TSTP Solution File: RNG105+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG105+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 08:57:16 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 159
% Syntax : Number of formulae : 473 ( 111 unt; 0 def)
% Number of atoms : 1748 ( 233 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 2015 ( 740 ~; 748 |; 327 &)
% ( 142 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 120 ( 118 usr; 100 prp; 0-3 aty)
% Number of functors : 35 ( 35 usr; 10 con; 0-4 aty)
% Number of variables : 839 ( 735 !; 104 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1033,plain,
$false,
inference(avatar_sat_refutation,[],[f309,f314,f319,f324,f329,f334,f339,f344,f353,f358,f363,f368,f372,f376,f391,f396,f401,f406,f411,f416,f424,f428,f433,f438,f442,f447,f451,f455,f459,f463,f467,f471,f475,f479,f483,f487,f491,f534,f556,f560,f564,f568,f572,f576,f580,f584,f588,f592,f596,f619,f653,f658,f663,f672,f676,f680,f684,f713,f718,f722,f726,f730,f734,f738,f742,f768,f772,f776,f780,f784,f785,f796,f800,f804,f808,f812,f816,f913,f917,f922,f930,f934,f938,f942,f946,f950,f954,f984,f988,f992,f996,f1001,f1011,f1015,f1019,f1023,f1027,f1031,f1032]) ).
fof(f1032,plain,
( ~ spl31_3
| ~ spl31_6
| ~ spl31_50
| spl31_81 ),
inference(avatar_split_clause,[],[f956,f919,f590,f331,f316]) ).
fof(f316,plain,
( spl31_3
<=> aElement0(xu) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_3])]) ).
fof(f331,plain,
( spl31_6
<=> aElement0(xz) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_6])]) ).
fof(f590,plain,
( spl31_50
<=> ! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_50])]) ).
fof(f919,plain,
( spl31_81
<=> aElement0(sdtasdt0(xu,xz)) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_81])]) ).
fof(f956,plain,
( ~ aElement0(xz)
| ~ aElement0(xu)
| ~ spl31_50
| spl31_81 ),
inference(resolution,[],[f921,f591]) ).
fof(f591,plain,
( ! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) )
| ~ spl31_50 ),
inference(avatar_component_clause,[],[f590]) ).
fof(f921,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| spl31_81 ),
inference(avatar_component_clause,[],[f919]) ).
fof(f1031,plain,
spl31_99,
inference(avatar_split_clause,[],[f301,f1029]) ).
fof(f1029,plain,
( spl31_99
<=> ! [X10,X0,X9,X2,X1] :
( aElementOf0(sdtpldt0(X9,X10),X2)
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_99])]) ).
fof(f301,plain,
! [X2,X10,X0,X1,X9] :
( aElementOf0(sdtpldt0(X9,X10),X2)
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1)
| ~ sP5(X0,X1,X2) ),
inference(equality_resolution,[],[f255]) ).
fof(f255,plain,
! [X2,X10,X0,X1,X8,X9] :
( aElementOf0(X8,X2)
| sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f159]) ).
fof(f159,plain,
! [X0,X1,X2] :
( ( sP5(X0,X1,X2)
| ( ( ! [X4,X5] :
( sdtpldt0(X4,X5) != sK20(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(sK20(X0,X1,X2),X2) )
& ( ( sK20(X0,X1,X2) = sdtpldt0(sK21(X0,X1,X2),sK22(X0,X1,X2))
& aElementOf0(sK22(X0,X1,X2),X0)
& aElementOf0(sK21(X0,X1,X2),X1) )
| aElementOf0(sK20(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( aElementOf0(X8,X2)
| ! [X9,X10] :
( sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1) ) )
& ( ( sdtpldt0(sK23(X0,X1,X8),sK24(X0,X1,X8)) = X8
& aElementOf0(sK24(X0,X1,X8),X0)
& aElementOf0(sK23(X0,X1,X8),X1) )
| ~ aElementOf0(X8,X2) ) )
| ~ sP5(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24])],[f155,f158,f157,f156]) ).
fof(f156,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X6,X7] :
( sdtpldt0(X6,X7) = X3
& aElementOf0(X7,X0)
& aElementOf0(X6,X1) )
| aElementOf0(X3,X2) ) )
=> ( ( ! [X5,X4] :
( sdtpldt0(X4,X5) != sK20(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(sK20(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( sdtpldt0(X6,X7) = sK20(X0,X1,X2)
& aElementOf0(X7,X0)
& aElementOf0(X6,X1) )
| aElementOf0(sK20(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f157,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( sdtpldt0(X6,X7) = sK20(X0,X1,X2)
& aElementOf0(X7,X0)
& aElementOf0(X6,X1) )
=> ( sK20(X0,X1,X2) = sdtpldt0(sK21(X0,X1,X2),sK22(X0,X1,X2))
& aElementOf0(sK22(X0,X1,X2),X0)
& aElementOf0(sK21(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f158,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( sdtpldt0(X11,X12) = X8
& aElementOf0(X12,X0)
& aElementOf0(X11,X1) )
=> ( sdtpldt0(sK23(X0,X1,X8),sK24(X0,X1,X8)) = X8
& aElementOf0(sK24(X0,X1,X8),X0)
& aElementOf0(sK23(X0,X1,X8),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f155,plain,
! [X0,X1,X2] :
( ( sP5(X0,X1,X2)
| ? [X3] :
( ( ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X6,X7] :
( sdtpldt0(X6,X7) = X3
& aElementOf0(X7,X0)
& aElementOf0(X6,X1) )
| aElementOf0(X3,X2) ) ) )
& ( ! [X8] :
( ( aElementOf0(X8,X2)
| ! [X9,X10] :
( sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1) ) )
& ( ? [X11,X12] :
( sdtpldt0(X11,X12) = X8
& aElementOf0(X12,X0)
& aElementOf0(X11,X1) )
| ~ aElementOf0(X8,X2) ) )
| ~ sP5(X0,X1,X2) ) ),
inference(rectify,[],[f154]) ).
fof(f154,plain,
! [X1,X0,X2] :
( ( sP5(X1,X0,X2)
| ? [X3] :
( ( ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X0) )
| ~ aElementOf0(X3,X2) )
& ( ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) )
| aElementOf0(X3,X2) ) ) )
& ( ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X0) ) )
& ( ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) )
| ~ aElementOf0(X3,X2) ) )
| ~ sP5(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X1,X0,X2] :
( sP5(X1,X0,X2)
<=> ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f1027,plain,
spl31_98,
inference(avatar_split_clause,[],[f277,f1025]) ).
fof(f1025,plain,
( spl31_98
<=> ! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_98])]) ).
fof(f277,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( sz00 = sdtasdt0(X0,X1)
=> ( sz00 = X1
| sz00 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCancel) ).
fof(f1023,plain,
spl31_97,
inference(avatar_split_clause,[],[f267,f1021]) ).
fof(f1021,plain,
( spl31_97
<=> ! [X0,X3,X2,X1] :
( sdteqdtlpzmzozddtrp0(sK25(X0,X1,X2,X3),X3,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_97])]) ).
fof(f267,plain,
! [X2,X3,X0,X1] :
( sdteqdtlpzmzozddtrp0(sK25(X0,X1,X2,X3),X3,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f165]) ).
fof(f165,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( sdteqdtlpzmzozddtrp0(sK25(X0,X1,X2,X3),X3,X0)
& sdteqdtlpzmzozddtrp0(sK25(X0,X1,X2,X3),X2,X1)
& aElement0(sK25(X0,X1,X2,X3)) )
| ~ aElement0(X3)
| ~ aElement0(X2) )
| ~ sP6(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f163,f164]) ).
fof(f164,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( sdteqdtlpzmzozddtrp0(X4,X3,X0)
& sdteqdtlpzmzozddtrp0(X4,X2,X1)
& aElement0(X4) )
=> ( sdteqdtlpzmzozddtrp0(sK25(X0,X1,X2,X3),X3,X0)
& sdteqdtlpzmzozddtrp0(sK25(X0,X1,X2,X3),X2,X1)
& aElement0(sK25(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f163,plain,
! [X0,X1] :
( ! [X2,X3] :
( ? [X4] :
( sdteqdtlpzmzozddtrp0(X4,X3,X0)
& sdteqdtlpzmzozddtrp0(X4,X2,X1)
& aElement0(X4) )
| ~ aElement0(X3)
| ~ aElement0(X2) )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f162]) ).
