TSTP Solution File: RNG112+4 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG112+4 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n028.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 : Tue May 21 02:43:15 EDT 2024
% Result : Theorem 1.48s 0.59s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 119
% Syntax : Number of formulae : 580 ( 70 unt; 0 def)
% Number of atoms : 2577 ( 488 equ)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 3034 (1037 ~;1037 |; 774 &)
% ( 84 <=>; 102 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 55 ( 53 usr; 30 prp; 0-3 aty)
% Number of functors : 55 ( 55 usr; 16 con; 0-4 aty)
% Number of variables : 1177 ( 923 !; 254 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4505,plain,
$false,
inference(avatar_sat_refutation,[],[f449,f463,f483,f490,f533,f537,f546,f586,f1312,f1315,f1333,f1336,f1853,f2114,f2123,f2368,f2371,f3967,f4081,f4084,f4225,f4265,f4492,f4501,f4504]) ).
fof(f4504,plain,
~ spl58_1,
inference(avatar_contradiction_clause,[],[f4503]) ).
fof(f4503,plain,
( $false
| ~ spl58_1 ),
inference(subsumption_resolution,[],[f4502,f499]) ).
fof(f499,plain,
( sP1(sK30)
| ~ spl58_1 ),
inference(subsumption_resolution,[],[f496,f493]) ).
fof(f493,plain,
( sz00 != sK30
| ~ spl58_1 ),
inference(subsumption_resolution,[],[f306,f443]) ).
fof(f443,plain,
( sP6
| ~ spl58_1 ),
inference(avatar_component_clause,[],[f442]) ).
fof(f442,plain,
( spl58_1
<=> sP6 ),
introduced(avatar_definition,[new_symbols(naming,[spl58_1])]) ).
fof(f306,plain,
( sz00 != sK30
| ~ sP6 ),
inference(cnf_transformation,[],[f173]) ).
fof(f173,plain,
( ( sP5(sK30)
& sz00 != sK30
& aElementOf0(sK30,xI)
& sP4(sK30) )
| ~ sP6 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f171,f172]) ).
fof(f172,plain,
( ? [X0] :
( sP5(X0)
& sz00 != X0
& aElementOf0(X0,xI)
& sP4(X0) )
=> ( sP5(sK30)
& sz00 != sK30
& aElementOf0(sK30,xI)
& sP4(sK30) ) ),
introduced(choice_axiom,[]) ).
fof(f171,plain,
( ? [X0] :
( sP5(X0)
& sz00 != X0
& aElementOf0(X0,xI)
& sP4(X0) )
| ~ sP6 ),
inference(rectify,[],[f170]) ).
fof(f170,plain,
( ? [X3] :
( sP5(X3)
& sz00 != X3
& aElementOf0(X3,xI)
& sP4(X3) )
| ~ sP6 ),
inference(nnf_transformation,[],[f126]) ).
fof(f126,plain,
( ? [X3] :
( sP5(X3)
& sz00 != X3
& aElementOf0(X3,xI)
& sP4(X3) )
| ~ sP6 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f496,plain,
( sz00 = sK30
| sP1(sK30)
| ~ spl58_1 ),
inference(resolution,[],[f253,f492]) ).
fof(f492,plain,
( aElementOf0(sK30,xI)
| ~ spl58_1 ),
inference(subsumption_resolution,[],[f305,f443]) ).
fof(f305,plain,
( aElementOf0(sK30,xI)
| ~ sP6 ),
inference(cnf_transformation,[],[f173]) ).
fof(f253,plain,
! [X0] :
( ~ aElementOf0(X0,xI)
| sz00 = X0
| sP1(X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
! [X0] :
( sP1(X0)
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f120]) ).
fof(f120,plain,
! [X0] :
( sP1(X0)
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X4,X5] :
( sdtpldt0(X4,X5) != X0
| ~ aElementOf0(X5,slsdtgt0(xb))
| ~ aElementOf0(X4,slsdtgt0(xa)) ) ) ),
inference(definition_folding,[],[f63,f119,f118]) ).
fof(f118,plain,
! [X1] :
( ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) )
| ~ sP0(X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f119,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI)
& sP0(X1) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f63,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X4,X5] :
( sdtpldt0(X4,X5) != X0
| ~ aElementOf0(X5,slsdtgt0(xb))
| ~ aElementOf0(X4,slsdtgt0(xa)) ) ) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X4,X5] :
( sdtpldt0(X4,X5) != X0
| ~ aElementOf0(X5,slsdtgt0(xb))
| ~ aElementOf0(X4,slsdtgt0(xa)) ) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
~ ? [X0] :
( ! [X1] :
( ( sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
& sz00 != X0
& ( aElementOf0(X0,xI)
| ? [X4,X5] :
( sdtpldt0(X4,X5) = X0
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f47]) ).
fof(f47,negated_conjecture,
~ ? [X0] :
( ! [X1] :
( ( sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
& sz00 != X0
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(negated_conjecture,[],[f46]) ).
fof(f46,conjecture,
? [X0] :
( ! [X1] :
( ( sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
& sz00 != X0
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f4502,plain,
( ~ sP1(sK30)
| ~ spl58_1 ),
inference(resolution,[],[f4367,f491]) ).
fof(f491,plain,
( sP5(sK30)
| ~ spl58_1 ),
inference(subsumption_resolution,[],[f307,f443]) ).
fof(f307,plain,
( sP5(sK30)
| ~ sP6 ),
inference(cnf_transformation,[],[f173]) ).
fof(f4367,plain,
! [X0] :
( ~ sP5(X0)
| ~ sP1(X0) ),
inference(subsumption_resolution,[],[f4366,f246]) ).
fof(f246,plain,
! [X0] :
( aElementOf0(sK16(X0),xI)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0] :
( ( iLess0(sbrdtbr0(sK16(X0)),sbrdtbr0(X0))
& sz00 != sK16(X0)
& aElementOf0(sK16(X0),xI)
& sP0(sK16(X0)) )
| ~ sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f143,f144]) ).
fof(f144,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI)
& sP0(X1) )
=> ( iLess0(sbrdtbr0(sK16(X0)),sbrdtbr0(X0))
& sz00 != sK16(X0)
& aElementOf0(sK16(X0),xI)
& sP0(sK16(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f143,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI)
& sP0(X1) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f4366,plain,
! [X0] :
( ~ aElementOf0(sK16(X0),xI)
| ~ sP5(X0)
| ~ sP1(X0) ),
inference(subsumption_resolution,[],[f4365,f247]) ).
fof(f247,plain,
! [X0] :
( sz00 != sK16(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f4365,plain,
! [X0] :
( sz00 = sK16(X0)
| ~ aElementOf0(sK16(X0),xI)
| ~ sP5(X0)
| ~ sP1(X0) ),
inference(resolution,[],[f309,f248]) ).
fof(f248,plain,
! [X0] :
( iLess0(sbrdtbr0(sK16(X0)),sbrdtbr0(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f309,plain,
! [X0,X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
| sz00 = X1
| ~ aElementOf0(X1,xI)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f175,plain,
! [X0] :
( ! [X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
| sz00 = X1
| ( ~ aElementOf0(X1,xI)
& ! [X2,X3] :
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa)) ) ) )
| ~ sP5(X0) ),
inference(rectify,[],[f174]) ).
fof(f174,plain,
! [X3] :
( ! [X4] :
( ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3))
| sz00 = X4
| ( ~ aElementOf0(X4,xI)
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) )
| ~ sP5(X3) ),
inference(nnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X3] :
( ! [X4] :
( ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3))
| sz00 = X4
| ( ~ aElementOf0(X4,xI)
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) )
| ~ sP5(X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f4501,plain,
( spl58_27
| spl58_28
| ~ spl58_6 ),
inference(avatar_split_clause,[],[f4429,f530,f4498,f4494]) ).
fof(f4494,plain,
( spl58_27
<=> sP1(sK34) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_27])]) ).
fof(f4498,plain,
( spl58_28
<=> sz00 = sK34 ),
introduced(avatar_definition,[new_symbols(naming,[spl58_28])]) ).
fof(f530,plain,
( spl58_6
<=> aElement0(sK34) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_6])]) ).
fof(f4429,plain,
( sz00 = sK34
| sP1(sK34)
| ~ spl58_6 ),
inference(resolution,[],[f4292,f253]) ).
fof(f4292,plain,
( aElementOf0(sK34,xI)
| ~ spl58_6 ),
inference(subsumption_resolution,[],[f4291,f321]) ).
fof(f321,plain,
aElementOf0(sK34,slsdtgt0(xa)),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
( sz00 != sK33
& aElementOf0(sK33,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& sK33 = sdtpldt0(sK34,sK35)
& aElementOf0(sK35,slsdtgt0(xb))
& aElementOf0(sK34,slsdtgt0(xa))
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ( sdtasdt0(xb,sK36(X3)) = X3
& aElement0(sK36(X3)) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xa))
| ! [X7] :
( sdtasdt0(xa,X7) != X6
| ~ aElement0(X7) ) )
& ( ( sdtasdt0(xa,sK37(X6)) = X6
& aElement0(sK37(X6)) )
| ~ aElementOf0(X6,slsdtgt0(xa)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34,sK35,sK36,sK37])],[f181,f185,f184,f183,f182]) ).
fof(f182,plain,
( ? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X5] :
( sdtasdt0(xb,X5) = X3
& aElement0(X5) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xa))
| ! [X7] :
( sdtasdt0(xa,X7) != X6
| ~ aElement0(X7) ) )
& ( ? [X8] :
( sdtasdt0(xa,X8) = X6
& aElement0(X8) )
| ~ aElementOf0(X6,slsdtgt0(xa)) ) ) )
=> ( sz00 != sK33
& aElementOf0(sK33,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X2,X1] :
( sdtpldt0(X1,X2) = sK33
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X5] :
( sdtasdt0(xb,X5) = X3
& aElement0(X5) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xa))
| ! [X7] :
( sdtasdt0(xa,X7) != X6
| ~ aElement0(X7) ) )
& ( ? [X8] :
( sdtasdt0(xa,X8) = X6
& aElement0(X8) )
| ~ aElementOf0(X6,slsdtgt0(xa)) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f183,plain,
( ? [X2,X1] :
( sdtpldt0(X1,X2) = sK33
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
=> ( sK33 = sdtpldt0(sK34,sK35)
& aElementOf0(sK35,slsdtgt0(xb))
& aElementOf0(sK34,slsdtgt0(xa)) ) ),
introduced(choice_axiom,[]) ).
fof(f184,plain,
! [X3] :
( ? [X5] :
( sdtasdt0(xb,X5) = X3
& aElement0(X5) )
=> ( sdtasdt0(xb,sK36(X3)) = X3
& aElement0(sK36(X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f185,plain,
! [X6] :
( ? [X8] :
( sdtasdt0(xa,X8) = X6
& aElement0(X8) )
=> ( sdtasdt0(xa,sK37(X6)) = X6
& aElement0(sK37(X6)) ) ),
introduced(choice_axiom,[]) ).
fof(f181,plain,
? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X5] :
( sdtasdt0(xb,X5) = X3
& aElement0(X5) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xa))
| ! [X7] :
( sdtasdt0(xa,X7) != X6
| ~ aElement0(X7) ) )
& ( ? [X8] :
( sdtasdt0(xa,X8) = X6
& aElement0(X8) )
| ~ aElementOf0(X6,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f180]) ).
fof(f180,plain,
? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xa))
| ! [X6] :
( sdtasdt0(xa,X6) != X5
| ~ aElement0(X6) ) )
& ( ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) )
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f53,plain,
? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xa))
<=> ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) ) ) ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( sdtasdt0(xb,X2) = X1
& aElement0(X2) ) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( sdtasdt0(xa,X2) = X1
& aElement0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2228) ).
fof(f4291,plain,
( aElementOf0(sK34,xI)
| ~ aElementOf0(sK34,slsdtgt0(xa))
| ~ spl58_6 ),
inference(subsumption_resolution,[],[f4207,f299]) ).
