TSTP Solution File: LCL642+1.001 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL642+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 08:26:59 EDT 2023
% Result : Theorem 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 76
% Syntax : Number of formulae : 289 ( 5 unt; 0 def)
% Number of atoms : 2193 ( 0 equ)
% Maximal formula atoms : 107 ( 7 avg)
% Number of connectives : 3213 (1309 ~;1347 |; 488 &)
% ( 41 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 52 ( 51 usr; 42 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 5 con; 0-1 aty)
% Number of variables : 826 (; 618 !; 208 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3878,plain,
$false,
inference(avatar_sat_refutation,[],[f134,f138,f145,f149,f153,f342,f591,f594,f606,f707,f719,f767,f1087,f1189,f1200,f1937,f1956,f2059,f2271,f2280,f2311,f2332,f2731,f2737,f2775,f2933,f2935,f3000,f3093,f3110,f3213,f3278,f3328,f3356,f3393,f3412,f3463,f3509,f3531,f3696,f3742,f3877]) ).
fof(f3877,plain,
( ~ spl36_4
| ~ spl36_32
| ~ spl36_645 ),
inference(avatar_contradiction_clause,[],[f3876]) ).
fof(f3876,plain,
( $false
| ~ spl36_4
| ~ spl36_32
| ~ spl36_645 ),
inference(resolution,[],[f3875,f141]) ).
fof(f141,plain,
( sP1(sK26)
| ~ spl36_4 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f140,plain,
( spl36_4
<=> sP1(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_4])]) ).
fof(f3875,plain,
( ~ sP1(sK26)
| ~ spl36_32
| ~ spl36_645 ),
inference(resolution,[],[f3874,f91]) ).
fof(f91,plain,
! [X0] :
( r1(sK20(X0),sK21(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ( ! [X1] :
( ( p2(sK18(X1))
& ~ p2(sK19(X1))
& r1(sK18(X1),sK19(X1))
& r1(X1,sK18(X1)) )
| p2(X1)
| ~ r1(X0,X1) )
& ! [X6] :
( ~ p2(X6)
| ! [X7] :
( p2(X7)
| ~ r1(X6,X7) )
| ~ r1(sK21(X0),X6) )
& ~ p2(sK21(X0))
& r1(sK20(X0),sK21(X0))
& r1(X0,sK20(X0)) )
| ~ sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21])],[f39,f43,f42,f41,f40]) ).
fof(f40,plain,
! [X1] :
( ? [X2] :
( p2(X2)
& ? [X3] :
( ~ p2(X3)
& r1(X2,X3) )
& r1(X1,X2) )
=> ( p2(sK18(X1))
& ? [X3] :
( ~ p2(X3)
& r1(sK18(X1),X3) )
& r1(X1,sK18(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f41,plain,
! [X1] :
( ? [X3] :
( ~ p2(X3)
& r1(sK18(X1),X3) )
=> ( ~ p2(sK19(X1))
& r1(sK18(X1),sK19(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ! [X6] :
( ~ p2(X6)
| ! [X7] :
( p2(X7)
| ~ r1(X6,X7) )
| ~ r1(X5,X6) )
& ~ p2(X5)
& r1(X4,X5) )
& r1(X0,X4) )
=> ( ? [X5] :
( ! [X6] :
( ~ p2(X6)
| ! [X7] :
( p2(X7)
| ~ r1(X6,X7) )
| ~ r1(X5,X6) )
& ~ p2(X5)
& r1(sK20(X0),X5) )
& r1(X0,sK20(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
! [X0] :
( ? [X5] :
( ! [X6] :
( ~ p2(X6)
| ! [X7] :
( p2(X7)
| ~ r1(X6,X7) )
| ~ r1(X5,X6) )
& ~ p2(X5)
& r1(sK20(X0),X5) )
=> ( ! [X6] :
( ~ p2(X6)
| ! [X7] :
( p2(X7)
| ~ r1(X6,X7) )
| ~ r1(sK21(X0),X6) )
& ~ p2(sK21(X0))
& r1(sK20(X0),sK21(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
! [X0] :
( ( ! [X1] :
( ? [X2] :
( p2(X2)
& ? [X3] :
( ~ p2(X3)
& r1(X2,X3) )
& r1(X1,X2) )
| p2(X1)
| ~ r1(X0,X1) )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ~ p2(X6)
| ! [X7] :
( p2(X7)
| ~ r1(X6,X7) )
| ~ r1(X5,X6) )
& ~ p2(X5)
& r1(X4,X5) )
& r1(X0,X4) ) )
| ~ sP1(X0) ),
inference(rectify,[],[f38]) ).
fof(f38,plain,
! [X5] :
( ( ! [X28] :
( ? [X29] :
( p2(X29)
& ? [X30] :
( ~ p2(X30)
& r1(X29,X30) )
& r1(X28,X29) )
| p2(X28)
| ~ r1(X5,X28) )
& ? [X31] :
( ? [X32] :
( ! [X33] :
( ~ p2(X33)
| ! [X34] :
( p2(X34)
| ~ r1(X33,X34) )
| ~ r1(X32,X33) )
& ~ p2(X32)
& r1(X31,X32) )
& r1(X5,X31) ) )
| ~ sP1(X5) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,plain,
! [X5] :
( ( ! [X28] :
( ? [X29] :
( p2(X29)
& ? [X30] :
( ~ p2(X30)
& r1(X29,X30) )
& r1(X28,X29) )
| p2(X28)
| ~ r1(X5,X28) )
& ? [X31] :
( ? [X32] :
( ! [X33] :
( ~ p2(X33)
| ! [X34] :
( p2(X34)
| ~ r1(X33,X34) )
| ~ r1(X32,X33) )
& ~ p2(X32)
& r1(X31,X32) )
& r1(X5,X31) ) )
| ~ sP1(X5) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f3874,plain,
( ~ r1(sK20(sK26),sK21(sK26))
| ~ spl36_32
| ~ spl36_645 ),
inference(resolution,[],[f3741,f263]) ).
fof(f263,plain,
( sP3(sK20(sK26))
| ~ spl36_32 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f262,plain,
( spl36_32
<=> sP3(sK20(sK26)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_32])]) ).
fof(f3741,plain,
( ! [X0] :
( ~ sP3(X0)
| ~ r1(X0,sK21(sK26)) )
| ~ spl36_645 ),
inference(avatar_component_clause,[],[f3740]) ).
fof(f3740,plain,
( spl36_645
<=> ! [X0] :
( ~ r1(X0,sK21(sK26))
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_645])]) ).
fof(f3742,plain,
( spl36_645
| spl36_127
| ~ spl36_634 ),
inference(avatar_split_clause,[],[f3731,f3694,f826,f3740]) ).
fof(f826,plain,
( spl36_127
<=> p2(sK21(sK26)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_127])]) ).
fof(f3694,plain,
( spl36_634
<=> p2(sK13(sK21(sK26))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_634])]) ).
fof(f3731,plain,
( ! [X0] :
( p2(sK21(sK26))
| ~ r1(X0,sK21(sK26))
| ~ sP3(X0) )
| ~ spl36_634 ),
inference(resolution,[],[f3695,f84]) ).
fof(f84,plain,
! [X0,X1] :
( ~ p2(sK13(X1))
| p2(X1)
| ~ r1(X0,X1)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] :
( ( ! [X1] :
( ( p2(sK12(X1))
& ~ p2(sK13(X1))
& r1(sK12(X1),sK13(X1))
& r1(X1,sK12(X1)) )
| p2(X1)
| ~ r1(X0,X1) )
& ! [X6] :
( ~ p2(X6)
| ! [X7] :
( p2(X7)
| ~ r1(X6,X7) )
| ~ r1(sK15(X0),X6) )
& ~ p2(sK15(X0))
& r1(sK14(X0),sK15(X0))
& r1(X0,sK14(X0)) )
| ~ sP3(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15])],[f27,f31,f30,f29,f28]) ).
fof(f28,plain,
! [X1] :
( ? [X2] :
( p2(X2)
& ? [X3] :
( ~ p2(X3)
& r1(X2,X3) )
& r1(X1,X2) )
=> ( p2(sK12(X1))
& ? [X3] :
( ~ p2(X3)
& r1(sK12(X1),X3) )
& r1(X1,sK12(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X1] :
( ? [X3] :
( ~ p2(X3)
& r1(sK12(X1),X3) )
=> ( ~ p2(sK13(X1))
& r1(sK12(X1),sK13(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ! [X6] :
( ~ p2(X6)
| ! [X7] :
( p2(X7)
| ~ r1(X6,X7) )
| ~ r1(X5,X6) )
& ~ p2(X5)
& r1(X4,X5) )
& r1(X0,X4) )
=> ( ? [X5] :
( ! [X6] :
( ~ p2(X6)
| ! [X7] :
( p2(X7)
| ~ r1(X6,X7) )
| ~ r1(X5,X6) )
& ~ p2(X5)
& r1(sK14(X0),X5) )
& r1(X0,sK14(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0] :
( ? [X5] :
( ! [X6] :
( ~ p2(X6)
| ! [X7] :
( p2(X7)
| ~ r1(X6,X7) )
| ~ r1(X5,X6) )
& ~ p2(X5)
& r1(sK14(X0),X5) )
=> ( ! [X6] :
( ~ p2(X6)
| ! [X7] :
( p2(X7)
| ~ r1(X6,X7) )
| ~ r1(sK15(X0),X6) )
& ~ p2(sK15(X0))
& r1(sK14(X0),sK15(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0] :
( ( ! [X1] :
( ? [X2] :
( p2(X2)
& ? [X3] :
( ~ p2(X3)
& r1(X2,X3) )
& r1(X1,X2) )
| p2(X1)
| ~ r1(X0,X1) )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ~ p2(X6)
| ! [X7] :
( p2(X7)
| ~ r1(X6,X7) )
| ~ r1(X5,X6) )
& ~ p2(X5)
& r1(X4,X5) )
& r1(X0,X4) ) )
| ~ sP3(X0) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X6] :
( ( ! [X9] :
( ? [X10] :
( p2(X10)
& ? [X11] :
( ~ p2(X11)
& r1(X10,X11) )
& r1(X9,X10) )
| p2(X9)
| ~ r1(X6,X9) )
& ? [X12] :
( ? [X13] :
( ! [X14] :
( ~ p2(X14)
| ! [X15] :
( p2(X15)
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
& ~ p2(X13)
& r1(X12,X13) )
& r1(X6,X12) ) )
| ~ sP3(X6) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,plain,
! [X6] :
( ( ! [X9] :
( ? [X10] :
( p2(X10)
& ? [X11] :
( ~ p2(X11)
& r1(X10,X11) )
& r1(X9,X10) )
| p2(X9)
| ~ r1(X6,X9) )
& ? [X12] :
( ? [X13] :
( ! [X14] :
( ~ p2(X14)
| ! [X15] :
( p2(X15)
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
& ~ p2(X13)
& r1(X12,X13) )
& r1(X6,X12) ) )
| ~ sP3(X6) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f3695,plain,
( p2(sK13(sK21(sK26)))
| ~ spl36_634 ),
inference(avatar_component_clause,[],[f3694]) ).
fof(f3696,plain,
( spl36_127
| ~ spl36_564
| spl36_634
| ~ spl36_32
| ~ spl36_591 ),
inference(avatar_split_clause,[],[f3685,f3480,f262,f3694,f3273,f826]) ).
fof(f3273,plain,
( spl36_564
<=> r1(sK20(sK26),sK21(sK26)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_564])]) ).