fof(f162,plain,
! [X1,X0] :
( ! [X3,X4] :
( ? [X5] :
( sdteqdtlpzmzozddtrp0(X5,X4,X1)
& sdteqdtlpzmzozddtrp0(X5,X3,X0)
& aElement0(X5) )
| ~ aElement0(X4)
| ~ aElement0(X3) )
| ~ sP6(X1,X0) ),
inference(nnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X1,X0] :
( ! [X3,X4] :
( ? [X5] :
( sdteqdtlpzmzozddtrp0(X5,X4,X1)
& sdteqdtlpzmzozddtrp0(X5,X3,X0)
& aElement0(X5) )
| ~ aElement0(X4)
| ~ aElement0(X3) )
| ~ sP6(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f1019,plain,
spl31_96,
inference(avatar_split_clause,[],[f266,f1017]) ).
fof(f1017,plain,
( spl31_96
<=> ! [X0,X3,X2,X1] :
( sdteqdtlpzmzozddtrp0(sK25(X0,X1,X2,X3),X2,X1)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_96])]) ).
fof(f266,plain,
! [X2,X3,X0,X1] :
( sdteqdtlpzmzozddtrp0(sK25(X0,X1,X2,X3),X2,X1)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f165]) ).
fof(f1015,plain,
spl31_95,
inference(avatar_split_clause,[],[f262,f1013]) ).
fof(f1013,plain,
( spl31_95
<=> ! [X2,X0,X1] :
( sdtpldt1(X0,X1) = X2
| ~ sP5(X1,X0,X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_95])]) ).
fof(f262,plain,
! [X2,X0,X1] :
( sdtpldt1(X0,X1) = X2
| ~ sP5(X1,X0,X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt1(X0,X1) = X2
| ~ sP5(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP5(X1,X0,X2)
& aSet0(X2) )
| sdtpldt1(X0,X1) != X2 ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f160]) ).
fof(f160,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt1(X0,X1) = X2
| ~ sP5(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP5(X1,X0,X2)
& aSet0(X2) )
| sdtpldt1(X0,X1) != X2 ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( sP5(X1,X0,X2)
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f73,f114]) ).
fof(f73,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSSum) ).
fof(f1011,plain,
spl31_94,
inference(avatar_split_clause,[],[f232,f1009]) ).
fof(f1009,plain,
( spl31_94
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ aElementOf0(sdtasdt0(sK14(X0,X1),X1),X0)
| aElementOf0(sK15(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_94])]) ).
fof(f232,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ aElementOf0(sdtasdt0(sK14(X0,X1),X1),X0)
| aElementOf0(sK15(X0,X1),X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ~ aElementOf0(sdtasdt0(sK14(X0,X1),X1),X0)
& aElement0(sK14(X0,X1)) )
| ( ~ aElementOf0(sdtpldt0(X1,sK15(X0,X1)),X0)
& aElementOf0(sK15(X0,X1),X0) ) )
& ( ( ! [X4] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4) )
& ! [X5] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0) ) )
| ~ sP2(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f136,f138,f137]) ).
fof(f137,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
=> ( ~ aElementOf0(sdtasdt0(sK14(X0,X1),X1),X0)
& aElement0(sK14(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f138,plain,
! [X0,X1] :
( ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) )
=> ( ~ aElementOf0(sdtpldt0(X1,sK15(X0,X1)),X0)
& aElementOf0(sK15(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f136,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& ( ( ! [X4] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4) )
& ! [X5] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0) ) )
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f135]) ).
fof(f135,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& ( ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) )
| ~ sP2(X0,X1) ) ),
inference(flattening,[],[f134]) ).
fof(f134,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& ( ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) )
| ~ sP2(X0,X1) ) ),
inference(nnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( sP2(X0,X1)
<=> ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f1001,plain,
( spl31_93
| ~ spl31_14
| ~ spl31_60 ),
inference(avatar_split_clause,[],[f842,f710,f370,f998]) ).
fof(f998,plain,
( spl31_93
<=> sP1(sdtpldt0(xu,xv)) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_93])]) ).
fof(f370,plain,
( spl31_14
<=> ! [X0] :
( sP1(X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_14])]) ).
fof(f710,plain,
( spl31_60
<=> aElement0(sdtpldt0(xu,xv)) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_60])]) ).
fof(f842,plain,
( sP1(sdtpldt0(xu,xv))
| ~ spl31_14
| ~ spl31_60 ),
inference(resolution,[],[f711,f371]) ).
fof(f371,plain,
( ! [X0] :
( ~ aElement0(X0)
| sP1(X0) )
| ~ spl31_14 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f711,plain,
( aElement0(sdtpldt0(xu,xv))
| ~ spl31_60 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f996,plain,
spl31_92,
inference(avatar_split_clause,[],[f281,f994]) ).
fof(f994,plain,
( spl31_92
<=> ! [X0,X1] :
( sdtasdt0(X0,sK29(X0,X1)) = X1
| ~ doDivides0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_92])]) ).
fof(f281,plain,
! [X0,X1] :
( sdtasdt0(X0,sK29(X0,X1)) = X1
| ~ doDivides0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f174]) ).
fof(f174,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aElement0(X2) ) )
& ( ( sdtasdt0(X0,sK29(X0,X1)) = X1
& aElement0(sK29(X0,X1)) )
| ~ doDivides0(X0,X1) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f172,f173]) ).
fof(f173,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aElement0(X3) )
=> ( sdtasdt0(X0,sK29(X0,X1)) = X1
& aElement0(sK29(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f172,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aElement0(X2) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aElement0(X3) )
| ~ doDivides0(X0,X1) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(rectify,[],[f171]) ).
fof(f171,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aElement0(X2) ) )
& ( ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(f992,plain,
spl31_91,
inference(avatar_split_clause,[],[f269,f990]) ).
fof(f990,plain,
( spl31_91
<=> ! [X0,X1] :
( sP6(X1,X0)
| ~ aElementOf0(sK26(X0,X1),sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_91])]) ).
fof(f269,plain,
! [X0,X1] :
( sP6(X1,X0)
| ~ aElementOf0(sK26(X0,X1),sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f167,plain,
! [X0,X1] :
( sP6(X1,X0)
| ( ~ aElementOf0(sK26(X0,X1),sdtpldt1(X0,X1))
& aElement0(sK26(X0,X1)) )
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f117,f166]) ).
fof(f166,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,sdtpldt1(X0,X1))
& aElement0(X2) )
=> ( ~ aElementOf0(sK26(X0,X1),sdtpldt1(X0,X1))
& aElement0(sK26(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
! [X0,X1] :
( sP6(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,sdtpldt1(X0,X1))
& aElement0(X2) )
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(definition_folding,[],[f79,f116]) ).
fof(f79,plain,
! [X0,X1] :
( ! [X3,X4] :
( ? [X5] :
( sdteqdtlpzmzozddtrp0(X5,X4,X1)
& sdteqdtlpzmzozddtrp0(X5,X3,X0)
& aElement0(X5) )
| ~ aElement0(X4)
| ~ aElement0(X3) )
| ? [X2] :
( ~ aElementOf0(X2,sdtpldt1(X0,X1))
& aElement0(X2) )
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ! [X3,X4] :
( ? [X5] :
( sdteqdtlpzmzozddtrp0(X5,X4,X1)
& sdteqdtlpzmzozddtrp0(X5,X3,X0)
& aElement0(X5) )
| ~ aElement0(X4)
| ~ aElement0(X3) )
| ? [X2] :
( ~ aElementOf0(X2,sdtpldt1(X0,X1))
& aElement0(X2) )
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( ( aIdeal0(X1)
& aIdeal0(X0) )
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(X2,sdtpldt1(X0,X1)) )
=> ! [X3,X4] :
( ( aElement0(X4)
& aElement0(X3) )
=> ? [X5] :
( sdteqdtlpzmzozddtrp0(X5,X4,X1)
& sdteqdtlpzmzozddtrp0(X5,X3,X0)
& aElement0(X5) ) ) ) ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( ( aIdeal0(X1)
& aIdeal0(X0) )
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(X2,sdtpldt1(X0,X1)) )
=> ! [X2,X3] :
( ( aElement0(X3)
& aElement0(X2) )
=> ? [X4] :
( sdteqdtlpzmzozddtrp0(X4,X3,X1)
& sdteqdtlpzmzozddtrp0(X4,X2,X0)
& aElement0(X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mChineseRemainder) ).