fof(f299,plain,
aElementOf0(sz00,slsdtgt0(xb)),
inference(cnf_transformation,[],[f169]) ).
fof(f169,plain,
( aElementOf0(xb,slsdtgt0(xb))
& xb = sdtasdt0(xb,sK26)
& aElement0(sK26)
& aElementOf0(sz00,slsdtgt0(xb))
& sz00 = sdtasdt0(xb,sK27)
& aElement0(sK27)
& aElementOf0(xa,slsdtgt0(xa))
& xa = sdtasdt0(xa,sK28)
& aElement0(sK28)
& aElementOf0(sz00,slsdtgt0(xa))
& sz00 = sdtasdt0(xa,sK29)
& aElement0(sK29) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27,sK28,sK29])],[f51,f168,f167,f166,f165]) ).
fof(f165,plain,
( ? [X0] :
( xb = sdtasdt0(xb,X0)
& aElement0(X0) )
=> ( xb = sdtasdt0(xb,sK26)
& aElement0(sK26) ) ),
introduced(choice_axiom,[]) ).
fof(f166,plain,
( ? [X1] :
( sz00 = sdtasdt0(xb,X1)
& aElement0(X1) )
=> ( sz00 = sdtasdt0(xb,sK27)
& aElement0(sK27) ) ),
introduced(choice_axiom,[]) ).
fof(f167,plain,
( ? [X2] :
( xa = sdtasdt0(xa,X2)
& aElement0(X2) )
=> ( xa = sdtasdt0(xa,sK28)
& aElement0(sK28) ) ),
introduced(choice_axiom,[]) ).
fof(f168,plain,
( ? [X3] :
( sz00 = sdtasdt0(xa,X3)
& aElement0(X3) )
=> ( sz00 = sdtasdt0(xa,sK29)
& aElement0(sK29) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
( aElementOf0(xb,slsdtgt0(xb))
& ? [X0] :
( xb = sdtasdt0(xb,X0)
& aElement0(X0) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [X1] :
( sz00 = sdtasdt0(xb,X1)
& aElement0(X1) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [X2] :
( xa = sdtasdt0(xa,X2)
& aElement0(X2) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [X3] :
( sz00 = sdtasdt0(xa,X3)
& aElement0(X3) ) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
( aElementOf0(xb,slsdtgt0(xb))
& ? [X0] :
( xb = sdtasdt0(xb,X0)
& aElement0(X0) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [X0] :
( sz00 = sdtasdt0(xb,X0)
& aElement0(X0) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [X0] :
( xa = sdtasdt0(xa,X0)
& aElement0(X0) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [X0] :
( sz00 = sdtasdt0(xa,X0)
& aElement0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).
fof(f4207,plain,
( aElementOf0(sK34,xI)
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(sK34,slsdtgt0(xa))
| ~ spl58_6 ),
inference(superposition,[],[f427,f653]) ).
fof(f653,plain,
( sK34 = sdtpldt0(sK34,sz00)
| ~ spl58_6 ),
inference(resolution,[],[f334,f532]) ).
fof(f532,plain,
( aElement0(sK34)
| ~ spl58_6 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f334,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,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/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(f427,plain,
! [X2,X1] :
( aElementOf0(sdtpldt0(X1,X2),xI)
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(equality_resolution,[],[f267]) ).
fof(f267,plain,
! [X2,X0,X1] :
( aElementOf0(X0,xI)
| sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( ( aElementOf0(X0,xI)
| ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
& ( ( sdtpldt0(sK19(X0),sK20(X0)) = X0
& aElementOf0(sK20(X0),slsdtgt0(xb))
& aElementOf0(sK19(X0),slsdtgt0(xa)) )
| ~ aElementOf0(X0,xI) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xb))
| ! [X6] :
( sdtasdt0(xb,X6) != X5
| ~ aElement0(X6) ) )
& ( ( sdtasdt0(xb,sK21(X5)) = X5
& aElement0(sK21(X5)) )
| ~ aElementOf0(X5,slsdtgt0(xb)) ) )
& ! [X8] :
( ( aElementOf0(X8,slsdtgt0(xa))
| ! [X9] :
( sdtasdt0(xa,X9) != X8
| ~ aElement0(X9) ) )
& ( ( sdtasdt0(xa,sK22(X8)) = X8
& aElement0(sK22(X8)) )
| ~ aElementOf0(X8,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X11] :
( ( ! [X12] :
( aElementOf0(sdtasdt0(X12,X11),xI)
| ~ aElement0(X12) )
& ! [X13] :
( aElementOf0(sdtpldt0(X11,X13),xI)
| ~ aElementOf0(X13,xI) ) )
| ~ aElementOf0(X11,xI) )
& aSet0(xI) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20,sK21,sK22])],[f152,f155,f154,f153]) ).
fof(f153,plain,
! [X0] :
( ? [X3,X4] :
( sdtpldt0(X3,X4) = X0
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) )
=> ( sdtpldt0(sK19(X0),sK20(X0)) = X0
& aElementOf0(sK20(X0),slsdtgt0(xb))
& aElementOf0(sK19(X0),slsdtgt0(xa)) ) ),
introduced(choice_axiom,[]) ).
fof(f154,plain,
! [X5] :
( ? [X7] :
( sdtasdt0(xb,X7) = X5
& aElement0(X7) )
=> ( sdtasdt0(xb,sK21(X5)) = X5
& aElement0(sK21(X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f155,plain,
! [X8] :
( ? [X10] :
( sdtasdt0(xa,X10) = X8
& aElement0(X10) )
=> ( sdtasdt0(xa,sK22(X8)) = X8
& aElement0(sK22(X8)) ) ),
introduced(choice_axiom,[]) ).
fof(f152,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( ( aElementOf0(X0,xI)
| ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
& ( ? [X3,X4] :
( sdtpldt0(X3,X4) = X0
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) )
| ~ aElementOf0(X0,xI) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xb))
| ! [X6] :
( sdtasdt0(xb,X6) != X5
| ~ aElement0(X6) ) )
& ( ? [X7] :
( sdtasdt0(xb,X7) = X5
& aElement0(X7) )
| ~ aElementOf0(X5,slsdtgt0(xb)) ) )
& ! [X8] :
( ( aElementOf0(X8,slsdtgt0(xa))
| ! [X9] :
( sdtasdt0(xa,X9) != X8
| ~ aElement0(X9) ) )
& ( ? [X10] :
( sdtasdt0(xa,X10) = X8
& aElement0(X10) )
| ~ aElementOf0(X8,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X11] :
( ( ! [X12] :
( aElementOf0(sdtasdt0(X12,X11),xI)
| ~ aElement0(X12) )
& ! [X13] :
( aElementOf0(sdtpldt0(X11,X13),xI)
| ~ aElementOf0(X13,xI) ) )
| ~ aElementOf0(X11,xI) )
& aSet0(xI) ),
inference(rectify,[],[f151]) ).
fof(f151,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( ( aElementOf0(X0,xI)
| ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
& ( ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
| ~ aElementOf0(X0,xI) ) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xa))
| ! [X6] :
( sdtasdt0(xa,X6) != X5
| ~ aElement0(X6) ) )
& ( ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) )
| ~ aElementOf0(X5,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X7] :
( ( ! [X8] :
( aElementOf0(sdtasdt0(X8,X7),xI)
| ~ aElement0(X8) )
& ! [X9] :
( aElementOf0(sdtpldt0(X7,X9),xI)
| ~ aElementOf0(X9,xI) ) )
| ~ aElementOf0(X7,xI) )
& aSet0(xI) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xa))
<=> ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) ) )
& aIdeal0(xI)
& ! [X7] :
( ( ! [X8] :
( aElementOf0(sdtasdt0(X8,X7),xI)
| ~ aElement0(X8) )
& ! [X9] :
( aElementOf0(sdtpldt0(X7,X9),xI)
| ~ aElementOf0(X9,xI) ) )
| ~ aElementOf0(X7,xI) )
& aSet0(xI) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xa))
<=> ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) ) )
& aIdeal0(xI)
& ! [X7] :
( aElementOf0(X7,xI)
=> ( ! [X8] :
( aElement0(X8)
=> aElementOf0(sdtasdt0(X8,X7),xI) )
& ! [X9] :
( aElementOf0(X9,xI)
=> aElementOf0(sdtpldt0(X7,X9),xI) ) ) )
& aSet0(xI) ),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xb))
<=> ? [X1] :
( sdtasdt0(xb,X1) = X0
& aElement0(X1) ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( sdtasdt0(xa,X1) = X0
& aElement0(X1) ) )
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) )
& ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(f4492,plain,
( spl58_25
| spl58_26
| ~ spl58_8 ),
inference(avatar_split_clause,[],[f4424,f543,f4489,f4485]) ).
fof(f4485,plain,
( spl58_25
<=> sP1(sK35) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_25])]) ).
fof(f4489,plain,
( spl58_26
<=> sz00 = sK35 ),
introduced(avatar_definition,[new_symbols(naming,[spl58_26])]) ).
fof(f543,plain,
( spl58_8
<=> aElement0(sK35) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_8])]) ).
fof(f4424,plain,
( sz00 = sK35
| sP1(sK35)
| ~ spl58_8 ),
inference(resolution,[],[f4251,f253]) ).
fof(f4251,plain,
( aElementOf0(sK35,xI)
| ~ spl58_8 ),
inference(subsumption_resolution,[],[f4250,f293]) ).
fof(f293,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cnf_transformation,[],[f169]) ).
fof(f4250,plain,
( aElementOf0(sK35,xI)
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ spl58_8 ),
inference(subsumption_resolution,[],[f4150,f322]) ).
fof(f322,plain,
aElementOf0(sK35,slsdtgt0(xb)),
inference(cnf_transformation,[],[f186]) ).
fof(f4150,plain,
( aElementOf0(sK35,xI)
| ~ aElementOf0(sK35,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ spl58_8 ),
inference(superposition,[],[f427,f692]) ).
fof(f692,plain,
( sK35 = sdtpldt0(sz00,sK35)
| ~ spl58_8 ),
inference(resolution,[],[f335,f545]) ).
fof(f545,plain,
( aElement0(sK35)
| ~ spl58_8 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f335,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f73]) ).
fof(f4265,plain,
spl58_16,
inference(avatar_contradiction_clause,[],[f4264]) ).
fof(f4264,plain,
( $false
| spl58_16 ),
inference(subsumption_resolution,[],[f4263,f296]) ).
fof(f296,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(cnf_transformation,[],[f169]) ).
fof(f4263,plain,
( ~ aElementOf0(xa,slsdtgt0(xa))
| spl58_16 ),
inference(subsumption_resolution,[],[f4262,f299]) ).
fof(f4262,plain,
( ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| spl58_16 ),
inference(subsumption_resolution,[],[f4174,f2112]) ).
fof(f2112,plain,
( ~ aElementOf0(xa,xI)
| spl58_16 ),
inference(avatar_component_clause,[],[f2111]) ).
fof(f2111,plain,
( spl58_16
<=> aElementOf0(xa,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_16])]) ).
fof(f4174,plain,
( aElementOf0(xa,xI)
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa)) ),
inference(superposition,[],[f427,f630]) ).
fof(f630,plain,
xa = sdtpldt0(xa,sz00),
inference(resolution,[],[f334,f289]) ).
fof(f289,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(f4225,plain,
spl58_18,
inference(avatar_contradiction_clause,[],[f4224]) ).
fof(f4224,plain,
( $false
| spl58_18 ),
inference(subsumption_resolution,[],[f4223,f293]) ).
fof(f4223,plain,
( ~ aElementOf0(sz00,slsdtgt0(xa))
| spl58_18 ),
inference(subsumption_resolution,[],[f4222,f302]) ).
fof(f302,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[],[f169]) ).
fof(f4222,plain,
( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xa))
| spl58_18 ),
inference(subsumption_resolution,[],[f4129,f2121]) ).