fof(f3480,plain,
( spl36_591
<=> ! [X0] :
( p2(X0)
| ~ r1(sK12(sK21(sK26)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_591])]) ).
fof(f3685,plain,
( p2(sK13(sK21(sK26)))
| ~ r1(sK20(sK26),sK21(sK26))
| p2(sK21(sK26))
| ~ spl36_32
| ~ spl36_591 ),
inference(resolution,[],[f3481,f3395]) ).
fof(f3395,plain,
( ! [X2] :
( r1(sK12(X2),sK13(X2))
| ~ r1(sK20(sK26),X2)
| p2(X2) )
| ~ spl36_32 ),
inference(resolution,[],[f263,f83]) ).
fof(f83,plain,
! [X0,X1] :
( ~ sP3(X0)
| p2(X1)
| ~ r1(X0,X1)
| r1(sK12(X1),sK13(X1)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f3481,plain,
( ! [X0] :
( ~ r1(sK12(sK21(sK26)),X0)
| p2(X0) )
| ~ spl36_591 ),
inference(avatar_component_clause,[],[f3480]) ).
fof(f3531,plain,
( ~ spl36_4
| spl36_598
| spl36_127
| ~ spl36_32 ),
inference(avatar_split_clause,[],[f3520,f262,f826,f3507,f140]) ).
fof(f3507,plain,
( spl36_598
<=> r1(sK21(sK26),sK12(sK21(sK26))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_598])]) ).
fof(f3520,plain,
( p2(sK21(sK26))
| r1(sK21(sK26),sK12(sK21(sK26)))
| ~ sP1(sK26)
| ~ spl36_32 ),
inference(resolution,[],[f3396,f91]) ).
fof(f3396,plain,
( ! [X3] :
( ~ r1(sK20(sK26),X3)
| p2(X3)
| r1(X3,sK12(X3)) )
| ~ spl36_32 ),
inference(resolution,[],[f263,f82]) ).
fof(f82,plain,
! [X0,X1] :
( ~ sP3(X0)
| p2(X1)
| ~ r1(X0,X1)
| r1(X1,sK12(X1)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f3509,plain,
( ~ spl36_598
| spl36_591
| ~ spl36_4
| ~ spl36_587 ),
inference(avatar_split_clause,[],[f3475,f3410,f140,f3480,f3507]) ).
fof(f3410,plain,
( spl36_587
<=> p2(sK12(sK21(sK26))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_587])]) ).
fof(f3475,plain,
( ! [X8] :
( ~ r1(sK12(sK21(sK26)),X8)
| ~ r1(sK21(sK26),sK12(sK21(sK26)))
| p2(X8) )
| ~ spl36_4
| ~ spl36_587 ),
inference(resolution,[],[f3411,f796]) ).
fof(f796,plain,
( ! [X0,X1] :
( ~ p2(X1)
| ~ r1(X1,X0)
| ~ r1(sK21(sK26),X1)
| p2(X0) )
| ~ spl36_4 ),
inference(resolution,[],[f141,f93]) ).
fof(f93,plain,
! [X0,X6,X7] :
( ~ sP1(X0)
| p2(X7)
| ~ r1(X6,X7)
| ~ r1(sK21(X0),X6)
| ~ p2(X6) ),
inference(cnf_transformation,[],[f44]) ).
fof(f3411,plain,
( p2(sK12(sK21(sK26)))
| ~ spl36_587 ),
inference(avatar_component_clause,[],[f3410]) ).
fof(f3463,plain,
( ~ spl36_4
| ~ spl36_31
| ~ spl36_577 ),
inference(avatar_split_clause,[],[f3461,f3354,f259,f140]) ).
fof(f259,plain,
( spl36_31
<=> sP4(sK20(sK26)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_31])]) ).
fof(f3354,plain,
( spl36_577
<=> ! [X0] :
( ~ r1(X0,sK21(sK26))
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_577])]) ).
fof(f3461,plain,
( ~ sP4(sK20(sK26))
| ~ sP1(sK26)
| ~ spl36_577 ),
inference(resolution,[],[f3355,f91]) ).
fof(f3355,plain,
( ! [X0] :
( ~ r1(X0,sK21(sK26))
| ~ sP4(X0) )
| ~ spl36_577 ),
inference(avatar_component_clause,[],[f3354]) ).
fof(f3412,plain,
( ~ spl36_4
| spl36_587
| spl36_127
| ~ spl36_32 ),
inference(avatar_split_clause,[],[f3399,f262,f826,f3410,f140]) ).
fof(f3399,plain,
( p2(sK21(sK26))
| p2(sK12(sK21(sK26)))
| ~ sP1(sK26)
| ~ spl36_32 ),
inference(resolution,[],[f3397,f91]) ).
fof(f3397,plain,
( ! [X4] :
( ~ r1(sK20(sK26),X4)
| p2(X4)
| p2(sK12(X4)) )
| ~ spl36_32 ),
inference(resolution,[],[f263,f85]) ).
fof(f85,plain,
! [X0,X1] :
( ~ sP3(X0)
| p2(X1)
| ~ r1(X0,X1)
| p2(sK12(X1)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f3393,plain,
( ~ spl36_4
| spl36_147
| spl36_32
| spl36_31
| spl36_29
| ~ spl36_2
| ~ spl36_4 ),
inference(avatar_split_clause,[],[f937,f140,f132,f253,f259,f262,f943,f140]) ).
fof(f943,plain,
( spl36_147
<=> ! [X3] :
( ~ r1(sK18(sK20(sK26)),X3)
| p2(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_147])]) ).
fof(f253,plain,
( spl36_29
<=> p2(sK20(sK26)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_29])]) ).
fof(f132,plain,
( spl36_2
<=> ! [X6,X7,X8] :
( ~ p2(X7)
| ~ r1(sK26,X6)
| sP4(X6)
| sP3(X6)
| ~ r1(X6,X7)
| ~ r1(X7,X8)
| p2(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_2])]) ).
fof(f937,plain,
( ! [X3] :
( p2(sK20(sK26))
| sP4(sK20(sK26))
| sP3(sK20(sK26))
| ~ r1(sK18(sK20(sK26)),X3)
| p2(X3)
| ~ sP1(sK26) )
| ~ spl36_2
| ~ spl36_4 ),
inference(resolution,[],[f847,f90]) ).
fof(f90,plain,
! [X0] :
( r1(X0,sK20(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f847,plain,
( ! [X0,X1] :
( ~ r1(sK26,X0)
| p2(X0)
| sP4(X0)
| sP3(X0)
| ~ r1(sK18(X0),X1)
| p2(X1) )
| ~ spl36_2
| ~ spl36_4 ),
inference(duplicate_literal_removal,[],[f846]) ).
fof(f846,plain,
( ! [X0,X1] :
( p2(X0)
| ~ r1(sK26,X0)
| sP4(X0)
| sP3(X0)
| ~ r1(sK26,X0)
| ~ r1(sK18(X0),X1)
| p2(X1)
| ~ r1(sK26,X0)
| p2(X0) )
| ~ spl36_2
| ~ spl36_4 ),
inference(resolution,[],[f305,f304]) ).
fof(f304,plain,
( ! [X0] :
( r1(X0,sK18(X0))
| ~ r1(sK26,X0)
| p2(X0) )
| ~ spl36_4 ),
inference(resolution,[],[f94,f141]) ).
fof(f94,plain,
! [X0,X1] :
( ~ sP1(X0)
| p2(X1)
| ~ r1(X0,X1)
| r1(X1,sK18(X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f305,plain,
( ! [X2,X0,X1] :
( ~ r1(X1,sK18(X0))
| p2(X0)
| ~ r1(sK26,X1)
| sP4(X1)
| sP3(X1)
| ~ r1(sK26,X0)
| ~ r1(sK18(X0),X2)
| p2(X2) )
| ~ spl36_2
| ~ spl36_4 ),
inference(resolution,[],[f303,f133]) ).
fof(f133,plain,
( ! [X8,X6,X7] :
( ~ p2(X7)
| ~ r1(sK26,X6)
| sP4(X6)
| sP3(X6)
| ~ r1(X6,X7)
| ~ r1(X7,X8)
| p2(X8) )
| ~ spl36_2 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f303,plain,
( ! [X0] :
( p2(sK18(X0))
| ~ r1(sK26,X0)
| p2(X0) )
| ~ spl36_4 ),
inference(resolution,[],[f97,f141]) ).
fof(f97,plain,
! [X0,X1] :
( ~ sP1(X0)
| p2(X1)
| ~ r1(X0,X1)
| p2(sK18(X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f3356,plain,
( spl36_577
| spl36_127
| ~ spl36_565 ),
inference(avatar_split_clause,[],[f3345,f3276,f826,f3354]) ).
fof(f3276,plain,
( spl36_565
<=> p2(sK10(sK21(sK26))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_565])]) ).
fof(f3345,plain,
( ! [X0] :
( p2(sK21(sK26))
| ~ r1(X0,sK21(sK26))
| ~ sP4(X0) )
| ~ spl36_565 ),
inference(resolution,[],[f3277,f76]) ).
fof(f76,plain,
! [X0,X1] :
( ~ p2(sK10(X1))
| p2(X1)
| ~ r1(X0,X1)
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0] :
( ! [X1] :
( ( ( ( p2(sK9(X1))
& ~ p2(sK10(X1))
& r1(sK9(X1),sK10(X1))
& r1(X1,sK9(X1)) )
| p2(X1) )
& ( ( ! [X5] :
( ~ p2(X5)
| ! [X6] :
( p2(X6)
| ~ r1(X5,X6) )
| ~ r1(sK11(X1),X5) )
& ~ p2(sK11(X1))
& r1(X1,sK11(X1)) )
| sP2(X1) ) )
| ~ r1(X0,X1) )
| ~ sP4(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f21,f24,f23,f22]) ).
fof(f22,plain,
! [X1] :
( ? [X2] :
( p2(X2)
& ? [X3] :
( ~ p2(X3)
& r1(X2,X3) )
& r1(X1,X2) )
=> ( p2(sK9(X1))
& ? [X3] :
( ~ p2(X3)
& r1(sK9(X1),X3) )
& r1(X1,sK9(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X1] :
( ? [X3] :
( ~ p2(X3)
& r1(sK9(X1),X3) )
=> ( ~ p2(sK10(X1))
& r1(sK9(X1),sK10(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X1] :
( ? [X4] :
( ! [X5] :
( ~ p2(X5)
| ! [X6] :
( p2(X6)
| ~ r1(X5,X6) )
| ~ r1(X4,X5) )
& ~ p2(X4)
& r1(X1,X4) )
=> ( ! [X5] :
( ~ p2(X5)
| ! [X6] :
( p2(X6)
| ~ r1(X5,X6) )
| ~ r1(sK11(X1),X5) )
& ~ p2(sK11(X1))
& r1(X1,sK11(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0] :
( ! [X1] :
( ( ( ? [X2] :
( p2(X2)
& ? [X3] :
( ~ p2(X3)
& r1(X2,X3) )
& r1(X1,X2) )
| p2(X1) )
& ( ? [X4] :
( ! [X5] :
( ~ p2(X5)
| ! [X6] :
( p2(X6)
| ~ r1(X5,X6) )
| ~ r1(X4,X5) )
& ~ p2(X4)
& r1(X1,X4) )
| sP2(X1) ) )
| ~ r1(X0,X1) )
| ~ sP4(X0) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
! [X6] :
( ! [X16] :
( ( ( ? [X17] :
( p2(X17)
& ? [X18] :
( ~ p2(X18)
& r1(X17,X18) )
& r1(X16,X17) )
| p2(X16) )
& ( ? [X19] :
( ! [X20] :
( ~ p2(X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
& ~ p2(X19)
& r1(X16,X19) )
| sP2(X16) ) )
| ~ r1(X6,X16) )
| ~ sP4(X6) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X6] :
( ! [X16] :
( ( ( ? [X17] :
( p2(X17)
& ? [X18] :
( ~ p2(X18)
& r1(X17,X18) )
& r1(X16,X17) )
| p2(X16) )
& ( ? [X19] :
( ! [X20] :
( ~ p2(X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
& ~ p2(X19)
& r1(X16,X19) )
| sP2(X16) ) )
| ~ r1(X6,X16) )
| ~ sP4(X6) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f3277,plain,
( p2(sK10(sK21(sK26)))
| ~ spl36_565 ),
inference(avatar_component_clause,[],[f3276]) ).