fof(f988,plain,
spl31_90,
inference(avatar_split_clause,[],[f231,f986]) ).
fof(f986,plain,
( spl31_90
<=> ! [X0,X1] :
( sP2(X0,X1)
| aElement0(sK14(X0,X1))
| ~ aElementOf0(sdtpldt0(X1,sK15(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_90])]) ).
fof(f231,plain,
! [X0,X1] :
( sP2(X0,X1)
| aElement0(sK14(X0,X1))
| ~ aElementOf0(sdtpldt0(X1,sK15(X0,X1)),X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f984,plain,
spl31_89,
inference(avatar_split_clause,[],[f224,f982]) ).
fof(f982,plain,
( spl31_89
<=> ! [X0,X1] :
( sP0(X0,X1)
| aElement0(sK12(X0,X1))
| aElementOf0(sK11(X0,X1),X1)
| ~ aSet0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_89])]) ).
fof(f224,plain,
! [X0,X1] :
( sP0(X0,X1)
| aElement0(sK12(X0,X1))
| aElementOf0(sK11(X0,X1),X1)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ! [X3] :
( sdtasdt0(X0,X3) != sK11(X0,X1)
| ~ aElement0(X3) )
| ~ aElementOf0(sK11(X0,X1),X1) )
& ( ( sK11(X0,X1) = sdtasdt0(X0,sK12(X0,X1))
& aElement0(sK12(X0,X1)) )
| aElementOf0(sK11(X0,X1),X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) ) )
& ( ( sdtasdt0(X0,sK13(X0,X5)) = X5
& aElement0(sK13(X0,X5)) )
| ~ aElementOf0(X5,X1) ) )
& aSet0(X1) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f129,f132,f131,f130]) ).
fof(f130,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| ~ aElementOf0(X2,X1) )
& ( ? [X4] :
( sdtasdt0(X0,X4) = X2
& aElement0(X4) )
| aElementOf0(X2,X1) ) )
=> ( ( ! [X3] :
( sdtasdt0(X0,X3) != sK11(X0,X1)
| ~ aElement0(X3) )
| ~ aElementOf0(sK11(X0,X1),X1) )
& ( ? [X4] :
( sdtasdt0(X0,X4) = sK11(X0,X1)
& aElement0(X4) )
| aElementOf0(sK11(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f131,plain,
! [X0,X1] :
( ? [X4] :
( sdtasdt0(X0,X4) = sK11(X0,X1)
& aElement0(X4) )
=> ( sK11(X0,X1) = sdtasdt0(X0,sK12(X0,X1))
& aElement0(sK12(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f132,plain,
! [X0,X5] :
( ? [X7] :
( sdtasdt0(X0,X7) = X5
& aElement0(X7) )
=> ( sdtasdt0(X0,sK13(X0,X5)) = X5
& aElement0(sK13(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f129,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| ~ aElementOf0(X2,X1) )
& ( ? [X4] :
( sdtasdt0(X0,X4) = X2
& aElement0(X4) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) ) )
& ( ? [X7] :
( sdtasdt0(X0,X7) = X5
& aElement0(X7) )
| ~ aElementOf0(X5,X1) ) )
& aSet0(X1) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f128]) ).
fof(f128,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) )
| ~ aElementOf0(X2,X1) ) )
& aSet0(X1) )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f127]) ).
fof(f127,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) )
| ~ aElementOf0(X2,X1) ) )
& aSet0(X1) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& aSet0(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f954,plain,
spl31_88,
inference(avatar_split_clause,[],[f304,f952]) ).
fof(f952,plain,
( spl31_88
<=> ! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aElement0(X2)
| ~ aElement0(sdtasdt0(X0,X2))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_88])]) ).
fof(f304,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aElement0(X2)
| ~ aElement0(sdtasdt0(X0,X2))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f282]) ).
fof(f282,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f174]) ).
fof(f950,plain,
spl31_87,
inference(avatar_split_clause,[],[f287,f948]) ).
fof(f948,plain,
( spl31_87
<=> ! [X2,X4,X0,X1] :
( doDivides0(X4,X0)
| ~ aDivisorOf0(X4,X1)
| ~ aDivisorOf0(X4,X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_87])]) ).
fof(f287,plain,
! [X2,X0,X1,X4] :
( doDivides0(X4,X0)
| ~ aDivisorOf0(X4,X1)
| ~ aDivisorOf0(X4,X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0,X1,X2] :
( ( sP7(X0,X1,X2)
| ( ~ doDivides0(sK30(X0,X1,X2),X0)
& aDivisorOf0(sK30(X0,X1,X2),X1)
& aDivisorOf0(sK30(X0,X1,X2),X2) )
| ~ aDivisorOf0(X0,X1)
| ~ aDivisorOf0(X0,X2) )
& ( ( ! [X4] :
( doDivides0(X4,X0)
| ~ aDivisorOf0(X4,X1)
| ~ aDivisorOf0(X4,X2) )
& aDivisorOf0(X0,X1)
& aDivisorOf0(X0,X2) )
| ~ sP7(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f178,f179]) ).
fof(f179,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ doDivides0(X3,X0)
& aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X2) )
=> ( ~ doDivides0(sK30(X0,X1,X2),X0)
& aDivisorOf0(sK30(X0,X1,X2),X1)
& aDivisorOf0(sK30(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f178,plain,
! [X0,X1,X2] :
( ( sP7(X0,X1,X2)
| ? [X3] :
( ~ doDivides0(X3,X0)
& aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X2) )
| ~ aDivisorOf0(X0,X1)
| ~ aDivisorOf0(X0,X2) )
& ( ( ! [X4] :
( doDivides0(X4,X0)
| ~ aDivisorOf0(X4,X1)
| ~ aDivisorOf0(X4,X2) )
& aDivisorOf0(X0,X1)
& aDivisorOf0(X0,X2) )
| ~ sP7(X0,X1,X2) ) ),
inference(rectify,[],[f177]) ).
fof(f177,plain,
! [X2,X1,X0] :
( ( sP7(X2,X1,X0)
| ? [X3] :
( ~ doDivides0(X3,X2)
& aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X0) )
| ~ aDivisorOf0(X2,X1)
| ~ aDivisorOf0(X2,X0) )
& ( ( ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) )
| ~ sP7(X2,X1,X0) ) ),
inference(flattening,[],[f176]) ).
fof(f176,plain,
! [X2,X1,X0] :
( ( sP7(X2,X1,X0)
| ? [X3] :
( ~ doDivides0(X3,X2)
& aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X0) )
| ~ aDivisorOf0(X2,X1)
| ~ aDivisorOf0(X2,X0) )
& ( ( ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) )
| ~ sP7(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X2,X1,X0] :
( sP7(X2,X1,X0)
<=> ( ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f946,plain,
spl31_86,
inference(avatar_split_clause,[],[f265,f944]) ).
fof(f944,plain,
( spl31_86
<=> ! [X0,X3,X2,X1] :
( aElement0(sK25(X0,X1,X2,X3))
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_86])]) ).
fof(f265,plain,
! [X2,X3,X0,X1] :
( aElement0(sK25(X0,X1,X2,X3))
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f165]) ).
fof(f942,plain,
spl31_85,
inference(avatar_split_clause,[],[f253,f940]) ).
fof(f940,plain,
( spl31_85
<=> ! [X0,X8,X2,X1] :
( aElementOf0(sK24(X0,X1,X8),X0)
| ~ aElementOf0(X8,X2)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_85])]) ).
