TSTP Solution File: LCL642+1.001 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : LCL642+1.001 : TPTP v8.1.0. Released v4.0.0.
% 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 : n019.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 17:48:55 EDT 2022
% Result : Theorem 0.21s 0.49s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 66
% Syntax : Number of formulae : 302 ( 5 unt; 0 def)
% Number of atoms : 2256 ( 0 equ)
% Maximal formula atoms : 107 ( 7 avg)
% Number of connectives : 3301 (1347 ~;1407 |; 488 &)
% ( 31 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 42 ( 41 usr; 32 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 5 con; 0-1 aty)
% Number of variables : 799 ( 591 !; 208 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f911,plain,
$false,
inference(avatar_sat_refutation,[],[f135,f139,f144,f153,f157,f309,f324,f329,f354,f488,f555,f581,f605,f629,f658,f672,f673,f675,f695,f721,f725,f745,f754,f797,f809,f823,f826,f851,f894,f899,f901,f910]) ).
fof(f910,plain,
( ~ spl36_5
| spl36_35
| ~ spl36_38
| ~ spl36_91
| ~ spl36_92
| ~ spl36_103 ),
inference(avatar_contradiction_clause,[],[f909]) ).
fof(f909,plain,
( $false
| ~ spl36_5
| spl36_35
| ~ spl36_38
| ~ spl36_91
| ~ spl36_92
| ~ spl36_103 ),
inference(subsumption_resolution,[],[f908,f730]) ).
fof(f730,plain,
( r1(sK29,sK20(sK29))
| ~ spl36_5 ),
inference(resolution,[],[f148,f101]) ).
fof(f101,plain,
! [X0] :
( ~ sP0(X0)
| r1(X0,sK20(X0)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ( r1(X0,sK20(X0))
& ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(sK21(X0),X3) )
& ~ p2(sK21(X0))
& r1(sK20(X0),sK21(X0))
& ! [X5] :
( ( r1(sK22(X5),sK23(X5))
& ~ p2(sK23(X5))
& r1(X5,sK22(X5))
& p2(sK22(X5)) )
| p2(X5)
| ~ r1(X0,X5) ) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23])],[f44,f48,f47,f46,f45]) ).
fof(f45,plain,
! [X0] :
( ? [X1] :
( r1(X0,X1)
& ? [X2] :
( ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
& ~ p2(X2)
& r1(X1,X2) ) )
=> ( r1(X0,sK20(X0))
& ? [X2] :
( ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
& ~ p2(X2)
& r1(sK20(X0),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0] :
( ? [X2] :
( ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
& ~ p2(X2)
& r1(sK20(X0),X2) )
=> ( ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(sK21(X0),X3) )
& ~ p2(sK21(X0))
& r1(sK20(X0),sK21(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
! [X5] :
( ? [X6] :
( ? [X7] :
( r1(X6,X7)
& ~ p2(X7) )
& r1(X5,X6)
& p2(X6) )
=> ( ? [X7] :
( r1(sK22(X5),X7)
& ~ p2(X7) )
& r1(X5,sK22(X5))
& p2(sK22(X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
! [X5] :
( ? [X7] :
( r1(sK22(X5),X7)
& ~ p2(X7) )
=> ( r1(sK22(X5),sK23(X5))
& ~ p2(sK23(X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
! [X0] :
( ( ? [X1] :
( r1(X0,X1)
& ? [X2] :
( ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
& ~ p2(X2)
& r1(X1,X2) ) )
& ! [X5] :
( ? [X6] :
( ? [X7] :
( r1(X6,X7)
& ~ p2(X7) )
& r1(X5,X6)
& p2(X6) )
| p2(X5)
| ~ r1(X0,X5) ) )
| ~ sP0(X0) ),
inference(rectify,[],[f43]) ).
fof(f43,plain,
! [X22] :
( ( ? [X46] :
( r1(X22,X46)
& ? [X47] :
( ! [X48] :
( ~ p2(X48)
| ! [X49] :
( p2(X49)
| ~ r1(X48,X49) )
| ~ r1(X47,X48) )
& ~ p2(X47)
& r1(X46,X47) ) )
& ! [X43] :
( ? [X44] :
( ? [X45] :
( r1(X44,X45)
& ~ p2(X45) )
& r1(X43,X44)
& p2(X44) )
| p2(X43)
| ~ r1(X22,X43) ) )
| ~ sP0(X22) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,plain,
! [X22] :
( ( ? [X46] :
( r1(X22,X46)
& ? [X47] :
( ! [X48] :
( ~ p2(X48)
| ! [X49] :
( p2(X49)
| ~ r1(X48,X49) )
| ~ r1(X47,X48) )
& ~ p2(X47)
& r1(X46,X47) ) )
& ! [X43] :
( ? [X44] :
( ? [X45] :
( r1(X44,X45)
& ~ p2(X45) )
& r1(X43,X44)
& p2(X44) )
| p2(X43)
| ~ r1(X22,X43) ) )
| ~ sP0(X22) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f148,plain,
( sP0(sK29)
| ~ spl36_5 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f146,plain,
( spl36_5
<=> sP0(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_5])]) ).
fof(f908,plain,
( ~ r1(sK29,sK20(sK29))
| ~ spl36_5
| spl36_35
| ~ spl36_38
| ~ spl36_91
| ~ spl36_92
| ~ spl36_103 ),
inference(resolution,[],[f907,f148]) ).
fof(f907,plain,
( ! [X0] :
( ~ sP0(X0)
| ~ r1(X0,sK20(sK29)) )
| spl36_35
| ~ spl36_38
| ~ spl36_91
| ~ spl36_92
| ~ spl36_103 ),
inference(subsumption_resolution,[],[f906,f341]) ).
fof(f341,plain,
( ~ p2(sK20(sK29))
| spl36_35 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f339,plain,
( spl36_35
<=> p2(sK20(sK29)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_35])]) ).
fof(f906,plain,
( ! [X0] :
( p2(sK20(sK29))
| ~ sP0(X0)
| ~ r1(X0,sK20(sK29)) )
| ~ spl36_38
| ~ spl36_91
| ~ spl36_92
| ~ spl36_103 ),
inference(resolution,[],[f905,f96]) ).
fof(f96,plain,
! [X0,X5] :
( ~ p2(sK23(X5))
| ~ r1(X0,X5)
| ~ sP0(X0)
| p2(X5) ),
inference(cnf_transformation,[],[f49]) ).
fof(f905,plain,
( p2(sK23(sK20(sK29)))
| ~ spl36_38
| ~ spl36_91
| ~ spl36_92
| ~ spl36_103 ),
inference(resolution,[],[f904,f898]) ).
fof(f898,plain,
( r1(sK22(sK20(sK29)),sK23(sK20(sK29)))
| ~ spl36_103 ),
inference(avatar_component_clause,[],[f896]) ).
fof(f896,plain,
( spl36_103
<=> r1(sK22(sK20(sK29)),sK23(sK20(sK29))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_103])]) ).
fof(f904,plain,
( ! [X1] :
( ~ r1(sK22(sK20(sK29)),X1)
| p2(X1) )
| ~ spl36_38
| ~ spl36_91
| ~ spl36_92 ),
inference(subsumption_resolution,[],[f903,f744]) ).
fof(f744,plain,
( p2(sK22(sK20(sK29)))
| ~ spl36_91 ),
inference(avatar_component_clause,[],[f742]) ).
fof(f742,plain,
( spl36_91
<=> p2(sK22(sK20(sK29))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_91])]) ).
fof(f903,plain,
( ! [X1] :
( ~ p2(sK22(sK20(sK29)))
| ~ r1(sK22(sK20(sK29)),X1)
| p2(X1) )
| ~ spl36_38
| ~ spl36_92 ),
inference(resolution,[],[f353,f753]) ).
fof(f753,plain,
( r1(sK20(sK29),sK22(sK20(sK29)))
| ~ spl36_92 ),
inference(avatar_component_clause,[],[f751]) ).
fof(f751,plain,
( spl36_92
<=> r1(sK20(sK29),sK22(sK20(sK29))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_92])]) ).
fof(f353,plain,
( ! [X0,X1] :
( ~ r1(sK20(sK29),X0)
| ~ p2(X0)
| ~ r1(X0,X1)
| p2(X1) )
| ~ spl36_38 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f352,plain,
( spl36_38
<=> ! [X0,X1] :
( p2(X1)
| ~ r1(sK20(sK29),X0)
| ~ p2(X0)
| ~ r1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_38])]) ).
fof(f901,plain,
( ~ spl36_35
| spl36_36
| ~ spl36_2
| ~ spl36_5
| spl36_37 ),
inference(avatar_split_clause,[],[f900,f347,f146,f133,f343,f339]) ).
fof(f343,plain,
( spl36_36
<=> sP3(sK20(sK29)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_36])]) ).
fof(f133,plain,
( spl36_2
<=> ! [X7] :
( sP3(X7)
| ~ r1(sK29,X7)
| sP2(X7)
| ~ p2(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_2])]) ).
fof(f347,plain,
( spl36_37
<=> sP2(sK20(sK29)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_37])]) ).
fof(f900,plain,
( sP3(sK20(sK29))
| ~ p2(sK20(sK29))
| ~ spl36_2
| ~ spl36_5
| spl36_37 ),
inference(subsumption_resolution,[],[f737,f348]) ).
fof(f348,plain,
( ~ sP2(sK20(sK29))
| spl36_37 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f737,plain,
( sP3(sK20(sK29))
| ~ p2(sK20(sK29))
| sP2(sK20(sK29))
| ~ spl36_2
| ~ spl36_5 ),
inference(resolution,[],[f730,f134]) ).
fof(f134,plain,
( ! [X7] :
( ~ r1(sK29,X7)
| sP2(X7)
| ~ p2(X7)
| sP3(X7) )
| ~ spl36_2 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f899,plain,
( spl36_103
| spl36_35
| ~ spl36_5 ),
inference(avatar_split_clause,[],[f758,f146,f339,f896]) ).
fof(f758,plain,
( p2(sK20(sK29))
| r1(sK22(sK20(sK29)),sK23(sK20(sK29)))
| ~ spl36_5 ),
inference(resolution,[],[f727,f730]) ).
fof(f727,plain,
( ! [X2] :
( ~ r1(sK29,X2)
| r1(sK22(X2),sK23(X2))
| p2(X2) )
| ~ spl36_5 ),
inference(resolution,[],[f148,f97]) ).
fof(f97,plain,
! [X0,X5] :
( ~ sP0(X0)
| ~ r1(X0,X5)
| r1(sK22(X5),sK23(X5))
| p2(X5) ),
inference(cnf_transformation,[],[f49]) ).
fof(f894,plain,
( ~ spl36_5
| ~ spl36_36
| spl36_98 ),
inference(avatar_contradiction_clause,[],[f893]) ).
fof(f893,plain,
( $false
| ~ spl36_5
| ~ spl36_36
| spl36_98 ),
inference(subsumption_resolution,[],[f892,f345]) ).
fof(f345,plain,
( sP3(sK20(sK29))
| ~ spl36_36 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f892,plain,
( ~ sP3(sK20(sK29))
| ~ spl36_5
| ~ spl36_36
| spl36_98 ),
inference(subsumption_resolution,[],[f891,f148]) ).
fof(f891,plain,
( ~ sP0(sK29)
| ~ sP3(sK20(sK29))
| ~ spl36_5
| ~ spl36_36
| spl36_98 ),
inference(resolution,[],[f888,f98]) ).
fof(f98,plain,
! [X0] :
( r1(sK20(X0),sK21(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f888,plain,
( ! [X0] :
( ~ r1(X0,sK21(sK29))
| ~ sP3(X0) )
| ~ spl36_5
| ~ spl36_36
| spl36_98 ),
inference(subsumption_resolution,[],[f887,f795]) ).
fof(f795,plain,
( ~ p2(sK21(sK29))
| spl36_98 ),
inference(avatar_component_clause,[],[f794]) ).
fof(f794,plain,
( spl36_98
<=> p2(sK21(sK29)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_98])]) ).
fof(f887,plain,
( ! [X0] :
( ~ sP3(X0)
| ~ r1(X0,sK21(sK29))
| p2(sK21(sK29)) )
| ~ spl36_5
| ~ spl36_36
| spl36_98 ),
inference(resolution,[],[f882,f81]) ).