fof(f2121,plain,
( ~ aElementOf0(xb,xI)
| spl58_18 ),
inference(avatar_component_clause,[],[f2120]) ).
fof(f2120,plain,
( spl58_18
<=> aElementOf0(xb,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_18])]) ).
fof(f4129,plain,
( aElementOf0(xb,xI)
| ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xa)) ),
inference(superposition,[],[f427,f669]) ).
fof(f669,plain,
xb = sdtpldt0(sz00,xb),
inference(resolution,[],[f335,f290]) ).
fof(f290,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f4084,plain,
spl58_23,
inference(avatar_contradiction_clause,[],[f4083]) ).
fof(f4083,plain,
( $false
| spl58_23 ),
inference(subsumption_resolution,[],[f4082,f275]) ).
fof(f275,plain,
aElement0(xc),
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
( aGcdOfAnd0(xc,xa,xb)
& ! [X0] :
( ( doDivides0(X0,xc)
& xc = sdtasdt0(X0,sK23(X0))
& aElement0(sK23(X0)) )
| sP3(X0)
| sP2(X0) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& xb = sdtasdt0(xc,sK24)
& aElement0(sK24)
& aElement0(xc)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& xa = sdtasdt0(xc,sK25)
& aElement0(sK25)
& aElement0(xc) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24,sK25])],[f160,f163,f162,f161]) ).
fof(f161,plain,
! [X0] :
( ? [X1] :
( sdtasdt0(X0,X1) = xc
& aElement0(X1) )
=> ( xc = sdtasdt0(X0,sK23(X0))
& aElement0(sK23(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f162,plain,
( ? [X2] :
( xb = sdtasdt0(xc,X2)
& aElement0(X2) )
=> ( xb = sdtasdt0(xc,sK24)
& aElement0(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f163,plain,
( ? [X3] :
( xa = sdtasdt0(xc,X3)
& aElement0(X3) )
=> ( xa = sdtasdt0(xc,sK25)
& aElement0(sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
( aGcdOfAnd0(xc,xa,xb)
& ! [X0] :
( ( doDivides0(X0,xc)
& ? [X1] :
( sdtasdt0(X0,X1) = xc
& aElement0(X1) ) )
| sP3(X0)
| sP2(X0) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& ? [X2] :
( xb = sdtasdt0(xc,X2)
& aElement0(X2) )
& aElement0(xc)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& ? [X3] :
( xa = sdtasdt0(xc,X3)
& aElement0(X3) )
& aElement0(xc) ),
inference(rectify,[],[f123]) ).
fof(f123,plain,
( aGcdOfAnd0(xc,xa,xb)
& ! [X0] :
( ( doDivides0(X0,xc)
& ? [X3] :
( sdtasdt0(X0,X3) = xc
& aElement0(X3) ) )
| sP3(X0)
| sP2(X0) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& ? [X4] :
( xb = sdtasdt0(xc,X4)
& aElement0(X4) )
& aElement0(xc)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& ? [X5] :
( xa = sdtasdt0(xc,X5)
& aElement0(X5) )
& aElement0(xc) ),
inference(definition_folding,[],[f66,f122,f121]) ).
fof(f121,plain,
! [X0] :
( ( ~ aDivisorOf0(X0,xa)
& ( ( ~ doDivides0(X0,xa)
& ! [X2] :
( sdtasdt0(X0,X2) != xa
| ~ aElement0(X2) ) )
| ~ aElement0(X0) ) )
| ~ sP2(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f122,plain,
! [X0] :
( ( ~ aDivisorOf0(X0,xb)
& ~ doDivides0(X0,xb)
& ! [X1] :
( sdtasdt0(X0,X1) != xb
| ~ aElement0(X1) ) )
| ~ sP3(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f66,plain,
( aGcdOfAnd0(xc,xa,xb)
& ! [X0] :
( ( doDivides0(X0,xc)
& ? [X3] :
( sdtasdt0(X0,X3) = xc
& aElement0(X3) ) )
| ( ~ aDivisorOf0(X0,xb)
& ~ doDivides0(X0,xb)
& ! [X1] :
( sdtasdt0(X0,X1) != xb
| ~ aElement0(X1) ) )
| ( ~ aDivisorOf0(X0,xa)
& ( ( ~ doDivides0(X0,xa)
& ! [X2] :
( sdtasdt0(X0,X2) != xa
| ~ aElement0(X2) ) )
| ~ aElement0(X0) ) ) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& ? [X4] :
( xb = sdtasdt0(xc,X4)
& aElement0(X4) )
& aElement0(xc)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& ? [X5] :
( xa = sdtasdt0(xc,X5)
& aElement0(X5) )
& aElement0(xc) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
( aGcdOfAnd0(xc,xa,xb)
& ! [X0] :
( ( doDivides0(X0,xc)
& ? [X3] :
( sdtasdt0(X0,X3) = xc
& aElement0(X3) ) )
| ( ~ aDivisorOf0(X0,xb)
& ~ doDivides0(X0,xb)
& ! [X1] :
( sdtasdt0(X0,X1) != xb
| ~ aElement0(X1) ) )
| ( ~ aDivisorOf0(X0,xa)
& ( ( ~ doDivides0(X0,xa)
& ! [X2] :
( sdtasdt0(X0,X2) != xa
| ~ aElement0(X2) ) )
| ~ aElement0(X0) ) ) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& ? [X4] :
( xb = sdtasdt0(xc,X4)
& aElement0(X4) )
& aElement0(xc)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& ? [X5] :
( xa = sdtasdt0(xc,X5)
& aElement0(X5) )
& aElement0(xc) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,plain,
( aGcdOfAnd0(xc,xa,xb)
& ! [X0] :
( ( ( aDivisorOf0(X0,xb)
| doDivides0(X0,xb)
| ? [X1] :
( sdtasdt0(X0,X1) = xb
& aElement0(X1) ) )
& ( aDivisorOf0(X0,xa)
| ( ( doDivides0(X0,xa)
| ? [X2] :
( sdtasdt0(X0,X2) = xa
& aElement0(X2) ) )
& aElement0(X0) ) ) )
=> ( doDivides0(X0,xc)
& ? [X3] :
( sdtasdt0(X0,X3) = xc
& aElement0(X3) ) ) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& ? [X4] :
( xb = sdtasdt0(xc,X4)
& aElement0(X4) )
& aElement0(xc)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& ? [X5] :
( xa = sdtasdt0(xc,X5)
& aElement0(X5) )
& aElement0(xc) ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
( aGcdOfAnd0(xc,xa,xb)
& ! [X0] :
( ( ( aDivisorOf0(X0,xb)
| doDivides0(X0,xb)
| ? [X1] :
( sdtasdt0(X0,X1) = xb
& aElement0(X1) ) )
& ( aDivisorOf0(X0,xa)
| ( ( doDivides0(X0,xa)
| ? [X1] :
( sdtasdt0(X0,X1) = xa
& aElement0(X1) ) )
& aElement0(X0) ) ) )
=> ( doDivides0(X0,xc)
& ? [X1] :
( sdtasdt0(X0,X1) = xc
& aElement0(X1) ) ) )
& aDivisorOf0(xc,xb)
& doDivides0(xc,xb)
& ? [X0] :
( xb = sdtasdt0(xc,X0)
& aElement0(X0) )
& aElement0(xc)
& aDivisorOf0(xc,xa)
& doDivides0(xc,xa)
& ? [X0] :
( xa = sdtasdt0(xc,X0)
& aElement0(X0) )
& aElement0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2129) ).
fof(f4082,plain,
( ~ aElement0(xc)
| spl58_23 ),
inference(resolution,[],[f4076,f354]) ).
fof(f354,plain,
! [X0] :
( sP8(X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0] :
( sP8(X0)
| ~ aElement0(X0) ),
inference(definition_folding,[],[f78,f129,f128]) ).
fof(f128,plain,
! [X0,X1] :
( sP7(X0,X1)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& aSet0(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( slsdtgt0(X0) = X1
<=> sP7(X0,X1) )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f78,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/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f4076,plain,
( ~ sP8(xc)
| spl58_23 ),
inference(avatar_component_clause,[],[f4074]) ).
fof(f4074,plain,
( spl58_23
<=> sP8(xc) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_23])]) ).
fof(f4081,plain,
( ~ spl58_23
| spl58_24 ),
inference(avatar_split_clause,[],[f3194,f4078,f4074]) ).
fof(f4078,plain,
( spl58_24
<=> aElementOf0(xb,slsdtgt0(xc)) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_24])]) ).
fof(f3194,plain,
( aElementOf0(xb,slsdtgt0(xc))
| ~ sP8(xc) ),
inference(resolution,[],[f3134,f434]) ).
fof(f434,plain,
! [X0] :
( sP7(X0,slsdtgt0(X0))
| ~ sP8(X0) ),
inference(equality_resolution,[],[f345]) ).
fof(f345,plain,
! [X0,X1] :
( sP7(X0,X1)
| slsdtgt0(X0) != X1
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f189]) ).
fof(f189,plain,
! [X0] :
( ! [X1] :
( ( slsdtgt0(X0) = X1
| ~ sP7(X0,X1) )
& ( sP7(X0,X1)
| slsdtgt0(X0) != X1 ) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f129]) ).
fof(f3134,plain,
! [X0] :
( ~ sP7(xc,X0)
| aElementOf0(xb,X0) ),
inference(subsumption_resolution,[],[f2962,f281]) ).
fof(f281,plain,
aElement0(sK24),
inference(cnf_transformation,[],[f164]) ).
fof(f2962,plain,
! [X0] :
( aElementOf0(xb,X0)
| ~ aElement0(sK24)
| ~ sP7(xc,X0) ),
inference(superposition,[],[f435,f282]) ).
fof(f282,plain,
xb = sdtasdt0(xc,sK24),
inference(cnf_transformation,[],[f164]) ).
fof(f435,plain,
! [X0,X1,X6] :
( aElementOf0(sdtasdt0(X0,X6),X1)
| ~ aElement0(X6)
| ~ sP7(X0,X1) ),
inference(equality_resolution,[],[f350]) ).
fof(f350,plain,
! [X0,X1,X6,X5] :
( aElementOf0(X5,X1)
| sdtasdt0(X0,X6) != X5
| ~ aElement0(X6)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0,X1] :
( ( sP7(X0,X1)
| ( ( ! [X3] :
( sdtasdt0(X0,X3) != sK38(X0,X1)
| ~ aElement0(X3) )
| ~ aElementOf0(sK38(X0,X1),X1) )
& ( ( sK38(X0,X1) = sdtasdt0(X0,sK39(X0,X1))
& aElement0(sK39(X0,X1)) )
| aElementOf0(sK38(X0,X1),X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) ) )
& ( ( sdtasdt0(X0,sK40(X0,X5)) = X5
& aElement0(sK40(X0,X5)) )
| ~ aElementOf0(X5,X1) ) )
& aSet0(X1) )
| ~ sP7(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39,sK40])],[f192,f195,f194,f193]) ).
fof(f193,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) != sK38(X0,X1)
| ~ aElement0(X3) )
| ~ aElementOf0(sK38(X0,X1),X1) )
& ( ? [X4] :
( sdtasdt0(X0,X4) = sK38(X0,X1)
& aElement0(X4) )
| aElementOf0(sK38(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f194,plain,
! [X0,X1] :
( ? [X4] :
( sdtasdt0(X0,X4) = sK38(X0,X1)
& aElement0(X4) )
=> ( sK38(X0,X1) = sdtasdt0(X0,sK39(X0,X1))
& aElement0(sK39(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f195,plain,
! [X0,X5] :
( ? [X7] :
( sdtasdt0(X0,X7) = X5
& aElement0(X7) )
=> ( sdtasdt0(X0,sK40(X0,X5)) = X5
& aElement0(sK40(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f192,plain,
! [X0,X1] :
( ( sP7(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) )
| ~ sP7(X0,X1) ) ),
inference(rectify,[],[f191]) ).