fof(f3328,plain,
( ~ spl36_4
| spl36_564 ),
inference(avatar_contradiction_clause,[],[f3327]) ).
fof(f3327,plain,
( $false
| ~ spl36_4
| spl36_564 ),
inference(resolution,[],[f3318,f141]) ).
fof(f3318,plain,
( ~ sP1(sK26)
| spl36_564 ),
inference(resolution,[],[f3274,f91]) ).
fof(f3274,plain,
( ~ r1(sK20(sK26),sK21(sK26))
| spl36_564 ),
inference(avatar_component_clause,[],[f3273]) ).
fof(f3278,plain,
( spl36_127
| ~ spl36_564
| spl36_565
| ~ spl36_31
| ~ spl36_547 ),
inference(avatar_split_clause,[],[f3263,f3186,f259,f3276,f3273,f826]) ).
fof(f3186,plain,
( spl36_547
<=> ! [X0] :
( p2(X0)
| ~ r1(sK9(sK21(sK26)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_547])]) ).
fof(f3263,plain,
( p2(sK10(sK21(sK26)))
| ~ r1(sK20(sK26),sK21(sK26))
| p2(sK21(sK26))
| ~ spl36_31
| ~ spl36_547 ),
inference(resolution,[],[f3187,f2937]) ).
fof(f2937,plain,
( ! [X3] :
( r1(sK9(X3),sK10(X3))
| ~ r1(sK20(sK26),X3)
| p2(X3) )
| ~ spl36_31 ),
inference(resolution,[],[f260,f75]) ).
fof(f75,plain,
! [X0,X1] :
( ~ sP4(X0)
| p2(X1)
| ~ r1(X0,X1)
| r1(sK9(X1),sK10(X1)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f260,plain,
( sP4(sK20(sK26))
| ~ spl36_31 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f3187,plain,
( ! [X0] :
( ~ r1(sK9(sK21(sK26)),X0)
| p2(X0) )
| ~ spl36_547 ),
inference(avatar_component_clause,[],[f3186]) ).
fof(f3213,plain,
( ~ spl36_533
| spl36_547
| ~ spl36_4
| ~ spl36_531 ),
inference(avatar_split_clause,[],[f3181,f3091,f140,f3186,f3108]) ).
fof(f3108,plain,
( spl36_533
<=> r1(sK21(sK26),sK9(sK21(sK26))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_533])]) ).
fof(f3091,plain,
( spl36_531
<=> p2(sK9(sK21(sK26))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_531])]) ).
fof(f3181,plain,
( ! [X8] :
( ~ r1(sK9(sK21(sK26)),X8)
| ~ r1(sK21(sK26),sK9(sK21(sK26)))
| p2(X8) )
| ~ spl36_4
| ~ spl36_531 ),
inference(resolution,[],[f3092,f796]) ).
fof(f3092,plain,
( p2(sK9(sK21(sK26)))
| ~ spl36_531 ),
inference(avatar_component_clause,[],[f3091]) ).
fof(f3110,plain,
( ~ spl36_4
| spl36_533
| spl36_127
| ~ spl36_31 ),
inference(avatar_split_clause,[],[f3098,f259,f826,f3108,f140]) ).
fof(f3098,plain,
( p2(sK21(sK26))
| r1(sK21(sK26),sK9(sK21(sK26)))
| ~ sP1(sK26)
| ~ spl36_31 ),
inference(resolution,[],[f2938,f91]) ).
fof(f2938,plain,
( ! [X4] :
( ~ r1(sK20(sK26),X4)
| p2(X4)
| r1(X4,sK9(X4)) )
| ~ spl36_31 ),
inference(resolution,[],[f260,f74]) ).
fof(f74,plain,
! [X0,X1] :
( ~ sP4(X0)
| p2(X1)
| ~ r1(X0,X1)
| r1(X1,sK9(X1)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f3093,plain,
( ~ spl36_4
| spl36_531
| spl36_127
| ~ spl36_31 ),
inference(avatar_split_clause,[],[f3081,f259,f826,f3091,f140]) ).
fof(f3081,plain,
( p2(sK21(sK26))
| p2(sK9(sK21(sK26)))
| ~ sP1(sK26)
| ~ spl36_31 ),
inference(resolution,[],[f2940,f91]) ).
fof(f2940,plain,
( ! [X6] :
( ~ r1(sK20(sK26),X6)
| p2(X6)
| p2(sK9(X6)) )
| ~ spl36_31 ),
inference(resolution,[],[f260,f77]) ).
fof(f77,plain,
! [X0,X1] :
( ~ sP4(X0)
| p2(X1)
| ~ r1(X0,X1)
| p2(sK9(X1)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f3000,plain,
( ~ spl36_4
| ~ spl36_127 ),
inference(avatar_contradiction_clause,[],[f2999]) ).
fof(f2999,plain,
( $false
| ~ spl36_4
| ~ spl36_127 ),
inference(resolution,[],[f2968,f141]) ).
fof(f2968,plain,
( ~ sP1(sK26)
| ~ spl36_127 ),
inference(resolution,[],[f827,f92]) ).
fof(f92,plain,
! [X0] :
( ~ p2(sK21(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f827,plain,
( p2(sK21(sK26))
| ~ spl36_127 ),
inference(avatar_component_clause,[],[f826]) ).
fof(f2935,plain,
( spl36_32
| spl36_31
| ~ spl36_175
| ~ spl36_3
| ~ spl36_29 ),
inference(avatar_split_clause,[],[f2901,f253,f136,f1082,f259,f262]) ).
fof(f1082,plain,
( spl36_175
<=> r1(sK26,sK20(sK26)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_175])]) ).
fof(f136,plain,
( spl36_3
<=> ! [X6] :
( ~ p2(X6)
| ~ r1(sK26,X6)
| sP4(X6)
| sP3(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_3])]) ).
fof(f2901,plain,
( ~ r1(sK26,sK20(sK26))
| sP4(sK20(sK26))
| sP3(sK20(sK26))
| ~ spl36_3
| ~ spl36_29 ),
inference(resolution,[],[f254,f137]) ).
fof(f137,plain,
( ! [X6] :
( ~ p2(X6)
| ~ r1(sK26,X6)
| sP4(X6)
| sP3(X6) )
| ~ spl36_3 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f254,plain,
( p2(sK20(sK26))
| ~ spl36_29 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f2933,plain,
( ~ spl36_4
| ~ spl36_203 ),
inference(avatar_contradiction_clause,[],[f2932]) ).
fof(f2932,plain,
( $false
| ~ spl36_4
| ~ spl36_203 ),
inference(resolution,[],[f2931,f141]) ).
fof(f2931,plain,
( ~ sP1(sK26)
| ~ spl36_4
| ~ spl36_203 ),
inference(resolution,[],[f2781,f90]) ).
fof(f2781,plain,
( ~ r1(sK26,sK20(sK26))
| ~ spl36_4
| ~ spl36_203 ),
inference(resolution,[],[f141,f1199]) ).
fof(f1199,plain,
( ! [X0] :
( ~ sP1(X0)
| ~ r1(X0,sK20(sK26)) )
| ~ spl36_203 ),
inference(avatar_component_clause,[],[f1198]) ).
fof(f1198,plain,
( spl36_203
<=> ! [X0] :
( ~ r1(X0,sK20(sK26))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_203])]) ).
fof(f2775,plain,
( ~ spl36_1
| spl36_50
| ~ spl36_79 ),
inference(avatar_split_clause,[],[f648,f586,f337,f129]) ).
fof(f129,plain,
( spl36_1
<=> sP5(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_1])]) ).
fof(f337,plain,
( spl36_50
<=> sP0(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_50])]) ).
fof(f586,plain,
( spl36_79
<=> p2(sK8(sK24)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_79])]) ).
fof(f648,plain,
( sP0(sK24)
| ~ sP5(sK24)
| ~ spl36_79 ),
inference(resolution,[],[f587,f65]) ).
fof(f65,plain,
! [X0] :
( ~ p2(sK8(X0))
| sP0(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0] :
( ( ( ( p2(sK6(X0))
& ~ p2(sK7(X0))
& r1(sK6(X0),sK7(X0))
& r1(X0,sK6(X0)) )
| p2(X0) )
& ( ( ! [X4] :
( ~ p2(X4)
| ! [X5] :
( p2(X5)
| ~ r1(X4,X5) )
| ~ r1(sK8(X0),X4) )
& ~ p2(sK8(X0))
& r1(X0,sK8(X0)) )
| sP0(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) )
& r1(X0,X1) )
=> ( p2(sK6(X0))
& ? [X2] :
( ~ p2(X2)
& r1(sK6(X0),X2) )
& r1(X0,sK6(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0] :
( ? [X2] :
( ~ p2(X2)
& r1(sK6(X0),X2) )
=> ( ~ p2(sK7(X0))
& r1(sK6(X0),sK7(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0] :
( ? [X3] :
( ! [X4] :
( ~ p2(X4)
| ! [X5] :
( p2(X5)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
& ~ p2(X3)
& r1(X0,X3) )
=> ( ! [X4] :
( ~ p2(X4)
| ! [X5] :
( p2(X5)
| ~ r1(X4,X5) )
| ~ r1(sK8(X0),X4) )
& ~ p2(sK8(X0))
& r1(X0,sK8(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
! [X0] :
( ( ( ? [X1] :
( p2(X1)
& ? [X2] :
( ~ p2(X2)
& r1(X1,X2) )
& r1(X0,X1) )
| p2(X0) )
& ( ? [X3] :
( ! [X4] :
( ~ p2(X4)
| ! [X5] :
( p2(X5)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
& ~ p2(X3)
& r1(X0,X3) )
| sP0(X0) ) )
| ~ sP5(X0) ),
inference(rectify,[],[f14]) ).
fof(f14,plain,
! [X0] :
( ( ( ? [X35] :
( p2(X35)
& ? [X36] :
( ~ p2(X36)
& r1(X35,X36) )
& r1(X0,X35) )
| p2(X0) )
& ( ? [X37] :
( ! [X38] :
( ~ p2(X38)
| ! [X39] :
( p2(X39)
| ~ r1(X38,X39) )
| ~ r1(X37,X38) )
& ~ p2(X37)
& r1(X0,X37) )
| sP0(X0) ) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0] :
( ( ( ? [X35] :
( p2(X35)
& ? [X36] :
( ~ p2(X36)
& r1(X35,X36) )
& r1(X0,X35) )
| p2(X0) )
& ( ? [X37] :
( ! [X38] :
( ~ p2(X38)
| ! [X39] :
( p2(X39)
| ~ r1(X38,X39) )
| ~ r1(X37,X38) )
& ~ p2(X37)
& r1(X0,X37) )
| sP0(X0) ) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f587,plain,
( p2(sK8(sK24))
| ~ spl36_79 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f2737,plain,
( ~ spl36_78
| spl36_79
| ~ spl36_81 ),
inference(avatar_split_clause,[],[f2732,f604,f586,f583]) ).