fof(f81,plain,
! [X0,X1] :
( ~ p2(sK12(X1))
| p2(X1)
| ~ sP3(X0)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| ( ( ( ~ p2(sK12(X1))
& r1(sK11(X1),sK12(X1))
& p2(sK11(X1))
& r1(X1,sK11(X1)) )
| p2(X1) )
& ( ( ! [X5] :
( ~ p2(X5)
| ~ r1(sK13(X1),X5)
| ! [X6] :
( p2(X6)
| ~ r1(X5,X6) ) )
& ~ p2(sK13(X1))
& r1(X1,sK13(X1)) )
| sP1(X1) ) ) )
| ~ sP3(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f26,f29,f28,f27]) ).
fof(f27,plain,
! [X1] :
( ? [X2] :
( ? [X3] :
( ~ p2(X3)
& r1(X2,X3) )
& p2(X2)
& r1(X1,X2) )
=> ( ? [X3] :
( ~ p2(X3)
& r1(sK11(X1),X3) )
& p2(sK11(X1))
& r1(X1,sK11(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X1] :
( ? [X3] :
( ~ p2(X3)
& r1(sK11(X1),X3) )
=> ( ~ p2(sK12(X1))
& r1(sK11(X1),sK12(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X1] :
( ? [X4] :
( ! [X5] :
( ~ p2(X5)
| ~ r1(X4,X5)
| ! [X6] :
( p2(X6)
| ~ r1(X5,X6) ) )
& ~ p2(X4)
& r1(X1,X4) )
=> ( ! [X5] :
( ~ p2(X5)
| ~ r1(sK13(X1),X5)
| ! [X6] :
( p2(X6)
| ~ r1(X5,X6) ) )
& ~ p2(sK13(X1))
& r1(X1,sK13(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
! [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| ( ( ? [X2] :
( ? [X3] :
( ~ p2(X3)
& r1(X2,X3) )
& p2(X2)
& r1(X1,X2) )
| p2(X1) )
& ( ? [X4] :
( ! [X5] :
( ~ p2(X5)
| ~ r1(X4,X5)
| ! [X6] :
( p2(X6)
| ~ r1(X5,X6) ) )
& ~ p2(X4)
& r1(X1,X4) )
| sP1(X1) ) ) )
| ~ sP3(X0) ),
inference(rectify,[],[f25]) ).
fof(f25,plain,
! [X23] :
( ! [X24] :
( ~ r1(X23,X24)
| ( ( ? [X32] :
( ? [X33] :
( ~ p2(X33)
& r1(X32,X33) )
& p2(X32)
& r1(X24,X32) )
| p2(X24) )
& ( ? [X29] :
( ! [X30] :
( ~ p2(X30)
| ~ r1(X29,X30)
| ! [X31] :
( p2(X31)
| ~ r1(X30,X31) ) )
& ~ p2(X29)
& r1(X24,X29) )
| sP1(X24) ) ) )
| ~ sP3(X23) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,plain,
! [X23] :
( ! [X24] :
( ~ r1(X23,X24)
| ( ( ? [X32] :
( ? [X33] :
( ~ p2(X33)
& r1(X32,X33) )
& p2(X32)
& r1(X24,X32) )
| p2(X24) )
& ( ? [X29] :
( ! [X30] :
( ~ p2(X30)
| ~ r1(X29,X30)
| ! [X31] :
( p2(X31)
| ~ r1(X30,X31) ) )
& ~ p2(X29)
& r1(X24,X29) )
| sP1(X24) ) ) )
| ~ sP3(X23) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f882,plain,
( p2(sK12(sK21(sK29)))
| ~ spl36_5
| ~ spl36_36
| spl36_98 ),
inference(resolution,[],[f881,f876]) ).
fof(f876,plain,
( r1(sK11(sK21(sK29)),sK12(sK21(sK29)))
| ~ spl36_5
| ~ spl36_36
| spl36_98 ),
inference(subsumption_resolution,[],[f875,f148]) ).
fof(f875,plain,
( ~ sP0(sK29)
| r1(sK11(sK21(sK29)),sK12(sK21(sK29)))
| ~ spl36_36
| spl36_98 ),
inference(subsumption_resolution,[],[f874,f795]) ).
fof(f874,plain,
( p2(sK21(sK29))
| ~ sP0(sK29)
| r1(sK11(sK21(sK29)),sK12(sK21(sK29)))
| ~ spl36_36 ),
inference(resolution,[],[f853,f98]) ).
fof(f853,plain,
( ! [X3] :
( ~ r1(sK20(sK29),X3)
| r1(sK11(X3),sK12(X3))
| p2(X3) )
| ~ spl36_36 ),
inference(resolution,[],[f345,f80]) ).
fof(f80,plain,
! [X0,X1] :
( ~ sP3(X0)
| ~ r1(X0,X1)
| p2(X1)
| r1(sK11(X1),sK12(X1)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f881,plain,
( ! [X0] :
( ~ r1(sK11(sK21(sK29)),X0)
| p2(X0) )
| ~ spl36_5
| ~ spl36_36
| spl36_98 ),
inference(subsumption_resolution,[],[f880,f859]) ).
fof(f859,plain,
( p2(sK11(sK21(sK29)))
| ~ spl36_5
| ~ spl36_36
| spl36_98 ),
inference(subsumption_resolution,[],[f858,f795]) ).
fof(f858,plain,
( p2(sK21(sK29))
| p2(sK11(sK21(sK29)))
| ~ spl36_5
| ~ spl36_36 ),
inference(subsumption_resolution,[],[f857,f148]) ).
fof(f857,plain,
( ~ sP0(sK29)
| p2(sK21(sK29))
| p2(sK11(sK21(sK29)))
| ~ spl36_36 ),
inference(resolution,[],[f856,f98]) ).
fof(f856,plain,
( ! [X6] :
( ~ r1(sK20(sK29),X6)
| p2(sK11(X6))
| p2(X6) )
| ~ spl36_36 ),
inference(resolution,[],[f345,f79]) ).
fof(f79,plain,
! [X0,X1] :
( ~ sP3(X0)
| ~ r1(X0,X1)
| p2(X1)
| p2(sK11(X1)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f880,plain,
( ! [X0] :
( p2(X0)
| ~ p2(sK11(sK21(sK29)))
| ~ r1(sK11(sK21(sK29)),X0) )
| ~ spl36_5
| ~ spl36_36
| spl36_98 ),
inference(resolution,[],[f862,f726]) ).
fof(f726,plain,
( ! [X0,X1] :
( ~ r1(sK21(sK29),X0)
| ~ p2(X0)
| ~ r1(X0,X1)
| p2(X1) )
| ~ spl36_5 ),
inference(resolution,[],[f148,f100]) ).
fof(f100,plain,
! [X3,X0,X4] :
( ~ sP0(X0)
| ~ r1(X3,X4)
| p2(X4)
| ~ r1(sK21(X0),X3)
| ~ p2(X3) ),
inference(cnf_transformation,[],[f49]) ).
fof(f862,plain,
( r1(sK21(sK29),sK11(sK21(sK29)))
| ~ spl36_5
| ~ spl36_36
| spl36_98 ),
inference(subsumption_resolution,[],[f861,f148]) ).
fof(f861,plain,
( r1(sK21(sK29),sK11(sK21(sK29)))
| ~ sP0(sK29)
| ~ spl36_36
| spl36_98 ),
inference(subsumption_resolution,[],[f860,f795]) ).
fof(f860,plain,
( p2(sK21(sK29))
| r1(sK21(sK29),sK11(sK21(sK29)))
| ~ sP0(sK29)
| ~ spl36_36 ),
inference(resolution,[],[f854,f98]) ).
fof(f854,plain,
( ! [X4] :
( ~ r1(sK20(sK29),X4)
| r1(X4,sK11(X4))
| p2(X4) )
| ~ spl36_36 ),
inference(resolution,[],[f345,f78]) ).
fof(f78,plain,
! [X0,X1] :
( ~ sP3(X0)
| r1(X1,sK11(X1))
| ~ r1(X0,X1)
| p2(X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f851,plain,
( ~ spl36_37
| ~ spl36_5
| ~ spl36_97
| spl36_98
| ~ spl36_99
| ~ spl36_100 ),
inference(avatar_split_clause,[],[f850,f820,f806,f794,f790,f146,f347]) ).
fof(f790,plain,
( spl36_97
<=> p2(sK16(sK21(sK29))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_97])]) ).
fof(f806,plain,
( spl36_99
<=> r1(sK21(sK29),sK16(sK21(sK29))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_99])]) ).
fof(f820,plain,
( spl36_100
<=> r1(sK16(sK21(sK29)),sK17(sK21(sK29))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_100])]) ).
fof(f850,plain,
( ~ sP2(sK20(sK29))
| ~ spl36_5
| ~ spl36_97
| spl36_98
| ~ spl36_99
| ~ spl36_100 ),
inference(subsumption_resolution,[],[f846,f148]) ).
fof(f846,plain,
( ~ sP2(sK20(sK29))
| ~ sP0(sK29)
| ~ spl36_5
| ~ spl36_97
| spl36_98
| ~ spl36_99
| ~ spl36_100 ),
inference(resolution,[],[f845,f98]) ).
fof(f845,plain,
( ! [X0] :
( ~ r1(X0,sK21(sK29))
| ~ sP2(X0) )
| ~ spl36_5
| ~ spl36_97
| spl36_98
| ~ spl36_99
| ~ spl36_100 ),
inference(subsumption_resolution,[],[f844,f795]) ).
fof(f844,plain,
( ! [X0] :
( p2(sK21(sK29))
| ~ sP2(X0)
| ~ r1(X0,sK21(sK29)) )
| ~ spl36_5
| ~ spl36_97
| ~ spl36_99
| ~ spl36_100 ),
inference(resolution,[],[f843,f85]) ).
fof(f85,plain,
! [X0,X5] :
( ~ p2(sK17(X5))
| ~ sP2(X0)
| ~ r1(X0,X5)
| p2(X5) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ( r1(X0,sK14(X0))
& ~ p2(sK15(X0))
& r1(sK14(X0),sK15(X0))
& ! [X3] :
( ! [X4] :
( ~ r1(X3,X4)
| p2(X4) )
| ~ r1(sK15(X0),X3)
| ~ p2(X3) )
& ! [X5] :
( ~ r1(X0,X5)
| p2(X5)
| ( ~ p2(sK17(X5))
& r1(sK16(X5),sK17(X5))
& p2(sK16(X5))
& r1(X5,sK16(X5)) ) ) )
| ~ sP2(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17])],[f32,f36,f35,f34,f33]) ).
fof(f33,plain,
! [X0] :
( ? [X1] :
( r1(X0,X1)
& ? [X2] :
( ~ p2(X2)
& r1(X1,X2)
& ! [X3] :
( ! [X4] :
( ~ r1(X3,X4)
| p2(X4) )
| ~ r1(X2,X3)
| ~ p2(X3) ) ) )
=> ( r1(X0,sK14(X0))
& ? [X2] :
( ~ p2(X2)
& r1(sK14(X0),X2)
& ! [X3] :
( ! [X4] :
( ~ r1(X3,X4)
| p2(X4) )
| ~ r1(X2,X3)
| ~ p2(X3) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0] :
( ? [X2] :
( ~ p2(X2)
& r1(sK14(X0),X2)
& ! [X3] :
( ! [X4] :
( ~ r1(X3,X4)
| p2(X4) )
| ~ r1(X2,X3)
| ~ p2(X3) ) )
=> ( ~ p2(sK15(X0))
& r1(sK14(X0),sK15(X0))
& ! [X3] :
( ! [X4] :
( ~ r1(X3,X4)
| p2(X4) )
| ~ r1(sK15(X0),X3)
| ~ p2(X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
! [X5] :
( ? [X6] :
( ? [X7] :
( ~ p2(X7)
& r1(X6,X7) )
& p2(X6)
& r1(X5,X6) )
=> ( ? [X7] :
( ~ p2(X7)
& r1(sK16(X5),X7) )
& p2(sK16(X5))
& r1(X5,sK16(X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
! [X5] :
( ? [X7] :
( ~ p2(X7)
& r1(sK16(X5),X7) )
=> ( ~ p2(sK17(X5))
& r1(sK16(X5),sK17(X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
! [X0] :
( ( ? [X1] :
( r1(X0,X1)
& ? [X2] :
( ~ p2(X2)
& r1(X1,X2)
& ! [X3] :
( ! [X4] :
( ~ r1(X3,X4)
| p2(X4) )
| ~ r1(X2,X3)
| ~ p2(X3) ) ) )
& ! [X5] :
( ~ r1(X0,X5)
| p2(X5)
| ? [X6] :
( ? [X7] :
( ~ p2(X7)
& r1(X6,X7) )
& p2(X6)
& r1(X5,X6) ) ) )
| ~ sP2(X0) ),
inference(rectify,[],[f31]) ).