fof(f191,plain,
! [X0,X1] :
( ( sP7(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) )
| ~ sP7(X0,X1) ) ),
inference(flattening,[],[f190]) ).
fof(f190,plain,
! [X0,X1] :
( ( sP7(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) )
| ~ sP7(X0,X1) ) ),
inference(nnf_transformation,[],[f128]) ).
fof(f3967,plain,
( ~ spl58_21
| ~ spl58_22 ),
inference(avatar_split_clause,[],[f3613,f3964,f3960]) ).
fof(f3960,plain,
( spl58_21
<=> sP2(xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_21])]) ).
fof(f3964,plain,
( spl58_22
<=> xa = sK35 ),
introduced(avatar_definition,[new_symbols(naming,[spl58_22])]) ).
fof(f3613,plain,
( xa != sK35
| ~ sP2(xb) ),
inference(subsumption_resolution,[],[f3612,f290]) ).
fof(f3612,plain,
( xa != sK35
| ~ aElement0(xb)
| ~ sP2(xb) ),
inference(subsumption_resolution,[],[f3418,f473]) ).
fof(f473,plain,
aElement0(sK21(sK35)),
inference(resolution,[],[f261,f322]) ).
fof(f261,plain,
! [X5] :
( ~ aElementOf0(X5,slsdtgt0(xb))
| aElement0(sK21(X5)) ),
inference(cnf_transformation,[],[f156]) ).
fof(f3418,plain,
( xa != sK35
| ~ aElement0(sK21(sK35))
| ~ aElement0(xb)
| ~ sP2(xb) ),
inference(superposition,[],[f272,f2131]) ).
fof(f2131,plain,
sK35 = sdtasdt0(xb,sK21(sK35)),
inference(resolution,[],[f262,f322]) ).
fof(f262,plain,
! [X5] :
( ~ aElementOf0(X5,slsdtgt0(xb))
| sdtasdt0(xb,sK21(X5)) = X5 ),
inference(cnf_transformation,[],[f156]) ).
fof(f272,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) != xa
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f159]) ).
fof(f159,plain,
! [X0] :
( ( ~ aDivisorOf0(X0,xa)
& ( ( ~ doDivides0(X0,xa)
& ! [X1] :
( sdtasdt0(X0,X1) != xa
| ~ aElement0(X1) ) )
| ~ aElement0(X0) ) )
| ~ sP2(X0) ),
inference(rectify,[],[f158]) ).
fof(f158,plain,
! [X0] :
( ( ~ aDivisorOf0(X0,xa)
& ( ( ~ doDivides0(X0,xa)
& ! [X2] :
( sdtasdt0(X0,X2) != xa
| ~ aElement0(X2) ) )
| ~ aElement0(X0) ) )
| ~ sP2(X0) ),
inference(nnf_transformation,[],[f121]) ).
fof(f2371,plain,
spl58_19,
inference(avatar_contradiction_clause,[],[f2370]) ).
fof(f2370,plain,
( $false
| spl58_19 ),
inference(subsumption_resolution,[],[f2369,f326]) ).
fof(f326,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f2369,plain,
( ~ aElement0(sz10)
| spl58_19 ),
inference(resolution,[],[f2363,f331]) ).
fof(f331,plain,
! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( aElement0(X0)
=> aElement0(smndt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).
fof(f2363,plain,
( ~ aElement0(smndt0(sz10))
| spl58_19 ),
inference(avatar_component_clause,[],[f2361]) ).
fof(f2361,plain,
( spl58_19
<=> aElement0(smndt0(sz10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_19])]) ).
fof(f2368,plain,
( ~ spl58_19
| spl58_20
| ~ spl58_5 ),
inference(avatar_split_clause,[],[f2353,f526,f2365,f2361]) ).
fof(f2365,plain,
( spl58_20
<=> aElement0(smndt0(xa)) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_20])]) ).
fof(f526,plain,
( spl58_5
<=> aSet0(slsdtgt0(xa)) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_5])]) ).
fof(f2353,plain,
( aElement0(smndt0(xa))
| ~ aElement0(smndt0(sz10))
| ~ spl58_5 ),
inference(superposition,[],[f900,f1786]) ).
fof(f1786,plain,
smndt0(xa) = sdtasdt0(xa,smndt0(sz10)),
inference(resolution,[],[f341,f289]) ).
fof(f341,plain,
! [X0] :
( ~ aElement0(X0)
| smndt0(X0) = sdtasdt0(X0,smndt0(sz10)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,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/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).
fof(f900,plain,
( ! [X0] :
( aElement0(sdtasdt0(xa,X0))
| ~ aElement0(X0) )
| ~ spl58_5 ),
inference(subsumption_resolution,[],[f895,f527]) ).
fof(f527,plain,
( aSet0(slsdtgt0(xa))
| ~ spl58_5 ),
inference(avatar_component_clause,[],[f526]) ).
fof(f895,plain,
! [X0] :
( ~ aElement0(X0)
| aElement0(sdtasdt0(xa,X0))
| ~ aSet0(slsdtgt0(xa)) ),
inference(resolution,[],[f429,f329]) ).
fof(f329,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,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/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f429,plain,
! [X9] :
( aElementOf0(sdtasdt0(xa,X9),slsdtgt0(xa))
| ~ aElement0(X9) ),
inference(equality_resolution,[],[f260]) ).
fof(f260,plain,
! [X8,X9] :
( aElementOf0(X8,slsdtgt0(xa))
| sdtasdt0(xa,X9) != X8
| ~ aElement0(X9) ),
inference(cnf_transformation,[],[f156]) ).
fof(f2123,plain,
( ~ spl58_17
| spl58_18 ),
inference(avatar_split_clause,[],[f2042,f2120,f2116]) ).
fof(f2116,plain,
( spl58_17
<=> aElementOf0(sK26,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_17])]) ).
fof(f2042,plain,
( aElementOf0(xb,xI)
| ~ aElementOf0(sK26,xI) ),
inference(subsumption_resolution,[],[f1938,f290]) ).
fof(f1938,plain,
( aElementOf0(xb,xI)
| ~ aElement0(xb)
| ~ aElementOf0(sK26,xI) ),
inference(superposition,[],[f256,f301]) ).
fof(f301,plain,
xb = sdtasdt0(xb,sK26),
inference(cnf_transformation,[],[f169]) ).
fof(f256,plain,
! [X11,X12] :
( aElementOf0(sdtasdt0(X12,X11),xI)
| ~ aElement0(X12)
| ~ aElementOf0(X11,xI) ),
inference(cnf_transformation,[],[f156]) ).
fof(f2114,plain,
( ~ spl58_15
| spl58_16 ),
inference(avatar_split_clause,[],[f2038,f2111,f2107]) ).
fof(f2107,plain,
( spl58_15
<=> aElementOf0(sK28,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_15])]) ).
fof(f2038,plain,
( aElementOf0(xa,xI)
| ~ aElementOf0(sK28,xI) ),
inference(subsumption_resolution,[],[f1934,f289]) ).
fof(f1934,plain,
( aElementOf0(xa,xI)
| ~ aElement0(xa)
| ~ aElementOf0(sK28,xI) ),
inference(superposition,[],[f256,f295]) ).
fof(f295,plain,
xa = sdtasdt0(xa,sK28),
inference(cnf_transformation,[],[f169]) ).
fof(f1853,plain,
( ~ spl58_13
| ~ spl58_14 ),
inference(avatar_split_clause,[],[f1634,f1850,f1846]) ).
fof(f1846,plain,
( spl58_13
<=> sP3(xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_13])]) ).
fof(f1850,plain,
( spl58_14
<=> xa = xb ),
introduced(avatar_definition,[new_symbols(naming,[spl58_14])]) ).
fof(f1634,plain,
( xa != xb
| ~ sP3(xa) ),
inference(subsumption_resolution,[],[f1510,f294]) ).
fof(f294,plain,
aElement0(sK28),
inference(cnf_transformation,[],[f169]) ).
fof(f1510,plain,
( xa != xb
| ~ aElement0(sK28)
| ~ sP3(xa) ),
inference(superposition,[],[f269,f295]) ).
fof(f269,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) != xb
| ~ aElement0(X1)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f157,plain,
! [X0] :
( ( ~ aDivisorOf0(X0,xb)
& ~ doDivides0(X0,xb)
& ! [X1] :
( sdtasdt0(X0,X1) != xb
| ~ aElement0(X1) ) )
| ~ sP3(X0) ),
inference(nnf_transformation,[],[f122]) ).
fof(f1336,plain,
spl58_12,
inference(avatar_contradiction_clause,[],[f1335]) ).
fof(f1335,plain,
( $false
| spl58_12 ),
inference(subsumption_resolution,[],[f1334,f290]) ).
fof(f1334,plain,
( ~ aElement0(xb)
| spl58_12 ),
inference(resolution,[],[f1331,f330]) ).
fof(f330,plain,
! [X0] :
( aIdeal0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( aIdeal0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( aElement0(X0)
=> aIdeal0(slsdtgt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrIdeal) ).
fof(f1331,plain,
( ~ aIdeal0(slsdtgt0(xb))
| spl58_12 ),
inference(avatar_component_clause,[],[f1330]) ).
fof(f1330,plain,
( spl58_12
<=> aIdeal0(slsdtgt0(xb)) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_12])]) ).
fof(f1333,plain,
( spl58_11
| spl58_12
| ~ spl58_7 ),
inference(avatar_split_clause,[],[f1052,f539,f1330,f1326]) ).
fof(f1326,plain,
( spl58_11
<=> aElement0(sK36(sK43(slsdtgt0(xb)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_11])]) ).
fof(f539,plain,
( spl58_7
<=> aSet0(slsdtgt0(xb)) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_7])]) ).
fof(f1052,plain,
( aIdeal0(slsdtgt0(xb))
| aElement0(sK36(sK43(slsdtgt0(xb))))
| ~ spl58_7 ),
inference(subsumption_resolution,[],[f1043,f540]) ).
fof(f540,plain,
( aSet0(slsdtgt0(xb))
| ~ spl58_7 ),
inference(avatar_component_clause,[],[f539]) ).
fof(f1043,plain,
( aIdeal0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xb))
| aElement0(sK36(sK43(slsdtgt0(xb)))) ),
inference(resolution,[],[f363,f318]) ).
fof(f318,plain,
! [X3] :
( ~ aElementOf0(X3,slsdtgt0(xb))
| aElement0(sK36(X3)) ),
inference(cnf_transformation,[],[f186]) ).
fof(f363,plain,
! [X0] :
( aElementOf0(sK43(X0),X0)
| aIdeal0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0] :
( ( aIdeal0(X0)
| ( ~ sP9(X0,sK43(X0))
& aElementOf0(sK43(X0),X0) )
| ~ aSet0(X0) )
& ( ( ! [X2] :
( sP9(X0,X2)
| ~ aElementOf0(X2,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f205,f206]) ).
fof(f206,plain,
! [X0] :
( ? [X1] :
( ~ sP9(X0,X1)
& aElementOf0(X1,X0) )
=> ( ~ sP9(X0,sK43(X0))
& aElementOf0(sK43(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f205,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ~ sP9(X0,X1)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X2] :
( sP9(X0,X2)
| ~ aElementOf0(X2,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(rectify,[],[f204]) ).
fof(f204,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ~ sP9(X0,X1)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X1] :
( sP9(X0,X1)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(flattening,[],[f203]) ).
fof(f203,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ~ sP9(X0,X1)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X1] :
( sP9(X0,X1)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(nnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( sP9(X0,X1)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) ) ),
inference(definition_folding,[],[f79,f131]) ).
fof(f131,plain,
! [X0,X1] :
( sP9(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,[sP9])]) ).
fof(f79,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,[],[f57]) ).
fof(f57,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/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f1315,plain,
spl58_10,
inference(avatar_contradiction_clause,[],[f1314]) ).