fof(f583,plain,
( spl36_78
<=> r1(sK24,sK8(sK24)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_78])]) ).
fof(f604,plain,
( spl36_81
<=> p2(sK31(sK8(sK24))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_81])]) ).
fof(f2732,plain,
( p2(sK8(sK24))
| ~ r1(sK24,sK8(sK24))
| ~ spl36_81 ),
inference(resolution,[],[f605,f112]) ).
fof(f112,plain,
! [X15] :
( ~ p2(sK31(X15))
| p2(X15)
| ~ r1(sK24,X15) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
( ! [X1] :
( ( ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(sK25(X1),X3) )
& ~ p2(sK25(X1))
& r1(X1,sK25(X1)) )
| p2(X1)
| ~ r1(sK24,X1) )
& ( ( ! [X6] :
( ( ! [X7] :
( ~ p2(X7)
| ! [X8] :
( p2(X8)
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
& ~ p2(X6) )
| sP3(X6)
| sP4(X6)
| ~ r1(sK26,X6) )
& ( ( ! [X9] :
( ~ p2(X9)
| ! [X10] :
( p2(X10)
| ~ r1(X9,X10) )
| ~ r1(sK26,X9) )
& ~ p2(sK26) )
| sP1(sK26) )
& r1(sK24,sK26) )
| sP5(sK24) )
& ! [X11] :
( ( p1(sK27(X11))
& ~ p1(sK28(X11))
& r1(sK27(X11),sK28(X11))
& r1(X11,sK27(X11)) )
| p1(X11)
| ~ r1(sK24,X11) )
& ~ p1(sK29)
& r1(sK24,sK29)
& ! [X15] :
( ( p2(sK30(X15))
& ~ p2(sK31(X15))
& r1(sK30(X15),sK31(X15))
& r1(X15,sK30(X15)) )
| p2(X15)
| ~ r1(sK24,X15) )
& ~ p2(sK32)
& r1(sK24,sK32)
& ! [X19] :
( ( p3(sK33(X19))
& ~ p3(sK34(X19))
& r1(sK33(X19),sK34(X19))
& r1(X19,sK33(X19)) )
| p3(X19)
| ~ r1(sK24,X19) )
& ~ p3(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] :
( ? [X2] :
( ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
& ~ p2(X2)
& r1(X1,X2) )
| p2(X1)
| ~ r1(X0,X1) )
& ( ? [X5] :
( ! [X6] :
( ( ! [X7] :
( ~ p2(X7)
| ! [X8] :
( p2(X8)
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
& ~ p2(X6) )
| sP3(X6)
| sP4(X6)
| ~ r1(X5,X6) )
& ( ( ! [X9] :
( ~ p2(X9)
| ! [X10] :
( p2(X10)
| ~ r1(X9,X10) )
| ~ r1(X5,X9) )
& ~ p2(X5) )
| sP1(X5) )
& r1(X0,X5) )
| sP5(X0) )
& ! [X11] :
( ? [X12] :
( p1(X12)
& ? [X13] :
( ~ p1(X13)
& r1(X12,X13) )
& r1(X11,X12) )
| p1(X11)
| ~ r1(X0,X11) )
& ? [X14] :
( ~ p1(X14)
& r1(X0,X14) )
& ! [X15] :
( ? [X16] :
( p2(X16)
& ? [X17] :
( ~ p2(X17)
& r1(X16,X17) )
& r1(X15,X16) )
| p2(X15)
| ~ r1(X0,X15) )
& ? [X18] :
( ~ p2(X18)
& r1(X0,X18) )
& ! [X19] :
( ? [X20] :
( p3(X20)
& ? [X21] :
( ~ p3(X21)
& r1(X20,X21) )
& r1(X19,X20) )
| p3(X19)
| ~ r1(X0,X19) )
& ? [X22] :
( ~ p3(X22)
& r1(X0,X22) ) )
=> ( ! [X1] :
( ? [X2] :
( ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
& ~ p2(X2)
& r1(X1,X2) )
| p2(X1)
| ~ r1(sK24,X1) )
& ( ? [X5] :
( ! [X6] :
( ( ! [X7] :
( ~ p2(X7)
| ! [X8] :
( p2(X8)
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
& ~ p2(X6) )
| sP3(X6)
| sP4(X6)
| ~ r1(X5,X6) )
& ( ( ! [X9] :
( ~ p2(X9)
| ! [X10] :
( p2(X10)
| ~ r1(X9,X10) )
| ~ r1(X5,X9) )
& ~ p2(X5) )
| sP1(X5) )
& r1(sK24,X5) )
| sP5(sK24) )
& ! [X11] :
( ? [X12] :
( p1(X12)
& ? [X13] :
( ~ p1(X13)
& r1(X12,X13) )
& r1(X11,X12) )
| p1(X11)
| ~ r1(sK24,X11) )
& ? [X14] :
( ~ p1(X14)
& r1(sK24,X14) )
& ! [X15] :
( ? [X16] :
( p2(X16)
& ? [X17] :
( ~ p2(X17)
& r1(X16,X17) )
& r1(X15,X16) )
| p2(X15)
| ~ r1(sK24,X15) )
& ? [X18] :
( ~ p2(X18)
& r1(sK24,X18) )
& ! [X19] :
( ? [X20] :
( p3(X20)
& ? [X21] :
( ~ p3(X21)
& r1(X20,X21) )
& r1(X19,X20) )
| p3(X19)
| ~ r1(sK24,X19) )
& ? [X22] :
( ~ p3(X22)
& r1(sK24,X22) ) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
! [X1] :
( ? [X2] :
( ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
& ~ p2(X2)
& r1(X1,X2) )
=> ( ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(sK25(X1),X3) )
& ~ p2(sK25(X1))
& r1(X1,sK25(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
( ? [X5] :
( ! [X6] :
( ( ! [X7] :
( ~ p2(X7)
| ! [X8] :
( p2(X8)
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
& ~ p2(X6) )
| sP3(X6)
| sP4(X6)
| ~ r1(X5,X6) )
& ( ( ! [X9] :
( ~ p2(X9)
| ! [X10] :
( p2(X10)
| ~ r1(X9,X10) )
| ~ r1(X5,X9) )
& ~ p2(X5) )
| sP1(X5) )
& r1(sK24,X5) )
=> ( ! [X6] :
( ( ! [X7] :
( ~ p2(X7)
| ! [X8] :
( p2(X8)
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
& ~ p2(X6) )
| sP3(X6)
| sP4(X6)
| ~ r1(sK26,X6) )
& ( ( ! [X9] :
( ~ p2(X9)
| ! [X10] :
( p2(X10)
| ~ r1(X9,X10) )
| ~ r1(sK26,X9) )
& ~ p2(sK26) )
| sP1(sK26) )
& r1(sK24,sK26) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X11] :
( ? [X12] :
( p1(X12)
& ? [X13] :
( ~ p1(X13)
& r1(X12,X13) )
& r1(X11,X12) )
=> ( p1(sK27(X11))
& ? [X13] :
( ~ p1(X13)
& r1(sK27(X11),X13) )
& r1(X11,sK27(X11)) ) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
! [X11] :
( ? [X13] :
( ~ p1(X13)
& r1(sK27(X11),X13) )
=> ( ~ p1(sK28(X11))
& r1(sK27(X11),sK28(X11)) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
( ? [X14] :
( ~ p1(X14)
& r1(sK24,X14) )
=> ( ~ p1(sK29)
& r1(sK24,sK29) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
! [X15] :
( ? [X16] :
( p2(X16)
& ? [X17] :
( ~ p2(X17)
& r1(X16,X17) )
& r1(X15,X16) )
=> ( p2(sK30(X15))
& ? [X17] :
( ~ p2(X17)
& r1(sK30(X15),X17) )
& r1(X15,sK30(X15)) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
! [X15] :
( ? [X17] :
( ~ p2(X17)
& r1(sK30(X15),X17) )
=> ( ~ p2(sK31(X15))
& r1(sK30(X15),sK31(X15)) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
( ? [X18] :
( ~ p2(X18)
& r1(sK24,X18) )
=> ( ~ p2(sK32)
& r1(sK24,sK32) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X19] :
( ? [X20] :
( p3(X20)
& ? [X21] :
( ~ p3(X21)
& r1(X20,X21) )
& r1(X19,X20) )
=> ( p3(sK33(X19))
& ? [X21] :
( ~ p3(X21)
& r1(sK33(X19),X21) )
& r1(X19,sK33(X19)) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
! [X19] :
( ? [X21] :
( ~ p3(X21)
& r1(sK33(X19),X21) )
=> ( ~ p3(sK34(X19))
& r1(sK33(X19),sK34(X19)) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
( ? [X22] :
( ~ p3(X22)
& r1(sK24,X22) )
=> ( ~ p3(sK35)
& r1(sK24,sK35) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
? [X0] :
( ! [X1] :
( ? [X2] :
( ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
& ~ p2(X2)
& r1(X1,X2) )
| p2(X1)
| ~ r1(X0,X1) )
& ( ? [X5] :
( ! [X6] :
( ( ! [X7] :
( ~ p2(X7)
| ! [X8] :
( p2(X8)
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
& ~ p2(X6) )
| sP3(X6)
| sP4(X6)
| ~ r1(X5,X6) )
& ( ( ! [X9] :
( ~ p2(X9)
| ! [X10] :
( p2(X10)
| ~ r1(X9,X10) )
| ~ r1(X5,X9) )
& ~ p2(X5) )
| sP1(X5) )
& r1(X0,X5) )
| sP5(X0) )
& ! [X11] :
( ? [X12] :
( p1(X12)
& ? [X13] :
( ~ p1(X13)
& r1(X12,X13) )
& r1(X11,X12) )
| p1(X11)
| ~ r1(X0,X11) )
& ? [X14] :
( ~ p1(X14)
& r1(X0,X14) )
& ! [X15] :
( ? [X16] :
( p2(X16)
& ? [X17] :
( ~ p2(X17)
& r1(X16,X17) )
& r1(X15,X16) )
| p2(X15)
| ~ r1(X0,X15) )
& ? [X18] :
( ~ p2(X18)
& r1(X0,X18) )
& ! [X19] :
( ? [X20] :
( p3(X20)
& ? [X21] :
( ~ p3(X21)
& r1(X20,X21) )
& r1(X19,X20) )
| p3(X19)
| ~ r1(X0,X19) )
& ? [X22] :
( ~ p3(X22)
& r1(X0,X22) ) ),
inference(rectify,[],[f13]) ).
fof(f13,plain,
? [X0] :
( ! [X1] :
( ? [X2] :
( ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
& ~ p2(X2)
& r1(X1,X2) )
| p2(X1)
| ~ r1(X0,X1) )
& ( ? [X5] :
( ! [X6] :
( ( ! [X7] :
( ~ p2(X7)
| ! [X8] :
( p2(X8)
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
& ~ p2(X6) )
| sP3(X6)
| sP4(X6)
| ~ r1(X5,X6) )
& ( ( ! [X26] :
( ~ p2(X26)
| ! [X27] :
( p2(X27)
| ~ r1(X26,X27) )
| ~ r1(X5,X26) )
& ~ p2(X5) )
| sP1(X5) )
& r1(X0,X5) )
| sP5(X0) )
& ! [X44] :
( ? [X45] :
( p1(X45)
& ? [X46] :
( ~ p1(X46)
& r1(X45,X46) )
& r1(X44,X45) )
| p1(X44)
| ~ r1(X0,X44) )
& ? [X47] :
( ~ p1(X47)
& r1(X0,X47) )
& ! [X48] :
( ? [X49] :
( p2(X49)
& ? [X50] :
( ~ p2(X50)
& r1(X49,X50) )
& r1(X48,X49) )
| p2(X48)
| ~ r1(X0,X48) )
& ? [X51] :
( ~ p2(X51)
& r1(X0,X51) )
& ! [X52] :
( ? [X53] :
( p3(X53)
& ? [X54] :
( ~ p3(X54)
& r1(X53,X54) )
& r1(X52,X53) )
| p3(X52)
| ~ r1(X0,X52) )
& ? [X55] :
( ~ p3(X55)
& r1(X0,X55) ) ),
inference(definition_folding,[],[f6,f12,f11,f10,f9,f8,f7]) ).