fof(f31,plain,
! [X23] :
( ( ? [X36] :
( r1(X23,X36)
& ? [X37] :
( ~ p2(X37)
& r1(X36,X37)
& ! [X38] :
( ! [X39] :
( ~ r1(X38,X39)
| p2(X39) )
| ~ r1(X37,X38)
| ~ p2(X38) ) ) )
& ! [X40] :
( ~ r1(X23,X40)
| p2(X40)
| ? [X41] :
( ? [X42] :
( ~ p2(X42)
& r1(X41,X42) )
& p2(X41)
& r1(X40,X41) ) ) )
| ~ sP2(X23) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,plain,
! [X23] :
( ( ? [X36] :
( r1(X23,X36)
& ? [X37] :
( ~ p2(X37)
& r1(X36,X37)
& ! [X38] :
( ! [X39] :
( ~ r1(X38,X39)
| p2(X39) )
| ~ r1(X37,X38)
| ~ p2(X38) ) ) )
& ! [X40] :
( ~ r1(X23,X40)
| p2(X40)
| ? [X41] :
( ? [X42] :
( ~ p2(X42)
& r1(X41,X42) )
& p2(X41)
& r1(X40,X41) ) ) )
| ~ sP2(X23) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f843,plain,
( p2(sK17(sK21(sK29)))
| ~ spl36_5
| ~ spl36_97
| ~ spl36_99
| ~ spl36_100 ),
inference(resolution,[],[f829,f822]) ).
fof(f822,plain,
( r1(sK16(sK21(sK29)),sK17(sK21(sK29)))
| ~ spl36_100 ),
inference(avatar_component_clause,[],[f820]) ).
fof(f829,plain,
( ! [X0] :
( ~ r1(sK16(sK21(sK29)),X0)
| p2(X0) )
| ~ spl36_5
| ~ spl36_97
| ~ spl36_99 ),
inference(subsumption_resolution,[],[f828,f792]) ).
fof(f792,plain,
( p2(sK16(sK21(sK29)))
| ~ spl36_97 ),
inference(avatar_component_clause,[],[f790]) ).
fof(f828,plain,
( ! [X0] :
( ~ r1(sK16(sK21(sK29)),X0)
| p2(X0)
| ~ p2(sK16(sK21(sK29))) )
| ~ spl36_5
| ~ spl36_99 ),
inference(resolution,[],[f808,f726]) ).
fof(f808,plain,
( r1(sK21(sK29),sK16(sK21(sK29)))
| ~ spl36_99 ),
inference(avatar_component_clause,[],[f806]) ).
fof(f826,plain,
( ~ spl36_5
| ~ spl36_98 ),
inference(avatar_contradiction_clause,[],[f825]) ).
fof(f825,plain,
( $false
| ~ spl36_5
| ~ spl36_98 ),
inference(subsumption_resolution,[],[f824,f148]) ).
fof(f824,plain,
( ~ sP0(sK29)
| ~ spl36_98 ),
inference(resolution,[],[f796,f99]) ).
fof(f99,plain,
! [X0] :
( ~ p2(sK21(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f796,plain,
( p2(sK21(sK29))
| ~ spl36_98 ),
inference(avatar_component_clause,[],[f794]) ).
fof(f823,plain,
( spl36_98
| spl36_100
| ~ spl36_5
| ~ spl36_37 ),
inference(avatar_split_clause,[],[f818,f347,f146,f820,f794]) ).
fof(f818,plain,
( r1(sK16(sK21(sK29)),sK17(sK21(sK29)))
| p2(sK21(sK29))
| ~ spl36_5
| ~ spl36_37 ),
inference(subsumption_resolution,[],[f816,f148]) ).
fof(f816,plain,
( p2(sK21(sK29))
| ~ sP0(sK29)
| r1(sK16(sK21(sK29)),sK17(sK21(sK29)))
| ~ spl36_37 ),
inference(resolution,[],[f732,f98]) ).
fof(f732,plain,
( ! [X2] :
( ~ r1(sK20(sK29),X2)
| p2(X2)
| r1(sK16(X2),sK17(X2)) )
| ~ spl36_37 ),
inference(resolution,[],[f349,f84]) ).
fof(f84,plain,
! [X0,X5] :
( ~ sP2(X0)
| p2(X5)
| ~ r1(X0,X5)
| r1(sK16(X5),sK17(X5)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f349,plain,
( sP2(sK20(sK29))
| ~ spl36_37 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f809,plain,
( spl36_99
| spl36_98
| ~ spl36_5
| ~ spl36_37 ),
inference(avatar_split_clause,[],[f804,f347,f146,f794,f806]) ).
fof(f804,plain,
( p2(sK21(sK29))
| r1(sK21(sK29),sK16(sK21(sK29)))
| ~ spl36_5
| ~ spl36_37 ),
inference(subsumption_resolution,[],[f802,f148]) ).
fof(f802,plain,
( r1(sK21(sK29),sK16(sK21(sK29)))
| ~ sP0(sK29)
| p2(sK21(sK29))
| ~ spl36_37 ),
inference(resolution,[],[f733,f98]) ).
fof(f733,plain,
( ! [X3] :
( ~ r1(sK20(sK29),X3)
| p2(X3)
| r1(X3,sK16(X3)) )
| ~ spl36_37 ),
inference(resolution,[],[f349,f82]) ).
fof(f82,plain,
! [X0,X5] :
( ~ sP2(X0)
| ~ r1(X0,X5)
| r1(X5,sK16(X5))
| p2(X5) ),
inference(cnf_transformation,[],[f37]) ).
fof(f797,plain,
( spl36_97
| spl36_98
| ~ spl36_5
| ~ spl36_37 ),
inference(avatar_split_clause,[],[f788,f347,f146,f794,f790]) ).
fof(f788,plain,
( p2(sK21(sK29))
| p2(sK16(sK21(sK29)))
| ~ spl36_5
| ~ spl36_37 ),
inference(subsumption_resolution,[],[f777,f148]) ).
fof(f777,plain,
( p2(sK16(sK21(sK29)))
| p2(sK21(sK29))
| ~ sP0(sK29)
| ~ spl36_37 ),
inference(resolution,[],[f734,f98]) ).
fof(f734,plain,
( ! [X4] :
( ~ r1(sK20(sK29),X4)
| p2(sK16(X4))
| p2(X4) )
| ~ spl36_37 ),
inference(resolution,[],[f349,f83]) ).
fof(f83,plain,
! [X0,X5] :
( ~ sP2(X0)
| p2(sK16(X5))
| ~ r1(X0,X5)
| p2(X5) ),
inference(cnf_transformation,[],[f37]) ).
fof(f754,plain,
( spl36_35
| spl36_92
| ~ spl36_5 ),
inference(avatar_split_clause,[],[f749,f146,f751,f339]) ).
fof(f749,plain,
( r1(sK20(sK29),sK22(sK20(sK29)))
| p2(sK20(sK29))
| ~ spl36_5 ),
inference(resolution,[],[f728,f730]) ).
fof(f728,plain,
( ! [X3] :
( ~ r1(sK29,X3)
| p2(X3)
| r1(X3,sK22(X3)) )
| ~ spl36_5 ),
inference(resolution,[],[f148,f95]) ).
fof(f95,plain,
! [X0,X5] :
( ~ sP0(X0)
| ~ r1(X0,X5)
| r1(X5,sK22(X5))
| p2(X5) ),
inference(cnf_transformation,[],[f49]) ).
fof(f745,plain,
( spl36_35
| spl36_91
| ~ spl36_5 ),
inference(avatar_split_clause,[],[f740,f146,f742,f339]) ).
fof(f740,plain,
( p2(sK22(sK20(sK29)))
| p2(sK20(sK29))
| ~ spl36_5 ),
inference(resolution,[],[f729,f730]) ).
fof(f729,plain,
( ! [X4] :
( ~ r1(sK29,X4)
| p2(X4)
| p2(sK22(X4)) )
| ~ spl36_5 ),
inference(resolution,[],[f148,f94]) ).
fof(f94,plain,
! [X0,X5] :
( ~ sP0(X0)
| ~ r1(X0,X5)
| p2(sK22(X5))
| p2(X5) ),
inference(cnf_transformation,[],[f49]) ).
fof(f725,plain,
( ~ spl36_4
| spl36_6
| ~ spl36_81 ),
inference(avatar_contradiction_clause,[],[f724]) ).
fof(f724,plain,
( $false
| ~ spl36_4
| spl36_6
| ~ spl36_81 ),
inference(subsumption_resolution,[],[f723,f152]) ).
fof(f152,plain,
( ~ p2(sK29)
| spl36_6 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f150,plain,
( spl36_6
<=> p2(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_6])]) ).
fof(f723,plain,
( p2(sK29)
| ~ spl36_4
| ~ spl36_81 ),
inference(subsumption_resolution,[],[f722,f143]) ).
fof(f143,plain,
( r1(sK24,sK29)
| ~ spl36_4 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f141,plain,
( spl36_4
<=> r1(sK24,sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_4])]) ).
fof(f722,plain,
( ~ r1(sK24,sK29)
| p2(sK29)
| ~ spl36_81 ),
inference(resolution,[],[f588,f107]) ).
fof(f107,plain,
! [X15] :
( ~ p2(sK33(X15))
| p2(X15)
| ~ r1(sK24,X15) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
( ~ p2(sK25)
& r1(sK24,sK25)
& ! [X2] :
( ( p1(sK26(X2))
& r1(X2,sK26(X2))
& ~ p1(sK27(X2))
& r1(sK26(X2),sK27(X2)) )
| p1(X2)
| ~ r1(sK24,X2) )
& r1(sK24,sK28)
& ~ p3(sK28)
& ( sP5(sK24)
| ( ! [X7] :
( ( ~ p2(X7)
& ! [X8] :
( ~ p2(X8)
| ~ r1(X7,X8)
| ! [X9] :
( p2(X9)
| ~ r1(X8,X9) ) ) )
| ~ r1(sK29,X7)
| sP3(X7)
| sP2(X7) )
& ( sP0(sK29)
| ( ! [X10] :
( ~ p2(X10)
| ! [X11] :
( ~ r1(X10,X11)
| p2(X11) )
| ~ r1(sK29,X10) )
& ~ p2(sK29) ) )
& r1(sK24,sK29) ) )
& ! [X12] :
( ~ r1(sK24,X12)
| p3(X12)
| ( p3(sK30(X12))
& r1(X12,sK30(X12))
& ~ p3(sK31(X12))
& r1(sK30(X12),sK31(X12)) ) )
& ! [X15] :
( ~ r1(sK24,X15)
| ( r1(X15,sK32(X15))
& p2(sK32(X15))
& r1(sK32(X15),sK33(X15))
& ~ p2(sK33(X15)) )
| p2(X15) )
& ! [X18] :
( ( ! [X20] :
( ~ p2(X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) )
| ~ r1(sK34(X18),X20) )
& r1(X18,sK34(X18))
& ~ p2(sK34(X18)) )
| p2(X18)
| ~ r1(sK24,X18) )
& ~ p1(sK35)
& r1(sK24,sK35) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25,sK26,sK27,sK28,sK29,sK30,sK31,sK32,sK33,sK34,sK35])],[f50,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51]) ).