fof(f1314,plain,
( $false
| spl58_10 ),
inference(subsumption_resolution,[],[f1313,f289]) ).
fof(f1313,plain,
( ~ aElement0(xa)
| spl58_10 ),
inference(resolution,[],[f1310,f330]) ).
fof(f1310,plain,
( ~ aIdeal0(slsdtgt0(xa))
| spl58_10 ),
inference(avatar_component_clause,[],[f1309]) ).
fof(f1309,plain,
( spl58_10
<=> aIdeal0(slsdtgt0(xa)) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_10])]) ).
fof(f1312,plain,
( spl58_9
| spl58_10
| ~ spl58_5 ),
inference(avatar_split_clause,[],[f1050,f526,f1309,f1305]) ).
fof(f1305,plain,
( spl58_9
<=> aElement0(sK37(sK43(slsdtgt0(xa)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_9])]) ).
fof(f1050,plain,
( aIdeal0(slsdtgt0(xa))
| aElement0(sK37(sK43(slsdtgt0(xa))))
| ~ spl58_5 ),
inference(subsumption_resolution,[],[f1041,f527]) ).
fof(f1041,plain,
( aIdeal0(slsdtgt0(xa))
| ~ aSet0(slsdtgt0(xa))
| aElement0(sK37(sK43(slsdtgt0(xa)))) ),
inference(resolution,[],[f363,f315]) ).
fof(f315,plain,
! [X6] :
( ~ aElementOf0(X6,slsdtgt0(xa))
| aElement0(sK37(X6)) ),
inference(cnf_transformation,[],[f186]) ).
fof(f586,plain,
spl58_7,
inference(avatar_contradiction_clause,[],[f585]) ).
fof(f585,plain,
( $false
| spl58_7 ),
inference(subsumption_resolution,[],[f584,f290]) ).
fof(f584,plain,
( ~ aElement0(xb)
| spl58_7 ),
inference(resolution,[],[f541,f454]) ).
fof(f454,plain,
! [X0] :
( aSet0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(resolution,[],[f330,f361]) ).
fof(f361,plain,
! [X0] :
( ~ aIdeal0(X0)
| aSet0(X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f541,plain,
( ~ aSet0(slsdtgt0(xb))
| spl58_7 ),
inference(avatar_component_clause,[],[f539]) ).
fof(f546,plain,
( ~ spl58_7
| spl58_8 ),
inference(avatar_split_clause,[],[f518,f543,f539]) ).
fof(f518,plain,
( aElement0(sK35)
| ~ aSet0(slsdtgt0(xb)) ),
inference(resolution,[],[f329,f322]) ).
fof(f537,plain,
spl58_5,
inference(avatar_contradiction_clause,[],[f536]) ).
fof(f536,plain,
( $false
| spl58_5 ),
inference(subsumption_resolution,[],[f535,f289]) ).
fof(f535,plain,
( ~ aElement0(xa)
| spl58_5 ),
inference(resolution,[],[f528,f454]) ).
fof(f528,plain,
( ~ aSet0(slsdtgt0(xa))
| spl58_5 ),
inference(avatar_component_clause,[],[f526]) ).
fof(f533,plain,
( ~ spl58_5
| spl58_6 ),
inference(avatar_split_clause,[],[f513,f530,f526]) ).
fof(f513,plain,
( aElement0(sK34)
| ~ aSet0(slsdtgt0(xa)) ),
inference(resolution,[],[f329,f321]) ).
fof(f490,plain,
spl58_1,
inference(avatar_contradiction_clause,[],[f489]) ).
fof(f489,plain,
( $false
| spl58_1 ),
inference(subsumption_resolution,[],[f487,f325]) ).
fof(f325,plain,
sz00 != sK33,
inference(cnf_transformation,[],[f186]) ).
fof(f487,plain,
( sz00 = sK33
| spl58_1 ),
inference(resolution,[],[f485,f480]) ).
fof(f480,plain,
aElementOf0(sK33,xI),
inference(forward_demodulation,[],[f324,f268]) ).
fof(f268,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f156]) ).
fof(f324,plain,
aElementOf0(sK33,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f186]) ).
fof(f485,plain,
( ! [X0] :
( ~ aElementOf0(X0,xI)
| sz00 = X0 )
| spl58_1 ),
inference(global_subsumption,[],[f248,f251,f250,f249,f426,f427,f266,f265,f264,f428,f262,f429,f259,f256,f255,f269,f273,f272,f286,f280,f307,f306,f305,f309,f430,f312,f311,f310,f314,f431,f324,f432,f319,f433,f316,f329,f333,f332,f335,f334,f337,f336,f339,f338,f341,f340,f344,f343,f342,f346,f353,f352,f351,f435,f349,f348,f360,f359,f358,f357,f356,f355,f364,f363,f362,f368,f367,f366,f365,f370,f436,f377,f376,f375,f374,f373,f372,f378,f386,f385,f384,f383,f437,f381,f380,f379,f389,f438,f439,f390,f391,f394,f393,f392,f396,f395,f400,f399,f398,f397,f401,f402,f403,f404,f405,f440,f409,f408,f411,f418,f417,f416,f415,f414,f413,f419,f420,f422,f423,f425,f424,f254,f257,f275,f276,f281,f289,f290,f291,f294,f297,f300,f326,f327,f278,f279,f283,f284,f325,f304,f444,f328,f288,f293,f296,f299,f302,f321,f322,f354,f361,f277,f282,f292,f295,f298,f301,f323,f245,f270,f451,f271,f274,f453,f330,f331,f347,f454,f303,f246,f247,f371,f434,f464,f258,f468,f469,f470,f261,f471,f472,f473,f268,f285,f287,f315,f474,f475,f476,f318,f477,f478,f479,f480,f484,f253]) ).
fof(f484,plain,
( ! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI) )
| spl58_1 ),
inference(subsumption_resolution,[],[f314,f444]) ).
fof(f479,plain,
aElement0(sK36(sK35)),
inference(resolution,[],[f318,f322]) ).
fof(f478,plain,
aElement0(sK36(xb)),
inference(resolution,[],[f318,f302]) ).
fof(f477,plain,
aElement0(sK36(sz00)),
inference(resolution,[],[f318,f299]) ).
fof(f476,plain,
aElement0(sK37(sK34)),
inference(resolution,[],[f315,f321]) ).
fof(f475,plain,
aElement0(sK37(xa)),
inference(resolution,[],[f315,f296]) ).
fof(f474,plain,
aElement0(sK37(sz00)),
inference(resolution,[],[f315,f293]) ).
fof(f287,plain,
! [X0] :
( doDivides0(X0,xc)
| sP3(X0)
| sP2(X0) ),
inference(cnf_transformation,[],[f164]) ).
fof(f285,plain,
! [X0] :
( aElement0(sK23(X0))
| sP3(X0)
| sP2(X0) ),
inference(cnf_transformation,[],[f164]) ).
fof(f472,plain,
aElement0(sK21(xb)),
inference(resolution,[],[f261,f302]) ).
fof(f471,plain,
aElement0(sK21(sz00)),
inference(resolution,[],[f261,f299]) ).
fof(f470,plain,
aElement0(sK22(sK34)),
inference(resolution,[],[f258,f321]) ).
fof(f469,plain,
aElement0(sK22(xa)),
inference(resolution,[],[f258,f296]) ).
fof(f468,plain,
aElement0(sK22(sz00)),
inference(resolution,[],[f258,f293]) ).
fof(f258,plain,
! [X8] :
( ~ aElementOf0(X8,slsdtgt0(xa))
| aElement0(sK22(X8)) ),
inference(cnf_transformation,[],[f156]) ).
fof(f464,plain,
! [X0] :
( aSet0(slsdtgt0(X0))
| ~ sP8(X0) ),
inference(resolution,[],[f434,f347]) ).
fof(f371,plain,
! [X2,X0,X1] :
( ~ sP10(X0,X1,X2)
| aSet0(X2) ),
inference(cnf_transformation,[],[f216]) ).
fof(f216,plain,
! [X0,X1,X2] :
( ( sP10(X0,X1,X2)
| ( ( ~ aElementOf0(sK46(X0,X1,X2),X0)
| ~ aElementOf0(sK46(X0,X1,X2),X1)
| ~ aElementOf0(sK46(X0,X1,X2),X2) )
& ( ( aElementOf0(sK46(X0,X1,X2),X0)
& aElementOf0(sK46(X0,X1,X2),X1) )
| aElementOf0(sK46(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) )
| ~ sP10(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f214,f215]) ).
fof(f215,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X0)
& aElementOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
=> ( ( ~ aElementOf0(sK46(X0,X1,X2),X0)
| ~ aElementOf0(sK46(X0,X1,X2),X1)
| ~ aElementOf0(sK46(X0,X1,X2),X2) )
& ( ( aElementOf0(sK46(X0,X1,X2),X0)
& aElementOf0(sK46(X0,X1,X2),X1) )
| aElementOf0(sK46(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f214,plain,
! [X0,X1,X2] :
( ( sP10(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) )
| ~ sP10(X0,X1,X2) ) ),
inference(rectify,[],[f213]) ).
fof(f213,plain,
! [X1,X0,X2] :
( ( sP10(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) )
| ~ sP10(X1,X0,X2) ) ),
inference(flattening,[],[f212]) ).
fof(f212,plain,
! [X1,X0,X2] :
( ( sP10(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) )
| ~ sP10(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X1,X0,X2] :
( sP10(X1,X0,X2)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f303,plain,
( sz00 != xb
| sz00 != xa ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
( sz00 != xb
| sz00 != xa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2110) ).
fof(f347,plain,
! [X0,X1] :
( ~ sP7(X0,X1)
| aSet0(X1) ),
inference(cnf_transformation,[],[f196]) ).
fof(f453,plain,
~ sP2(xc),
inference(resolution,[],[f274,f279]) ).
fof(f274,plain,
! [X0] :
( ~ aDivisorOf0(X0,xa)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f159]) ).
fof(f271,plain,
! [X0] :
( ~ aDivisorOf0(X0,xb)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f451,plain,
~ sP3(xc),
inference(resolution,[],[f270,f283]) ).
fof(f270,plain,
! [X0] :
( ~ doDivides0(X0,xb)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f245,plain,
! [X0] :
( sP0(sK16(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f323,plain,
sK33 = sdtpldt0(sK34,sK35),
inference(cnf_transformation,[],[f186]) ).
fof(f298,plain,
sz00 = sdtasdt0(xb,sK27),
inference(cnf_transformation,[],[f169]) ).
fof(f292,plain,
sz00 = sdtasdt0(xa,sK29),
inference(cnf_transformation,[],[f169]) ).
fof(f277,plain,
xa = sdtasdt0(xc,sK25),
inference(cnf_transformation,[],[f164]) ).
fof(f288,plain,
aGcdOfAnd0(xc,xa,xb),
inference(cnf_transformation,[],[f164]) ).
fof(f328,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
sz00 != sz10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).
fof(f444,plain,
( ~ sP6
| spl58_1 ),
inference(avatar_component_clause,[],[f442]) ).
fof(f304,plain,
( sP4(sK30)
| ~ sP6 ),
inference(cnf_transformation,[],[f173]) ).
fof(f284,plain,
aDivisorOf0(xc,xb),
inference(cnf_transformation,[],[f164]) ).
fof(f283,plain,
doDivides0(xc,xb),
inference(cnf_transformation,[],[f164]) ).
fof(f279,plain,
aDivisorOf0(xc,xa),
inference(cnf_transformation,[],[f164]) ).
fof(f278,plain,
doDivides0(xc,xa),
inference(cnf_transformation,[],[f164]) ).
fof(f327,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f300,plain,
aElement0(sK26),
inference(cnf_transformation,[],[f169]) ).
fof(f297,plain,
aElement0(sK27),
inference(cnf_transformation,[],[f169]) ).
fof(f291,plain,
aElement0(sK29),
inference(cnf_transformation,[],[f169]) ).