fof(f253,plain,
! [X2,X0,X1,X8] :
( aElementOf0(sK24(X0,X1,X8),X0)
| ~ aElementOf0(X8,X2)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f159]) ).
fof(f938,plain,
spl31_84,
inference(avatar_split_clause,[],[f252,f936]) ).
fof(f936,plain,
( spl31_84
<=> ! [X0,X8,X2,X1] :
( aElementOf0(sK23(X0,X1,X8),X1)
| ~ aElementOf0(X8,X2)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_84])]) ).
fof(f252,plain,
! [X2,X0,X1,X8] :
( aElementOf0(sK23(X0,X1,X8),X1)
| ~ aElementOf0(X8,X2)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f159]) ).
fof(f934,plain,
spl31_83,
inference(avatar_split_clause,[],[f247,f932]) ).
fof(f932,plain,
( spl31_83
<=> ! [X4,X0,X2,X1] :
( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_83])]) ).
fof(f247,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ( ( ~ aElementOf0(sK19(X0,X1,X2),X0)
| ~ aElementOf0(sK19(X0,X1,X2),X1)
| ~ aElementOf0(sK19(X0,X1,X2),X2) )
& ( ( aElementOf0(sK19(X0,X1,X2),X0)
& aElementOf0(sK19(X0,X1,X2),X1) )
| aElementOf0(sK19(X0,X1,X2),X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1) )
& ( ( aElementOf0(X4,X0)
& aElementOf0(X4,X1) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP3(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f151,f152]) ).
fof(f152,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X0)
& aElementOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
=> ( ( ~ aElementOf0(sK19(X0,X1,X2),X0)
| ~ aElementOf0(sK19(X0,X1,X2),X1)
| ~ aElementOf0(sK19(X0,X1,X2),X2) )
& ( ( aElementOf0(sK19(X0,X1,X2),X0)
& aElementOf0(sK19(X0,X1,X2),X1) )
| aElementOf0(sK19(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f151,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ? [X3] :
( ( ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X0)
& aElementOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1) )
& ( ( aElementOf0(X4,X0)
& aElementOf0(X4,X1) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP3(X0,X1,X2) ) ),
inference(rectify,[],[f150]) ).
fof(f150,plain,
! [X1,X0,X2] :
( ( sP3(X1,X0,X2)
| ? [X3] :
( ( ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0) )
& ( ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP3(X1,X0,X2) ) ),
inference(flattening,[],[f149]) ).
fof(f149,plain,
! [X1,X0,X2] :
( ( sP3(X1,X0,X2)
| ? [X3] :
( ( ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0) )
& ( ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP3(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X1,X0,X2] :
( sP3(X1,X0,X2)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f930,plain,
spl31_82,
inference(avatar_split_clause,[],[f222,f928]) ).
fof(f928,plain,
( spl31_82
<=> ! [X5,X0,X1] :
( sdtasdt0(X0,sK13(X0,X5)) = X5
| ~ aElementOf0(X5,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_82])]) ).
fof(f222,plain,
! [X0,X1,X5] :
( sdtasdt0(X0,sK13(X0,X5)) = X5
| ~ aElementOf0(X5,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f922,plain,
( ~ spl31_81
| ~ spl31_17
| ~ spl31_55 ),
inference(avatar_split_clause,[],[f792,f660,f389,f919]) ).
fof(f389,plain,
( spl31_17
<=> ! [X0] :
( sdtasdt0(xc,X0) != sdtasdt0(xz,xx)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_17])]) ).
fof(f660,plain,
( spl31_55
<=> sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_55])]) ).
fof(f792,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| ~ spl31_17
| ~ spl31_55 ),
inference(trivial_inequality_removal,[],[f787]) ).
fof(f787,plain,
( sdtasdt0(xz,xx) != sdtasdt0(xz,xx)
| ~ aElement0(sdtasdt0(xu,xz))
| ~ spl31_17
| ~ spl31_55 ),
inference(superposition,[],[f390,f662]) ).
fof(f662,plain,
( sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz))
| ~ spl31_55 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f390,plain,
( ! [X0] :
( sdtasdt0(xc,X0) != sdtasdt0(xz,xx)
| ~ aElement0(X0) )
| ~ spl31_17 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f917,plain,
spl31_80,
inference(avatar_split_clause,[],[f243,f915]) ).
fof(f915,plain,
( spl31_80
<=> ! [X2,X0,X1] :
( sdtasasdt0(X0,X1) = X2
| ~ sP3(X1,X0,X2)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_80])]) ).
fof(f243,plain,
! [X2,X0,X1] :
( sdtasasdt0(X0,X1) = X2
| ~ sP3(X1,X0,X2)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtasasdt0(X0,X1) = X2
| ~ sP3(X1,X0,X2) )
& ( sP3(X1,X0,X2)
| sdtasasdt0(X0,X1) != X2 ) )
| ~ sP4(X0,X1) ),
inference(nnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1] :
( ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> sP3(X1,X0,X2) )
| ~ sP4(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f913,plain,
spl31_79,
inference(avatar_split_clause,[],[f230,f911]) ).
fof(f911,plain,
( spl31_79
<=> ! [X0,X1] :
( sP2(X0,X1)
| aElement0(sK14(X0,X1))
| aElementOf0(sK15(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_79])]) ).
fof(f230,plain,
! [X0,X1] :
( sP2(X0,X1)
| aElement0(sK14(X0,X1))
| aElementOf0(sK15(X0,X1),X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f816,plain,
spl31_78,
inference(avatar_split_clause,[],[f284,f814]) ).
fof(f814,plain,
( spl31_78
<=> ! [X2,X0,X1] :
( aGcdOfAnd0(X2,X0,X1)
| ~ sP7(X2,X1,X0)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_78])]) ).
fof(f284,plain,
! [X2,X0,X1] :
( aGcdOfAnd0(X2,X0,X1)
| ~ sP7(X2,X1,X0)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
fof(f175,plain,
! [X0,X1] :
( ! [X2] :
( ( aGcdOfAnd0(X2,X0,X1)
| ~ sP7(X2,X1,X0) )
& ( sP7(X2,X1,X0)
| ~ aGcdOfAnd0(X2,X0,X1) ) )
| ~ sP8(X0,X1) ),
inference(nnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0,X1] :
( ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> sP7(X2,X1,X0) )
| ~ sP8(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f812,plain,
spl31_77,
inference(avatar_split_clause,[],[f283,f810]) ).
fof(f810,plain,
( spl31_77
<=> ! [X2,X0,X1] :
( sP7(X2,X1,X0)
| ~ aGcdOfAnd0(X2,X0,X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_77])]) ).
fof(f283,plain,
! [X2,X0,X1] :
( sP7(X2,X1,X0)
| ~ aGcdOfAnd0(X2,X0,X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
fof(f808,plain,
spl31_76,
inference(avatar_split_clause,[],[f280,f806]) ).
fof(f806,plain,
( spl31_76
<=> ! [X0,X1] :
( aElement0(sK29(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_76])]) ).
fof(f280,plain,
! [X0,X1] :
( aElement0(sK29(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f174]) ).
fof(f804,plain,
spl31_75,
inference(avatar_split_clause,[],[f279,f802]) ).
fof(f802,plain,
( spl31_75
<=> ! [X0,X1] :
( misRelativelyPrime0(X0,X1)
| ~ aGcdOfAnd0(sz10,X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_75])]) ).
fof(f279,plain,
! [X0,X1] :
( misRelativelyPrime0(X0,X1)
| ~ aGcdOfAnd0(sz10,X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f170,plain,
! [X0,X1] :
( ( ( misRelativelyPrime0(X0,X1)
| ~ aGcdOfAnd0(sz10,X0,X1) )
& ( aGcdOfAnd0(sz10,X0,X1)
| ~ misRelativelyPrime0(X0,X1) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( ( misRelativelyPrime0(X0,X1)
<=> aGcdOfAnd0(sz10,X0,X1) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ( misRelativelyPrime0(X0,X1)
<=> aGcdOfAnd0(sz10,X0,X1) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( misRelativelyPrime0(X0,X1)
<=> aGcdOfAnd0(sz10,X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefRel) ).