fof(f51,plain,
( ? [X0] :
( ? [X1] :
( ~ p2(X1)
& r1(X0,X1) )
& ! [X2] :
( ? [X3] :
( p1(X3)
& r1(X2,X3)
& ? [X4] :
( ~ p1(X4)
& r1(X3,X4) ) )
| p1(X2)
| ~ r1(X0,X2) )
& ? [X5] :
( r1(X0,X5)
& ~ p3(X5) )
& ( sP5(X0)
| ? [X6] :
( ! [X7] :
( ( ~ p2(X7)
& ! [X8] :
( ~ p2(X8)
| ~ r1(X7,X8)
| ! [X9] :
( p2(X9)
| ~ r1(X8,X9) ) ) )
| ~ r1(X6,X7)
| sP3(X7)
| sP2(X7) )
& ( sP0(X6)
| ( ! [X10] :
( ~ p2(X10)
| ! [X11] :
( ~ r1(X10,X11)
| p2(X11) )
| ~ r1(X6,X10) )
& ~ p2(X6) ) )
& r1(X0,X6) ) )
& ! [X12] :
( ~ r1(X0,X12)
| p3(X12)
| ? [X13] :
( p3(X13)
& r1(X12,X13)
& ? [X14] :
( ~ p3(X14)
& r1(X13,X14) ) ) )
& ! [X15] :
( ~ r1(X0,X15)
| ? [X16] :
( r1(X15,X16)
& p2(X16)
& ? [X17] :
( r1(X16,X17)
& ~ p2(X17) ) )
| p2(X15) )
& ! [X18] :
( ? [X19] :
( ! [X20] :
( ~ p2(X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
& r1(X18,X19)
& ~ p2(X19) )
| p2(X18)
| ~ r1(X0,X18) )
& ? [X22] :
( ~ p1(X22)
& r1(X0,X22) ) )
=> ( ? [X1] :
( ~ p2(X1)
& r1(sK24,X1) )
& ! [X2] :
( ? [X3] :
( p1(X3)
& r1(X2,X3)
& ? [X4] :
( ~ p1(X4)
& r1(X3,X4) ) )
| p1(X2)
| ~ r1(sK24,X2) )
& ? [X5] :
( r1(sK24,X5)
& ~ p3(X5) )
& ( sP5(sK24)
| ? [X6] :
( ! [X7] :
( ( ~ p2(X7)
& ! [X8] :
( ~ p2(X8)
| ~ r1(X7,X8)
| ! [X9] :
( p2(X9)
| ~ r1(X8,X9) ) ) )
| ~ r1(X6,X7)
| sP3(X7)
| sP2(X7) )
& ( sP0(X6)
| ( ! [X10] :
( ~ p2(X10)
| ! [X11] :
( ~ r1(X10,X11)
| p2(X11) )
| ~ r1(X6,X10) )
& ~ p2(X6) ) )
& r1(sK24,X6) ) )
& ! [X12] :
( ~ r1(sK24,X12)
| p3(X12)
| ? [X13] :
( p3(X13)
& r1(X12,X13)
& ? [X14] :
( ~ p3(X14)
& r1(X13,X14) ) ) )
& ! [X15] :
( ~ r1(sK24,X15)
| ? [X16] :
( r1(X15,X16)
& p2(X16)
& ? [X17] :
( r1(X16,X17)
& ~ p2(X17) ) )
| p2(X15) )
& ! [X18] :
( ? [X19] :
( ! [X20] :
( ~ p2(X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
& r1(X18,X19)
& ~ p2(X19) )
| p2(X18)
| ~ r1(sK24,X18) )
& ? [X22] :
( ~ p1(X22)
& r1(sK24,X22) ) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
( ? [X1] :
( ~ p2(X1)
& r1(sK24,X1) )
=> ( ~ p2(sK25)
& r1(sK24,sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
! [X2] :
( ? [X3] :
( p1(X3)
& r1(X2,X3)
& ? [X4] :
( ~ p1(X4)
& r1(X3,X4) ) )
=> ( p1(sK26(X2))
& r1(X2,sK26(X2))
& ? [X4] :
( ~ p1(X4)
& r1(sK26(X2),X4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X2] :
( ? [X4] :
( ~ p1(X4)
& r1(sK26(X2),X4) )
=> ( ~ p1(sK27(X2))
& r1(sK26(X2),sK27(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
( ? [X5] :
( r1(sK24,X5)
& ~ p3(X5) )
=> ( r1(sK24,sK28)
& ~ p3(sK28) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
( ? [X6] :
( ! [X7] :
( ( ~ p2(X7)
& ! [X8] :
( ~ p2(X8)
| ~ r1(X7,X8)
| ! [X9] :
( p2(X9)
| ~ r1(X8,X9) ) ) )
| ~ r1(X6,X7)
| sP3(X7)
| sP2(X7) )
& ( sP0(X6)
| ( ! [X10] :
( ~ p2(X10)
| ! [X11] :
( ~ r1(X10,X11)
| p2(X11) )
| ~ r1(X6,X10) )
& ~ p2(X6) ) )
& r1(sK24,X6) )
=> ( ! [X7] :
( ( ~ p2(X7)
& ! [X8] :
( ~ p2(X8)
| ~ r1(X7,X8)
| ! [X9] :
( p2(X9)
| ~ r1(X8,X9) ) ) )
| ~ r1(sK29,X7)
| sP3(X7)
| sP2(X7) )
& ( sP0(sK29)
| ( ! [X10] :
( ~ p2(X10)
| ! [X11] :
( ~ r1(X10,X11)
| p2(X11) )
| ~ r1(sK29,X10) )
& ~ p2(sK29) ) )
& r1(sK24,sK29) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
! [X12] :
( ? [X13] :
( p3(X13)
& r1(X12,X13)
& ? [X14] :
( ~ p3(X14)
& r1(X13,X14) ) )
=> ( p3(sK30(X12))
& r1(X12,sK30(X12))
& ? [X14] :
( ~ p3(X14)
& r1(sK30(X12),X14) ) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
! [X12] :
( ? [X14] :
( ~ p3(X14)
& r1(sK30(X12),X14) )
=> ( ~ p3(sK31(X12))
& r1(sK30(X12),sK31(X12)) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X15] :
( ? [X16] :
( r1(X15,X16)
& p2(X16)
& ? [X17] :
( r1(X16,X17)
& ~ p2(X17) ) )
=> ( r1(X15,sK32(X15))
& p2(sK32(X15))
& ? [X17] :
( r1(sK32(X15),X17)
& ~ p2(X17) ) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X15] :
( ? [X17] :
( r1(sK32(X15),X17)
& ~ p2(X17) )
=> ( r1(sK32(X15),sK33(X15))
& ~ p2(sK33(X15)) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
! [X18] :
( ? [X19] :
( ! [X20] :
( ~ p2(X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
& r1(X18,X19)
& ~ p2(X19) )
=> ( ! [X20] :
( ~ p2(X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) )
| ~ r1(sK34(X18),X20) )
& r1(X18,sK34(X18))
& ~ p2(sK34(X18)) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
( ? [X22] :
( ~ p1(X22)
& r1(sK24,X22) )
=> ( ~ p1(sK35)
& r1(sK24,sK35) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
? [X0] :
( ? [X1] :
( ~ p2(X1)
& r1(X0,X1) )
& ! [X2] :
( ? [X3] :
( p1(X3)
& r1(X2,X3)
& ? [X4] :
( ~ p1(X4)
& r1(X3,X4) ) )
| p1(X2)
| ~ r1(X0,X2) )
& ? [X5] :
( r1(X0,X5)
& ~ p3(X5) )
& ( sP5(X0)
| ? [X6] :
( ! [X7] :
( ( ~ p2(X7)
& ! [X8] :
( ~ p2(X8)
| ~ r1(X7,X8)
| ! [X9] :
( p2(X9)
| ~ r1(X8,X9) ) ) )
| ~ r1(X6,X7)
| sP3(X7)
| sP2(X7) )
& ( sP0(X6)
| ( ! [X10] :
( ~ p2(X10)
| ! [X11] :
( ~ r1(X10,X11)
| p2(X11) )
| ~ r1(X6,X10) )
& ~ p2(X6) ) )
& r1(X0,X6) ) )
& ! [X12] :
( ~ r1(X0,X12)
| p3(X12)
| ? [X13] :
( p3(X13)
& r1(X12,X13)
& ? [X14] :
( ~ p3(X14)
& r1(X13,X14) ) ) )
& ! [X15] :
( ~ r1(X0,X15)
| ? [X16] :
( r1(X15,X16)
& p2(X16)
& ? [X17] :
( r1(X16,X17)
& ~ p2(X17) ) )
| p2(X15) )
& ! [X18] :
( ? [X19] :
( ! [X20] :
( ~ p2(X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
& r1(X18,X19)
& ~ p2(X19) )
| p2(X18)
| ~ r1(X0,X18) )
& ? [X22] :
( ~ p1(X22)
& r1(X0,X22) ) ),
inference(rectify,[],[f13]) ).
fof(f13,plain,
? [X0] :
( ? [X9] :
( ~ p2(X9)
& r1(X0,X9) )
& ! [X1] :
( ? [X2] :
( p1(X2)
& r1(X1,X2)
& ? [X3] :
( ~ p1(X3)
& r1(X2,X3) ) )
| p1(X1)
| ~ r1(X0,X1) )
& ? [X7] :
( r1(X0,X7)
& ~ p3(X7) )
& ( sP5(X0)
| ? [X22] :
( ! [X23] :
( ( ~ p2(X23)
& ! [X34] :
( ~ p2(X34)
| ~ r1(X23,X34)
| ! [X35] :
( p2(X35)
| ~ r1(X34,X35) ) ) )
| ~ r1(X22,X23)
| sP3(X23)
| sP2(X23) )
& ( sP0(X22)
| ( ! [X50] :
( ~ p2(X50)
| ! [X51] :
( ~ r1(X50,X51)
| p2(X51) )
| ~ r1(X22,X50) )
& ~ p2(X22) ) )
& r1(X0,X22) ) )
& ! [X10] :
( ~ r1(X0,X10)
| p3(X10)
| ? [X11] :
( p3(X11)
& r1(X10,X11)
& ? [X12] :
( ~ p3(X12)
& r1(X11,X12) ) ) )
& ! [X4] :
( ~ r1(X0,X4)
| ? [X5] :
( r1(X4,X5)
& p2(X5)
& ? [X6] :
( r1(X5,X6)
& ~ p2(X6) ) )
| p2(X4) )
& ! [X52] :
( ? [X53] :
( ! [X54] :
( ~ p2(X54)
| ! [X55] :
( p2(X55)
| ~ r1(X54,X55) )
| ~ r1(X53,X54) )
& r1(X52,X53)
& ~ p2(X53) )
| p2(X52)
| ~ r1(X0,X52) )
& ? [X8] :
( ~ p1(X8)
& r1(X0,X8) ) ),
inference(definition_folding,[],[f6,f12,f11,f10,f9,f8,f7]) ).
