,plain,
( ! [X0] : sP0(X0)
| ~ spl52_69 ),
inference(avatar_component_clause,[],[f566]) ).
fof(f566,plain,
( spl52_69
<=> ! [X0] : sP0(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_69])]) ).
fof(f207,plain,
! [X0] :
( ~ sP0(X0)
| g(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ( ~ h(X0)
& g(X0)
& f(X0) )
| ~ sP0(X0) ),
inference(rectify,[],[f126]) ).
fof(f126,plain,
! [X52] :
( ( ~ h(X52)
& g(X52)
& f(X52) )
| ~ sP0(X52) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,plain,
! [X52] :
( ( ~ h(X52)
& g(X52)
& f(X52) )
| ~ sP0(X52) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f601,plain,
( ! [X0] : ~ g(X0)
| ~ spl52_51
| ~ spl52_69 ),
inference(subsumption_resolution,[],[f600,f594]) ).
fof(f594,plain,
( ! [X0] : f(X0)
| ~ spl52_69 ),
inference(subsumption_resolution,[],[f206,f567]) ).
fof(f206,plain,
! [X0] :
( ~ sP0(X0)
| f(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f600,plain,
( ! [X0] :
( ~ f(X0)
| ~ g(X0) )
| ~ spl52_51
| ~ spl52_69 ),
inference(subsumption_resolution,[],[f484,f596]) ).
fof(f596,plain,
( ! [X0] : ~ h(X0)
| ~ spl52_69 ),
inference(subsumption_resolution,[],[f208,f567]) ).
fof(f208,plain,
! [X0] :
( ~ sP0(X0)
| ~ h(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f593,plain,
( ~ spl52_3
| spl52_38 ),
inference(avatar_contradiction_clause,[],[f592]) ).
fof(f592,plain,
( $false
| ~ spl52_3
| spl52_38 ),
inference(subsumption_resolution,[],[f419,f239]) ).
fof(f419,plain,
( ~ p(sK40)
| spl52_38 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f417,plain,
( spl52_38
<=> p(sK40) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_38])]) ).
fof(f591,plain,
( ~ spl52_3
| spl52_39 ),
inference(avatar_contradiction_clause,[],[f590]) ).
fof(f590,plain,
( $false
| ~ spl52_3
| spl52_39 ),
inference(subsumption_resolution,[],[f424,f239]) ).
fof(f424,plain,
( ~ p(sK39)
| spl52_39 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f422,plain,
( spl52_39
<=> p(sK39) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_39])]) ).
fof(f589,plain,
( ~ spl52_3
| spl52_29 ),
inference(avatar_contradiction_clause,[],[f588]) ).
fof(f588,plain,
( $false
| ~ spl52_3
| spl52_29 ),
inference(subsumption_resolution,[],[f371,f239]) ).
fof(f371,plain,
( ~ p(sK34)
| spl52_29 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f369,plain,
( spl52_29
<=> p(sK34) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_29])]) ).
fof(f587,plain,
( ~ spl52_12
| ~ spl52_13 ),
inference(avatar_contradiction_clause,[],[f586]) ).
fof(f586,plain,
( $false
| ~ spl52_12
| ~ spl52_13 ),
inference(subsumption_resolution,[],[f287,f282]) ).
fof(f287,plain,
( q(sK26)
| ~ spl52_13 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f285,plain,
( spl52_13
<=> q(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_13])]) ).
fof(f585,plain,
( ~ spl52_3
| spl52_7 ),
inference(avatar_contradiction_clause,[],[f584]) ).
fof(f584,plain,
( $false
| ~ spl52_3
| spl52_7 ),
inference(subsumption_resolution,[],[f258,f239]) ).
fof(f258,plain,
( ~ p(sK23)
| spl52_7 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f256,plain,
( spl52_7
<=> p(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_7])]) ).
fof(f583,plain,
( ~ spl52_2
| ~ spl52_3 ),
inference(avatar_contradiction_clause,[],[f582]) ).
fof(f582,plain,
( $false
| ~ spl52_2
| ~ spl52_3 ),
inference(subsumption_resolution,[],[f235,f239]) ).
fof(f581,plain,
( ~ spl52_3
| spl52_5 ),
inference(avatar_contradiction_clause,[],[f580]) ).
fof(f580,plain,
( $false
| ~ spl52_3
| spl52_5 ),
inference(subsumption_resolution,[],[f248,f239]) ).
fof(f248,plain,
( ~ p(sK22)
| spl52_5 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f246,plain,
( spl52_5
<=> p(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_5])]) ).
fof(f579,plain,
( spl52_61
| spl52_56
| spl52_50
| spl52_19
| spl52_45
| spl52_15
| spl52_40
| spl52_6
| spl52_11
| spl52_4
| spl52_1
| spl52_8
| spl52_37
| spl52_34
| spl52_22
| spl52_31
| spl52_28
| spl52_25
| spl52_21 ),
inference(avatar_split_clause,[],[f213,f323,f344,f361,f378,f327,f395,f412,f262,f230,f242,f277,f252,f429,f295,f454,f313,f479,f503,f525]) ).
fof(f525,plain,
( spl52_61
<=> sP4 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_61])]) ).
fof(f503,plain,
( spl52_56
<=> sP5 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_56])]) ).
fof(f479,plain,
( spl52_50
<=> sP6 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_50])]) ).
fof(f313,plain,
( spl52_19
<=> sP15 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_19])]) ).
fof(f454,plain,
( spl52_45
<=> sP7 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_45])]) ).
fof(f295,plain,
( spl52_15
<=> sP16 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_15])]) ).
fof(f429,plain,
( spl52_40
<=> sP8 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_40])]) ).
fof(f252,plain,
( spl52_6
<=> sP19 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_6])]) ).
fof(f277,plain,
( spl52_11
<=> sP17 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_11])]) ).
fof(f242,plain,
( spl52_4
<=> sP20 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_4])]) ).
fof(f230,plain,
( spl52_1
<=> sP21 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_1])]) ).
fof(f262,plain,
( spl52_8
<=> sP18 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_8])]) ).
fof(f412,plain,
( spl52_37
<=> sP9 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_37])]) ).
fof(f395,plain,
( spl52_34
<=> sP10 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_34])]) ).
fof(f327,plain,
( spl52_22
<=> c ),
introduced(avatar_definition,[new_symbols(naming,[spl52_22])]) ).
fof(f378,plain,
( spl52_31
<=> sP11 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_31])]) ).
fof(f361,plain,
( spl52_28
<=> sP12 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_28])]) ).
fof(f344,plain,
( spl52_25
<=> sP13 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_25])]) ).
fof(f323,plain,
( spl52_21
<=> sP14 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_21])]) ).
fof(f213,plain,
( sP14
| sP13
| sP12
| sP11
| c
| sP10
| sP9
| sP18
| sP21
| sP20
| sP17
| sP19
| sP8
| sP16
| sP7
| sP15
| sP6
| sP5
| sP4 ),
inference(duplicate_literal_removal,[],[f209]) ).
fof(f209,plain,
( sP14
| sP13
| sP12
| sP11
| c
| c
| c
| c
| sP10
| sP9
| sP18
| sP21
| sP20
| sP17
| sP19
| sP8
| sP16
| sP7
| sP15
| sP6
| sP5
| sP4 ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
( sP14
| sP13
| sP12
| sP11
| ( ( ~ c
| ~ c )
& ( c
| c ) )
| ( ( ~ c
| ~ c )
& ( c
| c ) )
| sP10
| sP9
| sP18
| sP21
| sP20
| sP17
| sP19
| sP8
| sP16
| sP7
| sP15
| sP6
| sP5
| sP4 ),
inference(nnf_transformation,[],[f28]) ).
fof(f28,plain,
( sP14
| sP13
| sP12
| sP11
| ( c
<~> c )
| ( c
<~> c )
| sP10
| sP9
| sP18
| sP21
| sP20
| sP17
| sP19
| sP8
| sP16
| sP7
| sP15
| sP6
| sP5
| sP4 ),
inference(definition_folding,[],[f5,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13,f12,f11,f10,f9,f8,f7,f6]) ).