fof(f7,plain,
! [X0] :
( ! [X40] :
( ! [X41] :
( ? [X42] :
( p2(X42)
& ? [X43] :
( ~ p2(X43)
& r1(X42,X43) )
& r1(X41,X42) )
| p2(X41)
| ~ r1(X40,X41) )
| ~ r1(X0,X40) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f9,plain,
! [X16] :
( ! [X22] :
( ! [X23] :
( ? [X24] :
( p2(X24)
& ? [X25] :
( ~ p2(X25)
& r1(X24,X25) )
& r1(X23,X24) )
| p2(X23)
| ~ r1(X22,X23) )
| ~ r1(X16,X22) )
| ~ sP2(X16) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f6,plain,
? [X0] :
( ! [X1] :
( ? [X2] :
( ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
& ~ p2(X2)
& r1(X1,X2) )
| p2(X1)
| ~ r1(X0,X1) )
& ( ? [X5] :
( ! [X6] :
( ( ! [X7] :
( ~ p2(X7)
| ! [X8] :
( p2(X8)
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
& ~ p2(X6) )
| ( ! [X9] :
( ? [X10] :
( p2(X10)
& ? [X11] :
( ~ p2(X11)
& r1(X10,X11) )
& r1(X9,X10) )
| p2(X9)
| ~ r1(X6,X9) )
& ? [X12] :
( ? [X13] :
( ! [X14] :
( ~ p2(X14)
| ! [X15] :
( p2(X15)
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
& ~ p2(X13)
& r1(X12,X13) )
& r1(X6,X12) ) )
| ! [X16] :
( ( ( ? [X17] :
( p2(X17)
& ? [X18] :
( ~ p2(X18)
& r1(X17,X18) )
& r1(X16,X17) )
| p2(X16) )
& ( ? [X19] :
( ! [X20] :
( ~ p2(X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
& ~ p2(X19)
& r1(X16,X19) )
| ! [X22] :
( ! [X23] :
( ? [X24] :
( p2(X24)
& ? [X25] :
( ~ p2(X25)
& r1(X24,X25) )
& r1(X23,X24) )
| p2(X23)
| ~ r1(X22,X23) )
| ~ r1(X16,X22) ) ) )
| ~ r1(X6,X16) )
| ~ r1(X5,X6) )
& ( ( ! [X26] :
( ~ p2(X26)
| ! [X27] :
( p2(X27)
| ~ r1(X26,X27) )
| ~ r1(X5,X26) )
& ~ p2(X5) )
| ( ! [X28] :
( ? [X29] :
( p2(X29)
& ? [X30] :
( ~ p2(X30)
& r1(X29,X30) )
& r1(X28,X29) )
| p2(X28)
| ~ r1(X5,X28) )
& ? [X31] :
( ? [X32] :
( ! [X33] :
( ~ p2(X33)
| ! [X34] :
( p2(X34)
| ~ r1(X33,X34) )
| ~ r1(X32,X33) )
& ~ p2(X32)
& r1(X31,X32) )
& r1(X5,X31) ) ) )
& r1(X0,X5) )
| ( ( ? [X35] :
( p2(X35)
& ? [X36] :
( ~ p2(X36)
& r1(X35,X36) )
& r1(X0,X35) )
| p2(X0) )
& ( ? [X37] :
( ! [X38] :
( ~ p2(X38)
| ! [X39] :
( p2(X39)
| ~ r1(X38,X39) )
| ~ r1(X37,X38) )
& ~ p2(X37)
& r1(X0,X37) )
| ! [X40] :
( ! [X41] :
( ? [X42] :
( p2(X42)
& ? [X43] :
( ~ p2(X43)
& r1(X42,X43) )
& r1(X41,X42) )
| p2(X41)
| ~ r1(X40,X41) )
| ~ r1(X0,X40) ) ) ) )
& ! [X44] :
( ? [X45] :
( p1(X45)
& ? [X46] :
( ~ p1(X46)
& r1(X45,X46) )
& r1(X44,X45) )
| p1(X44)
| ~ r1(X0,X44) )
& ? [X47] :
( ~ p1(X47)
& r1(X0,X47) )
& ! [X48] :
( ? [X49] :
( p2(X49)
& ? [X50] :
( ~ p2(X50)
& r1(X49,X50) )
& r1(X48,X49) )
| p2(X48)
| ~ r1(X0,X48) )
& ? [X51] :
( ~ p2(X51)
& r1(X0,X51) )
& ! [X52] :
( ? [X53] :
( p3(X53)
& ? [X54] :
( ~ p3(X54)
& r1(X53,X54) )
& r1(X52,X53) )
| p3(X52)
| ~ r1(X0,X52) )
& ? [X55] :
( ~ p3(X55)
& r1(X0,X55) ) ),
inference(flattening,[],[f5]) ).
fof(f5,plain,
? [X0] :
( ! [X1] :
( ? [X2] :
( ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
& ~ p2(X2)
& r1(X1,X2) )
| p2(X1)
| ~ r1(X0,X1) )
& ( ? [X5] :
( ! [X6] :
( ( ! [X7] :
( ~ p2(X7)
| ! [X8] :
( p2(X8)
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
& ~ p2(X6) )
| ( ! [X9] :
( ? [X10] :
( p2(X10)
& ? [X11] :
( ~ p2(X11)
& r1(X10,X11) )
& r1(X9,X10) )
| p2(X9)
| ~ r1(X6,X9) )
& ? [X12] :
( ? [X13] :
( ! [X14] :
( ~ p2(X14)
| ! [X15] :
( p2(X15)
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
& ~ p2(X13)
& r1(X12,X13) )
& r1(X6,X12) ) )
| ! [X16] :
( ( ( ? [X17] :
( p2(X17)
& ? [X18] :
( ~ p2(X18)
& r1(X17,X18) )
& r1(X16,X17) )
| p2(X16) )
& ( ? [X19] :
( ! [X20] :
( ~ p2(X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
& ~ p2(X19)
& r1(X16,X19) )
| ! [X22] :
( ! [X23] :
( ? [X24] :
( p2(X24)
& ? [X25] :
( ~ p2(X25)
& r1(X24,X25) )
& r1(X23,X24) )
| p2(X23)
| ~ r1(X22,X23) )
| ~ r1(X16,X22) ) ) )
| ~ r1(X6,X16) )
| ~ r1(X5,X6) )
& ( ( ! [X26] :
( ~ p2(X26)
| ! [X27] :
( p2(X27)
| ~ r1(X26,X27) )
| ~ r1(X5,X26) )
& ~ p2(X5) )
| ( ! [X28] :
( ? [X29] :
( p2(X29)
& ? [X30] :
( ~ p2(X30)
& r1(X29,X30) )
& r1(X28,X29) )
| p2(X28)
| ~ r1(X5,X28) )
& ? [X31] :
( ? [X32] :
( ! [X33] :
( ~ p2(X33)
| ! [X34] :
( p2(X34)
| ~ r1(X33,X34) )
| ~ r1(X32,X33) )
& ~ p2(X32)
& r1(X31,X32) )
& r1(X5,X31) ) ) )
& r1(X0,X5) )
| ( ( ? [X35] :
( p2(X35)
& ? [X36] :
( ~ p2(X36)
& r1(X35,X36) )
& r1(X0,X35) )
| p2(X0) )
& ( ? [X37] :
( ! [X38] :
( ~ p2(X38)
| ! [X39] :
( p2(X39)
| ~ r1(X38,X39) )
| ~ r1(X37,X38) )
& ~ p2(X37)
& r1(X0,X37) )
| ! [X40] :
( ! [X41] :
( ? [X42] :
( p2(X42)
& ? [X43] :
( ~ p2(X43)
& r1(X42,X43) )
& r1(X41,X42) )
| p2(X41)
| ~ r1(X40,X41) )
| ~ r1(X0,X40) ) ) ) )
& ! [X44] :
( ? [X45] :
( p1(X45)
& ? [X46] :
( ~ p1(X46)
& r1(X45,X46) )
& r1(X44,X45) )
| p1(X44)
| ~ r1(X0,X44) )
& ? [X47] :
( ~ p1(X47)
& r1(X0,X47) )
& ! [X48] :
( ? [X49] :
( p2(X49)
& ? [X50] :
( ~ p2(X50)
& r1(X49,X50) )
& r1(X48,X49) )
| p2(X48)
| ~ r1(X0,X48) )
& ? [X51] :
( ~ p2(X51)
& r1(X0,X51) )
& ! [X52] :
( ? [X53] :
( p3(X53)
& ? [X54] :
( ~ p3(X54)
& r1(X53,X54) )
& r1(X52,X53) )
| p3(X52)
| ~ r1(X0,X52) )
& ? [X55] :
( ~ p3(X55)
& r1(X0,X55) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,plain,
? [X0] :
~ ( ~ ( ! [X1] :
( ~ ! [X2] :
( ~ ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| p2(X2)
| ~ r1(X1,X2) )
| p2(X1)
| ~ r1(X0,X1) )
& ( ~ ! [X5] :
( ~ ! [X6] :
( ~ ( ( ~ ! [X7] :
( ~ p2(X7)
| ! [X8] :
( p2(X8)
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
| p2(X6) )
& ( ~ ! [X9] :
( ~ ! [X10] :
( ~ p2(X10)
| ! [X11] :
( p2(X11)
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| p2(X9)
| ~ r1(X6,X9) )
| ! [X12] :
( ! [X13] :
( ~ ! [X14] :
( ~ p2(X14)
| ! [X15] :
( p2(X15)
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
| p2(X13)
| ~ r1(X12,X13) )
| ~ r1(X6,X12) ) ) )
| ! [X16] :
( ( ( ~ ! [X17] :
( ~ p2(X17)
| ! [X18] :
( p2(X18)
| ~ r1(X17,X18) )
| ~ r1(X16,X17) )
| p2(X16) )
& ( ~ ! [X19] :
( ~ ! [X20] :
( ~ p2(X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| p2(X19)
| ~ r1(X16,X19) )
| ! [X22] :
( ! [X23] :
( ~ ! [X24] :
( ~ p2(X24)
| ! [X25] :
( p2(X25)
| ~ r1(X24,X25) )
| ~ r1(X23,X24) )
| p2(X23)
| ~ r1(X22,X23) )
| ~ r1(X16,X22) ) ) )
| ~ r1(X6,X16) )
| ~ r1(X5,X6) )
| ( ( ~ ! [X26] :
( ~ p2(X26)
| ! [X27] :
( p2(X27)
| ~ r1(X26,X27) )
| ~ r1(X5,X26) )
| p2(X5) )
& ( ~ ! [X28] :
( ~ ! [X29] :
( ~ p2(X29)
| ! [X30] :
( p2(X30)
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| p2(X28)
| ~ r1(X5,X28) )
| ! [X31] :
( ! [X32] :
( ~ ! [X33] :
( ~ p2(X33)
| ! [X34] :
( p2(X34)
| ~ r1(X33,X34) )
| ~ r1(X32,X33) )
| p2(X32)
| ~ r1(X31,X32) )
| ~ r1(X5,X31) ) ) )
| ~ r1(X0,X5) )
| ( ( ~ ! [X35] :
( ~ p2(X35)
| ! [X36] :
( p2(X36)
| ~ r1(X35,X36) )
| ~ r1(X0,X35) )
| p2(X0) )
& ( ~ ! [X37] :
( ~ ! [X38] :
( ~ p2(X38)
| ! [X39] :
( p2(X39)
| ~ r1(X38,X39) )
| ~ r1(X37,X38) )
| p2(X37)
| ~ r1(X0,X37) )
| ! [X40] :
( ! [X41] :
( ~ ! [X42] :
( ~ p2(X42)
| ! [X43] :
( p2(X43)
| ~ r1(X42,X43) )
| ~ r1(X41,X42) )
| p2(X41)
| ~ r1(X40,X41) )
| ~ r1(X0,X40) ) ) ) ) )
| ~ ! [X44] :
( ~ ! [X45] :
( ~ p1(X45)
| ! [X46] :
( p1(X46)
| ~ r1(X45,X46) )
| ~ r1(X44,X45) )
| p1(X44)
| ~ r1(X0,X44) )
| ! [X47] :
( p1(X47)
| ~ r1(X0,X47) )
| ~ ! [X48] :
( ~ ! [X49] :
( ~ p2(X49)
| ! [X50] :
( p2(X50)
| ~ r1(X49,X50) )
| ~ r1(X48,X49) )
| p2(X48)
| ~ r1(X0,X48) )
| ! [X51] :
( p2(X51)
| ~ r1(X0,X51) )
| ~ ! [X52] :
( ~ ! [X53] :
( ~ p3(X53)
| ! [X54] :
( p3(X54)
| ~ r1(X53,X54) )
| ~ r1(X52,X53) )
| p3(X52)
| ~ r1(X0,X52) )
| ! [X55] :
( p3(X55)
| ~ r1(X0,X55) ) ),
inference(flattening,[],[f3]) ).