fof(f800,plain,
spl31_74,
inference(avatar_split_clause,[],[f278,f798]) ).
fof(f798,plain,
( spl31_74
<=> ! [X0,X1] :
( aGcdOfAnd0(sz10,X0,X1)
| ~ misRelativelyPrime0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_74])]) ).
fof(f278,plain,
! [X0,X1] :
( aGcdOfAnd0(sz10,X0,X1)
| ~ misRelativelyPrime0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f796,plain,
spl31_73,
inference(avatar_split_clause,[],[f276,f794]) ).
fof(f794,plain,
( spl31_73
<=> ! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_73])]) ).
fof(f276,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f785,plain,
( ~ spl31_3
| ~ spl31_2
| ~ spl31_49
| spl31_60 ),
inference(avatar_split_clause,[],[f744,f710,f586,f311,f316]) ).
fof(f311,plain,
( spl31_2
<=> aElement0(xv) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_2])]) ).
fof(f586,plain,
( spl31_49
<=> ! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_49])]) ).
fof(f744,plain,
( ~ aElement0(xv)
| ~ aElement0(xu)
| ~ spl31_49
| spl31_60 ),
inference(resolution,[],[f712,f587]) ).
fof(f587,plain,
( ! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) )
| ~ spl31_49 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f712,plain,
( ~ aElement0(sdtpldt0(xu,xv))
| spl31_60 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f784,plain,
spl31_72,
inference(avatar_split_clause,[],[f275,f782]) ).
fof(f782,plain,
( spl31_72
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_72])]) ).
fof(f275,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(f780,plain,
spl31_71,
inference(avatar_split_clause,[],[f271,f778]) ).
fof(f778,plain,
( spl31_71
<=> ! [X0,X1] :
( aElement0(sK28(X0,X1))
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_71])]) ).
fof(f271,plain,
! [X0,X1] :
( aElement0(sK28(X0,X1))
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f169,plain,
! [X0,X1] :
( ( sdtpldt0(sdtasdt0(sK27(X0,X1),X1),sK28(X0,X1)) = X0
& aElement0(sK28(X0,X1))
& aElement0(sK27(X0,X1)) )
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f81,f168]) ).
fof(f168,plain,
! [X0,X1] :
( ? [X2,X3] :
( sdtpldt0(sdtasdt0(X2,X1),X3) = X0
& aElement0(X3)
& aElement0(X2) )
=> ( sdtpldt0(sdtasdt0(sK27(X0,X1),X1),sK28(X0,X1)) = X0
& aElement0(sK28(X0,X1))
& aElement0(sK27(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0,X1] :
( ? [X2,X3] :
( sdtpldt0(sdtasdt0(X2,X1),X3) = X0
& aElement0(X3)
& aElement0(X2) )
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ? [X2,X3] :
( sdtpldt0(sdtasdt0(X2,X1),X3) = X0
& aElement0(X3)
& aElement0(X2) )
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ( sz00 != X1
& aElement0(X1)
& aElement0(X0) )
=> ? [X2,X3] :
( sdtpldt0(sdtasdt0(X2,X1),X3) = X0
& aElement0(X3)
& aElement0(X2) ) ),
inference(pure_predicate_removal,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( ( sz00 != X1
& aElement0(X1)
& aElement0(X0) )
=> ? [X2,X3] :
( ( sz00 != X3
=> iLess0(sbrdtbr0(X3),sbrdtbr0(X1)) )
& sdtpldt0(sdtasdt0(X2,X1),X3) = X0
& aElement0(X3)
& aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivision) ).
fof(f776,plain,
spl31_70,
inference(avatar_split_clause,[],[f270,f774]) ).
fof(f774,plain,
( spl31_70
<=> ! [X0,X1] :
( aElement0(sK27(X0,X1))
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_70])]) ).
fof(f270,plain,
! [X0,X1] :
( aElement0(sK27(X0,X1))
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f772,plain,
spl31_69,
inference(avatar_split_clause,[],[f268,f770]) ).
fof(f770,plain,
( spl31_69
<=> ! [X0,X1] :
( sP6(X1,X0)
| aElement0(sK26(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_69])]) ).
fof(f268,plain,
! [X0,X1] :
( sP6(X1,X0)
| aElement0(sK26(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f768,plain,
spl31_68,
inference(avatar_split_clause,[],[f228,f766]) ).
fof(f766,plain,
( spl31_68
<=> ! [X5,X0,X1] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_68])]) ).
fof(f228,plain,
! [X0,X1,X5] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f742,plain,
spl31_67,
inference(avatar_split_clause,[],[f302,f740]) ).
fof(f740,plain,
( spl31_67
<=> ! [X0,X1] :
( sP5(X1,X0,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_67])]) ).
fof(f302,plain,
! [X0,X1] :
( sP5(X1,X0,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f261]) ).
fof(f261,plain,
! [X2,X0,X1] :
( sP5(X1,X0,X2)
| sdtpldt1(X0,X1) != X2
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f738,plain,
spl31_66,
inference(avatar_split_clause,[],[f299,f736]) ).
fof(f736,plain,
( spl31_66
<=> ! [X6,X0,X1] :
( aElementOf0(sdtasdt0(X0,X6),X1)
| ~ aElement0(X6)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_66])]) ).
fof(f299,plain,
! [X0,X1,X6] :
( aElementOf0(sdtasdt0(X0,X6),X1)
| ~ aElement0(X6)
| ~ sP0(X0,X1) ),
inference(equality_resolution,[],[f223]) ).
fof(f223,plain,
! [X0,X1,X6,X5] :
( aElementOf0(X5,X1)
| sdtasdt0(X0,X6) != X5
| ~ aElement0(X6)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f734,plain,
spl31_65,
inference(avatar_split_clause,[],[f246,f732]) ).
fof(f732,plain,
( spl31_65
<=> ! [X4,X0,X2,X1] :
( aElementOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_65])]) ).
fof(f246,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f153]) ).
fof(f730,plain,
spl31_64,
inference(avatar_split_clause,[],[f245,f728]) ).
fof(f728,plain,
( spl31_64
<=> ! [X4,X0,X1,X2] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_64])]) ).
fof(f245,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f153]) ).
fof(f726,plain,
spl31_63,
inference(avatar_split_clause,[],[f229,f724]) ).
fof(f724,plain,
( spl31_63
<=> ! [X4,X0,X1] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_63])]) ).
fof(f229,plain,
! [X0,X1,X4] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f722,plain,
spl31_62,
inference(avatar_split_clause,[],[f221,f720]) ).
fof(f720,plain,
( spl31_62
<=> ! [X5,X0,X1] :
( aElement0(sK13(X0,X5))
| ~ aElementOf0(X5,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_62])]) ).
fof(f221,plain,
! [X0,X1,X5] :
( aElement0(sK13(X0,X5))
| ~ aElementOf0(X5,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f718,plain,
spl31_61,
inference(avatar_split_clause,[],[f217,f716]) ).
fof(f716,plain,
( spl31_61
<=> ! [X0,X1] :
( aDivisorOf0(X1,X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_61])]) ).
fof(f217,plain,
! [X0,X1] :
( aDivisorOf0(X1,X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1) )
& ( ( doDivides0(X1,X0)
& aElement0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aElement0(X0) ),
inference(flattening,[],[f124]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1) )
& ( ( doDivides0(X1,X0)
& aElement0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( doDivides0(X1,X0)
& aElement0(X1) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( doDivides0(X1,X0)
& aElement0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDvs) ).
fof(f713,plain,
( ~ spl31_60
| ~ spl31_16
| ~ spl31_53 ),
inference(avatar_split_clause,[],[f666,f650,f386,f710]) ).
fof(f386,plain,
( spl31_16
<=> ! [X1] :
( sdtpldt0(xx,xy) != sdtasdt0(xc,X1)
| ~ aElement0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_16])]) ).
fof(f650,plain,
( spl31_53
<=> sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_53])]) ).