fof(f7,plain,
( ! [X52] :
( ? [X53] :
( ~ g(X53)
& f(X53) )
| sP0(X52) )
| ~ sP1 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f8,plain,
( ? [X39] :
( ~ h(X39)
& g(X39)
& f(X39) )
| ~ sP2 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f9,plain,
( ? [X40] :
( ~ g(X40)
& f(X40) )
| sP2
| ~ sP3 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f10,plain,
( ( ! [X55] :
( h(X55)
| ~ g(X55)
| ~ f(X55) )
& ! [X54] :
( g(X54)
| ~ h(X54)
| ~ f(X54) )
& ( ! [X50] :
( h(X50)
| ~ f(X50) )
| ! [X51] :
( g(X51)
| ~ f(X51) ) )
& sP1 )
| ~ sP4 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f11,plain,
( ( ? [X48,X49] :
( ~ r(X48,X48)
& r(X48,X49) )
& ! [X43,X44,X45] :
( r(X43,X45)
| ~ r(X44,X45)
| ~ r(X43,X44) )
& ! [X46,X47] :
( r(X47,X46)
| ~ r(X46,X47) ) )
| ~ sP5 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f12,plain,
( ( ! [X42] :
( h(X42)
| ~ g(X42)
| ~ f(X42) )
& ! [X41] :
( g(X41)
| ~ h(X41)
| ~ f(X41) )
& ( ! [X37] :
( h(X37)
| ~ f(X37) )
| ! [X38] :
( g(X38)
| ~ f(X38) ) )
& sP3 )
| ~ sP6 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f13,plain,
( ( ! [X32] :
( q(X32)
& p(X32) )
<~> ( ! [X33] : q(X33)
& ! [X34] : p(X34) ) )
| ~ sP7 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f14,plain,
( ( ? [X26] :
( q(X26)
| p(X26) )
<~> ( ? [X27] : q(X27)
| ? [X28] : p(X28) ) )
| ~ sP8 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f15,plain,
( ( ! [X12] :
( c
| p(X12) )
<~> ( c
| ! [X13] : p(X13) ) )
| ~ sP9 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f16,plain,
( ( ? [X10] :
( c
& p(X10) )
<~> ( c
& ? [X11] : p(X11) ) )
| ~ sP10 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f17,plain,
( ( ? [X6] :
( p(X6)
| ~ c )
<~> ( ? [X7] : p(X7)
| ~ c ) )
| ~ sP11 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f18,plain,
( ( ? [X4] :
( c
| ~ p(X4) )
<~> ( c
| ? [X5] : ~ p(X5) ) )
| ~ sP12 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f19,plain,
( ( ! [X2] :
( p(X2)
| ~ c )
<~> ( ! [X3] : p(X3)
| ~ c ) )
| ~ sP13 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f20,plain,
( ( ! [X0] :
( c
| ~ p(X0) )
<~> ( c
| ! [X1] : ~ p(X1) ) )
| ~ sP14 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f21,plain,
( ! [X35] :
? [X36] :
( ~ q(X35)
& p(X35)
& ( q(X35)
| ~ p(X36) ) )
| ~ sP15 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f22,plain,
( ( ? [X31] :
( ~ q(X31)
& ~ p(X31) )
& ( ! [X29] : q(X29)
| ! [X30] : p(X30) ) )
| ~ sP16 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f23,plain,
( ( ( ! [X22] : ~ q(X22)
| ! [X23] : ~ p(X23) )
& ? [X21] :
( q(X21)
& p(X21) ) )
| ~ sP17 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f24,plain,
( ( ? [X15] :
( ~ p(X15)
& ? [X16] : p(X16) )
& ! [X14] : ~ p(X14) )
| ~ sP18 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f25,plain,
( ! [X24] :
( ? [X25] : ~ p(X25)
& p(X24) )
| ~ sP19 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
fof(f26,plain,
( ? [X19] :
( ~ p(X19)
& ! [X20] : p(X20) )
| ~ sP20 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).
fof(f27,plain,
( ( ! [X18] : ~ p(X18)
& ! [X17] : p(X17) )
| ~ sP21 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).
fof(f5,plain,
( ( ! [X0] :
( c
| ~ p(X0) )
<~> ( c
| ! [X1] : ~ p(X1) ) )
| ( ! [X2] :
( p(X2)
| ~ c )
<~> ( ! [X3] : p(X3)
| ~ c ) )
| ( ? [X4] :
( c
| ~ p(X4) )
<~> ( c
| ? [X5] : ~ p(X5) ) )
| ( ? [X6] :
( p(X6)
| ~ c )
<~> ( ? [X7] : p(X7)
| ~ c ) )
| ( c
<~> c )
| ( c
<~> c )
| ( ? [X10] :
( c
& p(X10) )
<~> ( c
& ? [X11] : p(X11) ) )
| ( ! [X12] :
( c
| p(X12) )
<~> ( c
| ! [X13] : p(X13) ) )
| ( ? [X15] :
( ~ p(X15)
& ? [X16] : p(X16) )
& ! [X14] : ~ p(X14) )
| ( ! [X18] : ~ p(X18)
& ! [X17] : p(X17) )
| ? [X19] :
( ~ p(X19)
& ! [X20] : p(X20) )
| ( ( ! [X22] : ~ q(X22)
| ! [X23] : ~ p(X23) )
& ? [X21] :
( q(X21)
& p(X21) ) )
| ! [X24] :
( ? [X25] : ~ p(X25)
& p(X24) )
| ( ? [X26] :
( q(X26)
| p(X26) )
<~> ( ? [X27] : q(X27)
| ? [X28] : p(X28) ) )
| ( ? [X31] :
( ~ q(X31)
& ~ p(X31) )
& ( ! [X29] : q(X29)
| ! [X30] : p(X30) ) )
| ( ! [X32] :
( q(X32)
& p(X32) )
<~> ( ! [X33] : q(X33)
& ! [X34] : p(X34) ) )
| ! [X35] :
? [X36] :
( ~ q(X35)
& p(X35)
& ( q(X35)
| ~ p(X36) ) )
| ( ! [X42] :
( h(X42)
| ~ g(X42)
| ~ f(X42) )
& ! [X41] :
( g(X41)
| ~ h(X41)
| ~ f(X41) )
& ( ! [X37] :
( h(X37)
| ~ f(X37) )
| ! [X38] :
( g(X38)
| ~ f(X38) ) )
& ( ? [X40] :
( ~ g(X40)
& f(X40) )
| ? [X39] :
( ~ h(X39)
& g(X39)
& f(X39) ) ) )
| ( ? [X48,X49] :
( ~ r(X48,X48)
& r(X48,X49) )
& ! [X43,X44,X45] :
( r(X43,X45)
| ~ r(X44,X45)
| ~ r(X43,X44) )
& ! [X46,X47] :
( r(X47,X46)
| ~ r(X46,X47) ) )
| ( ! [X55] :
( h(X55)
| ~ g(X55)
| ~ f(X55) )
& ! [X54] :
( g(X54)
| ~ h(X54)
| ~ f(X54) )
& ( ! [X50] :
( h(X50)
| ~ f(X50) )
| ! [X51] :
( g(X51)
| ~ f(X51) ) )
& ! [X52] :
( ? [X53] :
( ~ g(X53)
& f(X53) )
| ( ~ h(X52)
& g(X52)
& f(X52) ) ) ) ),
inference(flattening,[],[f4]) ).
fof(f4,plain,
( ( ! [X0] :
( c
| ~ p(X0) )
<~> ( c
| ! [X1] : ~ p(X1) ) )
| ( ! [X2] :
( p(X2)
| ~ c )
<~> ( ! [X3] : p(X3)
| ~ c ) )
| ( ? [X4] :
( c
| ~ p(X4) )
<~> ( c
| ? [X5] : ~ p(X5) ) )
| ( ? [X6] :
( p(X6)
| ~ c )
<~> ( ? [X7] : p(X7)
| ~ c ) )
| ( c
<~> c )
| ( c
<~> c )
| ( ? [X10] :
( c
& p(X10) )
<~> ( c
& ? [X11] : p(X11) ) )
| ( ! [X12] :
( c
| p(X12) )
<~> ( c
| ! [X13] : p(X13) ) )
| ( ? [X15] :
( ~ p(X15)
& ? [X16] : p(X16) )
& ! [X14] : ~ p(X14) )
| ( ! [X18] : ~ p(X18)
& ! [X17] : p(X17) )
| ? [X19] :
( ~ p(X19)
& ! [X20] : p(X20) )
| ( ( ! [X22] : ~ q(X22)
| ! [X23] : ~ p(X23) )
& ? [X21] :
( q(X21)
& p(X21) ) )
| ! [X24] :
( ? [X25] : ~ p(X25)
& p(X24) )
| ( ? [X26] :
( q(X26)
| p(X26) )
<~> ( ? [X27] : q(X27)
| ? [X28] : p(X28) ) )
| ( ? [X31] :
( ~ q(X31)
& ~ p(X31) )
& ( ! [X29] : q(X29)
| ! [X30] : p(X30) ) )
| ( ! [X32] :
( q(X32)
& p(X32) )
<~> ( ! [X33] : q(X33)
& ! [X34] : p(X34) ) )
| ! [X35] :
? [X36] :
( ~ q(X35)
& p(X35)
& ( q(X35)
| ~ p(X36) ) )
| ( ! [X42] :
( h(X42)
| ~ g(X42)
| ~ f(X42) )
& ! [X41] :
( g(X41)
| ~ h(X41)