fof(f3,plain,
~ ~ ? [X0] :
~ ( ~ ( ! [X1] :
( ~ ! [X2] :
( ~ ! [X3] :
( ~ p2(X3)
| ! [X4] :
( p2(X4)
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| p2(X2)
| ~ r1(X1,X2) )
| p2(X1)
| ~ r1(X0,X1) )
& ( ~ ! [X5] :
( ~ ! [X6] :
( ~ ( ( ~ ! [X7] :
( ~ p2(X7)
| ! [X8] :
( p2(X8)
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
| p2(X6) )
& ( ~ ! [X9] :
( ~ ! [X10] :
( ~ p2(X10)
| ! [X11] :
( p2(X11)
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| p2(X9)
| ~ r1(X6,X9) )
| ! [X12] :
( ! [X13] :
( ~ ! [X14] :
( ~ p2(X14)
| ! [X15] :
( p2(X15)
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
| p2(X13)
| ~ r1(X12,X13) )
| ~ r1(X6,X12) ) ) )
| ! [X16] :
( ( ( ~ ! [X17] :
( ~ p2(X17)
| ! [X18] :
( p2(X18)
| ~ r1(X17,X18) )
| ~ r1(X16,X17) )
| p2(X16) )
& ( ~ ! [X19] :
( ~ ! [X20] :
( ~ p2(X20)
| ! [X21] :
( p2(X21)
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| p2(X19)
| ~ r1(X16,X19) )
| ! [X22] :
( ! [X23] :
( ~ ! [X24] :
( ~ p2(X24)
| ! [X25] :
( p2(X25)
| ~ r1(X24,X25) )
| ~ r1(X23,X24) )
| p2(X23)
| ~ r1(X22,X23) )
| ~ r1(X16,X22) ) ) )
| ~ r1(X6,X16) )
| ~ r1(X5,X6) )
| ( ( ~ ! [X26] :
( ~ p2(X26)
| ! [X27] :
( p2(X27)
| ~ r1(X26,X27) )
| ~ r1(X5,X26) )
| p2(X5) )
& ( ~ ! [X28] :
( ~ ! [X29] :
( ~ p2(X29)
| ! [X30] :
( p2(X30)
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| p2(X28)
| ~ r1(X5,X28) )
| ! [X31] :
( ! [X32] :
( ~ ! [X33] :
( ~ p2(X33)
| ! [X34] :
( p2(X34)
| ~ r1(X33,X34) )
| ~ r1(X32,X33) )
| p2(X32)
| ~ r1(X31,X32) )
| ~ r1(X5,X31) ) ) )
| ~ r1(X0,X5) )
| ( ( ~ ! [X35] :
( ~ p2(X35)
| ! [X36] :
( p2(X36)
| ~ r1(X35,X36) )
| ~ r1(X0,X35) )
| p2(X0) )
& ( ~ ! [X37] :
( ~ ! [X38] :
( ~ p2(X38)
| ! [X39] :
( p2(X39)
| ~ r1(X38,X39) )
| ~ r1(X37,X38) )
| p2(X37)
| ~ r1(X0,X37) )
| ! [X40] :
( ! [X41] :
( ~ ! [X42] :
( ~ p2(X42)
| ! [X43] :
( p2(X43)
| ~ r1(X42,X43) )
| ~ r1(X41,X42) )
| p2(X41)
| ~ r1(X40,X41) )
| ~ r1(X0,X40) ) ) ) ) )
| ~ ! [X44] :
( ~ ! [X45] :
( ~ p1(X45)
| ! [X46] :
( p1(X46)
| ~ r1(X45,X46) )
| ~ r1(X44,X45) )
| p1(X44)
| ~ r1(X0,X44) )
| ! [X47] :
( p1(X47)
| ~ r1(X0,X47) )
| ~ ! [X48] :
( ~ ! [X49] :
( ~ p2(X49)
| ! [X50] :
( p2(X50)
| ~ r1(X49,X50) )
| ~ r1(X48,X49) )
| p2(X48)
| ~ r1(X0,X48) )
| ! [X51] :
( p2(X51)
| ~ r1(X0,X51) )
| ~ ! [X52] :
( ~ ! [X53] :
( ~ p3(X53)
| ! [X54] :
( p3(X54)
| ~ r1(X53,X54) )
| ~ r1(X52,X53) )
| p3(X52)
| ~ r1(X0,X52) )
| ! [X55] :
( p3(X55)
| ~ r1(X0,X55) ) ),
inference(rectify,[],[f2]) ).
fof(f2,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ( ! [X1] :
( ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| p2(X0)
| ~ r1(X1,X0) )
| p2(X1)
| ~ r1(X0,X1) )
& ( ~ ! [X1] :
( ~ ! [X0] :
( ~ ( ( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| p2(X0) )
& ( ~ ! [X1] :
( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p2(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) ) )
| ! [X1] :
( ( ( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p2(X1) )
& ( ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| p2(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ! [X1] :
( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) ) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ( ( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p2(X1) )
& ( ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| p2(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ! [X1] :
( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) ) )
| ~ r1(X0,X1) )
| ( ( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| p2(X0) )
& ( ~ ! [X1] :
( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p2(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) ) ) ) )
| ~ ! [X1] :
( ~ ! [X0] :
( ~ p1(X0)
| ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p1(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p2(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ! [X0] :
( ~ p3(X0)
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p3(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
~ ? [X0] :
~ ( ~ ( ! [X1] :
( ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| p2(X0)
| ~ r1(X1,X0) )
| p2(X1)
| ~ r1(X0,X1) )
& ( ~ ! [X1] :
( ~ ! [X0] :
( ~ ( ( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| p2(X0) )
& ( ~ ! [X1] :
( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p2(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) ) )
| ! [X1] :
( ( ( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p2(X1) )
& ( ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| p2(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ! [X1] :
( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) ) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ( ( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p2(X1) )
& ( ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| p2(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ! [X1] :
( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) ) )
| ~ r1(X0,X1) )
| ( ( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| p2(X0) )
& ( ~ ! [X1] :
( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p2(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) ) ) ) )
| ~ ! [X1] :
( ~ ! [X0] :
( ~ p1(X0)
| ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p1(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p2(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ! [X0] :
( ~ p3(X0)
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| p3(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.QX6SZBzdIb/Vampire---4.8_19934',main) ).
fof(f605,plain,
( p2(sK31(sK8(sK24)))
| ~ spl36_81 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f2731,plain,
( spl36_308
| ~ spl36_307
| ~ spl36_50
| ~ spl36_385 ),
inference(avatar_split_clause,[],[f2730,f2278,f337,f1926,f1929]) ).
fof(f1929,plain,
( spl36_308
<=> p2(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_308])]) ).
fof(f1926,plain,
( spl36_307
<=> r1(sK24,sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_307])]) ).
fof(f2278,plain,
( spl36_385
<=> ! [X0,X1] :
( ~ r1(X0,sK25(sK32))
| ~ sP0(X1)
| ~ r1(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_385])]) ).
fof(f2730,plain,
( ~ r1(sK24,sK32)
| p2(sK32)
| ~ spl36_50
| ~ spl36_385 ),
inference(duplicate_literal_removal,[],[f2729]) ).
fof(f2729,plain,
( ~ r1(sK24,sK32)
| p2(sK32)
| ~ r1(sK24,sK32)
| ~ spl36_50
| ~ spl36_385 ),
inference(resolution,[],[f2627,f125]) ).
fof(f125,plain,
! [X1] :
( r1(X1,sK25(X1))
| p2(X1)
| ~ r1(sK24,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f2627,plain,
( ! [X0] :
( ~ r1(X0,sK25(sK32))
| ~ r1(sK24,X0) )
| ~ spl36_50
| ~ spl36_385 ),
inference(resolution,[],[f2279,f338]) ).
fof(f338,plain,
( sP0(sK24)
| ~ spl36_50 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f2279,plain,
( ! [X0,X1] :
( ~ sP0(X1)
| ~ r1(X0,sK25(sK32))
| ~ r1(X1,X0) )
| ~ spl36_385 ),
inference(avatar_component_clause,[],[f2278]) ).
fof(f2332,plain,
~ spl36_308,
inference(avatar_contradiction_clause,[],[f2327]) ).
fof(f2327,plain,
( $false
| ~ spl36_308 ),
inference(resolution,[],[f1930,f109]) ).
fof(f109,plain,
~ p2(sK32),
inference(cnf_transformation,[],[f63]) ).
fof(f1930,plain,
( p2(sK32)
| ~ spl36_308 ),
inference(avatar_component_clause,[],[f1929]) ).
fof(f2311,plain,
( ~ spl36_307
| spl36_308
| ~ spl36_309 ),
inference(avatar_split_clause,[],[f2306,f1932,f1929,f1926]) ).
fof(f1932,plain,
( spl36_309
<=> p2(sK25(sK32)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_309])]) ).
fof(f2306,plain,
( p2(sK32)
| ~ r1(sK24,sK32)
| ~ spl36_309 ),
inference(resolution,[],[f1933,f126]) ).
fof(f126,plain,
! [X1] :
( ~ p2(sK25(X1))
| p2(X1)
| ~ r1(sK24,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f1933,plain,
( p2(sK25(sK32))
| ~ spl36_309 ),
inference(avatar_component_clause,[],[f1932]) ).