fof(f8,plain,
! [X24] :
( ! [X25] :
( ~ r1(X24,X25)
| ! [X26] :
( ~ r1(X25,X26)
| ? [X27] :
( p2(X27)
& r1(X26,X27)
& ? [X28] :
( ~ p2(X28)
& r1(X27,X28) ) )
| p2(X26) ) )
| ~ sP1(X24) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f11,plain,
! [X0] :
( ! [X15] :
( ~ r1(X0,X15)
| ! [X16] :
( p2(X16)
| ? [X17] :
( ? [X18] :
( ~ p2(X18)
& r1(X17,X18) )
& p2(X17)
& r1(X16,X17) )
| ~ r1(X15,X16) ) )
| ~ sP4(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f12,plain,
! [X0] :
( ( ( sP4(X0)
| ? [X19] :
( ~ p2(X19)
& ! [X20] :
( ~ p2(X20)
| ~ r1(X19,X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) ) )
& r1(X0,X19) ) )
& ( ? [X13] :
( ? [X14] :
( r1(X13,X14)
& ~ p2(X14) )
& p2(X13)
& r1(X0,X13) )
| p2(X0) ) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f6,plain,
? [X0] :
( ? [X9] :
( ~ p2(X9)
& r1(X0,X9) )
& ! [X1] :
( ? [X2] :
( p1(X2)
& r1(X1,X2)
& ? [X3] :
( ~ p1(X3)
& r1(X2,X3) ) )
| p1(X1)
| ~ r1(X0,X1) )
& ? [X7] :
( r1(X0,X7)
& ~ p3(X7) )
& ( ( ( ! [X15] :
( ~ r1(X0,X15)
| ! [X16] :
( p2(X16)
| ? [X17] :
( ? [X18] :
( ~ p2(X18)
& r1(X17,X18) )
& p2(X17)
& r1(X16,X17) )
| ~ r1(X15,X16) ) )
| ? [X19] :
( ~ p2(X19)
& ! [X20] :
( ~ p2(X20)
| ~ r1(X19,X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) ) )
& r1(X0,X19) ) )
& ( ? [X13] :
( ? [X14] :
( r1(X13,X14)
& ~ p2(X14) )
& p2(X13)
& r1(X0,X13) )
| p2(X0) ) )
| ? [X22] :
( ! [X23] :
( ( ~ p2(X23)
& ! [X34] :
( ~ p2(X34)
| ~ r1(X23,X34)
| ! [X35] :
( p2(X35)
| ~ r1(X34,X35) ) ) )
| ~ r1(X22,X23)
| ! [X24] :
( ~ r1(X23,X24)
| ( ( ? [X32] :
( ? [X33] :
( ~ p2(X33)
& r1(X32,X33) )
& p2(X32)
& r1(X24,X32) )
| p2(X24) )
& ( ? [X29] :
( ! [X30] :
( ~ p2(X30)
| ~ r1(X29,X30)
| ! [X31] :
( p2(X31)
| ~ r1(X30,X31) ) )
& ~ p2(X29)
& r1(X24,X29) )
| ! [X25] :
( ~ r1(X24,X25)
| ! [X26] :
( ~ r1(X25,X26)
| ? [X27] :
( p2(X27)
& r1(X26,X27)
& ? [X28] :
( ~ p2(X28)
& r1(X27,X28) ) )
| p2(X26) ) ) ) ) )
| ( ? [X36] :
( r1(X23,X36)
& ? [X37] :
( ~ p2(X37)
& r1(X36,X37)
& ! [X38] :
( ! [X39] :
( ~ r1(X38,X39)
| p2(X39) )
| ~ r1(X37,X38)
| ~ p2(X38) ) ) )
& ! [X40] :
( ~ r1(X23,X40)
| p2(X40)
| ? [X41] :
( ? [X42] :
( ~ p2(X42)
& r1(X41,X42) )
& p2(X41)
& r1(X40,X41) ) ) ) )
& ( ( ? [X46] :
( r1(X22,X46)
& ? [X47] :
( ! [X48] :
( ~ p2(X48)
| ! [X49] :
( p2(X49)
| ~ r1(X48,X49) )
| ~ r1(X47,X48) )
& ~ p2(X47)
& r1(X46,X47) ) )
& ! [X43] :
( ? [X44] :
( ? [X45] :
( r1(X44,X45)
& ~ p2(X45) )
& r1(X43,X44)
& p2(X44) )
| p2(X43)
| ~ r1(X22,X43) ) )
| ( ! [X50] :
( ~ p2(X50)
| ! [X51] :
( ~ r1(X50,X51)
| p2(X51) )
| ~ r1(X22,X50) )
& ~ p2(X22) ) )
& r1(X0,X22) ) )
& ! [X10] :
( ~ r1(X0,X10)
| p3(X10)
| ? [X11] :
( p3(X11)
& r1(X10,X11)
& ? [X12] :
( ~ p3(X12)
& r1(X11,X12) ) ) )
& ! [X4] :
( ~ r1(X0,X4)
| ? [X5] :
( r1(X4,X5)
& p2(X5)
& ? [X6] :
( r1(X5,X6)
& ~ p2(X6) ) )
| p2(X4) )
& ! [X52] :
( ? [X53] :
( ! [X54] :
( ~ p2(X54)
| ! [X55] :
( p2(X55)
| ~ r1(X54,X55) )
| ~ r1(X53,X54) )
& r1(X52,X53)
& ~ p2(X53) )
| p2(X52)
| ~ r1(X0,X52) )
& ? [X8] :
( ~ p1(X8)
& r1(X0,X8) ) ),
inference(flattening,[],[f5]) ).
fof(f5,plain,
? [X0] :
( ? [X9] :
( ~ p2(X9)
& r1(X0,X9) )
& ? [X8] :
( ~ p1(X8)
& r1(X0,X8) )
& ? [X7] :
( r1(X0,X7)
& ~ p3(X7) )
& ! [X1] :
( ? [X2] :
( p1(X2)
& r1(X1,X2)
& ? [X3] :
( ~ p1(X3)
& r1(X2,X3) ) )
| p1(X1)
| ~ r1(X0,X1) )
& ! [X10] :
( ~ r1(X0,X10)
| p3(X10)
| ? [X11] :
( p3(X11)
& r1(X10,X11)
& ? [X12] :
( ~ p3(X12)
& r1(X11,X12) ) ) )
& ! [X52] :
( ? [X53] :
( ! [X54] :
( ~ p2(X54)
| ! [X55] :
( p2(X55)
| ~ r1(X54,X55) )
| ~ r1(X53,X54) )
& r1(X52,X53)
& ~ p2(X53) )
| p2(X52)
| ~ r1(X0,X52) )
& ( ? [X22] :
( ! [X23] :
( ~ r1(X22,X23)
| ! [X24] :
( ~ r1(X23,X24)
| ( ( ? [X32] :
( ? [X33] :
( ~ p2(X33)
& r1(X32,X33) )
& p2(X32)
& r1(X24,X32) )
| p2(X24) )
& ( ? [X29] :
( ! [X30] :
( ~ p2(X30)
| ~ r1(X29,X30)
| ! [X31] :
( p2(X31)
| ~ r1(X30,X31) ) )
& ~ p2(X29)
& r1(X24,X29) )
| ! [X25] :
( ~ r1(X24,X25)
| ! [X26] :
( ~ r1(X25,X26)
| ? [X27] :
( p2(X27)
& r1(X26,X27)
& ? [X28] :
( ~ p2(X28)
& r1(X27,X28) ) )
| p2(X26) ) ) ) ) )
| ( ? [X36] :
( r1(X23,X36)
& ? [X37] :
( ~ p2(X37)
& r1(X36,X37)
& ! [X38] :
( ! [X39] :
( ~ r1(X38,X39)
| p2(X39) )
| ~ r1(X37,X38)
| ~ p2(X38) ) ) )
& ! [X40] :
( ~ r1(X23,X40)
| p2(X40)
| ? [X41] :
( ? [X42] :
( ~ p2(X42)
& r1(X41,X42) )
& p2(X41)
& r1(X40,X41) ) ) )
| ( ~ p2(X23)
& ! [X34] :
( ~ p2(X34)
| ~ r1(X23,X34)
| ! [X35] :
( p2(X35)
| ~ r1(X34,X35) ) ) ) )
& ( ( ? [X46] :
( r1(X22,X46)
& ? [X47] :
( ! [X48] :
( ~ p2(X48)
| ! [X49] :
( p2(X49)
| ~ r1(X48,X49) )
| ~ r1(X47,X48) )
& ~ p2(X47)
& r1(X46,X47) ) )
& ! [X43] :
( ? [X44] :
( ? [X45] :
( r1(X44,X45)
& ~ p2(X45) )
& r1(X43,X44)
& p2(X44) )
| p2(X43)
| ~ r1(X22,X43) ) )
| ( ! [X50] :
( ~ p2(X50)
| ! [X51] :
( ~ r1(X50,X51)
| p2(X51) )
| ~ r1(X22,X50) )
& ~ p2(X22) ) )
& r1(X0,X22) )
| ( ( ! [X15] :
( ~ r1(X0,X15)
| ! [X16] :
( p2(X16)
| ? [X17] :
( ? [X18] :
( ~ p2(X18)
& r1(X17,X18) )
& p2(X17)
& r1(X16,X17) )
| ~ r1(X15,X16) ) )
| ? [X19] :
( ~ p2(X19)
& ! [X20] :
( ~ p2(X20)
| ~ r1(X19,X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) ) )
& r1(X0,X19) ) )
& ( ? [X13] :
( ? [X14] :
( r1(X13,X14)
& ~ p2(X14) )
& p2(X13)
& r1(X0,X13) )
| p2(X0) ) ) )
& ! [X4] :
( ~ r1(X0,X4)
| ? [X5] :
( r1(X4,X5)
& p2(X5)
& ? [X6] :
( r1(X5,X6)
& ~ p2(X6) ) )
| p2(X4) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,plain,
? [X0] :
~ ( ! [X9] :
( p2(X9)
| ~ r1(X0,X9) )
| ! [X8] :
( ~ r1(X0,X8)
| p1(X8) )
| ! [X7] :
( ~ r1(X0,X7)
| p3(X7) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X2] :
( ~ p1(X2)
| ~ r1(X1,X2)
| ! [X3] :
( p1(X3)
| ~ r1(X2,X3) ) )
| p1(X1) )
| ~ ! [X10] :
( p3(X10)
| ~ ! [X11] :
( ~ p3(X11)
| ! [X12] :
( ~ r1(X11,X12)
| p3(X12) )
| ~ r1(X10,X11) )
| ~ r1(X0,X10) )
| ~ ( ! [X52] :
( ~ ! [X53] :
( ~ r1(X52,X53)
| ~ ! [X54] :
( ~ p2(X54)
| ! [X55] :
( p2(X55)
| ~ r1(X54,X55) )
| ~ r1(X53,X54) )
| p2(X53) )
| ~ r1(X0,X52)
| p2(X52) )
& ( ~ ! [X22] :
( ~ ! [X23] :
( ~ r1(X22,X23)
| ! [X24] :
( ( ( p2(X24)
| ~ ! [X32] :
( ~ r1(X24,X32)
| ! [X33] :
( p2(X33)
| ~ r1(X32,X33) )
| ~ p2(X32) ) )
& ( ~ ! [X29] :
( ~ ! [X30] :
( ~ p2(X30)
| ~ r1(X29,X30)
| ! [X31] :
( p2(X31)
| ~ r1(X30,X31) ) )
| p2(X29)
| ~ r1(X24,X29) )
| ! [X25] :
( ! [X26] :
( ~ r1(X25,X26)
| ~ ! [X27] :
( ~ p2(X27)
| ! [X28] :
( p2(X28)
| ~ r1(X27,X28) )
| ~ r1(X26,X27) )
| p2(X26) )
| ~ r1(X24,X25) ) ) )
| ~ r1(X23,X24) )
| ~ ( ( ~ ! [X40] :
( ~ ! [X41] :
( ! [X42] :
( ~ r1(X41,X42)
| p2(X42) )
| ~ p2(X41)
| ~ r1(X40,X41) )
| p2(X40)
| ~ r1(X23,X40) )
| ! [X36] :
( ! [X37] :
( ~ ! [X38] :
( ! [X39] :
( ~ r1(X38,X39)
| p2(X39) )
| ~ r1(X37,X38)
| ~ p2(X38) )
| p2(X37)
| ~ r1(X36,X37) )
| ~ r1(X23,X36) ) )
& ( ~ ! [X34] :
( ~ p2(X34)
| ~ r1(X23,X34)
| ! [X35] :
( p2(X35)
| ~ r1(X34,X35) ) )
| p2(X23) ) ) )
| ( ( ~ ! [X50] :
( ~ p2(X50)
| ! [X51] :
( ~ r1(X50,X51)
| p2(X51) )
| ~ r1(X22,X50) )
| p2(X22) )
& ( ! [X46] :
( ~ r1(X22,X46)
| ! [X47] :
( p2(X47)
| ~ ! [X48] :
( ~ p2(X48)
| ! [X49] :
( p2(X49)
| ~ r1(X48,X49) )
| ~ r1(X47,X48) )
| ~ r1(X46,X47) ) )
| ~ ! [X43] :
( ~ ! [X44] :
( ! [X45] :
( ~ r1(X44,X45)
| p2(X45) )
| ~ p2(X44)
| ~ r1(X43,X44) )
| ~ r1(X22,X43)
| p2(X43) ) ) )
| ~ r1(X0,X22) )
| ( ( ~ ! [X19] :
( p2(X19)
| ~ ! [X20] :
( ~ p2(X20)
| ~ r1(X19,X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) ) )
| ~ r1(X0,X19) )
| ! [X15] :
( ! [X16] :
( ~ ! [X17] :
( ~ r1(X16,X17)
| ! [X18] :
( p2(X18)
| ~ r1(X17,X18) )
| ~ p2(X17) )
| p2(X16)
| ~ r1(X15,X16) )
| ~ r1(X0,X15) ) )
& ( ~ ! [X13] :
( ! [X14] :
( p2(X14)
| ~ r1(X13,X14) )
| ~ p2(X13)
| ~ r1(X0,X13) )
| p2(X0) ) ) ) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| p2(X4)
| ~ ! [X5] :
( ~ p2(X5)
| ! [X6] :
( p2(X6)
| ~ r1(X5,X6) )
| ~ r1(X4,X5) ) ) ),
inference(flattening,[],[f3]) ).