| ~ f(X41) )
& ( ! [X37] :
( h(X37)
| ~ f(X37) )
| ! [X38] :
( g(X38)
| ~ f(X38) ) )
& ( ? [X40] :
( ~ g(X40)
& f(X40) )
| ? [X39] :
( ~ h(X39)
& g(X39)
& f(X39) ) ) )
| ( ? [X48,X49] :
( ~ r(X48,X48)
& r(X48,X49) )
& ! [X43,X44,X45] :
( r(X43,X45)
| ~ r(X44,X45)
| ~ r(X43,X44) )
& ! [X46,X47] :
( r(X47,X46)
| ~ r(X46,X47) ) )
| ( ! [X55] :
( h(X55)
| ~ g(X55)
| ~ f(X55) )
& ! [X54] :
( g(X54)
| ~ h(X54)
| ~ f(X54) )
& ( ! [X50] :
( h(X50)
| ~ f(X50) )
| ! [X51] :
( g(X51)
| ~ f(X51) ) )
& ! [X52] :
( ? [X53] :
( ~ g(X53)
& f(X53) )
| ( ~ h(X52)
& g(X52)
& f(X52) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,plain,
~ ( ( ! [X0] :
( p(X0)
=> c )
<=> ( ? [X1] : p(X1)
=> c ) )
& ( ! [X2] :
( c
=> p(X2) )
<=> ( c
=> ! [X3] : p(X3) ) )
& ( ? [X4] :
( p(X4)
=> c )
<=> ( ! [X5] : p(X5)
=> c ) )
& ( ? [X6] :
( c
=> p(X6) )
<=> ( c
=> ? [X7] : p(X7) ) )
& ( c
<=> c )
& ( c
<=> c )
& ( ? [X10] :
( c
& p(X10) )
<=> ( c
& ? [X11] : p(X11) ) )
& ( ! [X12] :
( c
| p(X12) )
<=> ( c
| ! [X13] : p(X13) ) )
& ( ~ ? [X14] : p(X14)
=> ! [X15] :
( ? [X16] : p(X16)
=> p(X15) ) )
& ( ! [X17] : p(X17)
=> ? [X18] : p(X18) )
& ! [X19] :
( ! [X20] : p(X20)
=> p(X19) )
& ( ? [X21] :
( q(X21)
& p(X21) )
=> ( ? [X22] : q(X22)
& ? [X23] : p(X23) ) )
& ? [X24] :
( p(X24)
=> ! [X25] : p(X25) )
& ( ? [X26] :
( q(X26)
| p(X26) )
<=> ( ? [X27] : q(X27)
| ? [X28] : p(X28) ) )
& ( ( ! [X29] : q(X29)
| ! [X30] : p(X30) )
=> ! [X31] :
( q(X31)
| p(X31) ) )
& ( ! [X32] :
( q(X32)
& p(X32) )
<=> ( ! [X33] : q(X33)
& ! [X34] : p(X34) ) )
& ? [X35] :
! [X36] :
( ( p(X36)
=> q(X35) )
=> ( p(X35)
=> q(X35) ) )
& ( ( ( ! [X37] :
( f(X37)
=> h(X37) )
| ! [X38] :
( f(X38)
=> g(X38) ) )
& ( ! [X39] :
( ( g(X39)
& f(X39) )
=> h(X39) )
=> ? [X40] :
( ~ g(X40)
& f(X40) ) ) )
=> ( ! [X41] :
( ( h(X41)
& f(X41) )
=> g(X41) )
=> ? [X42] :
( ~ h(X42)
& g(X42)
& f(X42) ) ) )
& ( ( ! [X43,X44,X45] :
( ( r(X44,X45)
& r(X43,X44) )
=> r(X43,X45) )
& ! [X46,X47] :
( r(X46,X47)
=> r(X47,X46) ) )
=> ! [X48,X49] :
( r(X48,X49)
=> r(X48,X48) ) )
& ( ( ( ! [X50] :
( f(X50)
=> h(X50) )
| ! [X51] :
( f(X51)
=> g(X51) ) )
& ! [X52] :
( ( ( g(X52)
& f(X52) )
=> h(X52) )
=> ? [X53] :
( ~ g(X53)
& f(X53) ) ) )
=> ( ! [X54] :
( ( h(X54)
& f(X54) )
=> g(X54) )
=> ? [X55] :
( ~ h(X55)
& g(X55)
& f(X55) ) ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,negated_conjecture,
~ ( ( ! [X0] :
( p(X0)
=> c )
<=> ( ? [X0] : p(X0)
=> c ) )
& ( ! [X0] :
( c
=> p(X0) )
<=> ( c
=> ! [X0] : p(X0) ) )
& ( ? [X0] :
( p(X0)
=> c )
<=> ( ! [X0] : p(X0)
=> c ) )
& ( ? [X0] :
( c
=> p(X0) )
<=> ( c
=> ? [X0] : p(X0) ) )
& ( ! [X0] : c
<=> c )
& ( ? [X0] : c
<=> c )
& ( ? [X0] :
( c
& p(X0) )
<=> ( c
& ? [X0] : p(X0) ) )
& ( ! [X0] :
( c
| p(X0) )
<=> ( c
| ! [X0] : p(X0) ) )
& ( ~ ? [X1] : p(X1)
=> ! [X1] :
( ? [X0] : p(X0)
=> p(X1) ) )
& ( ! [X0] : p(X0)
=> ? [X0] : p(X0) )
& ! [X1] :
( ! [X0] : p(X0)
=> p(X1) )
& ( ? [X0] :
( q(X0)
& p(X0) )
=> ( ? [X0] : q(X0)
& ? [X0] : p(X0) ) )
& ? [X1] :
( p(X1)
=> ! [X0] : p(X0) )
& ( ? [X0] :
( q(X0)
| p(X0) )
<=> ( ? [X0] : q(X0)
| ? [X0] : p(X0) ) )
& ( ( ! [X0] : q(X0)
| ! [X0] : p(X0) )
=> ! [X0] :
( q(X0)
| p(X0) ) )
& ( ! [X0] :
( q(X0)
& p(X0) )
<=> ( ! [X0] : q(X0)
& ! [X0] : p(X0) ) )
& ? [X0] :
! [X1] :
( ( p(X1)
=> q(X0) )
=> ( p(X0)
=> q(X0) ) )
& ( ( ( ! [X3] :
( f(X3)
=> h(X3) )
| ! [X2] :
( f(X2)
=> g(X2) ) )
& ( ! [X0] :
( ( g(X0)
& f(X0) )
=> h(X0) )
=> ? [X0] :
( ~ g(X0)
& f(X0) ) ) )
=> ( ! [X4] :
( ( h(X4)
& f(X4) )
=> g(X4) )
=> ? [X5] :
( ~ h(X5)
& g(X5)
& f(X5) ) ) )
& ( ( ! [X0,X1,X3] :
( ( r(X1,X3)
& r(X0,X1) )
=> r(X0,X3) )
& ! [X0,X1] :
( r(X0,X1)
=> r(X1,X0) ) )
=> ! [X0,X1] :
( r(X0,X1)
=> r(X0,X0) ) )
& ( ( ( ! [X3] :
( f(X3)
=> h(X3) )
| ! [X2] :
( f(X2)
=> g(X2) ) )
& ! [X0] :
( ( ( g(X0)
& f(X0) )
=> h(X0) )
=> ? [X1] :
( ~ g(X1)
& f(X1) ) ) )
=> ( ! [X4] :
( ( h(X4)
& f(X4) )
=> g(X4) )
=> ? [X5] :
( ~ h(X5)
& g(X5)
& f(X5) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
( ( ! [X0] :
( p(X0)
=> c )
<=> ( ? [X0] : p(X0)
=> c ) )
& ( ! [X0] :
( c
=> p(X0) )
<=> ( c
=> ! [X0] : p(X0) ) )
& ( ? [X0] :
( p(X0)
=> c )
<=> ( ! [X0] : p(X0)
=> c ) )
& ( ? [X0] :
( c
=> p(X0) )
<=> ( c
=> ? [X0] : p(X0) ) )
& ( ! [X0] : c
<=> c )
& ( ? [X0] : c
<=> c )
& ( ? [X0] :
( c
& p(X0) )
<=> ( c
& ? [X0] : p(X0) ) )
& ( ! [X0] :
( c
| p(X0) )
<=> ( c
| ! [X0] : p(X0) ) )
& ( ~ ? [X1] : p(X1)
=> ! [X1] :
( ? [X0] : p(X0)
=> p(X1) ) )
& ( ! [X0] : p(X0)
=> ? [X0] : p(X0) )
& ! [X1] :
( ! [X0] : p(X0)
=> p(X1) )
& ( ? [X0] :
( q(X0)
& p(X0) )
=> ( ? [X0] : q(X0)
& ? [X0] : p(X0) ) )
& ? [X1] :
( p(X1)
=> ! [X0] : p(X0) )
& ( ? [X0] :
( q(X0)
| p(X0) )
<=> ( ? [X0] : q(X0)
| ? [X0] : p(X0) ) )
& ( ( ! [X0] : q(X0)
| ! [X0] : p(X0) )
=> ! [X0] :
( q(X0)
| p(X0) ) )
& ( ! [X0] :
( q(X0)
& p(X0) )
<=> ( ! [X0] : q(X0)
& ! [X0] : p(X0) ) )
& ? [X0] :
! [X1] :
( ( p(X1)
=> q(X0) )
=> ( p(X0)
=> q(X0) ) )
& ( ( ( ! [X3] :
( f(X3)
=> h(X3) )
| ! [X2] :
( f(X2)
=> g(X2) ) )
& ( ! [X0] :
( ( g(X0)
& f(X0) )
=> h(X0) )
=> ? [X0] :
( ~ g(X0)
& f(X0) ) ) )
=> ( ! [X4] :
( ( h(X4)
& f(X4) )
=> g(X4) )
=> ? [X5] :
( ~ h(X5)
& g(X5)
& f(X5) ) ) )
& ( ( ! [X0,X1,X3] :
( ( r(X1,X3)
& r(X0,X1) )
=> r(X0,X3) )
& ! [X0,X1] :
( r(X0,X1)
=> r(X1,X0) ) )
=> ! [X0,X1] :
( r(X0,X1)
=> r(X0,X0) ) )
& ( ( ( ! [X3] :
( f(X3)
=> h(X3) )
| ! [X2] :
( f(X2)
=> g(X2) ) )
& ! [X0] :
( ( ( g(X0)
& f(X0) )
=> h(X0) )
=> ? [X1] :
( ~ g(X1)
& f(X1) ) ) )
=> ( ! [X4] :
( ( h(X4)
& f(X4) )
=> g(X4) )
=> ? [X5] :
( ~ h(X5)
& g(X5)
& f(X5) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f578,plain,
( spl52_61
| spl52_56
| spl52_50
| spl52_19
| spl52_45
| spl52_15
| spl52_40
| spl52_6
| spl52_11
| spl52_4
| spl52_1
| spl52_8
| spl52_37
| spl52_34
| ~ spl52_22
| spl52_31
| spl52_28
| spl52_25
| spl52_21 ),
inference(avatar_split_clause,[],[f216,f323,f344,f361,f378,f327,f395,f412,f262,f230,f242,f277,f252,f429,f295,f454,f313,f479,f503,f525]) ).