fof(f2280,plain,
( spl36_385
| spl36_309
| ~ spl36_333 ),
inference(avatar_split_clause,[],[f2272,f2053,f1932,f2278]) ).
fof(f2053,plain,
( spl36_333
<=> p2(sK23(sK25(sK32))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_333])]) ).
fof(f2272,plain,
( ! [X0,X1] :
( p2(sK25(sK32))
| ~ r1(X0,sK25(sK32))
| ~ r1(X1,X0)
| ~ sP0(X1) )
| ~ spl36_333 ),
inference(resolution,[],[f2054,f100]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ p2(sK23(X2))
| p2(X2)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( p2(sK22(X2))
& ~ p2(sK23(X2))
& r1(sK22(X2),sK23(X2))
& r1(X2,sK22(X2)) )
| p2(X2)
| ~ r1(X1,X2) )
| ~ r1(X0,X1) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f46,f48,f47]) ).
fof(f47,plain,
! [X2] :
( ? [X3] :
( p2(X3)
& ? [X4] :
( ~ p2(X4)
& r1(X3,X4) )
& r1(X2,X3) )
=> ( p2(sK22(X2))
& ? [X4] :
( ~ p2(X4)
& r1(sK22(X2),X4) )
& r1(X2,sK22(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
! [X2] :
( ? [X4] :
( ~ p2(X4)
& r1(sK22(X2),X4) )
=> ( ~ p2(sK23(X2))
& r1(sK22(X2),sK23(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ? [X3] :
( p2(X3)
& ? [X4] :
( ~ p2(X4)
& r1(X3,X4) )
& r1(X2,X3) )
| p2(X2)
| ~ r1(X1,X2) )
| ~ r1(X0,X1) )
| ~ sP0(X0) ),
inference(rectify,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ! [X40] :
( ! [X41] :
( ? [X42] :
( p2(X42)
& ? [X43] :
( ~ p2(X43)
& r1(X42,X43) )
& r1(X41,X42) )
| p2(X41)
| ~ r1(X40,X41) )
| ~ r1(X0,X40) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f7]) ).
fof(f2054,plain,
( p2(sK23(sK25(sK32)))
| ~ spl36_333 ),
inference(avatar_component_clause,[],[f2053]) ).
fof(f2271,plain,
( ~ spl36_307
| spl36_308
| spl36_334 ),
inference(avatar_split_clause,[],[f2270,f2057,f1929,f1926]) ).
fof(f2057,plain,
( spl36_334
<=> r1(sK32,sK25(sK32)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_334])]) ).
fof(f2270,plain,
( p2(sK32)
| ~ r1(sK24,sK32)
| spl36_334 ),
inference(resolution,[],[f2058,f125]) ).
fof(f2058,plain,
( ~ r1(sK32,sK25(sK32))
| spl36_334 ),
inference(avatar_component_clause,[],[f2057]) ).
fof(f2059,plain,
( ~ spl36_334
| spl36_309
| spl36_333
| ~ spl36_50
| ~ spl36_310 ),
inference(avatar_split_clause,[],[f2035,f1935,f337,f2053,f1932,f2057]) ).
fof(f1935,plain,
( spl36_310
<=> ! [X0] :
( p2(X0)
| ~ r1(sK22(sK25(sK32)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_310])]) ).
fof(f2035,plain,
( p2(sK23(sK25(sK32)))
| p2(sK25(sK32))
| ~ r1(sK32,sK25(sK32))
| ~ spl36_50
| ~ spl36_310 ),
inference(resolution,[],[f1936,f394]) ).
fof(f394,plain,
( ! [X2] :
( r1(sK22(X2),sK23(X2))
| p2(X2)
| ~ r1(sK32,X2) )
| ~ spl36_50 ),
inference(resolution,[],[f343,f108]) ).
fof(f108,plain,
r1(sK24,sK32),
inference(cnf_transformation,[],[f63]) ).
fof(f343,plain,
( ! [X0,X1] :
( ~ r1(sK24,X1)
| ~ r1(X1,X0)
| p2(X0)
| r1(sK22(X0),sK23(X0)) )
| ~ spl36_50 ),
inference(resolution,[],[f338,f99]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ sP0(X0)
| p2(X2)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| r1(sK22(X2),sK23(X2)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f1936,plain,
( ! [X0] :
( ~ r1(sK22(sK25(sK32)),X0)
| p2(X0) )
| ~ spl36_310 ),
inference(avatar_component_clause,[],[f1935]) ).
fof(f1956,plain,
spl36_307,
inference(avatar_contradiction_clause,[],[f1955]) ).
fof(f1955,plain,
( $false
| spl36_307 ),
inference(resolution,[],[f1927,f108]) ).
fof(f1927,plain,
( ~ r1(sK24,sK32)
| spl36_307 ),
inference(avatar_component_clause,[],[f1926]) ).
fof(f1937,plain,
( ~ spl36_307
| spl36_308
| spl36_309
| spl36_310
| ~ spl36_50 ),
inference(avatar_split_clause,[],[f1924,f337,f1935,f1932,f1929,f1926]) ).
fof(f1924,plain,
( ! [X0] :
( p2(X0)
| ~ r1(sK22(sK25(sK32)),X0)
| p2(sK25(sK32))
| p2(sK32)
| ~ r1(sK24,sK32) )
| ~ spl36_50 ),
inference(duplicate_literal_removal,[],[f1923]) ).
fof(f1923,plain,
( ! [X0] :
( p2(X0)
| ~ r1(sK22(sK25(sK32)),X0)
| p2(sK25(sK32))
| p2(sK32)
| ~ r1(sK24,sK32)
| p2(sK32)
| ~ r1(sK24,sK32) )
| ~ spl36_50 ),
inference(resolution,[],[f455,f125]) ).
fof(f455,plain,
( ! [X2,X3] :
( ~ r1(sK32,sK25(X2))
| p2(X3)
| ~ r1(sK22(sK25(X2)),X3)
| p2(sK25(X2))
| p2(X2)
| ~ r1(sK24,X2) )
| ~ spl36_50 ),
inference(duplicate_literal_removal,[],[f450]) ).
fof(f450,plain,
( ! [X2,X3] :
( ~ r1(sK32,sK25(X2))
| p2(X3)
| ~ r1(sK22(sK25(X2)),X3)
| p2(sK25(X2))
| p2(X2)
| ~ r1(sK24,X2)
| p2(sK25(X2))
| ~ r1(sK32,sK25(X2)) )
| ~ spl36_50 ),
inference(resolution,[],[f408,f383]) ).
fof(f383,plain,
( ! [X2] :
( r1(X2,sK22(X2))
| p2(X2)
| ~ r1(sK32,X2) )
| ~ spl36_50 ),
inference(resolution,[],[f344,f108]) ).
fof(f344,plain,
( ! [X2,X3] :
( ~ r1(sK24,X3)
| ~ r1(X3,X2)
| p2(X2)
| r1(X2,sK22(X2)) )
| ~ spl36_50 ),
inference(resolution,[],[f338,f98]) ).
fof(f98,plain,
! [X2,X0,X1] :
( ~ sP0(X0)
| p2(X2)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| r1(X2,sK22(X2)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f408,plain,
( ! [X3,X4,X5] :
( ~ r1(sK25(X5),sK22(X3))
| ~ r1(sK32,X3)
| p2(X4)
| ~ r1(sK22(X3),X4)
| p2(X3)
| p2(X5)
| ~ r1(sK24,X5) )
| ~ spl36_50 ),
inference(resolution,[],[f348,f127]) ).
fof(f127,plain,
! [X3,X1,X4] :
( ~ p2(X3)
| p2(X4)
| ~ r1(X3,X4)
| ~ r1(sK25(X1),X3)
| p2(X1)
| ~ r1(sK24,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f348,plain,
( ! [X2] :
( p2(sK22(X2))
| p2(X2)
| ~ r1(sK32,X2) )
| ~ spl36_50 ),
inference(resolution,[],[f345,f108]) ).
fof(f345,plain,
( ! [X4,X5] :
( ~ r1(sK24,X5)
| ~ r1(X5,X4)
| p2(X4)
| p2(sK22(X4)) )
| ~ spl36_50 ),
inference(resolution,[],[f338,f101]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ sP0(X0)
| p2(X2)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| p2(sK22(X2)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f1200,plain,
( spl36_203
| spl36_29
| ~ spl36_176 ),
inference(avatar_split_clause,[],[f1190,f1085,f253,f1198]) ).
fof(f1085,plain,
( spl36_176
<=> p2(sK19(sK20(sK26))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_176])]) ).
fof(f1190,plain,
( ! [X0] :
( p2(sK20(sK26))
| ~ r1(X0,sK20(sK26))
| ~ sP1(X0) )
| ~ spl36_176 ),
inference(resolution,[],[f1086,f96]) ).
fof(f96,plain,
! [X0,X1] :
( ~ p2(sK19(X1))
| p2(X1)
| ~ r1(X0,X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f1086,plain,
( p2(sK19(sK20(sK26)))
| ~ spl36_176 ),
inference(avatar_component_clause,[],[f1085]) ).
fof(f1189,plain,
( ~ spl36_4
| spl36_175 ),
inference(avatar_contradiction_clause,[],[f1188]) ).
fof(f1188,plain,
( $false
| ~ spl36_4
| spl36_175 ),
inference(resolution,[],[f1186,f141]) ).
fof(f1186,plain,
( ~ sP1(sK26)
| spl36_175 ),
inference(resolution,[],[f1083,f90]) ).
fof(f1083,plain,
( ~ r1(sK26,sK20(sK26))
| spl36_175 ),
inference(avatar_component_clause,[],[f1082]) ).
fof(f1087,plain,
( spl36_29
| ~ spl36_175
| spl36_176
| ~ spl36_4
| ~ spl36_147 ),
inference(avatar_split_clause,[],[f1072,f943,f140,f1085,f1082,f253]) ).
fof(f1072,plain,
( p2(sK19(sK20(sK26)))
| ~ r1(sK26,sK20(sK26))
| p2(sK20(sK26))
| ~ spl36_4
| ~ spl36_147 ),
inference(resolution,[],[f944,f310]) ).
fof(f310,plain,
( ! [X0] :
( r1(sK18(X0),sK19(X0))
| ~ r1(sK26,X0)
| p2(X0) )
| ~ spl36_4 ),
inference(resolution,[],[f95,f141]) ).
fof(f95,plain,
! [X0,X1] :
( ~ sP1(X0)
| p2(X1)
| ~ r1(X0,X1)
| r1(sK18(X1),sK19(X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f944,plain,
( ! [X3] :
( ~ r1(sK18(sK20(sK26)),X3)
| p2(X3) )
| ~ spl36_147 ),
inference(avatar_component_clause,[],[f943]) ).
fof(f767,plain,
( ~ spl36_7
| spl36_6
| ~ spl36_105 ),
inference(avatar_split_clause,[],[f761,f717,f147,f151]) ).
fof(f151,plain,
( spl36_7
<=> r1(sK24,sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_7])]) ).
fof(f147,plain,
( spl36_6
<=> p2(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_6])]) ).
fof(f717,plain,
( spl36_105
<=> p2(sK31(sK26)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_105])]) ).
fof(f761,plain,
( p2(sK26)
| ~ r1(sK24,sK26)
| ~ spl36_105 ),
inference(resolution,[],[f718,f112]) ).
fof(f718,plain,
( p2(sK31(sK26))
| ~ spl36_105 ),
inference(avatar_component_clause,[],[f717]) ).
fof(f719,plain,
( ~ spl36_7
| spl36_6
| spl36_105
| ~ spl36_104 ),
inference(avatar_split_clause,[],[f708,f705,f717,f147,f151]) ).