fof(f666,plain,
( ~ aElement0(sdtpldt0(xu,xv))
| ~ spl31_16
| ~ spl31_53 ),
inference(trivial_inequality_removal,[],[f664]) ).
fof(f664,plain,
( sdtpldt0(xx,xy) != sdtpldt0(xx,xy)
| ~ aElement0(sdtpldt0(xu,xv))
| ~ spl31_16
| ~ spl31_53 ),
inference(superposition,[],[f387,f652]) ).
fof(f652,plain,
( sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv))
| ~ spl31_53 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f387,plain,
( ! [X1] :
( sdtpldt0(xx,xy) != sdtasdt0(xc,X1)
| ~ aElement0(X1) )
| ~ spl31_16 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f684,plain,
spl31_59,
inference(avatar_split_clause,[],[f300,f682]) ).
fof(f682,plain,
( spl31_59
<=> ! [X0,X1] :
( sP3(X1,X0,sdtasasdt0(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_59])]) ).
fof(f300,plain,
! [X0,X1] :
( sP3(X1,X0,sdtasasdt0(X0,X1))
| ~ sP4(X0,X1) ),
inference(equality_resolution,[],[f242]) ).
fof(f242,plain,
! [X2,X0,X1] :
( sP3(X1,X0,X2)
| sdtasasdt0(X0,X1) != X2
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f148]) ).
fof(f680,plain,
spl31_58,
inference(avatar_split_clause,[],[f219,f678]) ).
fof(f678,plain,
( spl31_58
<=> ! [X0,X1] :
( slsdtgt0(X0) = X1
| ~ sP0(X0,X1)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_58])]) ).
fof(f219,plain,
! [X0,X1] :
( slsdtgt0(X0) = X1
| ~ sP0(X0,X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ( slsdtgt0(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| slsdtgt0(X0) != X1 ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( slsdtgt0(X0) = X1
<=> sP0(X0,X1) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f676,plain,
spl31_57,
inference(avatar_split_clause,[],[f214,f674]) ).
fof(f674,plain,
( spl31_57
<=> ! [X0] :
( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_57])]) ).
fof(f214,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
& smndt0(X0) = sdtasdt0(smndt0(sz10),X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( aElement0(X0)
=> ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
& smndt0(X0) = sdtasdt0(smndt0(sz10),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMnOne) ).
fof(f672,plain,
spl31_56,
inference(avatar_split_clause,[],[f213,f670]) ).
fof(f670,plain,
( spl31_56
<=> ! [X0] :
( smndt0(X0) = sdtasdt0(smndt0(sz10),X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_56])]) ).
fof(f213,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(smndt0(sz10),X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f663,plain,
spl31_55,
inference(avatar_split_clause,[],[f188,f660]) ).
fof(f188,plain,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2043) ).
fof(f658,plain,
( spl31_54
| ~ spl31_3
| ~ spl31_14 ),
inference(avatar_split_clause,[],[f381,f370,f316,f655]) ).
fof(f655,plain,
( spl31_54
<=> sP1(xu) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_54])]) ).
fof(f381,plain,
( sP1(xu)
| ~ spl31_3
| ~ spl31_14 ),
inference(resolution,[],[f371,f318]) ).
fof(f318,plain,
( aElement0(xu)
| ~ spl31_3 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f653,plain,
spl31_53,
inference(avatar_split_clause,[],[f187,f650]) ).
fof(f187,plain,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2010) ).
fof(f619,plain,
( spl31_52
| ~ spl31_6
| ~ spl31_14 ),
inference(avatar_split_clause,[],[f380,f370,f331,f616]) ).
fof(f616,plain,
( spl31_52
<=> sP1(xz) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_52])]) ).
fof(f380,plain,
( sP1(xz)
| ~ spl31_6
| ~ spl31_14 ),
inference(resolution,[],[f371,f333]) ).
fof(f333,plain,
( aElement0(xz)
| ~ spl31_6 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f596,plain,
spl31_51,
inference(avatar_split_clause,[],[f303,f594]) ).
fof(f594,plain,
( spl31_51
<=> ! [X0,X1] :
( aSet0(sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_51])]) ).
fof(f303,plain,
! [X0,X1] :
( aSet0(sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f260]) ).
fof(f260,plain,
! [X2,X0,X1] :
( aSet0(X2)
| sdtpldt1(X0,X1) != X2
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f592,plain,
spl31_50,
inference(avatar_split_clause,[],[f274,f590]) ).
fof(f274,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f588,plain,
spl31_49,
inference(avatar_split_clause,[],[f273,f586]) ).
fof(f273,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f584,plain,
spl31_48,
inference(avatar_split_clause,[],[f264,f582]) ).
fof(f582,plain,
( spl31_48
<=> ! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_48])]) ).
fof(f264,plain,
! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] :
( ( aIdeal0(X1)
& aIdeal0(X0) )
=> aIdeal0(sdtpldt1(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIdeSum) ).
fof(f580,plain,
spl31_47,
inference(avatar_split_clause,[],[f263,f578]) ).
fof(f578,plain,
( spl31_47
<=> ! [X0,X1] :
( aIdeal0(sdtasasdt0(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_47])]) ).
fof(f263,plain,
! [X0,X1] :
( aIdeal0(sdtasasdt0(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( aIdeal0(sdtasasdt0(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( aIdeal0(sdtasasdt0(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0,X1] :
( ( aIdeal0(X1)
& aIdeal0(X0) )
=> aIdeal0(sdtasasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIdeInt) ).
fof(f576,plain,
spl31_46,
inference(avatar_split_clause,[],[f237,f574]) ).
fof(f574,plain,
( spl31_46
<=> ! [X0] :
( aIdeal0(X0)
| ~ sP2(X0,sK16(X0))
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_46])]) ).
fof(f237,plain,
! [X0] :
( aIdeal0(X0)
| ~ sP2(X0,sK16(X0))
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0] :
( ( aIdeal0(X0)
| ( ~ sP2(X0,sK16(X0))
& aElementOf0(sK16(X0),X0) )
| ~ aSet0(X0) )
& ( ( ! [X2] :
( sP2(X0,X2)
| ~ aElementOf0(X2,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f142,f143]) ).
fof(f143,plain,
! [X0] :
( ? [X1] :
( ~ sP2(X0,X1)
& aElementOf0(X1,X0) )
=> ( ~ sP2(X0,sK16(X0))
& aElementOf0(sK16(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f142,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ~ sP2(X0,X1)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X2] :
( sP2(X0,X2)
| ~ aElementOf0(X2,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(rectify,[],[f141]) ).
fof(f141,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ~ sP2(X0,X1)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X1] :
( sP2(X0,X1)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(flattening,[],[f140]) ).
fof(f140,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ~ sP2(X0,X1)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X1] :
( sP2(X0,X1)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(nnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( sP2(X0,X1)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) ) ),
inference(definition_folding,[],[f67,f109]) ).
fof(f67,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) )
| ~ aElementOf0(X1,X0) )
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X3] :
( aElementOf0(X3,X0)
=> aElementOf0(sdtpldt0(X1,X3),X0) ) ) )
& aSet0(X0) ) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f572,plain,
spl31_45,
inference(avatar_split_clause,[],[f236,f570]) ).
fof(f570,plain,
( spl31_45
<=> ! [X0] :
( aIdeal0(X0)
| aElementOf0(sK16(X0),X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_45])]) ).
fof(f236,plain,
! [X0] :
( aIdeal0(X0)
| aElementOf0(sK16(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f568,plain,
spl31_44,
inference(avatar_split_clause,[],[f235,f566]) ).
fof(f566,plain,
( spl31_44
<=> ! [X2,X0] :
( sP2(X0,X2)
| ~ aElementOf0(X2,X0)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_44])]) ).
fof(f235,plain,
! [X2,X0] :
( sP2(X0,X2)
| ~ aElementOf0(X2,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f564,plain,
spl31_43,
inference(avatar_split_clause,[],[f216,f562]) ).
fof(f562,plain,
( spl31_43
<=> ! [X0,X1] :
( doDivides0(X1,X0)
| ~ aDivisorOf0(X1,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_43])]) ).