fof(f216,plain,
( sP14
| sP13
| sP12
| sP11
| ~ c
| sP10
| sP9
| sP18
| sP21
| sP20
| sP17
| sP19
| sP8
| sP16
| sP7
| sP15
| sP6
| sP5
| sP4 ),
inference(duplicate_literal_removal,[],[f212]) ).
fof(f212,plain,
( sP14
| sP13
| sP12
| sP11
| ~ c
| ~ c
| ~ c
| ~ c
| sP10
| sP9
| sP18
| sP21
| sP20
| sP17
| sP19
| sP8
| sP16
| sP7
| sP15
| sP6
| sP5
| sP4 ),
inference(cnf_transformation,[],[f128]) ).
fof(f577,plain,
( ~ spl52_62
| spl52_69
| spl52_71 ),
inference(avatar_split_clause,[],[f204,f574,f566,f532]) ).
fof(f532,plain,
( spl52_62
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_62])]) ).
fof(f204,plain,
! [X0] :
( f(sK51)
| sP0(X0)
| ~ sP1 ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
( ! [X0] :
( ( ~ g(sK51)
& f(sK51) )
| sP0(X0) )
| ~ sP1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f123,f124]) ).
fof(f124,plain,
( ? [X1] :
( ~ g(X1)
& f(X1) )
=> ( ~ g(sK51)
& f(sK51) ) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
( ! [X0] :
( ? [X1] :
( ~ g(X1)
& f(X1) )
| sP0(X0) )
| ~ sP1 ),
inference(rectify,[],[f122]) ).
fof(f122,plain,
( ! [X52] :
( ? [X53] :
( ~ g(X53)
& f(X53) )
| sP0(X52) )
| ~ sP1 ),
inference(nnf_transformation,[],[f7]) ).
fof(f572,plain,
( ~ spl52_62
| spl52_69
| ~ spl52_70 ),
inference(avatar_split_clause,[],[f205,f569,f566,f532]) ).
fof(f205,plain,
! [X0] :
( ~ g(sK51)
| sP0(X0)
| ~ sP1 ),
inference(cnf_transformation,[],[f125]) ).
fof(f564,plain,
( ~ spl52_63
| spl52_68 ),
inference(avatar_split_clause,[],[f201,f561,f537]) ).
fof(f537,plain,
( spl52_63
<=> sP2 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_63])]) ).
fof(f201,plain,
( f(sK50)
| ~ sP2 ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
( ( ~ h(sK50)
& g(sK50)
& f(sK50) )
| ~ sP2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50])],[f119,f120]) ).
fof(f120,plain,
( ? [X0] :
( ~ h(X0)
& g(X0)
& f(X0) )
=> ( ~ h(sK50)
& g(sK50)
& f(sK50) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
( ? [X0] :
( ~ h(X0)
& g(X0)
& f(X0) )
| ~ sP2 ),
inference(rectify,[],[f118]) ).
fof(f118,plain,
( ? [X39] :
( ~ h(X39)
& g(X39)
& f(X39) )
| ~ sP2 ),
inference(nnf_transformation,[],[f8]) ).
fof(f559,plain,
( ~ spl52_63
| spl52_67 ),
inference(avatar_split_clause,[],[f202,f556,f537]) ).
fof(f202,plain,
( g(sK50)
| ~ sP2 ),
inference(cnf_transformation,[],[f121]) ).
fof(f554,plain,
( ~ spl52_63
| ~ spl52_66 ),
inference(avatar_split_clause,[],[f203,f551,f537]) ).
fof(f203,plain,
( ~ h(sK50)
| ~ sP2 ),
inference(cnf_transformation,[],[f121]) ).
fof(f549,plain,
( ~ spl52_55
| spl52_63
| spl52_65 ),
inference(avatar_split_clause,[],[f199,f546,f537,f498]) ).
fof(f498,plain,
( spl52_55
<=> sP3 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_55])]) ).
fof(f199,plain,
( f(sK49)
| sP2
| ~ sP3 ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
( ( ~ g(sK49)
& f(sK49) )
| sP2
| ~ sP3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49])],[f115,f116]) ).
fof(f116,plain,
( ? [X0] :
( ~ g(X0)
& f(X0) )
=> ( ~ g(sK49)
& f(sK49) ) ),
introduced(choice_axiom,[]) ).
fof(f115,plain,
( ? [X0] :
( ~ g(X0)
& f(X0) )
| sP2
| ~ sP3 ),
inference(rectify,[],[f114]) ).
fof(f114,plain,
( ? [X40] :
( ~ g(X40)
& f(X40) )
| sP2
| ~ sP3 ),
inference(nnf_transformation,[],[f9]) ).
fof(f544,plain,
( ~ spl52_55
| spl52_63
| ~ spl52_64 ),
inference(avatar_split_clause,[],[f200,f541,f537,f498]) ).
fof(f200,plain,
( ~ g(sK49)
| sP2
| ~ sP3 ),
inference(cnf_transformation,[],[f117]) ).
fof(f535,plain,
( ~ spl52_61
| spl52_62 ),
inference(avatar_split_clause,[],[f195,f532,f525]) ).
fof(f195,plain,
( sP1
| ~ sP4 ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
( ( ! [X0] :
( h(X0)
| ~ g(X0)
| ~ f(X0) )
& ! [X1] :
( g(X1)
| ~ h(X1)
| ~ f(X1) )
& ( ! [X2] :
( h(X2)
| ~ f(X2) )
| ! [X3] :
( g(X3)
| ~ f(X3) ) )
& sP1 )
| ~ sP4 ),
inference(rectify,[],[f112]) ).
fof(f112,plain,
( ( ! [X55] :
( h(X55)
| ~ g(X55)
| ~ f(X55) )
& ! [X54] :
( g(X54)
| ~ h(X54)
| ~ f(X54) )
& ( ! [X50] :
( h(X50)
| ~ f(X50) )
| ! [X51] :
( g(X51)
| ~ f(X51) ) )
& sP1 )
| ~ sP4 ),
inference(nnf_transformation,[],[f10]) ).
fof(f530,plain,
( ~ spl52_61
| spl52_53
| spl52_54 ),
inference(avatar_split_clause,[],[f196,f494,f491,f525]) ).
fof(f196,plain,
! [X2,X3] :
( h(X2)
| ~ f(X2)
| g(X3)
| ~ f(X3)
| ~ sP4 ),
inference(cnf_transformation,[],[f113]) ).
fof(f529,plain,
( ~ spl52_61
| spl52_52 ),
inference(avatar_split_clause,[],[f197,f487,f525]) ).
fof(f197,plain,
! [X1] :
( g(X1)
| ~ h(X1)
| ~ f(X1)
| ~ sP4 ),
inference(cnf_transformation,[],[f113]) ).
fof(f528,plain,
( ~ spl52_61
| spl52_51 ),
inference(avatar_split_clause,[],[f198,f483,f525]) ).
fof(f198,plain,
! [X0] :
( h(X0)
| ~ g(X0)
| ~ f(X0)
| ~ sP4 ),
inference(cnf_transformation,[],[f113]) ).
fof(f523,plain,
( ~ spl52_56
| spl52_60 ),
inference(avatar_split_clause,[],[f191,f521,f503]) ).
fof(f191,plain,
! [X6,X5] :
( r(X6,X5)
| ~ r(X5,X6)
| ~ sP5 ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
( ( ~ r(sK47,sK47)
& r(sK47,sK48)
& ! [X2,X3,X4] :
( r(X2,X4)
| ~ r(X3,X4)
| ~ r(X2,X3) )
& ! [X5,X6] :
( r(X6,X5)
| ~ r(X5,X6) ) )
| ~ sP5 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48])],[f109,f110]) ).
fof(f110,plain,
( ? [X0,X1] :
( ~ r(X0,X0)
& r(X0,X1) )
=> ( ~ r(sK47,sK47)
& r(sK47,sK48) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
( ( ? [X0,X1] :
( ~ r(X0,X0)
& r(X0,X1) )
& ! [X2,X3,X4] :
( r(X2,X4)
| ~ r(X3,X4)
| ~ r(X2,X3) )
& ! [X5,X6] :
( r(X6,X5)
| ~ r(X5,X6) ) )
| ~ sP5 ),
inference(rectify,[],[f108]) ).