fof(f276,plain,
aElement0(sK25),
inference(cnf_transformation,[],[f164]) ).
fof(f257,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f156]) ).
fof(f254,plain,
aSet0(xI),
inference(cnf_transformation,[],[f156]) ).
fof(f424,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(f425,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f423,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f114]) ).
fof(f114,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(f422,plain,
! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f112]) ).
fof(f112,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(f420,plain,
! [X2,X0,X1] :
( aElementOf0(sdtpldt0(X0,smndt0(X1)),X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aIdeal0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f244]) ).
fof(f244,plain,
! [X0,X1,X2] :
( ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aElementOf0(sdtpldt0(X0,smndt0(X1)),X2) )
& ( aElementOf0(sdtpldt0(X0,smndt0(X1)),X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ) )
| ~ aIdeal0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aElementOf0(sdtpldt0(X0,smndt0(X1)),X2) )
| ~ aIdeal0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f110]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aElementOf0(sdtpldt0(X0,smndt0(X1)),X2) )
| ~ aIdeal0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1,X2] :
( ( aIdeal0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aElementOf0(sdtpldt0(X0,smndt0(X1)),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMod) ).
fof(f419,plain,
! [X0,X1] :
( sP15(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0,X1] :
( sP15(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(definition_folding,[],[f109,f141,f140]) ).
fof(f140,plain,
! [X2,X1,X0] :
( sP14(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,[sP14])]) ).
fof(f141,plain,
! [X0,X1] :
( ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> sP14(X2,X1,X0) )
| ~ sP15(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f109,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,[],[f108]) ).
fof(f108,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/sandbox2/benchmark/theBenchmark.p',mDefGCD) ).
fof(f413,plain,
! [X2,X0,X1] :
( ~ sP14(X0,X1,X2)
| aDivisorOf0(X0,X2) ),
inference(cnf_transformation,[],[f243]) ).
fof(f243,plain,
! [X0,X1,X2] :
( ( sP14(X0,X1,X2)
| ( ~ doDivides0(sK57(X0,X1,X2),X0)
& aDivisorOf0(sK57(X0,X1,X2),X1)
& aDivisorOf0(sK57(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) )
| ~ sP14(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f241,f242]) ).
fof(f242,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ doDivides0(X3,X0)
& aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X2) )
=> ( ~ doDivides0(sK57(X0,X1,X2),X0)
& aDivisorOf0(sK57(X0,X1,X2),X1)
& aDivisorOf0(sK57(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f241,plain,
! [X0,X1,X2] :
( ( sP14(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) )
| ~ sP14(X0,X1,X2) ) ),
inference(rectify,[],[f240]) ).
fof(f240,plain,
! [X2,X1,X0] :
( ( sP14(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) )
| ~ sP14(X2,X1,X0) ) ),
inference(flattening,[],[f239]) ).
fof(f239,plain,
! [X2,X1,X0] :
( ( sP14(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) )
| ~ sP14(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f140]) ).
fof(f414,plain,
! [X2,X0,X1] :
( ~ sP14(X0,X1,X2)
| aDivisorOf0(X0,X1) ),
inference(cnf_transformation,[],[f243]) ).
fof(f415,plain,
! [X2,X0,X1,X4] :
( doDivides0(X4,X0)
| ~ aDivisorOf0(X4,X1)
| ~ aDivisorOf0(X4,X2)
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f243]) ).
fof(f416,plain,
! [X2,X0,X1] :
( sP14(X0,X1,X2)
| aDivisorOf0(sK57(X0,X1,X2),X2)
| ~ aDivisorOf0(X0,X1)
| ~ aDivisorOf0(X0,X2) ),
inference(cnf_transformation,[],[f243]) ).
fof(f417,plain,
! [X2,X0,X1] :
( sP14(X0,X1,X2)
| aDivisorOf0(sK57(X0,X1,X2),X1)
| ~ aDivisorOf0(X0,X1)
| ~ aDivisorOf0(X0,X2) ),
inference(cnf_transformation,[],[f243]) ).
fof(f418,plain,
! [X2,X0,X1] :
( sP14(X0,X1,X2)
| ~ doDivides0(sK57(X0,X1,X2),X0)
| ~ aDivisorOf0(X0,X1)
| ~ aDivisorOf0(X0,X2) ),
inference(cnf_transformation,[],[f243]) ).
fof(f411,plain,
! [X2,X0,X1] :
( sP14(X2,X1,X0)
| ~ aGcdOfAnd0(X2,X0,X1)
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f238,plain,
! [X0,X1] :
( ! [X2] :
( ( aGcdOfAnd0(X2,X0,X1)
| ~ sP14(X2,X1,X0) )
& ( sP14(X2,X1,X0)
| ~ aGcdOfAnd0(X2,X0,X1) ) )
| ~ sP15(X0,X1) ),
inference(nnf_transformation,[],[f141]) ).
fof(f408,plain,
! [X0,X1] :
( aElement0(sK56(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f237]) ).
fof(f237,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aElement0(X2) ) )
& ( ( sdtasdt0(X0,sK56(X0,X1)) = X1
& aElement0(sK56(X0,X1)) )
| ~ doDivides0(X0,X1) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56])],[f235,f236]) ).
fof(f236,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aElement0(X3) )
=> ( sdtasdt0(X0,sK56(X0,X1)) = X1
& aElement0(sK56(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f235,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,[],[f234]) ).
fof(f234,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,[],[f107]) ).
fof(f107,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f106]) ).
fof(f106,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/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f409,plain,
! [X0,X1] :
( sdtasdt0(X0,sK56(X0,X1)) = X1
| ~ doDivides0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f237]) ).
fof(f440,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aElement0(X2)
| ~ aElement0(sdtasdt0(X0,X2))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f410]) ).
fof(f410,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f237]) ).
fof(f405,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f102]) ).
fof(f102,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/sandbox2/benchmark/theBenchmark.p',mCancel) ).
fof(f404,plain,
! [X0,X1] :
( ~ aElement0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f100]) ).
fof(f100,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/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f403,plain,
! [X0,X1] :
( ~ aElement0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f98]) ).
fof(f98,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/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f402,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f96]) ).
fof(f96,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/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f401,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f94]) ).
fof(f94,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/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f397,plain,
! [X0,X1] :
( aElement0(sK54(X0,X1))
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f232]) ).
fof(f232,plain,
! [X0,X1] :
( ( ( iLess0(sbrdtbr0(sK55(X0,X1)),sbrdtbr0(X1))
| sz00 = sK55(X0,X1) )
& sdtpldt0(sdtasdt0(sK54(X0,X1),X1),sK55(X0,X1)) = X0
& aElement0(sK55(X0,X1))
& aElement0(sK54(X0,X1)) )
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55])],[f93,f231]) ).
fof(f231,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( iLess0(sbrdtbr0(X3),sbrdtbr0(X1))
| sz00 = X3 )
& sdtpldt0(sdtasdt0(X2,X1),X3) = X0
& aElement0(X3)
& aElement0(X2) )
=> ( ( iLess0(sbrdtbr0(sK55(X0,X1)),sbrdtbr0(X1))
| sz00 = sK55(X0,X1) )
& sdtpldt0(sdtasdt0(sK54(X0,X1),X1),sK55(X0,X1)) = X0
& aElement0(sK55(X0,X1))
& aElement0(sK54(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( iLess0(sbrdtbr0(X3),sbrdtbr0(X1))
| sz00 = X3 )
& sdtpldt0(sdtasdt0(X2,X1),X3) = X0
& aElement0(X3)
& aElement0(X2) )
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( iLess0(sbrdtbr0(X3),sbrdtbr0(X1))
| sz00 = X3 )
& sdtpldt0(sdtasdt0(X2,X1),X3) = X0
& aElement0(X3)
& aElement0(X2) )
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[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/sandbox2/benchmark/theBenchmark.p',mDivision) ).
fof(f398,plain,
! [X0,X1] :
( aElement0(sK55(X0,X1))
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f232]) ).
fof(f399,plain,
! [X0,X1] :
( sdtpldt0(sdtasdt0(sK54(X0,X1),X1),sK55(X0,X1)) = X0
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f232]) ).
fof(f400,plain,
! [X0,X1] :
( iLess0(sbrdtbr0(sK55(X0,X1)),sbrdtbr0(X1))
| sz00 = sK55(X0,X1)
| sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f232]) ).
fof(f395,plain,
! [X0,X1] :
( aElement0(sK53(X0,X1))
| sP13(X1,X0)
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f230]) ).
fof(f230,plain,
! [X0,X1] :
( sP13(X1,X0)
| ( ~ aElementOf0(sK53(X0,X1),sdtpldt1(X0,X1))
& aElement0(sK53(X0,X1)) )
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53])],[f139,f229]) ).
fof(f229,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,sdtpldt1(X0,X1))
& aElement0(X2) )
=> ( ~ aElementOf0(sK53(X0,X1),sdtpldt1(X0,X1))
& aElement0(sK53(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f139,plain,
! [X0,X1] :
( sP13(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,sdtpldt1(X0,X1))
& aElement0(X2) )
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(definition_folding,[],[f91,f138]) ).
fof(f138,plain,
! [X1,X0] :
( ! [X3,X4] :
( ? [X5] :
( sdteqdtlpzmzozddtrp0(X5,X4,X1)
& sdteqdtlpzmzozddtrp0(X5,X3,X0)
& aElement0(X5) )
| ~ aElement0(X4)
| ~ aElement0(X3) )
| ~ sP13(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f91,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,[],[f90]) ).
fof(f90,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,[],[f60]) ).
fof(f60,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/sandbox2/benchmark/theBenchmark.p',mChineseRemainder) ).
fof(f396,plain,
! [X0,X1] :
( sP13(X1,X0)
| ~ aElementOf0(sK53(X0,X1),sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f230]) ).
fof(f392,plain,
! [X2,X3,X0,X1] :
( aElement0(sK52(X0,X1,X2,X3))
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ sP13(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( sdteqdtlpzmzozddtrp0(sK52(X0,X1,X2,X3),X3,X0)
& sdteqdtlpzmzozddtrp0(sK52(X0,X1,X2,X3),X2,X1)
& aElement0(sK52(X0,X1,X2,X3)) )
| ~ aElement0(X3)
| ~ aElement0(X2) )
| ~ sP13(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f226,f227]) ).
fof(f227,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( sdteqdtlpzmzozddtrp0(X4,X3,X0)
& sdteqdtlpzmzozddtrp0(X4,X2,X1)
& aElement0(X4) )
=> ( sdteqdtlpzmzozddtrp0(sK52(X0,X1,X2,X3),X3,X0)
& sdteqdtlpzmzozddtrp0(sK52(X0,X1,X2,X3),X2,X1)
& aElement0(sK52(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f226,plain,
! [X0,X1] :
( ! [X2,X3] :
( ? [X4] :
( sdteqdtlpzmzozddtrp0(X4,X3,X0)
& sdteqdtlpzmzozddtrp0(X4,X2,X1)
& aElement0(X4) )
| ~ aElement0(X3)
| ~ aElement0(X2) )
| ~ sP13(X0,X1) ),
inference(rectify,[],[f225]) ).
fof(f225,plain,
! [X1,X0] :
( ! [X3,X4] :
( ? [X5] :
( sdteqdtlpzmzozddtrp0(X5,X4,X1)
& sdteqdtlpzmzozddtrp0(X5,X3,X0)
& aElement0(X5) )
| ~ aElement0(X4)
| ~ aElement0(X3) )
| ~ sP13(X1,X0) ),
inference(nnf_transformation,[],[f138]) ).
fof(f393,plain,
! [X2,X3,X0,X1] :
( sdteqdtlpzmzozddtrp0(sK52(X0,X1,X2,X3),X2,X1)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ sP13(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f394,plain,
! [X2,X3,X0,X1] :
( sdteqdtlpzmzozddtrp0(sK52(X0,X1,X2,X3),X3,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ sP13(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f391,plain,
! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(flattening,[],[f88]) ).