fof(f3,plain,
~ ~ ? [X0] :
~ ( ! [X9] :
( p2(X9)
| ~ r1(X0,X9) )
| ! [X8] :
( ~ r1(X0,X8)
| p1(X8) )
| ! [X7] :
( ~ r1(X0,X7)
| p3(X7) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X2] :
( ~ p1(X2)
| ~ r1(X1,X2)
| ! [X3] :
( p1(X3)
| ~ r1(X2,X3) ) )
| p1(X1) )
| ~ ! [X10] :
( p3(X10)
| ~ ! [X11] :
( ~ p3(X11)
| ! [X12] :
( ~ r1(X11,X12)
| p3(X12) )
| ~ r1(X10,X11) )
| ~ r1(X0,X10) )
| ~ ( ! [X52] :
( ~ ! [X53] :
( ~ r1(X52,X53)
| ~ ! [X54] :
( ~ p2(X54)
| ! [X55] :
( p2(X55)
| ~ r1(X54,X55) )
| ~ r1(X53,X54) )
| p2(X53) )
| ~ r1(X0,X52)
| p2(X52) )
& ( ~ ! [X22] :
( ~ ! [X23] :
( ~ r1(X22,X23)
| ! [X24] :
( ( ( p2(X24)
| ~ ! [X32] :
( ~ r1(X24,X32)
| ! [X33] :
( p2(X33)
| ~ r1(X32,X33) )
| ~ p2(X32) ) )
& ( ~ ! [X29] :
( ~ ! [X30] :
( ~ p2(X30)
| ~ r1(X29,X30)
| ! [X31] :
( p2(X31)
| ~ r1(X30,X31) ) )
| p2(X29)
| ~ r1(X24,X29) )
| ! [X25] :
( ! [X26] :
( ~ r1(X25,X26)
| ~ ! [X27] :
( ~ p2(X27)
| ! [X28] :
( p2(X28)
| ~ r1(X27,X28) )
| ~ r1(X26,X27) )
| p2(X26) )
| ~ r1(X24,X25) ) ) )
| ~ r1(X23,X24) )
| ~ ( ( ~ ! [X40] :
( ~ ! [X41] :
( ! [X42] :
( ~ r1(X41,X42)
| p2(X42) )
| ~ p2(X41)
| ~ r1(X40,X41) )
| p2(X40)
| ~ r1(X23,X40) )
| ! [X36] :
( ! [X37] :
( ~ ! [X38] :
( ! [X39] :
( ~ r1(X38,X39)
| p2(X39) )
| ~ r1(X37,X38)
| ~ p2(X38) )
| p2(X37)
| ~ r1(X36,X37) )
| ~ r1(X23,X36) ) )
& ( ~ ! [X34] :
( ~ p2(X34)
| ~ r1(X23,X34)
| ! [X35] :
( p2(X35)
| ~ r1(X34,X35) ) )
| p2(X23) ) ) )
| ( ( ~ ! [X50] :
( ~ p2(X50)
| ! [X51] :
( ~ r1(X50,X51)
| p2(X51) )
| ~ r1(X22,X50) )
| p2(X22) )
& ( ! [X46] :
( ~ r1(X22,X46)
| ! [X47] :
( p2(X47)
| ~ ! [X48] :
( ~ p2(X48)
| ! [X49] :
( p2(X49)
| ~ r1(X48,X49) )
| ~ r1(X47,X48) )
| ~ r1(X46,X47) ) )
| ~ ! [X43] :
( ~ ! [X44] :
( ! [X45] :
( ~ r1(X44,X45)
| p2(X45) )
| ~ p2(X44)
| ~ r1(X43,X44) )
| ~ r1(X22,X43)
| p2(X43) ) ) )
| ~ r1(X0,X22) )
| ( ( ~ ! [X19] :
( p2(X19)
| ~ ! [X20] :
( ~ p2(X20)
| ~ r1(X19,X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) ) )
| ~ r1(X0,X19) )
| ! [X15] :
( ! [X16] :
( ~ ! [X17] :
( ~ r1(X16,X17)
| ! [X18] :
( p2(X18)
| ~ r1(X17,X18) )
| ~ p2(X17) )
| p2(X16)
| ~ r1(X15,X16) )
| ~ r1(X0,X15) ) )
& ( ~ ! [X13] :
( ! [X14] :
( p2(X14)
| ~ r1(X13,X14) )
| ~ p2(X13)
| ~ r1(X0,X13) )
| p2(X0) ) ) ) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| p2(X4)
| ~ ! [X5] :
( ~ p2(X5)
| ! [X6] :
( p2(X6)
| ~ r1(X5,X6) )
| ~ r1(X4,X5) ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1) )
| ~ p1(X0) ) )
| ~ ! [X1] :
( ~ ! [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ r1(X1,X0)
| ~ p2(X0) )
| p2(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| p3(X1)
| ~ ! [X0] :
( ~ p3(X0)
| ! [X1] :
( ~ r1(X0,X1)
| p3(X1) )
| ~ r1(X1,X0) ) )
| ~ ( ( ( ( p2(X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ p2(X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) ) ) )
& ( ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ~ r1(X0,X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) ) )
| p2(X0)
| ~ r1(X1,X0) ) )
| ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ p2(X0) ) ) ) )
| ~ ! [X1] :
( ~ ! [X0] :
( ! [X1] :
( ( ( ! [X0] :
( ! [X1] :
( p2(X1)
| ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ p2(X0) ) )
| ~ r1(X1,X0) )
| ~ ! [X0] :
( ~ ! [X1] :
( ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1)
| ~ p2(X1) )
| p2(X0)
| ~ r1(X1,X0) ) )
& ( p2(X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| ~ p2(X0)
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ) ) )
| ~ r1(X0,X1) )
| ~ ( ( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( ~ r1(X1,X0)
| p2(X0) )
| ~ r1(X0,X1) )
| p2(X0) )
& ( ! [X1] :
( ! [X0] :
( p2(X0)
| ~ r1(X1,X0)
| ~ ! [X1] :
( ! [X0] :
( ~ r1(X1,X0)
| p2(X0) )
| ~ p2(X1)
| ~ r1(X0,X1) ) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ p2(X0)
| ! [X1] :
( ~ r1(X0,X1)
| p2(X1) ) )
| p2(X1)
| ~ r1(X0,X1) ) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1)
| ( ( ~ ! [X0] :
( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ p2(X1)
| ! [X0] :
( ~ r1(X1,X0)
| p2(X0) ) )
| ~ r1(X1,X0)
| p2(X0) )
| ! [X0] :
( ! [X1] :
( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ r1(X1,X0) )
| p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
& ( p2(X1)
| ~ ! [X0] :
( ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0)
| ~ p2(X0) ) ) ) ) )
& ! [X1] :
( ~ r1(X0,X1)
| p2(X1)
| ~ ! [X0] :
( ~ ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ p2(X1) )
| p2(X0)
| ~ r1(X1,X0) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1) )
| ~ p1(X0) ) )
| ~ ! [X1] :
( ~ ! [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ r1(X1,X0)
| ~ p2(X0) )
| p2(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| p3(X1)
| ~ ! [X0] :
( ~ p3(X0)
| ! [X1] :
( ~ r1(X0,X1)
| p3(X1) )
| ~ r1(X1,X0) ) )
| ~ ( ( ( ( p2(X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ p2(X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) ) ) )
& ( ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ~ r1(X0,X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) ) )
| p2(X0)
| ~ r1(X1,X0) ) )
| ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ p2(X0) ) ) ) )
| ~ ! [X1] :
( ~ ! [X0] :
( ! [X1] :
( ( ( ! [X0] :
( ! [X1] :
( p2(X1)
| ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ p2(X0) ) )
| ~ r1(X1,X0) )
| ~ ! [X0] :
( ~ ! [X1] :
( ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1)
| ~ p2(X1) )
| p2(X0)
| ~ r1(X1,X0) ) )
& ( p2(X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| ~ p2(X0)
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ) ) )
| ~ r1(X0,X1) )
| ~ ( ( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( ~ r1(X1,X0)
| p2(X0) )
| ~ r1(X0,X1) )
| p2(X0) )
& ( ! [X1] :
( ! [X0] :
( p2(X0)
| ~ r1(X1,X0)
| ~ ! [X1] :
( ! [X0] :
( ~ r1(X1,X0)
| p2(X0) )
| ~ p2(X1)
| ~ r1(X0,X1) ) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ p2(X0)
| ! [X1] :
( ~ r1(X0,X1)
| p2(X1) ) )
| p2(X1)
| ~ r1(X0,X1) ) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1)
| ( ( ~ ! [X0] :
( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ p2(X1)
| ! [X0] :
( ~ r1(X1,X0)
| p2(X0) ) )
| ~ r1(X1,X0)
| p2(X0) )
| ! [X0] :
( ! [X1] :
( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ r1(X1,X0) )
| p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
& ( p2(X1)
| ~ ! [X0] :
( ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0)
| ~ p2(X0) ) ) ) ) )
& ! [X1] :
( ~ r1(X0,X1)
| p2(X1)
| ~ ! [X0] :
( ~ ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ p2(X1) )
| p2(X0)
| ~ r1(X1,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f588,plain,
( p2(sK33(sK29))
| ~ spl36_81 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f587,plain,
( spl36_81
<=> p2(sK33(sK29)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_81])]) ).
fof(f721,plain,
( ~ spl36_29
| ~ spl36_79
| spl36_81 ),
inference(avatar_contradiction_clause,[],[f720]) ).
fof(f720,plain,
( $false
| ~ spl36_29
| ~ spl36_79
| spl36_81 ),
inference(subsumption_resolution,[],[f719,f589]) ).
fof(f589,plain,
( ~ p2(sK33(sK29))
| spl36_81 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f719,plain,
( p2(sK33(sK29))
| ~ spl36_29
| ~ spl36_79 ),
inference(resolution,[],[f580,f308]) ).
fof(f308,plain,
( r1(sK32(sK29),sK33(sK29))
| ~ spl36_29 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f306,plain,
( spl36_29
<=> r1(sK32(sK29),sK33(sK29)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_29])]) ).
fof(f580,plain,
( ! [X0] :
( ~ r1(sK32(sK29),X0)
| p2(X0) )
| ~ spl36_79 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f579,plain,
( spl36_79
<=> ! [X0] :
( p2(X0)
| ~ r1(sK32(sK29),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_79])]) ).
fof(f695,plain,
( ~ spl36_1
| spl36_62
| ~ spl36_63
| spl36_65
| ~ spl36_68
| ~ spl36_72
| ~ spl36_75 ),
inference(avatar_contradiction_clause,[],[f694]) ).
fof(f694,plain,
( $false
| ~ spl36_1
| spl36_62
| ~ spl36_63
| spl36_65
| ~ spl36_68
| ~ spl36_72
| ~ spl36_75 ),
inference(subsumption_resolution,[],[f693,f487]) ).
fof(f487,plain,
( r1(sK24,sK6(sK24))
| ~ spl36_63 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f485,plain,
( spl36_63
<=> r1(sK24,sK6(sK24)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_63])]) ).
fof(f693,plain,
( ~ r1(sK24,sK6(sK24))
| ~ spl36_1
| spl36_62
| spl36_65
| ~ spl36_68
| ~ spl36_72
| ~ spl36_75 ),
inference(subsumption_resolution,[],[f692,f505]) ).
fof(f505,plain,
( ~ p2(sK6(sK24))
| spl36_65 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f504,plain,
( spl36_65
<=> p2(sK6(sK24)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_65])]) ).
fof(f692,plain,
( p2(sK6(sK24))
| ~ r1(sK24,sK6(sK24))
| ~ spl36_1
| spl36_62
| ~ spl36_68
| ~ spl36_72
| ~ spl36_75 ),
inference(resolution,[],[f691,f107]) ).