fof(f108,plain,
( ( ? [X48,X49] :
( ~ r(X48,X48)
& r(X48,X49) )
& ! [X43,X44,X45] :
( r(X43,X45)
| ~ r(X44,X45)
| ~ r(X43,X44) )
& ! [X46,X47] :
( r(X47,X46)
| ~ r(X46,X47) ) )
| ~ sP5 ),
inference(nnf_transformation,[],[f11]) ).
fof(f519,plain,
( ~ spl52_56
| spl52_59 ),
inference(avatar_split_clause,[],[f192,f517,f503]) ).
fof(f192,plain,
! [X2,X3,X4] :
( r(X2,X4)
| ~ r(X3,X4)
| ~ r(X2,X3)
| ~ sP5 ),
inference(cnf_transformation,[],[f111]) ).
fof(f515,plain,
( ~ spl52_56
| spl52_58 ),
inference(avatar_split_clause,[],[f193,f512,f503]) ).
fof(f193,plain,
( r(sK47,sK48)
| ~ sP5 ),
inference(cnf_transformation,[],[f111]) ).
fof(f510,plain,
( ~ spl52_56
| ~ spl52_57 ),
inference(avatar_split_clause,[],[f194,f507,f503]) ).
fof(f194,plain,
( ~ r(sK47,sK47)
| ~ sP5 ),
inference(cnf_transformation,[],[f111]) ).
fof(f501,plain,
( ~ spl52_50
| spl52_55 ),
inference(avatar_split_clause,[],[f187,f498,f479]) ).
fof(f187,plain,
( sP3
| ~ sP6 ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
( ( ! [X0] :
( h(X0)
| ~ g(X0)
| ~ f(X0) )
& ! [X1] :
( g(X1)
| ~ h(X1)
| ~ f(X1) )
& ( ! [X2] :
( h(X2)
| ~ f(X2) )
| ! [X3] :
( g(X3)
| ~ f(X3) ) )
& sP3 )
| ~ sP6 ),
inference(rectify,[],[f106]) ).
fof(f106,plain,
( ( ! [X42] :
( h(X42)
| ~ g(X42)
| ~ f(X42) )
& ! [X41] :
( g(X41)
| ~ h(X41)
| ~ f(X41) )
& ( ! [X37] :
( h(X37)
| ~ f(X37) )
| ! [X38] :
( g(X38)
| ~ f(X38) ) )
& sP3 )
| ~ sP6 ),
inference(nnf_transformation,[],[f12]) ).
fof(f496,plain,
( ~ spl52_50
| spl52_53
| spl52_54 ),
inference(avatar_split_clause,[],[f188,f494,f491,f479]) ).
fof(f188,plain,
! [X2,X3] :
( h(X2)
| ~ f(X2)
| g(X3)
| ~ f(X3)
| ~ sP6 ),
inference(cnf_transformation,[],[f107]) ).
fof(f489,plain,
( ~ spl52_50
| spl52_52 ),
inference(avatar_split_clause,[],[f189,f487,f479]) ).
fof(f189,plain,
! [X1] :
( g(X1)
| ~ h(X1)
| ~ f(X1)
| ~ sP6 ),
inference(cnf_transformation,[],[f107]) ).
fof(f485,plain,
( ~ spl52_50
| spl52_51 ),
inference(avatar_split_clause,[],[f190,f483,f479]) ).
fof(f190,plain,
! [X0] :
( h(X0)
| ~ g(X0)
| ~ f(X0)
| ~ sP6 ),
inference(cnf_transformation,[],[f107]) ).
fof(f477,plain,
( ~ spl52_45
| spl52_3
| spl52_3 ),
inference(avatar_split_clause,[],[f182,f238,f238,f454]) ).
fof(f182,plain,
! [X4,X5] :
( p(X4)
| p(X5)
| ~ sP7 ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
( ( ( ~ q(sK44)
| ~ p(sK45)
| ~ q(sK46)
| ~ p(sK46) )
& ( ( ! [X3] : q(X3)
& ! [X4] : p(X4) )
| ! [X5] :
( q(X5)
& p(X5) ) ) )
| ~ sP7 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45,sK46])],[f101,f104,f103,f102]) ).
fof(f102,plain,
( ? [X0] : ~ q(X0)
=> ~ q(sK44) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
( ? [X1] : ~ p(X1)
=> ~ p(sK45) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
( ? [X2] :
( ~ q(X2)
| ~ p(X2) )
=> ( ~ q(sK46)
| ~ p(sK46) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
( ( ( ? [X0] : ~ q(X0)
| ? [X1] : ~ p(X1)
| ? [X2] :
( ~ q(X2)
| ~ p(X2) ) )
& ( ( ! [X3] : q(X3)
& ! [X4] : p(X4) )
| ! [X5] :
( q(X5)
& p(X5) ) ) )
| ~ sP7 ),
inference(rectify,[],[f100]) ).
fof(f100,plain,
( ( ( ? [X33] : ~ q(X33)
| ? [X34] : ~ p(X34)
| ? [X32] :
( ~ q(X32)
| ~ p(X32) ) )
& ( ( ! [X33] : q(X33)
& ! [X34] : p(X34) )
| ! [X32] :
( q(X32)
& p(X32) ) ) )
| ~ sP7 ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
( ( ( ? [X33] : ~ q(X33)
| ? [X34] : ~ p(X34)
| ? [X32] :
( ~ q(X32)
| ~ p(X32) ) )
& ( ( ! [X33] : q(X33)
& ! [X34] : p(X34) )
| ! [X32] :
( q(X32)
& p(X32) ) ) )
| ~ sP7 ),
inference(nnf_transformation,[],[f13]) ).
fof(f474,plain,
( ~ spl52_45
| spl52_18
| spl52_18 ),
inference(avatar_split_clause,[],[f185,f309,f309,f454]) ).
fof(f185,plain,
! [X3,X5] :
( q(X3)
| q(X5)
| ~ sP7 ),
inference(cnf_transformation,[],[f105]) ).
fof(f473,plain,
( ~ spl52_45
| ~ spl52_46
| ~ spl52_47
| ~ spl52_48
| ~ spl52_49 ),
inference(avatar_split_clause,[],[f186,f470,f466,f462,f458,f454]) ).
fof(f186,plain,
( ~ q(sK44)
| ~ p(sK45)
| ~ q(sK46)
| ~ p(sK46)
| ~ sP7 ),
inference(cnf_transformation,[],[f105]) ).
fof(f452,plain,
( ~ spl52_40
| spl52_41
| spl52_42
| spl52_43
| spl52_44 ),
inference(avatar_split_clause,[],[f177,f449,f445,f441,f437,f429]) ).
fof(f177,plain,
( q(sK41)
| p(sK42)
| q(sK43)
| p(sK43)
| ~ sP8 ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
( ( ( ( ! [X0] : ~ q(X0)
& ! [X1] : ~ p(X1) )
| ! [X2] :
( ~ q(X2)
& ~ p(X2) ) )
& ( q(sK41)
| p(sK42)
| q(sK43)
| p(sK43) ) )
| ~ sP8 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42,sK43])],[f94,f97,f96,f95]) ).
fof(f95,plain,
( ? [X3] : q(X3)
=> q(sK41) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
( ? [X4] : p(X4)
=> p(sK42) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
( ? [X5] :
( q(X5)
| p(X5) )
=> ( q(sK43)
| p(sK43) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
( ( ( ( ! [X0] : ~ q(X0)
& ! [X1] : ~ p(X1) )
| ! [X2] :
( ~ q(X2)
& ~ p(X2) ) )
& ( ? [X3] : q(X3)
| ? [X4] : p(X4)
| ? [X5] :
( q(X5)
| p(X5) ) ) )
| ~ sP8 ),
inference(rectify,[],[f93]) ).
fof(f93,plain,
( ( ( ( ! [X27] : ~ q(X27)
& ! [X28] : ~ p(X28) )
| ! [X26] :
( ~ q(X26)
& ~ p(X26) ) )
& ( ? [X27] : q(X27)
| ? [X28] : p(X28)
| ? [X26] :
( q(X26)
| p(X26) ) ) )
| ~ sP8 ),
inference(flattening,[],[f92]) ).
fof(f92,plain,
( ( ( ( ! [X27] : ~ q(X27)
& ! [X28] : ~ p(X28) )
| ! [X26] :
( ~ q(X26)
& ~ p(X26) ) )
& ( ? [X27] : q(X27)
| ? [X28] : p(X28)
| ? [X26] :
( q(X26)
| p(X26) ) ) )
| ~ sP8 ),
inference(nnf_transformation,[],[f14]) ).
fof(f435,plain,
( ~ spl52_40
| spl52_2
| spl52_2 ),
inference(avatar_split_clause,[],[f178,f234,f234,f429]) ).
fof(f178,plain,
! [X2,X1] :
( ~ p(X1)
| ~ p(X2)
| ~ sP8 ),
inference(cnf_transformation,[],[f98]) ).
fof(f432,plain,
( ~ spl52_40
| spl52_12
| spl52_12 ),
inference(avatar_split_clause,[],[f181,f281,f281,f429]) ).