fof(f88,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/sandbox2/benchmark/theBenchmark.p',mIdeSum) ).
fof(f390,plain,
! [X0,X1] :
( aIdeal0(sdtasasdt0(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( aIdeal0(sdtasasdt0(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(flattening,[],[f86]) ).
fof(f86,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/sandbox2/benchmark/theBenchmark.p',mIdeInt) ).
fof(f439,plain,
! [X0,X1] :
( aSet0(sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f387]) ).
fof(f387,plain,
! [X2,X0,X1] :
( aSet0(X2)
| sdtpldt1(X0,X1) != X2
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f224]) ).
fof(f224,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt1(X0,X1) = X2
| ~ sP12(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP12(X1,X0,X2)
& aSet0(X2) )
| sdtpldt1(X0,X1) != X2 ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f223]) ).
fof(f223,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt1(X0,X1) = X2
| ~ sP12(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP12(X1,X0,X2)
& aSet0(X2) )
| sdtpldt1(X0,X1) != X2 ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( sP12(X1,X0,X2)
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f85,f136]) ).
fof(f136,plain,
! [X1,X0,X2] :
( sP12(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,[sP12])]) ).
fof(f85,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,[],[f84]) ).
fof(f84,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/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).
fof(f438,plain,
! [X0,X1] :
( sP12(X1,X0,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f388]) ).
fof(f388,plain,
! [X2,X0,X1] :
( sP12(X1,X0,X2)
| sdtpldt1(X0,X1) != X2
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f224]) ).
fof(f389,plain,
! [X2,X0,X1] :
( sdtpldt1(X0,X1) = X2
| ~ sP12(X1,X0,X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f224]) ).
fof(f379,plain,
! [X2,X0,X1,X8] :
( aElementOf0(sK50(X0,X1,X8),X1)
| ~ aElementOf0(X8,X2)
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f222]) ).
fof(f222,plain,
! [X0,X1,X2] :
( ( sP12(X0,X1,X2)
| ( ( ! [X4,X5] :
( sdtpldt0(X4,X5) != sK47(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(sK47(X0,X1,X2),X2) )
& ( ( sK47(X0,X1,X2) = sdtpldt0(sK48(X0,X1,X2),sK49(X0,X1,X2))
& aElementOf0(sK49(X0,X1,X2),X0)
& aElementOf0(sK48(X0,X1,X2),X1) )
| aElementOf0(sK47(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( aElementOf0(X8,X2)
| ! [X9,X10] :
( sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1) ) )
& ( ( sdtpldt0(sK50(X0,X1,X8),sK51(X0,X1,X8)) = X8
& aElementOf0(sK51(X0,X1,X8),X0)
& aElementOf0(sK50(X0,X1,X8),X1) )
| ~ aElementOf0(X8,X2) ) )
| ~ sP12(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48,sK49,sK50,sK51])],[f218,f221,f220,f219]) ).
fof(f219,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) != sK47(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(sK47(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( sdtpldt0(X6,X7) = sK47(X0,X1,X2)
& aElementOf0(X7,X0)
& aElementOf0(X6,X1) )
| aElementOf0(sK47(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f220,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( sdtpldt0(X6,X7) = sK47(X0,X1,X2)
& aElementOf0(X7,X0)
& aElementOf0(X6,X1) )
=> ( sK47(X0,X1,X2) = sdtpldt0(sK48(X0,X1,X2),sK49(X0,X1,X2))
& aElementOf0(sK49(X0,X1,X2),X0)
& aElementOf0(sK48(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f221,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( sdtpldt0(X11,X12) = X8
& aElementOf0(X12,X0)
& aElementOf0(X11,X1) )
=> ( sdtpldt0(sK50(X0,X1,X8),sK51(X0,X1,X8)) = X8
& aElementOf0(sK51(X0,X1,X8),X0)
& aElementOf0(sK50(X0,X1,X8),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f218,plain,
! [X0,X1,X2] :
( ( sP12(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) ) )
| ~ sP12(X0,X1,X2) ) ),
inference(rectify,[],[f217]) ).
fof(f217,plain,
! [X1,X0,X2] :
( ( sP12(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) ) )
| ~ sP12(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f136]) ).
fof(f380,plain,
! [X2,X0,X1,X8] :
( aElementOf0(sK51(X0,X1,X8),X0)
| ~ aElementOf0(X8,X2)
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f222]) ).
fof(f381,plain,
! [X2,X0,X1,X8] :
( sdtpldt0(sK50(X0,X1,X8),sK51(X0,X1,X8)) = X8
| ~ aElementOf0(X8,X2)
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f222]) ).
fof(f437,plain,
! [X2,X10,X0,X1,X9] :
( aElementOf0(sdtpldt0(X9,X10),X2)
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1)
| ~ sP12(X0,X1,X2) ),
inference(equality_resolution,[],[f382]) ).
fof(f382,plain,
! [X2,X10,X0,X1,X8,X9] :
( aElementOf0(X8,X2)
| sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1)
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f222]) ).
fof(f383,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| aElementOf0(sK48(X0,X1,X2),X1)
| aElementOf0(sK47(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f222]) ).
fof(f384,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| aElementOf0(sK49(X0,X1,X2),X0)
| aElementOf0(sK47(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f222]) ).
fof(f385,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| sK47(X0,X1,X2) = sdtpldt0(sK48(X0,X1,X2),sK49(X0,X1,X2))
| aElementOf0(sK47(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f222]) ).
fof(f386,plain,
! [X2,X0,X1,X4,X5] :
( sP12(X0,X1,X2)
| sdtpldt0(X4,X5) != sK47(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(sK47(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f222]) ).
fof(f378,plain,
! [X0,X1] :
( sP11(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0,X1] :
( sP11(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f83,f134,f133]) ).
fof(f134,plain,
! [X0,X1] :
( ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> sP10(X1,X0,X2) )
| ~ sP11(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f83,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,[],[f82]) ).
fof(f82,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/sandbox2/benchmark/theBenchmark.p',mDefSInt) ).
fof(f372,plain,
! [X2,X0,X1,X4] :
( ~ sP10(X0,X1,X2)
| ~ aElementOf0(X4,X2)
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f216]) ).
fof(f373,plain,
! [X2,X0,X1,X4] :
( ~ sP10(X0,X1,X2)
| ~ aElementOf0(X4,X2)
| aElementOf0(X4,X0) ),
inference(cnf_transformation,[],[f216]) ).
fof(f374,plain,
! [X2,X0,X1,X4] :
( ~ sP10(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1)
| aElementOf0(X4,X2) ),
inference(cnf_transformation,[],[f216]) ).
fof(f375,plain,
! [X2,X0,X1] :
( sP10(X0,X1,X2)
| aElementOf0(sK46(X0,X1,X2),X1)
| aElementOf0(sK46(X0,X1,X2),X2)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f216]) ).
fof(f376,plain,
! [X2,X0,X1] :
( sP10(X0,X1,X2)
| aElementOf0(sK46(X0,X1,X2),X0)
| aElementOf0(sK46(X0,X1,X2),X2)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f216]) ).
fof(f377,plain,
! [X2,X0,X1] :
( sP10(X0,X1,X2)
| ~ aElementOf0(sK46(X0,X1,X2),X0)
| ~ aElementOf0(sK46(X0,X1,X2),X1)
| ~ aElementOf0(sK46(X0,X1,X2),X2)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f216]) ).
fof(f436,plain,
! [X0,X1] :
( sP10(X1,X0,sdtasasdt0(X0,X1))
| ~ sP11(X0,X1) ),
inference(equality_resolution,[],[f369]) ).
fof(f369,plain,
! [X2,X0,X1] :
( sP10(X1,X0,X2)
| sdtasasdt0(X0,X1) != X2
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtasasdt0(X0,X1) = X2
| ~ sP10(X1,X0,X2) )
& ( sP10(X1,X0,X2)
| sdtasasdt0(X0,X1) != X2 ) )
| ~ sP11(X0,X1) ),
inference(nnf_transformation,[],[f134]) ).
fof(f370,plain,
! [X2,X0,X1] :
( ~ sP10(X1,X0,X2)
| sdtasasdt0(X0,X1) = X2
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f211]) ).
fof(f365,plain,
! [X0,X1] :
( X0 = X1
| aElementOf0(sK44(X0,X1),X1)
| aElementOf0(sK45(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f210]) ).
fof(f210,plain,
! [X0,X1] :
( X0 = X1
| ( ~ aElementOf0(sK44(X0,X1),X0)
& aElementOf0(sK44(X0,X1),X1) )
| ( ~ aElementOf0(sK45(X0,X1),X1)
& aElementOf0(sK45(X0,X1),X0) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45])],[f81,f209,f208]) ).
fof(f208,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK44(X0,X1),X0)
& aElementOf0(sK44(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f209,plain,
! [X0,X1] :
( ? [X3] :
( ~ aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
=> ( ~ aElementOf0(sK45(X0,X1),X1)
& aElementOf0(sK45(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ? [X3] :
( ~ aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ? [X3] :
( ~ aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ( ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(X3,X0)
=> aElementOf0(X3,X1) ) )
=> X0 = X1 ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ( ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(X2,X1) ) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetEq) ).
fof(f366,plain,
! [X0,X1] :
( X0 = X1
| aElementOf0(sK44(X0,X1),X1)
| ~ aElementOf0(sK45(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f210]) ).
fof(f367,plain,
! [X0,X1] :
( X0 = X1
| ~ aElementOf0(sK44(X0,X1),X0)
| aElementOf0(sK45(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f210]) ).
fof(f368,plain,
! [X0,X1] :
( X0 = X1
| ~ aElementOf0(sK44(X0,X1),X0)
| ~ aElementOf0(sK45(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f210]) ).
fof(f362,plain,
! [X2,X0] :
( sP9(X0,X2)
| ~ aElementOf0(X2,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f364,plain,
! [X0] :
( ~ sP9(X0,sK43(X0))
| aIdeal0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f355,plain,
! [X0,X1,X5] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0)
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0,X1] :
( ( sP9(X0,X1)
| ( ~ aElementOf0(sdtasdt0(sK41(X0,X1),X1),X0)
& aElement0(sK41(X0,X1)) )
| ( ~ aElementOf0(sdtpldt0(X1,sK42(X0,X1)),X0)
& aElementOf0(sK42(X0,X1),X0) ) )
& ( ( ! [X4] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4) )
& ! [X5] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0) ) )
| ~ sP9(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42])],[f199,f201,f200]) ).
fof(f200,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
=> ( ~ aElementOf0(sdtasdt0(sK41(X0,X1),X1),X0)
& aElement0(sK41(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f201,plain,
! [X0,X1] :
( ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) )
=> ( ~ aElementOf0(sdtpldt0(X1,sK42(X0,X1)),X0)
& aElementOf0(sK42(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f199,plain,
! [X0,X1] :
( ( sP9(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) ) )
| ~ sP9(X0,X1) ) ),
inference(rectify,[],[f198]) ).
fof(f198,plain,
! [X0,X1] :
( ( sP9(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) ) )
| ~ sP9(X0,X1) ) ),
inference(flattening,[],[f197]) ).
fof(f197,plain,
! [X0,X1] :
( ( sP9(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) ) )
| ~ sP9(X0,X1) ) ),
inference(nnf_transformation,[],[f131]) ).
fof(f356,plain,
! [X0,X1,X4] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4)
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f202]) ).
fof(f357,plain,
! [X0,X1] :
( aElementOf0(sK42(X0,X1),X0)
| aElement0(sK41(X0,X1))
| sP9(X0,X1) ),
inference(cnf_transformation,[],[f202]) ).