fof(f216,plain,
! [X0,X1] :
( doDivides0(X1,X0)
| ~ aDivisorOf0(X1,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f560,plain,
spl31_42,
inference(avatar_split_clause,[],[f212,f558]) ).
fof(f558,plain,
( spl31_42
<=> ! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_42])]) ).
fof(f212,plain,
! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ( sz00 = sdtpldt0(smndt0(X0),X0)
& sz00 = sdtpldt0(X0,smndt0(X0)) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( aElement0(X0)
=> ( sz00 = sdtpldt0(smndt0(X0),X0)
& sz00 = sdtpldt0(X0,smndt0(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddInvr) ).
fof(f556,plain,
spl31_41,
inference(avatar_split_clause,[],[f211,f554]) ).
fof(f554,plain,
( spl31_41
<=> ! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_41])]) ).
fof(f211,plain,
! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f534,plain,
( ~ spl31_3
| ~ spl31_40
| ~ spl31_16
| ~ spl31_19 ),
inference(avatar_split_clause,[],[f418,f398,f386,f531,f316]) ).
fof(f531,plain,
( spl31_40
<=> xx = sdtpldt0(xx,xy) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_40])]) ).
fof(f398,plain,
( spl31_19
<=> xx = sdtasdt0(xc,xu) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_19])]) ).
fof(f418,plain,
( xx != sdtpldt0(xx,xy)
| ~ aElement0(xu)
| ~ spl31_16
| ~ spl31_19 ),
inference(superposition,[],[f387,f400]) ).
fof(f400,plain,
( xx = sdtasdt0(xc,xu)
| ~ spl31_19 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f491,plain,
spl31_39,
inference(avatar_split_clause,[],[f291,f489]) ).
fof(f489,plain,
( spl31_39
<=> ! [X0,X1] :
( sP8(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_39])]) ).
fof(f291,plain,
! [X0,X1] :
( sP8(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1] :
( sP8(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(definition_folding,[],[f97,f119,f118]) ).
fof(f97,plain,
! [X0,X1] :
( ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> ( ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f96]) ).
fof(f96,plain,
! [X0,X1] :
( ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> ( ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> ( ! [X3] :
( ( aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X0) )
=> doDivides0(X3,X2) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefGCD) ).
fof(f487,plain,
spl31_38,
inference(avatar_split_clause,[],[f286,f485]) ).
fof(f485,plain,
( spl31_38
<=> ! [X2,X0,X1] :
( aDivisorOf0(X0,X1)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_38])]) ).
fof(f286,plain,
! [X2,X0,X1] :
( aDivisorOf0(X0,X1)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f180]) ).
fof(f483,plain,
spl31_37,
inference(avatar_split_clause,[],[f285,f481]) ).
fof(f481,plain,
( spl31_37
<=> ! [X2,X0,X1] :
( aDivisorOf0(X0,X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_37])]) ).
fof(f285,plain,
! [X2,X0,X1] :
( aDivisorOf0(X0,X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f180]) ).
fof(f479,plain,
spl31_36,
inference(avatar_split_clause,[],[f251,f477]) ).
fof(f477,plain,
( spl31_36
<=> ! [X0,X1] :
( sP4(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_36])]) ).
fof(f251,plain,
! [X0,X1] :
( sP4(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1] :
( sP4(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f71,f112,f111]) ).
fof(f71,plain,
! [X0,X1] :
( ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSInt) ).
fof(f475,plain,
spl31_35,
inference(avatar_split_clause,[],[f215,f473]) ).
fof(f473,plain,
( spl31_35
<=> ! [X0,X1] :
( aElement0(X1)
| ~ aDivisorOf0(X1,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_35])]) ).
fof(f215,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aDivisorOf0(X1,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f471,plain,
spl31_34,
inference(avatar_split_clause,[],[f210,f469]) ).
fof(f469,plain,
( spl31_34
<=> ! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_34])]) ).
fof(f210,plain,
! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).
fof(f467,plain,
spl31_33,
inference(avatar_split_clause,[],[f209,f465]) ).
fof(f465,plain,
( spl31_33
<=> ! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_33])]) ).
fof(f209,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f463,plain,
spl31_32,
inference(avatar_split_clause,[],[f208,f461]) ).
fof(f461,plain,
( spl31_32
<=> ! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_32])]) ).
fof(f208,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(f459,plain,
spl31_31,
inference(avatar_split_clause,[],[f207,f457]) ).
fof(f457,plain,
( spl31_31
<=> ! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_31])]) ).
fof(f207,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f455,plain,
spl31_30,
inference(avatar_split_clause,[],[f206,f453]) ).
fof(f453,plain,
( spl31_30
<=> ! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_30])]) ).
fof(f206,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( aElement0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(f451,plain,
spl31_29,
inference(avatar_split_clause,[],[f205,f449]) ).
fof(f449,plain,
( spl31_29
<=> ! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_29])]) ).
fof(f205,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f447,plain,
spl31_28,
inference(avatar_split_clause,[],[f203,f445]) ).
fof(f445,plain,
( spl31_28
<=> ! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_28])]) ).
fof(f203,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f442,plain,
spl31_27,
inference(avatar_split_clause,[],[f298,f440]) ).
fof(f440,plain,
( spl31_27
<=> ! [X0] :
( sP0(X0,slsdtgt0(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_27])]) ).
fof(f298,plain,
! [X0] :
( sP0(X0,slsdtgt0(X0))
| ~ sP1(X0) ),
inference(equality_resolution,[],[f218]) ).
fof(f218,plain,
! [X0,X1] :
( sP0(X0,X1)
| slsdtgt0(X0) != X1
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f438,plain,
( ~ spl31_2
| ~ spl31_26
| ~ spl31_16
| ~ spl31_18 ),
inference(avatar_split_clause,[],[f417,f393,f386,f435,f311]) ).
fof(f435,plain,
( spl31_26
<=> xy = sdtpldt0(xx,xy) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_26])]) ).
fof(f393,plain,
( spl31_18
<=> xy = sdtasdt0(xc,xv) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_18])]) ).
fof(f417,plain,
( xy != sdtpldt0(xx,xy)
| ~ aElement0(xv)
| ~ spl31_16
| ~ spl31_18 ),
inference(superposition,[],[f387,f395]) ).
fof(f395,plain,
( xy = sdtasdt0(xc,xv)
| ~ spl31_18 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f433,plain,
spl31_25,
inference(avatar_split_clause,[],[f244,f431]) ).
fof(f431,plain,
( spl31_25
<=> ! [X2,X0,X1] :
( aSet0(X2)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_25])]) ).
fof(f244,plain,
! [X2,X0,X1] :
( aSet0(X2)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f153]) ).
fof(f428,plain,
spl31_24,
inference(avatar_split_clause,[],[f220,f426]) ).
fof(f426,plain,
( spl31_24
<=> ! [X0,X1] :
( aSet0(X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_24])]) ).
fof(f220,plain,
! [X0,X1] :
( aSet0(X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f424,plain,
spl31_23,
inference(avatar_split_clause,[],[f204,f422]) ).
fof(f422,plain,
( spl31_23
<=> ! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_23])]) ).
fof(f204,plain,
! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( aElement0(X0)
=> aElement0(smndt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsU) ).
fof(f416,plain,
spl31_22,
inference(avatar_split_clause,[],[f197,f413]) ).
fof(f413,plain,
( spl31_22
<=> xy = sdtasdt0(xc,sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_22])]) ).
fof(f197,plain,
xy = sdtasdt0(xc,sK9),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& xy = sdtasdt0(xc,sK9)
& aElement0(sK9)
& aElementOf0(xx,slsdtgt0(xc))
& xx = sdtasdt0(xc,sK10)
& aElement0(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f47,f122,f121]) ).