fof(f181,plain,
! [X2,X0] :
( ~ q(X0)
| ~ q(X2)
| ~ sP8 ),
inference(cnf_transformation,[],[f98]) ).
fof(f427,plain,
( ~ spl52_37
| spl52_3
| spl52_3
| spl52_22 ),
inference(avatar_split_clause,[],[f217,f327,f238,f238,f412]) ).
fof(f217,plain,
! [X2,X3] :
( c
| p(X2)
| p(X3)
| ~ sP9 ),
inference(duplicate_literal_removal,[],[f172]) ).
fof(f172,plain,
! [X2,X3] :
( c
| p(X2)
| c
| p(X3)
| ~ sP9 ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
( ( ( ( ~ c
& ~ p(sK39) )
| ( ~ c
& ~ p(sK40) ) )
& ( c
| ! [X2] : p(X2)
| ! [X3] :
( c
| p(X3) ) ) )
| ~ sP9 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39,sK40])],[f88,f90,f89]) ).
fof(f89,plain,
( ? [X0] : ~ p(X0)
=> ~ p(sK39) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
( ? [X1] :
( ~ c
& ~ p(X1) )
=> ( ~ c
& ~ p(sK40) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
( ( ( ( ~ c
& ? [X0] : ~ p(X0) )
| ? [X1] :
( ~ c
& ~ p(X1) ) )
& ( c
| ! [X2] : p(X2)
| ! [X3] :
( c
| p(X3) ) ) )
| ~ sP9 ),
inference(rectify,[],[f87]) ).
fof(f87,plain,
( ( ( ( ~ c
& ? [X13] : ~ p(X13) )
| ? [X12] :
( ~ c
& ~ p(X12) ) )
& ( c
| ! [X13] : p(X13)
| ! [X12] :
( c
| p(X12) ) ) )
| ~ sP9 ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
( ( ( ( ~ c
& ? [X13] : ~ p(X13) )
| ? [X12] :
( ~ c
& ~ p(X12) ) )
& ( c
| ! [X13] : p(X13)
| ! [X12] :
( c
| p(X12) ) ) )
| ~ sP9 ),
inference(nnf_transformation,[],[f15]) ).
fof(f426,plain,
( ~ spl52_37
| ~ spl52_38
| ~ spl52_39 ),
inference(avatar_split_clause,[],[f173,f422,f417,f412]) ).
fof(f173,plain,
( ~ p(sK39)
| ~ p(sK40)
| ~ sP9 ),
inference(cnf_transformation,[],[f91]) ).
fof(f415,plain,
( ~ spl52_37
| ~ spl52_22 ),
inference(avatar_split_clause,[],[f218,f327,f412]) ).
fof(f218,plain,
( ~ c
| ~ sP9 ),
inference(duplicate_literal_removal,[],[f176]) ).
fof(f176,plain,
( ~ c
| ~ c
| ~ sP9 ),
inference(cnf_transformation,[],[f91]) ).
fof(f410,plain,
( ~ spl52_34
| spl52_35
| spl52_36 ),
inference(avatar_split_clause,[],[f167,f406,f401,f395]) ).
fof(f167,plain,
( p(sK37)
| p(sK38)
| ~ sP10 ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
( ( ( ~ c
| ! [X0] : ~ p(X0)
| ! [X1] :
( ~ c
| ~ p(X1) ) )
& ( ( c
& p(sK37) )
| ( c
& p(sK38) ) ) )
| ~ sP10 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38])],[f82,f84,f83]) ).
fof(f83,plain,
( ? [X2] : p(X2)
=> p(sK37) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
( ? [X3] :
( c
& p(X3) )
=> ( c
& p(sK38) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
( ( ( ~ c
| ! [X0] : ~ p(X0)
| ! [X1] :
( ~ c
| ~ p(X1) ) )
& ( ( c
& ? [X2] : p(X2) )
| ? [X3] :
( c
& p(X3) ) ) )
| ~ sP10 ),
inference(rectify,[],[f81]) ).
fof(f81,plain,
( ( ( ~ c
| ! [X11] : ~ p(X11)
| ! [X10] :
( ~ c
| ~ p(X10) ) )
& ( ( c
& ? [X11] : p(X11) )
| ? [X10] :
( c
& p(X10) ) ) )
| ~ sP10 ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
( ( ( ~ c
| ! [X11] : ~ p(X11)
| ! [X10] :
( ~ c
| ~ p(X10) ) )
& ( ( c
& ? [X11] : p(X11) )
| ? [X10] :
( c
& p(X10) ) ) )
| ~ sP10 ),
inference(nnf_transformation,[],[f16]) ).
fof(f399,plain,
( ~ spl52_34
| spl52_22 ),
inference(avatar_split_clause,[],[f219,f327,f395]) ).
fof(f219,plain,
( c
| ~ sP10 ),
inference(duplicate_literal_removal,[],[f170]) ).
fof(f170,plain,
( c
| c
| ~ sP10 ),
inference(cnf_transformation,[],[f85]) ).
fof(f398,plain,
( ~ spl52_34
| spl52_2
| spl52_2
| ~ spl52_22 ),
inference(avatar_split_clause,[],[f220,f327,f234,f234,f395]) ).
fof(f220,plain,
! [X0,X1] :
( ~ c
| ~ p(X0)
| ~ p(X1)
| ~ sP10 ),
inference(duplicate_literal_removal,[],[f171]) ).
fof(f171,plain,
! [X0,X1] :
( ~ c
| ~ p(X0)
| ~ c
| ~ p(X1)
| ~ sP10 ),
inference(cnf_transformation,[],[f85]) ).
fof(f393,plain,
( ~ spl52_31
| spl52_32
| ~ spl52_22
| spl52_33 ),
inference(avatar_split_clause,[],[f221,f390,f327,f386,f378]) ).
fof(f221,plain,
( p(sK35)
| ~ c
| p(sK36)
| ~ sP11 ),
inference(duplicate_literal_removal,[],[f162]) ).
fof(f162,plain,
( p(sK35)
| ~ c
| p(sK36)
| ~ c
| ~ sP11 ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
( ( ( ( ! [X0] : ~ p(X0)
& c )
| ! [X1] :
( ~ p(X1)
& c ) )
& ( p(sK35)
| ~ c
| p(sK36)
| ~ c ) )
| ~ sP11 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36])],[f76,f78,f77]) ).
fof(f77,plain,
( ? [X2] : p(X2)
=> p(sK35) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
( ? [X3] :
( p(X3)
| ~ c )
=> ( p(sK36)
| ~ c ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
( ( ( ( ! [X0] : ~ p(X0)
& c )
| ! [X1] :
( ~ p(X1)
& c ) )
& ( ? [X2] : p(X2)
| ~ c
| ? [X3] :
( p(X3)
| ~ c ) ) )
| ~ sP11 ),
inference(rectify,[],[f75]) ).
fof(f75,plain,
( ( ( ( ! [X7] : ~ p(X7)
& c )
| ! [X6] :
( ~ p(X6)
& c ) )
& ( ? [X7] : p(X7)
| ~ c
| ? [X6] :
( p(X6)
| ~ c ) ) )
| ~ sP11 ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
( ( ( ( ! [X7] : ~ p(X7)
& c )
| ! [X6] :
( ~ p(X6)
& c ) )
& ( ? [X7] : p(X7)
| ~ c
| ? [X6] :
( p(X6)
| ~ c ) ) )
| ~ sP11 ),
inference(nnf_transformation,[],[f17]) ).
fof(f384,plain,
( ~ spl52_31
| spl52_22 ),
inference(avatar_split_clause,[],[f222,f327,f378]) ).
fof(f222,plain,
( c
| ~ sP11 ),
inference(duplicate_literal_removal,[],[f163]) ).
fof(f163,plain,
( c
| c
| ~ sP11 ),
inference(cnf_transformation,[],[f79]) ).
fof(f381,plain,
( ~ spl52_31
| spl52_2
| spl52_2 ),
inference(avatar_split_clause,[],[f166,f234,f234,f378]) ).
fof(f166,plain,
! [X0,X1] :
( ~ p(X0)
| ~ p(X1)
| ~ sP11 ),
inference(cnf_transformation,[],[f79]) ).
fof(f376,plain,
( ~ spl52_28
| ~ spl52_29
| ~ spl52_30
| spl52_22 ),
inference(avatar_split_clause,[],[f223,f327,f373,f369,f361]) ).
fof(f223,plain,
( c
| ~ p(sK33)
| ~ p(sK34)
| ~ sP12 ),
inference(duplicate_literal_removal,[],[f157]) ).
fof(f157,plain,
( c
| ~ p(sK33)
| c
| ~ p(sK34)
| ~ sP12 ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
( ( ( ( ~ c
& ! [X0] : p(X0) )
| ! [X1] :
( ~ c
& p(X1) ) )
& ( c
| ~ p(sK33)
| c
| ~ p(sK34) ) )
| ~ sP12 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34])],[f70,f72,f71]) ).
fof(f71,plain,
( ? [X2] : ~ p(X2)
=> ~ p(sK33) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
( ? [X3] :
( c
| ~ p(X3) )
=> ( c
| ~ p(sK34) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
( ( ( ( ~ c
& ! [X0] : p(X0) )
| ! [X1] :
( ~ c
& p(X1) ) )
& ( c
| ? [X2] : ~ p(X2)
| ? [X3] :
( c
| ~ p(X3) ) ) )
| ~ sP12 ),
inference(rectify,[],[f69]) ).