fof(f691,plain,
( p2(sK33(sK6(sK24)))
| ~ spl36_1
| spl36_62
| ~ spl36_68
| ~ spl36_72
| ~ spl36_75 ),
inference(resolution,[],[f690,f520]) ).
fof(f520,plain,
( r1(sK32(sK6(sK24)),sK33(sK6(sK24)))
| ~ spl36_68 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f518,plain,
( spl36_68
<=> r1(sK32(sK6(sK24)),sK33(sK6(sK24))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_68])]) ).
fof(f690,plain,
( ! [X0] :
( ~ r1(sK32(sK6(sK24)),X0)
| p2(X0) )
| ~ spl36_1
| spl36_62
| ~ spl36_72
| ~ spl36_75 ),
inference(subsumption_resolution,[],[f689,f482]) ).
fof(f482,plain,
( ~ sP4(sK24)
| spl36_62 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f481,plain,
( spl36_62
<=> sP4(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_62])]) ).
fof(f689,plain,
( ! [X0] :
( p2(X0)
| ~ r1(sK32(sK6(sK24)),X0)
| sP4(sK24) )
| ~ spl36_1
| ~ spl36_72
| ~ spl36_75 ),
inference(subsumption_resolution,[],[f688,f131]) ).
fof(f131,plain,
( sP5(sK24)
| ~ spl36_1 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f129,plain,
( spl36_1
<=> sP5(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_1])]) ).
fof(f688,plain,
( ! [X0] :
( p2(X0)
| ~ sP5(sK24)
| sP4(sK24)
| ~ r1(sK32(sK6(sK24)),X0) )
| ~ spl36_72
| ~ spl36_75 ),
inference(subsumption_resolution,[],[f687,f554]) ).
fof(f554,plain,
( p2(sK32(sK6(sK24)))
| ~ spl36_75 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f552,plain,
( spl36_75
<=> p2(sK32(sK6(sK24))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_75])]) ).
fof(f687,plain,
( ! [X0] :
( ~ p2(sK32(sK6(sK24)))
| sP4(sK24)
| ~ r1(sK32(sK6(sK24)),X0)
| ~ sP5(sK24)
| p2(X0) )
| ~ spl36_72 ),
inference(resolution,[],[f539,f69]) ).
fof(f69,plain,
! [X2,X3,X0] :
( ~ r1(sK6(X0),X2)
| ~ sP5(X0)
| ~ p2(X2)
| sP4(X0)
| ~ r1(X2,X3)
| p2(X3) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0] :
( ( ( sP4(X0)
| ( ~ p2(sK6(X0))
& ! [X2] :
( ~ p2(X2)
| ~ r1(sK6(X0),X2)
| ! [X3] :
( p2(X3)
| ~ r1(X2,X3) ) )
& r1(X0,sK6(X0)) ) )
& ( ( r1(sK7(X0),sK8(X0))
& ~ p2(sK8(X0))
& p2(sK7(X0))
& r1(X0,sK7(X0)) )
| p2(X0) ) )
| ~ sP5(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f15,f18,f17,f16]) ).
fof(f16,plain,
! [X0] :
( ? [X1] :
( ~ p2(X1)
& ! [X2] :
( ~ p2(X2)
| ~ r1(X1,X2)
| ! [X3] :
( p2(X3)
| ~ r1(X2,X3) ) )
& r1(X0,X1) )
=> ( ~ p2(sK6(X0))
& ! [X2] :
( ~ p2(X2)
| ~ r1(sK6(X0),X2)
| ! [X3] :
( p2(X3)
| ~ r1(X2,X3) ) )
& r1(X0,sK6(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( r1(X4,X5)
& ~ p2(X5) )
& p2(X4)
& r1(X0,X4) )
=> ( ? [X5] :
( r1(sK7(X0),X5)
& ~ p2(X5) )
& p2(sK7(X0))
& r1(X0,sK7(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0] :
( ? [X5] :
( r1(sK7(X0),X5)
& ~ p2(X5) )
=> ( r1(sK7(X0),sK8(X0))
& ~ p2(sK8(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
! [X0] :
( ( ( sP4(X0)
| ? [X1] :
( ~ p2(X1)
& ! [X2] :
( ~ p2(X2)
| ~ r1(X1,X2)
| ! [X3] :
( p2(X3)
| ~ r1(X2,X3) ) )
& r1(X0,X1) ) )
& ( ? [X4] :
( ? [X5] :
( r1(X4,X5)
& ~ p2(X5) )
& p2(X4)
& r1(X0,X4) )
| p2(X0) ) )
| ~ sP5(X0) ),
inference(rectify,[],[f14]) ).
fof(f14,plain,
! [X0] :
( ( ( sP4(X0)
| ? [X19] :
( ~ p2(X19)
& ! [X20] :
( ~ p2(X20)
| ~ r1(X19,X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) ) )
& r1(X0,X19) ) )
& ( ? [X13] :
( ? [X14] :
( r1(X13,X14)
& ~ p2(X14) )
& p2(X13)
& r1(X0,X13) )
| p2(X0) ) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f12]) ).
fof(f539,plain,
( r1(sK6(sK24),sK32(sK6(sK24)))
| ~ spl36_72 ),
inference(avatar_component_clause,[],[f537]) ).
fof(f537,plain,
( spl36_72
<=> r1(sK6(sK24),sK32(sK6(sK24))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_72])]) ).
fof(f675,plain,
( spl36_72
| spl36_65
| ~ spl36_63 ),
inference(avatar_split_clause,[],[f662,f485,f504,f537]) ).
fof(f662,plain,
( p2(sK6(sK24))
| r1(sK6(sK24),sK32(sK6(sK24)))
| ~ spl36_63 ),
inference(resolution,[],[f487,f110]) ).
fof(f110,plain,
! [X15] :
( ~ r1(sK24,X15)
| p2(X15)
| r1(X15,sK32(X15)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f673,plain,
( spl36_65
| spl36_68
| ~ spl36_63 ),
inference(avatar_split_clause,[],[f660,f485,f518,f504]) ).
fof(f660,plain,
( r1(sK32(sK6(sK24)),sK33(sK6(sK24)))
| p2(sK6(sK24))
| ~ spl36_63 ),
inference(resolution,[],[f487,f108]) ).
fof(f108,plain,
! [X15] :
( ~ r1(sK24,X15)
| r1(sK32(X15),sK33(X15))
| p2(X15) ),
inference(cnf_transformation,[],[f63]) ).
fof(f672,plain,
( ~ spl36_1
| spl36_62
| ~ spl36_65 ),
inference(avatar_contradiction_clause,[],[f671]) ).
fof(f671,plain,
( $false
| ~ spl36_1
| spl36_62
| ~ spl36_65 ),
inference(subsumption_resolution,[],[f670,f131]) ).
fof(f670,plain,
( ~ sP5(sK24)
| spl36_62
| ~ spl36_65 ),
inference(subsumption_resolution,[],[f669,f482]) ).
fof(f669,plain,
( sP4(sK24)
| ~ sP5(sK24)
| ~ spl36_65 ),
inference(resolution,[],[f506,f70]) ).
fof(f70,plain,
! [X0] :
( ~ p2(sK6(X0))
| sP4(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f506,plain,
( p2(sK6(sK24))
| ~ spl36_65 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f658,plain,
( ~ spl36_62
| spl36_82
| ~ spl36_83 ),
inference(avatar_contradiction_clause,[],[f657]) ).
fof(f657,plain,
( $false
| ~ spl36_62
| spl36_82
| ~ spl36_83 ),
inference(subsumption_resolution,[],[f656,f126]) ).
fof(f126,plain,
r1(sK24,sK25),
inference(cnf_transformation,[],[f63]) ).
fof(f656,plain,
( ~ r1(sK24,sK25)
| ~ spl36_62
| spl36_82
| ~ spl36_83 ),
inference(resolution,[],[f655,f227]) ).
fof(f227,plain,
r1(sK25,sK34(sK25)),
inference(subsumption_resolution,[],[f226,f127]) ).
fof(f127,plain,
~ p2(sK25),
inference(cnf_transformation,[],[f63]) ).
fof(f226,plain,
( r1(sK25,sK34(sK25))
| p2(sK25) ),
inference(resolution,[],[f105,f126]) ).
fof(f105,plain,
! [X18] :
( ~ r1(sK24,X18)
| r1(X18,sK34(X18))
| p2(X18) ),
inference(cnf_transformation,[],[f63]) ).
fof(f655,plain,
( ! [X0] :
( ~ r1(X0,sK34(sK25))
| ~ r1(sK24,X0) )
| ~ spl36_62
| spl36_82
| ~ spl36_83 ),
inference(resolution,[],[f654,f483]) ).
fof(f483,plain,
( sP4(sK24)
| ~ spl36_62 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f654,plain,
( ! [X0,X1] :
( ~ sP4(X0)
| ~ r1(X1,sK34(sK25))
| ~ r1(X0,X1) )
| ~ spl36_62
| spl36_82
| ~ spl36_83 ),
inference(subsumption_resolution,[],[f653,f599]) ).
fof(f599,plain,
( ~ p2(sK34(sK25))
| spl36_82 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f598,plain,
( spl36_82
<=> p2(sK34(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_82])]) ).
fof(f653,plain,
( ! [X0,X1] :
( ~ r1(X1,sK34(sK25))
| p2(sK34(sK25))
| ~ sP4(X0)
| ~ r1(X0,X1) )
| ~ spl36_62
| spl36_82
| ~ spl36_83 ),
inference(resolution,[],[f652,f74]) ).
fof(f74,plain,
! [X2,X0,X1] :
( ~ p2(sK10(X2))
| ~ r1(X0,X1)
| ~ sP4(X0)
| p2(X2)
| ~ r1(X1,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| ! [X2] :
( p2(X2)
| ( ~ p2(sK10(X2))
& r1(sK9(X2),sK10(X2))
& p2(sK9(X2))
& r1(X2,sK9(X2)) )
| ~ r1(X1,X2) ) )
| ~ sP4(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f21,f23,f22]) ).
fof(f22,plain,
! [X2] :
( ? [X3] :
( ? [X4] :
( ~ p2(X4)
& r1(X3,X4) )
& p2(X3)
& r1(X2,X3) )
=> ( ? [X4] :
( ~ p2(X4)
& r1(sK9(X2),X4) )
& p2(sK9(X2))
& r1(X2,sK9(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X2] :
( ? [X4] :
( ~ p2(X4)
& r1(sK9(X2),X4) )
=> ( ~ p2(sK10(X2))
& r1(sK9(X2),sK10(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| ! [X2] :
( p2(X2)
| ? [X3] :
( ? [X4] :
( ~ p2(X4)
& r1(X3,X4) )
& p2(X3)
& r1(X2,X3) )
| ~ r1(X1,X2) ) )
| ~ sP4(X0) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
! [X0] :
( ! [X15] :
( ~ r1(X0,X15)
| ! [X16] :
( p2(X16)
| ? [X17] :
( ? [X18] :
( ~ p2(X18)
& r1(X17,X18) )
& p2(X17)
& r1(X16,X17) )
| ~ r1(X15,X16) ) )
| ~ sP4(X0) ),
inference(nnf_transformation,[],[f11]) ).
fof(f652,plain,
( p2(sK10(sK34(sK25)))
| ~ spl36_62
| spl36_82
| ~ spl36_83 ),
inference(resolution,[],[f649,f642]) ).
fof(f642,plain,
( ! [X0] :
( ~ r1(sK9(sK34(sK25)),X0)
| p2(X0) )
| ~ spl36_62
| spl36_82
| ~ spl36_83 ),
inference(subsumption_resolution,[],[f641,f127]) ).
fof(f641,plain,
( ! [X0] :
( p2(X0)
| ~ r1(sK9(sK34(sK25)),X0)
| p2(sK25) )
| ~ spl36_62
| spl36_82
| ~ spl36_83 ),
inference(subsumption_resolution,[],[f640,f604]) ).
fof(f604,plain,
( p2(sK9(sK34(sK25)))
| ~ spl36_83 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f602,plain,
( spl36_83
<=> p2(sK9(sK34(sK25))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_83])]) ).
fof(f640,plain,
( ! [X0] :
( ~ r1(sK9(sK34(sK25)),X0)
| ~ p2(sK9(sK34(sK25)))
| p2(sK25)
| p2(X0) )
| ~ spl36_62
| spl36_82 ),
inference(subsumption_resolution,[],[f639,f126]) ).