fof(f705,plain,
( spl36_104
<=> ! [X0] :
( ~ r1(sK30(sK26),X0)
| p2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_104])]) ).
fof(f708,plain,
( p2(sK31(sK26))
| p2(sK26)
| ~ r1(sK24,sK26)
| ~ spl36_104 ),
inference(resolution,[],[f706,f111]) ).
fof(f111,plain,
! [X15] :
( r1(sK30(X15),sK31(X15))
| p2(X15)
| ~ r1(sK24,X15) ),
inference(cnf_transformation,[],[f63]) ).
fof(f706,plain,
( ! [X0] :
( ~ r1(sK30(sK26),X0)
| p2(X0) )
| ~ spl36_104 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f707,plain,
( ~ spl36_7
| spl36_6
| spl36_104
| ~ spl36_5 ),
inference(avatar_split_clause,[],[f703,f143,f705,f147,f151]) ).
fof(f143,plain,
( spl36_5
<=> ! [X9,X10] :
( ~ p2(X9)
| ~ r1(sK26,X9)
| ~ r1(X9,X10)
| p2(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_5])]) ).
fof(f703,plain,
( ! [X0] :
( ~ r1(sK30(sK26),X0)
| p2(X0)
| p2(sK26)
| ~ r1(sK24,sK26) )
| ~ spl36_5 ),
inference(duplicate_literal_removal,[],[f702]) ).
fof(f702,plain,
( ! [X0] :
( ~ r1(sK30(sK26),X0)
| p2(X0)
| p2(sK26)
| ~ r1(sK24,sK26)
| p2(sK26)
| ~ r1(sK24,sK26) )
| ~ spl36_5 ),
inference(resolution,[],[f694,f110]) ).
fof(f110,plain,
! [X15] :
( r1(X15,sK30(X15))
| p2(X15)
| ~ r1(sK24,X15) ),
inference(cnf_transformation,[],[f63]) ).
fof(f694,plain,
( ! [X2,X3] :
( ~ r1(sK26,sK30(X2))
| ~ r1(sK30(X2),X3)
| p2(X3)
| p2(X2)
| ~ r1(sK24,X2) )
| ~ spl36_5 ),
inference(resolution,[],[f144,f113]) ).
fof(f113,plain,
! [X15] :
( p2(sK30(X15))
| p2(X15)
| ~ r1(sK24,X15) ),
inference(cnf_transformation,[],[f63]) ).
fof(f144,plain,
( ! [X10,X9] :
( ~ p2(X9)
| ~ r1(sK26,X9)
| ~ r1(X9,X10)
| p2(X10) )
| ~ spl36_5 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f606,plain,
( ~ spl36_78
| spl36_79
| spl36_81
| ~ spl36_80 ),
inference(avatar_split_clause,[],[f595,f589,f604,f586,f583]) ).
fof(f589,plain,
( spl36_80
<=> ! [X0] :
( p2(X0)
| ~ r1(sK30(sK8(sK24)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_80])]) ).
fof(f595,plain,
( p2(sK31(sK8(sK24)))
| p2(sK8(sK24))
| ~ r1(sK24,sK8(sK24))
| ~ spl36_80 ),
inference(resolution,[],[f590,f111]) ).
fof(f590,plain,
( ! [X0] :
( ~ r1(sK30(sK8(sK24)),X0)
| p2(X0) )
| ~ spl36_80 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f594,plain,
( ~ spl36_1
| spl36_50
| spl36_78 ),
inference(avatar_split_clause,[],[f592,f583,f337,f129]) ).
fof(f592,plain,
( sP0(sK24)
| ~ sP5(sK24)
| spl36_78 ),
inference(resolution,[],[f584,f64]) ).
fof(f64,plain,
! [X0] :
( r1(X0,sK8(X0))
| sP0(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f584,plain,
( ~ r1(sK24,sK8(sK24))
| spl36_78 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f591,plain,
( ~ spl36_78
| spl36_79
| spl36_80
| ~ spl36_51 ),
inference(avatar_split_clause,[],[f581,f340,f589,f586,f583]) ).
fof(f340,plain,
( spl36_51
<=> ! [X0,X1] :
( p2(X0)
| ~ p2(X1)
| ~ r1(sK8(sK24),X1)
| ~ r1(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_51])]) ).
fof(f581,plain,
( ! [X0] :
( p2(X0)
| ~ r1(sK30(sK8(sK24)),X0)
| p2(sK8(sK24))
| ~ r1(sK24,sK8(sK24)) )
| ~ spl36_51 ),
inference(duplicate_literal_removal,[],[f580]) ).
fof(f580,plain,
( ! [X0] :
( p2(X0)
| ~ r1(sK30(sK8(sK24)),X0)
| p2(sK8(sK24))
| ~ r1(sK24,sK8(sK24))
| p2(sK8(sK24))
| ~ r1(sK24,sK8(sK24)) )
| ~ spl36_51 ),
inference(resolution,[],[f575,f110]) ).
fof(f575,plain,
( ! [X2,X1] :
( ~ r1(sK8(sK24),sK30(X2))
| p2(X1)
| ~ r1(sK30(X2),X1)
| p2(X2)
| ~ r1(sK24,X2) )
| ~ spl36_51 ),
inference(resolution,[],[f341,f113]) ).
fof(f341,plain,
( ! [X0,X1] :
( ~ p2(X1)
| p2(X0)
| ~ r1(sK8(sK24),X1)
| ~ r1(X1,X0) )
| ~ spl36_51 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f342,plain,
( spl36_50
| spl36_51
| ~ spl36_1 ),
inference(avatar_split_clause,[],[f335,f129,f340,f337]) ).
fof(f335,plain,
( ! [X0,X1] :
( p2(X0)
| ~ r1(X1,X0)
| ~ r1(sK8(sK24),X1)
| sP0(sK24)
| ~ p2(X1) )
| ~ spl36_1 ),
inference(resolution,[],[f66,f130]) ).
fof(f130,plain,
( sP5(sK24)
| ~ spl36_1 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f66,plain,
! [X0,X4,X5] :
( ~ sP5(X0)
| p2(X5)
| ~ r1(X4,X5)
| ~ r1(sK8(X0),X4)
| sP0(X0)
| ~ p2(X4) ),
inference(cnf_transformation,[],[f19]) ).
fof(f153,plain,
( spl36_1
| spl36_7 ),
inference(avatar_split_clause,[],[f120,f151,f129]) ).
fof(f120,plain,
( r1(sK24,sK26)
| sP5(sK24) ),
inference(cnf_transformation,[],[f63]) ).
fof(f149,plain,
( spl36_1
| spl36_4
| ~ spl36_6 ),
inference(avatar_split_clause,[],[f121,f147,f140,f129]) ).
fof(f121,plain,
( ~ p2(sK26)
| sP1(sK26)
| sP5(sK24) ),
inference(cnf_transformation,[],[f63]) ).
fof(f145,plain,
( spl36_1
| spl36_4
| spl36_5 ),
inference(avatar_split_clause,[],[f122,f143,f140,f129]) ).
fof(f122,plain,
! [X10,X9] :
( ~ p2(X9)
| p2(X10)
| ~ r1(X9,X10)
| ~ r1(sK26,X9)
| sP1(sK26)
| sP5(sK24) ),
inference(cnf_transformation,[],[f63]) ).
fof(f138,plain,
( spl36_1
| spl36_3 ),
inference(avatar_split_clause,[],[f123,f136,f129]) ).
fof(f123,plain,
! [X6] :
( ~ p2(X6)
| sP3(X6)
| sP4(X6)
| ~ r1(sK26,X6)
| sP5(sK24) ),
inference(cnf_transformation,[],[f63]) ).
fof(f134,plain,
( spl36_1
| spl36_2 ),
inference(avatar_split_clause,[],[f124,f132,f129]) ).
fof(f124,plain,
! [X8,X6,X7] :
( ~ p2(X7)
| p2(X8)
| ~ r1(X7,X8)
| ~ r1(X6,X7)
| sP3(X6)
| sP4(X6)
| ~ r1(sK26,X6)
| sP5(sK24) ),
inference(cnf_transformation,[],[f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL642+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 17:55:53 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a FOF_THM_RFO_NEQ problem
% 0.14/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.QX6SZBzdIb/Vampire---4.8_19934
% 0.14/0.36 % (20056)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (20060)dis-1_128_add=large:amm=sco:anc=all_dependent:bs=on:bsr=on:bce=on:cond=fast:fsr=off:gsp=on:gs=on:gsem=off:lcm=predicate:lma=on:nm=32:nwc=4.0:nicw=on:sac=on:sp=weighted_frequency_692 on Vampire---4 for (692ds/0Mi)
% 0.21/0.42 % (20059)lrs+11_4:3_aac=none:add=off:amm=off:anc=none:bd=preordered:bs=on:bce=on:flr=on:fsd=off:fsr=off:fde=none:nwc=2.5:sims=off:sp=reverse_arity:tgt=full:stl=188_1106 on Vampire---4 for (1106ds/0Mi)
% 0.21/0.42 % (20061)ott-1010_5_add=off:amm=off:anc=none:bce=on:cond=fast:flr=on:lma=on:nm=2:nwc=1.1:sp=occurrence:tgt=ground_470 on Vampire---4 for (470ds/0Mi)
% 0.21/0.42 % (20062)ott+10_8_br=off:cond=on:fsr=off:gsp=on:nm=16:nwc=3.0:sims=off:sp=reverse_frequency:urr=on_415 on Vampire---4 for (415ds/0Mi)
% 0.21/0.42 % (20058)dis-1002_1_av=off:bsr=on:cond=on:flr=on:fsr=off:gsp=on:nwc=2.0:sims=off_1218 on Vampire---4 for (1218ds/0Mi)
% 0.21/0.42 % (20057)lrs-1_7_acc=on:amm=off:anc=all:bs=on:bsr=on:cond=fast:flr=on:fsr=off:gsp=on:lcm=reverse:lma=on:msp=off:nm=0:nwc=1.2:sp=frequency:stl=188_1354 on Vampire---4 for (1354ds/0Mi)
% 0.21/0.42 % (20063)dis+3_1024_av=off:fsr=off:gsp=on:lcm=predicate:nm=4:sos=all:sp=weighted_frequency_338 on Vampire---4 for (338ds/0Mi)
% 0.21/0.43 % (20062)Refutation not found, incomplete strategy% (20062)------------------------------
% 0.21/0.43 % (20062)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.43 % (20062)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.43 % (20062)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.43
% 0.21/0.43 % (20062)Memory used [KB]: 6140
% 0.21/0.43 % (20062)Time elapsed: 0.014 s
% 0.21/0.43 % (20062)------------------------------
% 0.21/0.43 % (20062)------------------------------
% 0.21/0.47 % (20059)First to succeed.
% 0.21/0.48 % (20059)Refutation found. Thanks to Tanya!
% 0.21/0.48 % SZS status Theorem for Vampire---4
% 0.21/0.48 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.48 % (20059)------------------------------
% 0.21/0.48 % (20059)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.48 % (20059)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.48 % (20059)Termination reason: Refutation
% 0.21/0.48
% 0.21/0.48 % (20059)Memory used [KB]: 8059
% 0.21/0.48 % (20059)Time elapsed: 0.061 s
% 0.21/0.48 % (20059)------------------------------
% 0.21/0.48 % (20059)------------------------------
% 0.21/0.48 % (20056)Success in time 0.12 s
% 0.21/0.48 % Vampire---4.8 exiting
%------------------------------------------------------------------------------