fof(f69,plain,
( ( ( ( ~ c
& ! [X5] : p(X5) )
| ! [X4] :
( ~ c
& p(X4) ) )
& ( c
| ? [X5] : ~ p(X5)
| ? [X4] :
( c
| ~ p(X4) ) ) )
| ~ sP12 ),
inference(flattening,[],[f68]) ).
fof(f68,plain,
( ( ( ( ~ c
& ! [X5] : p(X5) )
| ! [X4] :
( ~ c
& p(X4) ) )
& ( c
| ? [X5] : ~ p(X5)
| ? [X4] :
( c
| ~ p(X4) ) ) )
| ~ sP12 ),
inference(nnf_transformation,[],[f18]) ).
fof(f367,plain,
( ~ spl52_28
| spl52_3
| spl52_3 ),
inference(avatar_split_clause,[],[f158,f238,f238,f361]) ).
fof(f158,plain,
! [X0,X1] :
( p(X0)
| p(X1)
| ~ sP12 ),
inference(cnf_transformation,[],[f73]) ).
fof(f364,plain,
( ~ spl52_28
| ~ spl52_22 ),
inference(avatar_split_clause,[],[f224,f327,f361]) ).
fof(f224,plain,
( ~ c
| ~ sP12 ),
inference(duplicate_literal_removal,[],[f161]) ).
fof(f161,plain,
( ~ c
| ~ c
| ~ sP12 ),
inference(cnf_transformation,[],[f73]) ).
fof(f359,plain,
( ~ spl52_25
| spl52_3
| ~ spl52_22
| spl52_3 ),
inference(avatar_split_clause,[],[f225,f238,f327,f238,f344]) ).
fof(f225,plain,
! [X2,X3] :
( p(X2)
| ~ c
| p(X3)
| ~ sP13 ),
inference(duplicate_literal_removal,[],[f152]) ).
fof(f152,plain,
! [X2,X3] :
( p(X2)
| ~ c
| p(X3)
| ~ c
| ~ sP13 ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
( ( ( ( ~ p(sK31)
& c )
| ( ~ p(sK32)
& c ) )
& ( ! [X2] : p(X2)
| ~ c
| ! [X3] :
( p(X3)
| ~ c ) ) )
| ~ sP13 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32])],[f64,f66,f65]) ).
fof(f65,plain,
( ? [X0] : ~ p(X0)
=> ~ p(sK31) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
( ? [X1] :
( ~ p(X1)
& c )
=> ( ~ p(sK32)
& c ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
( ( ( ( ? [X0] : ~ p(X0)
& c )
| ? [X1] :
( ~ p(X1)
& c ) )
& ( ! [X2] : p(X2)
| ~ c
| ! [X3] :
( p(X3)
| ~ c ) ) )
| ~ sP13 ),
inference(rectify,[],[f63]) ).
fof(f63,plain,
( ( ( ( ? [X3] : ~ p(X3)
& c )
| ? [X2] :
( ~ p(X2)
& c ) )
& ( ! [X3] : p(X3)
| ~ c
| ! [X2] :
( p(X2)
| ~ c ) ) )
| ~ sP13 ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
( ( ( ( ? [X3] : ~ p(X3)
& c )
| ? [X2] :
( ~ p(X2)
& c ) )
& ( ! [X3] : p(X3)
| ~ c
| ! [X2] :
( p(X2)
| ~ c ) ) )
| ~ sP13 ),
inference(nnf_transformation,[],[f19]) ).
fof(f358,plain,
( ~ spl52_25
| spl52_22 ),
inference(avatar_split_clause,[],[f226,f327,f344]) ).
fof(f226,plain,
( c
| ~ sP13 ),
inference(duplicate_literal_removal,[],[f153]) ).
fof(f153,plain,
( c
| c
| ~ sP13 ),
inference(cnf_transformation,[],[f67]) ).
fof(f355,plain,
( ~ spl52_25
| ~ spl52_26
| ~ spl52_27 ),
inference(avatar_split_clause,[],[f156,f352,f348,f344]) ).
fof(f156,plain,
( ~ p(sK31)
| ~ p(sK32)
| ~ sP13 ),
inference(cnf_transformation,[],[f67]) ).
fof(f342,plain,
( ~ spl52_21
| spl52_2
| spl52_2
| spl52_22 ),
inference(avatar_split_clause,[],[f227,f327,f234,f234,f323]) ).
fof(f227,plain,
! [X2,X3] :
( c
| ~ p(X2)
| ~ p(X3)
| ~ sP14 ),
inference(duplicate_literal_removal,[],[f147]) ).
fof(f147,plain,
! [X2,X3] :
( c
| ~ p(X2)
| c
| ~ p(X3)
| ~ sP14 ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
( ( ( ( ~ c
& p(sK29) )
| ( ~ c
& p(sK30) ) )
& ( c
| ! [X2] : ~ p(X2)
| ! [X3] :
( c
| ~ p(X3) ) ) )
| ~ sP14 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30])],[f58,f60,f59]) ).
fof(f59,plain,
( ? [X0] : p(X0)
=> p(sK29) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
( ? [X1] :
( ~ c
& p(X1) )
=> ( ~ c
& p(sK30) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
( ( ( ( ~ c
& ? [X0] : p(X0) )
| ? [X1] :
( ~ c
& p(X1) ) )
& ( c
| ! [X2] : ~ p(X2)
| ! [X3] :
( c
| ~ p(X3) ) ) )
| ~ sP14 ),
inference(rectify,[],[f57]) ).
fof(f57,plain,
( ( ( ( ~ c
& ? [X1] : p(X1) )
| ? [X0] :
( ~ c
& p(X0) ) )
& ( c
| ! [X1] : ~ p(X1)
| ! [X0] :
( c
| ~ p(X0) ) ) )
| ~ sP14 ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
( ( ( ( ~ c
& ? [X1] : p(X1) )
| ? [X0] :
( ~ c
& p(X0) ) )
& ( c
| ! [X1] : ~ p(X1)
| ! [X0] :
( c
| ~ p(X0) ) ) )
| ~ sP14 ),
inference(nnf_transformation,[],[f20]) ).
fof(f341,plain,
( ~ spl52_21
| spl52_23
| spl52_24 ),
inference(avatar_split_clause,[],[f148,f337,f332,f323]) ).
fof(f148,plain,
( p(sK29)
| p(sK30)
| ~ sP14 ),
inference(cnf_transformation,[],[f61]) ).
fof(f330,plain,
( ~ spl52_21
| ~ spl52_22 ),
inference(avatar_split_clause,[],[f228,f327,f323]) ).
fof(f228,plain,
( ~ c
| ~ sP14 ),
inference(duplicate_literal_removal,[],[f151]) ).
fof(f151,plain,
( ~ c
| ~ c
| ~ sP14 ),
inference(cnf_transformation,[],[f61]) ).
fof(f321,plain,
( ~ spl52_19
| spl52_20 ),
inference(avatar_split_clause,[],[f144,f319,f313]) ).
fof(f144,plain,
! [X0] :
( q(X0)
| ~ p(sK28(X0))
| ~ sP15 ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
( ! [X0] :
( ~ q(X0)
& p(X0)
& ( q(X0)
| ~ p(sK28(X0)) ) )
| ~ sP15 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f53,f54]) ).
fof(f54,plain,
! [X0] :
( ? [X1] :
( ~ q(X0)
& p(X0)
& ( q(X0)
| ~ p(X1) ) )
=> ( ~ q(X0)
& p(X0)
& ( q(X0)
| ~ p(sK28(X0)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
( ! [X0] :
? [X1] :
( ~ q(X0)
& p(X0)
& ( q(X0)
| ~ p(X1) ) )
| ~ sP15 ),
inference(rectify,[],[f52]) ).
fof(f52,plain,
( ! [X35] :
? [X36] :
( ~ q(X35)
& p(X35)
& ( q(X35)
| ~ p(X36) ) )
| ~ sP15 ),
inference(nnf_transformation,[],[f21]) ).
fof(f317,plain,
( ~ spl52_19
| spl52_3 ),
inference(avatar_split_clause,[],[f145,f238,f313]) ).
fof(f145,plain,
! [X0] :
( p(X0)
| ~ sP15 ),
inference(cnf_transformation,[],[f55]) ).
fof(f316,plain,
( ~ spl52_19
| spl52_12 ),
inference(avatar_split_clause,[],[f146,f281,f313]) ).
fof(f146,plain,
! [X0] :
( ~ q(X0)
| ~ sP15 ),
inference(cnf_transformation,[],[f55]) ).
fof(f311,plain,
( ~ spl52_15
| spl52_3
| spl52_18 ),
inference(avatar_split_clause,[],[f141,f309,f238,f295]) ).
fof(f141,plain,
! [X2,X1] :
( q(X1)
| p(X2)
| ~ sP16 ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
( ( ~ q(sK27)
& ~ p(sK27)
& ( ! [X1] : q(X1)
| ! [X2] : p(X2) ) )
| ~ sP16 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f49,f50]) ).