fof(f121,plain,
( ? [X0] :
( sdtasdt0(xc,X0) = xy
& aElement0(X0) )
=> ( xy = sdtasdt0(xc,sK9)
& aElement0(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f122,plain,
( ? [X1] :
( xx = sdtasdt0(xc,X1)
& aElement0(X1) )
=> ( xx = sdtasdt0(xc,sK10)
& aElement0(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& ? [X0] :
( sdtasdt0(xc,X0) = xy
& aElement0(X0) )
& aElementOf0(xx,slsdtgt0(xc))
& ? [X1] :
( xx = sdtasdt0(xc,X1)
& aElement0(X1) ) ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& ? [X0] :
( sdtasdt0(xc,X0) = xy
& aElement0(X0) )
& aElementOf0(xx,slsdtgt0(xc))
& ? [X0] :
( sdtasdt0(xc,X0) = xx
& aElement0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1933) ).
fof(f411,plain,
( spl31_21
| ~ spl31_1
| ~ spl31_14 ),
inference(avatar_split_clause,[],[f379,f370,f306,f408]) ).
fof(f408,plain,
( spl31_21
<=> sP1(xc) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_21])]) ).
fof(f306,plain,
( spl31_1
<=> aElement0(xc) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_1])]) ).
fof(f379,plain,
( sP1(xc)
| ~ spl31_1
| ~ spl31_14 ),
inference(resolution,[],[f371,f308]) ).
fof(f308,plain,
( aElement0(xc)
| ~ spl31_1 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f406,plain,
spl31_20,
inference(avatar_split_clause,[],[f194,f403]) ).
fof(f403,plain,
( spl31_20
<=> xx = sdtasdt0(xc,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_20])]) ).
fof(f194,plain,
xx = sdtasdt0(xc,sK10),
inference(cnf_transformation,[],[f123]) ).
fof(f401,plain,
spl31_19,
inference(avatar_split_clause,[],[f192,f398]) ).
fof(f192,plain,
xx = sdtasdt0(xc,xu),
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
( xx = sdtasdt0(xc,xu)
& aElement0(xu) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1956) ).
fof(f396,plain,
spl31_18,
inference(avatar_split_clause,[],[f190,f393]) ).
fof(f190,plain,
xy = sdtasdt0(xc,xv),
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
( xy = sdtasdt0(xc,xv)
& aElement0(xv) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1979) ).
fof(f391,plain,
( spl31_16
| spl31_17 ),
inference(avatar_split_clause,[],[f182,f389,f386]) ).
fof(f182,plain,
! [X0,X1] :
( sdtasdt0(xc,X0) != sdtasdt0(xz,xx)
| ~ aElement0(X0)
| sdtpldt0(xx,xy) != sdtasdt0(xc,X1)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
( ( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
& ! [X0] :
( sdtasdt0(xc,X0) != sdtasdt0(xz,xx)
| ~ aElement0(X0) ) )
| ( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
& ! [X1] :
( sdtpldt0(xx,xy) != sdtasdt0(xc,X1)
| ~ aElement0(X1) ) ) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,plain,
~ ( ( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ? [X0] :
( sdtasdt0(xc,X0) = sdtasdt0(xz,xx)
& aElement0(X0) ) )
& ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ? [X1] :
( sdtpldt0(xx,xy) = sdtasdt0(xc,X1)
& aElement0(X1) ) ) ),
inference(rectify,[],[f45]) ).
fof(f45,negated_conjecture,
~ ( ( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ? [X0] :
( sdtasdt0(xc,X0) = sdtasdt0(xz,xx)
& aElement0(X0) ) )
& ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ? [X0] :
( sdtasdt0(xc,X0) = sdtpldt0(xx,xy)
& aElement0(X0) ) ) ),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
( ( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ? [X0] :
( sdtasdt0(xc,X0) = sdtasdt0(xz,xx)
& aElement0(X0) ) )
& ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ? [X0] :
( sdtasdt0(xc,X0) = sdtpldt0(xx,xy)
& aElement0(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f376,plain,
spl31_15,
inference(avatar_split_clause,[],[f234,f374]) ).
fof(f374,plain,
( spl31_15
<=> ! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_15])]) ).
fof(f234,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f372,plain,
spl31_14,
inference(avatar_split_clause,[],[f227,f370]) ).
fof(f227,plain,
! [X0] :
( sP1(X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( sP1(X0)
| ~ aElement0(X0) ),
inference(definition_folding,[],[f66,f107,f106]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( slsdtgt0(X0) = X1
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& aSet0(X1) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( slsdtgt0(X0) = X1
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f368,plain,
spl31_13,
inference(avatar_split_clause,[],[f198,f365]) ).
fof(f365,plain,
( spl31_13
<=> aElementOf0(xy,slsdtgt0(xc)) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_13])]) ).
fof(f198,plain,
aElementOf0(xy,slsdtgt0(xc)),
inference(cnf_transformation,[],[f123]) ).
fof(f363,plain,
spl31_12,
inference(avatar_split_clause,[],[f195,f360]) ).
fof(f360,plain,
( spl31_12
<=> aElementOf0(xx,slsdtgt0(xc)) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_12])]) ).
fof(f195,plain,
aElementOf0(xx,slsdtgt0(xc)),
inference(cnf_transformation,[],[f123]) ).
fof(f358,plain,
~ spl31_11,
inference(avatar_split_clause,[],[f202,f355]) ).
fof(f355,plain,
( spl31_11
<=> sz00 = sz10 ),
introduced(avatar_definition,[new_symbols(naming,[spl31_11])]) ).
fof(f202,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
sz00 != sz10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnNeZr) ).
fof(f353,plain,
( ~ spl31_9
| ~ spl31_10 ),
inference(avatar_split_clause,[],[f185,f350,f346]) ).
fof(f346,plain,
( spl31_9
<=> aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_9])]) ).
fof(f350,plain,
( spl31_10
<=> aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_10])]) ).
fof(f185,plain,
( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f344,plain,
spl31_8,
inference(avatar_split_clause,[],[f201,f341]) ).
fof(f341,plain,
( spl31_8
<=> aElement0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_8])]) ).
fof(f201,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f339,plain,
spl31_7,
inference(avatar_split_clause,[],[f200,f336]) ).
fof(f336,plain,
( spl31_7
<=> aElement0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_7])]) ).
fof(f200,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f334,plain,
spl31_6,
inference(avatar_split_clause,[],[f199,f331]) ).
fof(f199,plain,
aElement0(xz),
inference(cnf_transformation,[],[f123]) ).
fof(f329,plain,
spl31_5,
inference(avatar_split_clause,[],[f196,f326]) ).
fof(f326,plain,
( spl31_5
<=> aElement0(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_5])]) ).
fof(f196,plain,
aElement0(sK9),
inference(cnf_transformation,[],[f123]) ).
fof(f324,plain,
spl31_4,
inference(avatar_split_clause,[],[f193,f321]) ).
fof(f321,plain,
( spl31_4
<=> aElement0(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl31_4])]) ).
fof(f193,plain,
aElement0(sK10),
inference(cnf_transformation,[],[f123]) ).
fof(f319,plain,
spl31_3,
inference(avatar_split_clause,[],[f191,f316]) ).
fof(f191,plain,
aElement0(xu),
inference(cnf_transformation,[],[f40]) ).
fof(f314,plain,
spl31_2,
inference(avatar_split_clause,[],[f189,f311]) ).
fof(f189,plain,
aElement0(xv),
inference(cnf_transformation,[],[f41]) ).
fof(f309,plain,
spl31_1,
inference(avatar_split_clause,[],[f186,f306]) ).
fof(f186,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
aElement0(xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1905) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG105+2 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n029.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 : Fri May 3 18:20:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (19932)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (19936)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (19935)WARNING: value z3 for option sas not known
% 0.14/0.37 % (19933)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (19934)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (19935)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (19937)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 % (19938)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 % (19939)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 % (19937)First to succeed.
% 0.14/0.40 % (19938)Also succeeded, but the first one will report.
% 0.14/0.40 % (19937)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19932"
% 0.14/0.40 % (19937)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.41 % (19937)------------------------------
% 0.14/0.41 % (19937)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.41 % (19937)Termination reason: Refutation
% 0.14/0.41
% 0.14/0.41 % (19937)Memory used [KB]: 1359
% 0.14/0.41 % (19937)Time elapsed: 0.031 s
% 0.14/0.41 % (19937)Instructions burned: 47 (million)
% 0.14/0.41 % (19932)Success in time 0.048 s
%------------------------------------------------------------------------------