fof(f639,plain,
( ! [X0] :
( p2(X0)
| ~ r1(sK9(sK34(sK25)),X0)
| ~ r1(sK24,sK25)
| p2(sK25)
| ~ p2(sK9(sK34(sK25))) )
| ~ spl36_62
| spl36_82 ),
inference(resolution,[],[f636,f106]) ).
fof(f106,plain,
! [X21,X18,X20] :
( ~ r1(sK34(X18),X20)
| ~ r1(X20,X21)
| ~ r1(sK24,X18)
| p2(X21)
| p2(X18)
| ~ p2(X20) ),
inference(cnf_transformation,[],[f63]) ).
fof(f636,plain,
( r1(sK34(sK25),sK9(sK34(sK25)))
| ~ spl36_62
| spl36_82 ),
inference(subsumption_resolution,[],[f634,f599]) ).
fof(f634,plain,
( r1(sK34(sK25),sK9(sK34(sK25)))
| p2(sK34(sK25))
| ~ spl36_62 ),
inference(resolution,[],[f631,f227]) ).
fof(f631,plain,
( ! [X0] :
( ~ r1(sK25,X0)
| r1(X0,sK9(X0))
| p2(X0) )
| ~ spl36_62 ),
inference(resolution,[],[f630,f126]) ).
fof(f630,plain,
( ! [X0,X1] :
( ~ r1(sK24,X1)
| r1(X0,sK9(X0))
| p2(X0)
| ~ r1(X1,X0) )
| ~ spl36_62 ),
inference(resolution,[],[f71,f483]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ sP4(X0)
| p2(X2)
| r1(X2,sK9(X2))
| ~ r1(X0,X1)
| ~ r1(X1,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f649,plain,
( r1(sK9(sK34(sK25)),sK10(sK34(sK25)))
| ~ spl36_62
| spl36_82 ),
inference(subsumption_resolution,[],[f647,f599]) ).
fof(f647,plain,
( p2(sK34(sK25))
| r1(sK9(sK34(sK25)),sK10(sK34(sK25)))
| ~ spl36_62 ),
inference(resolution,[],[f644,f227]) ).
fof(f644,plain,
( ! [X0] :
( ~ r1(sK25,X0)
| r1(sK9(X0),sK10(X0))
| p2(X0) )
| ~ spl36_62 ),
inference(resolution,[],[f643,f126]) ).
fof(f643,plain,
( ! [X0,X1] :
( ~ r1(sK24,X0)
| r1(sK9(X1),sK10(X1))
| p2(X1)
| ~ r1(X0,X1) )
| ~ spl36_62 ),
inference(resolution,[],[f73,f483]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ sP4(X0)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| p2(X2)
| r1(sK9(X2),sK10(X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f629,plain,
~ spl36_82,
inference(avatar_contradiction_clause,[],[f628]) ).
fof(f628,plain,
( $false
| ~ spl36_82 ),
inference(subsumption_resolution,[],[f627,f126]) ).
fof(f627,plain,
( ~ r1(sK24,sK25)
| ~ spl36_82 ),
inference(subsumption_resolution,[],[f626,f127]) ).
fof(f626,plain,
( p2(sK25)
| ~ r1(sK24,sK25)
| ~ spl36_82 ),
inference(resolution,[],[f600,f104]) ).
fof(f104,plain,
! [X18] :
( ~ p2(sK34(X18))
| ~ r1(sK24,X18)
| p2(X18) ),
inference(cnf_transformation,[],[f63]) ).
fof(f600,plain,
( p2(sK34(sK25))
| ~ spl36_82 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f605,plain,
( spl36_82
| spl36_83
| ~ spl36_62 ),
inference(avatar_split_clause,[],[f595,f481,f602,f598]) ).
fof(f595,plain,
( p2(sK9(sK34(sK25)))
| p2(sK34(sK25))
| ~ spl36_62 ),
inference(resolution,[],[f592,f227]) ).
fof(f592,plain,
( ! [X0] :
( ~ r1(sK25,X0)
| p2(X0)
| p2(sK9(X0)) )
| ~ spl36_62 ),
inference(resolution,[],[f591,f126]) ).
fof(f591,plain,
( ! [X0,X1] :
( ~ r1(sK24,X1)
| ~ r1(X1,X0)
| p2(sK9(X0))
| p2(X0) )
| ~ spl36_62 ),
inference(resolution,[],[f72,f483]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ sP4(X0)
| p2(sK9(X2))
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| p2(X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f581,plain,
( spl36_79
| ~ spl36_33
| ~ spl36_7
| ~ spl36_32 ),
inference(avatar_split_clause,[],[f379,f321,f155,f326,f579]) ).
fof(f326,plain,
( spl36_33
<=> p2(sK32(sK29)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_33])]) ).
fof(f155,plain,
( spl36_7
<=> ! [X11,X10] :
( ~ p2(X10)
| ~ r1(X10,X11)
| ~ r1(sK29,X10)
| p2(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_7])]) ).
fof(f321,plain,
( spl36_32
<=> r1(sK29,sK32(sK29)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_32])]) ).
fof(f379,plain,
( ! [X0] :
( ~ p2(sK32(sK29))
| p2(X0)
| ~ r1(sK32(sK29),X0) )
| ~ spl36_7
| ~ spl36_32 ),
inference(resolution,[],[f323,f156]) ).
fof(f156,plain,
( ! [X10,X11] :
( ~ r1(sK29,X10)
| p2(X11)
| ~ r1(X10,X11)
| ~ p2(X10) )
| ~ spl36_7 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f323,plain,
( r1(sK29,sK32(sK29))
| ~ spl36_32 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f555,plain,
( spl36_75
| spl36_65
| ~ spl36_63 ),
inference(avatar_split_clause,[],[f491,f485,f504,f552]) ).
fof(f491,plain,
( p2(sK6(sK24))
| p2(sK32(sK6(sK24)))
| ~ spl36_63 ),
inference(resolution,[],[f487,f109]) ).
fof(f109,plain,
! [X15] :
( ~ r1(sK24,X15)
| p2(sK32(X15))
| p2(X15) ),
inference(cnf_transformation,[],[f63]) ).
fof(f488,plain,
( spl36_62
| spl36_63
| ~ spl36_1 ),
inference(avatar_split_clause,[],[f479,f129,f485,f481]) ).
fof(f479,plain,
( r1(sK24,sK6(sK24))
| sP4(sK24)
| ~ spl36_1 ),
inference(resolution,[],[f68,f131]) ).
fof(f68,plain,
! [X0] :
( ~ sP5(X0)
| sP4(X0)
| r1(X0,sK6(X0)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f354,plain,
( spl36_37
| spl36_38
| spl36_36
| ~ spl36_3
| ~ spl36_5 ),
inference(avatar_split_clause,[],[f336,f146,f137,f343,f352,f347]) ).
fof(f137,plain,
( spl36_3
<=> ! [X9,X8,X7] :
( ~ r1(X7,X8)
| p2(X9)
| ~ r1(X8,X9)
| ~ r1(sK29,X7)
| sP2(X7)
| sP3(X7)
| ~ p2(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_3])]) ).
fof(f336,plain,
( ! [X0,X1] :
( sP3(sK20(sK29))
| p2(X1)
| sP2(sK20(sK29))
| ~ p2(X0)
| ~ r1(X0,X1)
| ~ r1(sK20(sK29),X0) )
| ~ spl36_3
| ~ spl36_5 ),
inference(resolution,[],[f335,f138]) ).
fof(f138,plain,
( ! [X8,X9,X7] :
( ~ r1(sK29,X7)
| ~ p2(X8)
| sP3(X7)
| sP2(X7)
| ~ r1(X8,X9)
| ~ r1(X7,X8)
| p2(X9) )
| ~ spl36_3 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f335,plain,
( r1(sK29,sK20(sK29))
| ~ spl36_5 ),
inference(resolution,[],[f101,f148]) ).
fof(f329,plain,
( spl36_6
| spl36_33
| ~ spl36_4 ),
inference(avatar_split_clause,[],[f269,f141,f326,f150]) ).
fof(f269,plain,
( p2(sK32(sK29))
| p2(sK29)
| ~ spl36_4 ),
inference(resolution,[],[f143,f109]) ).
fof(f324,plain,
( spl36_32
| spl36_6
| ~ spl36_4 ),
inference(avatar_split_clause,[],[f270,f141,f150,f321]) ).
fof(f270,plain,
( p2(sK29)
| r1(sK29,sK32(sK29))
| ~ spl36_4 ),
inference(resolution,[],[f143,f110]) ).
fof(f309,plain,
( spl36_29
| spl36_6
| ~ spl36_4 ),
inference(avatar_split_clause,[],[f268,f141,f150,f306]) ).
fof(f268,plain,
( p2(sK29)
| r1(sK32(sK29),sK33(sK29))
| ~ spl36_4 ),
inference(resolution,[],[f143,f108]) ).
fof(f157,plain,
( spl36_5
| spl36_1
| spl36_7 ),
inference(avatar_split_clause,[],[f117,f155,f129,f146]) ).
fof(f117,plain,
! [X10,X11] :
( ~ p2(X10)
| sP5(sK24)
| sP0(sK29)
| p2(X11)
| ~ r1(sK29,X10)
| ~ r1(X10,X11) ),
inference(cnf_transformation,[],[f63]) ).
fof(f153,plain,
( spl36_5
| spl36_1
| ~ spl36_6 ),
inference(avatar_split_clause,[],[f116,f150,f129,f146]) ).
fof(f116,plain,
( ~ p2(sK29)
| sP5(sK24)
| sP0(sK29) ),
inference(cnf_transformation,[],[f63]) ).
fof(f144,plain,
( spl36_1
| spl36_4 ),
inference(avatar_split_clause,[],[f115,f141,f129]) ).
fof(f115,plain,
( r1(sK24,sK29)
| sP5(sK24) ),
inference(cnf_transformation,[],[f63]) ).
fof(f139,plain,
( spl36_1
| spl36_3 ),
inference(avatar_split_clause,[],[f118,f137,f129]) ).
fof(f118,plain,
! [X8,X9,X7] :
( ~ r1(X7,X8)
| ~ p2(X8)
| sP3(X7)
| sP2(X7)
| ~ r1(sK29,X7)
| ~ r1(X8,X9)
| sP5(sK24)
| p2(X9) ),
inference(cnf_transformation,[],[f63]) ).
fof(f135,plain,
( spl36_1
| spl36_2 ),
inference(avatar_split_clause,[],[f119,f133,f129]) ).
fof(f119,plain,
! [X7] :
( sP3(X7)
| sP5(sK24)
| ~ p2(X7)
| sP2(X7)
| ~ r1(sK29,X7) ),
inference(cnf_transformation,[],[f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL642+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.13 % 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 : n019.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 02:16:35 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.44 % (14472)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.21/0.45 % (14464)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.21/0.45 % (14456)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.47 % (14456)Instruction limit reached!
% 0.21/0.47 % (14456)------------------------------
% 0.21/0.47 % (14456)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.47 % (14456)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.47 % (14456)Termination reason: Unknown
% 0.21/0.47 % (14456)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (14456)Memory used [KB]: 5756
% 0.21/0.47 % (14456)Time elapsed: 0.054 s
% 0.21/0.47 % (14456)Instructions burned: 7 (million)
% 0.21/0.47 % (14456)------------------------------
% 0.21/0.47 % (14456)------------------------------
% 0.21/0.47 % (14472)First to succeed.
% 0.21/0.49 % (14472)Refutation found. Thanks to Tanya!
% 0.21/0.49 % SZS status Theorem for theBenchmark
% 0.21/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.49 % (14472)------------------------------
% 0.21/0.49 % (14472)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.49 % (14472)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.49 % (14472)Termination reason: Refutation
% 0.21/0.49
% 0.21/0.49 % (14472)Memory used [KB]: 6012
% 0.21/0.49 % (14472)Time elapsed: 0.058 s
% 0.21/0.49 % (14472)Instructions burned: 17 (million)
% 0.21/0.49 % (14472)------------------------------
% 0.21/0.49 % (14472)------------------------------
% 0.21/0.49 % (14448)Success in time 0.139 s
%------------------------------------------------------------------------------