fof(f50,plain,
( ? [X0] :
( ~ q(X0)
& ~ p(X0) )
=> ( ~ q(sK27)
& ~ p(sK27) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
( ( ? [X0] :
( ~ q(X0)
& ~ p(X0) )
& ( ! [X1] : q(X1)
| ! [X2] : p(X2) ) )
| ~ sP16 ),
inference(rectify,[],[f48]) ).
fof(f48,plain,
( ( ? [X31] :
( ~ q(X31)
& ~ p(X31) )
& ( ! [X29] : q(X29)
| ! [X30] : p(X30) ) )
| ~ sP16 ),
inference(nnf_transformation,[],[f22]) ).
fof(f307,plain,
( ~ spl52_15
| ~ spl52_17 ),
inference(avatar_split_clause,[],[f142,f304,f295]) ).
fof(f142,plain,
( ~ p(sK27)
| ~ sP16 ),
inference(cnf_transformation,[],[f51]) ).
fof(f302,plain,
( ~ spl52_15
| ~ spl52_16 ),
inference(avatar_split_clause,[],[f143,f299,f295]) ).
fof(f143,plain,
( ~ q(sK27)
| ~ sP16 ),
inference(cnf_transformation,[],[f51]) ).
fof(f293,plain,
( ~ spl52_11
| spl52_14 ),
inference(avatar_split_clause,[],[f138,f290,f277]) ).
fof(f138,plain,
( p(sK26)
| ~ sP17 ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
( ( ( ! [X0] : ~ q(X0)
| ! [X1] : ~ p(X1) )
& q(sK26)
& p(sK26) )
| ~ sP17 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f45,f46]) ).
fof(f46,plain,
( ? [X2] :
( q(X2)
& p(X2) )
=> ( q(sK26)
& p(sK26) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
( ( ( ! [X0] : ~ q(X0)
| ! [X1] : ~ p(X1) )
& ? [X2] :
( q(X2)
& p(X2) ) )
| ~ sP17 ),
inference(rectify,[],[f44]) ).
fof(f44,plain,
( ( ( ! [X22] : ~ q(X22)
| ! [X23] : ~ p(X23) )
& ? [X21] :
( q(X21)
& p(X21) ) )
| ~ sP17 ),
inference(nnf_transformation,[],[f23]) ).
fof(f288,plain,
( ~ spl52_11
| spl52_13 ),
inference(avatar_split_clause,[],[f139,f285,f277]) ).
fof(f139,plain,
( q(sK26)
| ~ sP17 ),
inference(cnf_transformation,[],[f47]) ).
fof(f283,plain,
( ~ spl52_11
| spl52_2
| spl52_12 ),
inference(avatar_split_clause,[],[f140,f281,f234,f277]) ).
fof(f140,plain,
! [X0,X1] :
( ~ q(X0)
| ~ p(X1)
| ~ sP17 ),
inference(cnf_transformation,[],[f47]) ).
fof(f275,plain,
( ~ spl52_8
| spl52_2 ),
inference(avatar_split_clause,[],[f135,f234,f262]) ).
fof(f135,plain,
! [X2] :
( ~ p(X2)
| ~ sP18 ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
( ( ~ p(sK24)
& p(sK25)
& ! [X2] : ~ p(X2) )
| ~ sP18 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f40,f42,f41]) ).
fof(f41,plain,
( ? [X0] :
( ~ p(X0)
& ? [X1] : p(X1) )
=> ( ~ p(sK24)
& ? [X1] : p(X1) ) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
( ? [X1] : p(X1)
=> p(sK25) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
( ( ? [X0] :
( ~ p(X0)
& ? [X1] : p(X1) )
& ! [X2] : ~ p(X2) )
| ~ sP18 ),
inference(rectify,[],[f39]) ).
fof(f39,plain,
( ( ? [X15] :
( ~ p(X15)
& ? [X16] : p(X16) )
& ! [X14] : ~ p(X14) )
| ~ sP18 ),
inference(nnf_transformation,[],[f24]) ).
fof(f274,plain,
( ~ spl52_8
| spl52_10 ),
inference(avatar_split_clause,[],[f136,f271,f262]) ).
fof(f136,plain,
( p(sK25)
| ~ sP18 ),
inference(cnf_transformation,[],[f43]) ).
fof(f260,plain,
( ~ spl52_6
| spl52_3 ),
inference(avatar_split_clause,[],[f133,f238,f252]) ).
fof(f133,plain,
! [X0] :
( p(X0)
| ~ sP19 ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
( ! [X0] :
( ~ p(sK23)
& p(X0) )
| ~ sP19 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f36,f37]) ).
fof(f37,plain,
( ? [X1] : ~ p(X1)
=> ~ p(sK23) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
( ! [X0] :
( ? [X1] : ~ p(X1)
& p(X0) )
| ~ sP19 ),
inference(rectify,[],[f35]) ).
fof(f35,plain,
( ! [X24] :
( ? [X25] : ~ p(X25)
& p(X24) )
| ~ sP19 ),
inference(nnf_transformation,[],[f25]) ).
fof(f259,plain,
( ~ spl52_6
| ~ spl52_7 ),
inference(avatar_split_clause,[],[f134,f256,f252]) ).
fof(f134,plain,
( ~ p(sK23)
| ~ sP19 ),
inference(cnf_transformation,[],[f38]) ).
fof(f250,plain,
( ~ spl52_4
| spl52_3 ),
inference(avatar_split_clause,[],[f131,f238,f242]) ).
fof(f131,plain,
! [X1] :
( p(X1)
| ~ sP20 ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
( ( ~ p(sK22)
& ! [X1] : p(X1) )
| ~ sP20 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f32,f33]) ).
fof(f33,plain,
( ? [X0] :
( ~ p(X0)
& ! [X1] : p(X1) )
=> ( ~ p(sK22)
& ! [X1] : p(X1) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
( ? [X0] :
( ~ p(X0)
& ! [X1] : p(X1) )
| ~ sP20 ),
inference(rectify,[],[f31]) ).
fof(f31,plain,
( ? [X19] :
( ~ p(X19)
& ! [X20] : p(X20) )
| ~ sP20 ),
inference(nnf_transformation,[],[f26]) ).
fof(f249,plain,
( ~ spl52_4
| ~ spl52_5 ),
inference(avatar_split_clause,[],[f132,f246,f242]) ).
fof(f132,plain,
( ~ p(sK22)
| ~ sP20 ),
inference(cnf_transformation,[],[f34]) ).
fof(f240,plain,
( ~ spl52_1
| spl52_3 ),
inference(avatar_split_clause,[],[f129,f238,f230]) ).
fof(f129,plain,
! [X1] :
( p(X1)
| ~ sP21 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
( ( ! [X0] : ~ p(X0)
& ! [X1] : p(X1) )
| ~ sP21 ),
inference(rectify,[],[f29]) ).
fof(f29,plain,
( ( ! [X18] : ~ p(X18)
& ! [X17] : p(X17) )
| ~ sP21 ),
inference(nnf_transformation,[],[f27]) ).
fof(f236,plain,
( ~ spl52_1
| spl52_2 ),
inference(avatar_split_clause,[],[f130,f234,f230]) ).
fof(f130,plain,
! [X0] :
( ~ p(X0)
| ~ sP21 ),
inference(cnf_transformation,[],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN917+1 : TPTP v8.1.2. Released v3.1.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n029.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 17:16:08 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (4397)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (4402)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.38 % (4400)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)
% 0.15/0.38 % (4401)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.38 % (4398)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.38 % (4403)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.38 % (4404)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)
% 0.15/0.38 % (4399)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 Detected minimum model sizes of [1,1,1]
% 0.15/0.38 Detected maximum model sizes of [max,2,3]
% 0.15/0.38 TRYING [1,1,1]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [2,1,1]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 Detected minimum model sizes of [1,1,1]
% 0.15/0.38 Detected maximum model sizes of [max,2,3]
% 0.15/0.38 TRYING [1,1,1]
% 0.15/0.38 % (4403)First to succeed.
% 0.15/0.38 TRYING [3,1,1]
% 0.15/0.38 TRYING [4]
% 0.15/0.38 TRYING [2,1,1]
% 0.15/0.38 TRYING [4]
% 0.15/0.39 TRYING [3,1,1]
% 0.15/0.39 TRYING [2,2,1]
% 0.15/0.39 TRYING [5]
% 0.15/0.39 TRYING [5]
% 0.15/0.39 TRYING [2,1,2]
% 0.15/0.39 TRYING [2,2,1]
% 0.15/0.39 TRYING [3,2,1]
% 0.15/0.39 TRYING [2,1,2]
% 0.15/0.39 TRYING [6]
% 0.15/0.39 % (4403)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4397"
% 0.15/0.39 % (4400)Also succeeded, but the first one will report.
% 0.15/0.39 TRYING [2,2,2]
% 0.15/0.39 TRYING [3,2,1]
% 0.15/0.39 TRYING [6]
% 0.15/0.39 % (4403)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40 % (4403)------------------------------
% 0.15/0.40 % (4403)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.40 % (4403)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (4403)Memory used [KB]: 1071
% 0.15/0.40 % (4403)Time elapsed: 0.015 s
% 0.15/0.40 % (4403)Instructions burned: 22 (million)
% 0.15/0.40 % (4397)Success in time 0.031 s
%------------------------------------------------------------------------------