fof(f358,plain,
! [X0,X1] :
( sP9(X0,X1)
| aElement0(sK41(X0,X1))
| ~ aElementOf0(sdtpldt0(X1,sK42(X0,X1)),X0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f359,plain,
! [X0,X1] :
( sP9(X0,X1)
| ~ aElementOf0(sdtasdt0(sK41(X0,X1),X1),X0)
| aElementOf0(sK42(X0,X1),X0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f360,plain,
! [X0,X1] :
( sP9(X0,X1)
| ~ aElementOf0(sdtasdt0(sK41(X0,X1),X1),X0)
| ~ aElementOf0(sdtpldt0(X1,sK42(X0,X1)),X0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f348,plain,
! [X0,X1,X5] :
( ~ sP7(X0,X1)
| ~ aElementOf0(X5,X1)
| aElement0(sK40(X0,X5)) ),
inference(cnf_transformation,[],[f196]) ).
fof(f349,plain,
! [X0,X1,X5] :
( ~ sP7(X0,X1)
| ~ aElementOf0(X5,X1)
| sdtasdt0(X0,sK40(X0,X5)) = X5 ),
inference(cnf_transformation,[],[f196]) ).
fof(f351,plain,
! [X0,X1] :
( sP7(X0,X1)
| aElement0(sK39(X0,X1))
| aElementOf0(sK38(X0,X1),X1)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f196]) ).
fof(f352,plain,
! [X0,X1] :
( sP7(X0,X1)
| sK38(X0,X1) = sdtasdt0(X0,sK39(X0,X1))
| aElementOf0(sK38(X0,X1),X1)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f196]) ).
fof(f353,plain,
! [X3,X0,X1] :
( sP7(X0,X1)
| sdtasdt0(X0,X3) != sK38(X0,X1)
| ~ aElement0(X3)
| ~ aElementOf0(sK38(X0,X1),X1)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f196]) ).
fof(f346,plain,
! [X0,X1] :
( ~ sP7(X0,X1)
| slsdtgt0(X0) = X1
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f189]) ).
fof(f342,plain,
! [X0,X1] :
( ~ aDivisorOf0(X1,X0)
| aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f188,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1) )
& ( ( doDivides0(X1,X0)
& aElement0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aElement0(X0) ),
inference(flattening,[],[f187]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1) )
& ( ( doDivides0(X1,X0)
& aElement0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f77]) ).
fof(f77,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/sandbox2/benchmark/theBenchmark.p',mDefDvs) ).
fof(f343,plain,
! [X0,X1] :
( ~ aDivisorOf0(X1,X0)
| doDivides0(X1,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f344,plain,
! [X0,X1] :
( aDivisorOf0(X1,X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f340,plain,
! [X0] :
( ~ aElement0(X0)
| smndt0(X0) = sdtasdt0(smndt0(sz10),X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f338,plain,
! [X0] :
( ~ aElement0(X0)
| sz00 = sdtpldt0(X0,smndt0(X0)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,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/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).
fof(f339,plain,
! [X0] :
( ~ aElement0(X0)
| sz00 = sdtpldt0(smndt0(X0),X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f336,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,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/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).
fof(f337,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(sz10,X0) = X0 ),
inference(cnf_transformation,[],[f74]) ).
fof(f332,plain,
! [X0] :
( ~ aElement0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,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/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(f333,plain,
! [X0] :
( ~ aElement0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f316,plain,
! [X6] :
( ~ aElementOf0(X6,slsdtgt0(xa))
| sdtasdt0(xa,sK37(X6)) = X6 ),
inference(cnf_transformation,[],[f186]) ).
fof(f433,plain,
! [X7] :
( aElementOf0(sdtasdt0(xa,X7),slsdtgt0(xa))
| ~ aElement0(X7) ),
inference(equality_resolution,[],[f317]) ).
fof(f317,plain,
! [X6,X7] :
( aElementOf0(X6,slsdtgt0(xa))
| sdtasdt0(xa,X7) != X6
| ~ aElement0(X7) ),
inference(cnf_transformation,[],[f186]) ).
fof(f319,plain,
! [X3] :
( ~ aElementOf0(X3,slsdtgt0(xb))
| sdtasdt0(xb,sK36(X3)) = X3 ),
inference(cnf_transformation,[],[f186]) ).
fof(f432,plain,
! [X4] :
( aElementOf0(sdtasdt0(xb,X4),slsdtgt0(xb))
| ~ aElement0(X4) ),
inference(equality_resolution,[],[f320]) ).
fof(f320,plain,
! [X3,X4] :
( aElementOf0(X3,slsdtgt0(xb))
| sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ),
inference(cnf_transformation,[],[f186]) ).
fof(f431,plain,
! [X2,X1] :
( sP6
| sz00 = sdtpldt0(X1,X2)
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(equality_resolution,[],[f313]) ).
fof(f313,plain,
! [X2,X0,X1] :
( sP6
| sz00 = X0
| sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( sP6
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(definition_folding,[],[f68,f126,f125,f124]) ).
fof(f124,plain,
! [X3] :
( ? [X7,X8] :
( sdtpldt0(X7,X8) = X3
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) )
| ~ sP4(X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f68,plain,
! [X0] :
( ? [X3] :
( ! [X4] :
( ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3))
| sz00 = X4
| ( ~ aElementOf0(X4,xI)
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X3
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) )
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ? [X3] :
( ! [X4] :
( ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3))
| sz00 = X4
| ( ~ aElementOf0(X4,xI)
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X3
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) )
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ( sz00 != X0
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) )
=> ? [X3] :
( ! [X4] :
( ( sz00 != X4
& ( aElementOf0(X4,xI)
| ? [X5,X6] :
( sdtpldt0(X5,X6) = X4
& aElementOf0(X6,slsdtgt0(xb))
& aElementOf0(X5,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3)) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X3
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ( sz00 != X0
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) )
=> ? [X1] :
( ! [X2] :
( ( sz00 != X2
& ( aElementOf0(X2,xI)
| ? [X3,X4] :
( sdtpldt0(X3,X4) = X2
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) )
& sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2351) ).
fof(f314,plain,
! [X0] :
( sP6
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f127]) ).
fof(f310,plain,
! [X0] :
( aElementOf0(sK31(X0),slsdtgt0(xa))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ( sdtpldt0(sK31(X0),sK32(X0)) = X0
& aElementOf0(sK32(X0),slsdtgt0(xb))
& aElementOf0(sK31(X0),slsdtgt0(xa)) )
| ~ sP4(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32])],[f177,f178]) ).
fof(f178,plain,
! [X0] :
( ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
=> ( sdtpldt0(sK31(X0),sK32(X0)) = X0
& aElementOf0(sK32(X0),slsdtgt0(xb))
& aElementOf0(sK31(X0),slsdtgt0(xa)) ) ),
introduced(choice_axiom,[]) ).
fof(f177,plain,
! [X0] :
( ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
| ~ sP4(X0) ),
inference(rectify,[],[f176]) ).
fof(f176,plain,
! [X3] :
( ? [X7,X8] :
( sdtpldt0(X7,X8) = X3
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) )
| ~ sP4(X3) ),
inference(nnf_transformation,[],[f124]) ).
fof(f311,plain,
! [X0] :
( aElementOf0(sK32(X0),slsdtgt0(xb))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f312,plain,
! [X0] :
( ~ sP4(X0)
| sdtpldt0(sK31(X0),sK32(X0)) = X0 ),
inference(cnf_transformation,[],[f179]) ).
fof(f430,plain,
! [X2,X3,X0] :
( ~ iLess0(sbrdtbr0(sdtpldt0(X2,X3)),sbrdtbr0(X0))
| sz00 = sdtpldt0(X2,X3)
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa))
| ~ sP5(X0) ),
inference(equality_resolution,[],[f308]) ).
fof(f308,plain,
! [X2,X3,X0,X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
| sz00 = X1
| sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f280,plain,
aElement0(xc),
inference(cnf_transformation,[],[f164]) ).
fof(f286,plain,
! [X0] :
( sP3(X0)
| xc = sdtasdt0(X0,sK23(X0))
| sP2(X0) ),
inference(cnf_transformation,[],[f164]) ).
fof(f273,plain,
! [X0] :
( ~ doDivides0(X0,xa)
| ~ aElement0(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f159]) ).
fof(f255,plain,
! [X11,X13] :
( aElementOf0(sdtpldt0(X11,X13),xI)
| ~ aElementOf0(X13,xI)
| ~ aElementOf0(X11,xI) ),
inference(cnf_transformation,[],[f156]) ).
fof(f259,plain,
! [X8] :
( ~ aElementOf0(X8,slsdtgt0(xa))
| sdtasdt0(xa,sK22(X8)) = X8 ),
inference(cnf_transformation,[],[f156]) ).
fof(f428,plain,
! [X6] :
( aElementOf0(sdtasdt0(xb,X6),slsdtgt0(xb))
| ~ aElement0(X6) ),
inference(equality_resolution,[],[f263]) ).
fof(f263,plain,
! [X6,X5] :
( aElementOf0(X5,slsdtgt0(xb))
| sdtasdt0(xb,X6) != X5
| ~ aElement0(X6) ),
inference(cnf_transformation,[],[f156]) ).
fof(f264,plain,
! [X0] :
( aElementOf0(sK19(X0),slsdtgt0(xa))
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f156]) ).
fof(f265,plain,
! [X0] :
( aElementOf0(sK20(X0),slsdtgt0(xb))
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f156]) ).
fof(f266,plain,
! [X0] :
( ~ aElementOf0(X0,xI)
| sdtpldt0(sK19(X0),sK20(X0)) = X0 ),
inference(cnf_transformation,[],[f156]) ).
fof(f426,plain,
! [X2,X1] :
( sP1(sdtpldt0(X1,X2))
| sz00 = sdtpldt0(X1,X2)
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(equality_resolution,[],[f252]) ).
fof(f252,plain,
! [X2,X0,X1] :
( sP1(X0)
| sz00 = X0
| sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(cnf_transformation,[],[f150]) ).
fof(f249,plain,
! [X0] :
( aElementOf0(sK17(X0),slsdtgt0(xa))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f149,plain,
! [X0] :
( ( sdtpldt0(sK17(X0),sK18(X0)) = X0
& aElementOf0(sK18(X0),slsdtgt0(xb))
& aElementOf0(sK17(X0),slsdtgt0(xa)) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f147,f148]) ).
fof(f148,plain,
! [X0] :
( ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
=> ( sdtpldt0(sK17(X0),sK18(X0)) = X0
& aElementOf0(sK18(X0),slsdtgt0(xb))
& aElementOf0(sK17(X0),slsdtgt0(xa)) ) ),
introduced(choice_axiom,[]) ).
fof(f147,plain,
! [X0] :
( ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
| ~ sP0(X0) ),
inference(rectify,[],[f146]) ).
fof(f146,plain,
! [X1] :
( ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) )
| ~ sP0(X1) ),
inference(nnf_transformation,[],[f118]) ).
fof(f250,plain,
! [X0] :
( aElementOf0(sK18(X0),slsdtgt0(xb))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f251,plain,
! [X0] :
( ~ sP0(X0)
| sdtpldt0(sK17(X0),sK18(X0)) = X0 ),
inference(cnf_transformation,[],[f149]) ).
fof(f483,plain,
spl58_2,
inference(avatar_contradiction_clause,[],[f482]) ).
fof(f482,plain,
( $false
| spl58_2 ),
inference(subsumption_resolution,[],[f481,f325]) ).
fof(f481,plain,
( sz00 = sK33
| spl58_2 ),
inference(resolution,[],[f480,f465]) ).
fof(f465,plain,
( ! [X0] :
( ~ aElementOf0(X0,xI)
| sz00 = X0 )
| spl58_2 ),
inference(global_subsumption,[],[f248,f251,f250,f249,f426,f268,f427,f266,f265,f264,f428,f262,f261,f429,f259,f258,f256,f255,f269,f273,f272,f287,f286,f285,f280,f307,f306,f305,f309,f430,f312,f311,f310,f314,f431,f324,f432,f319,f318,f433,f316,f315,f329,f333,f332,f335,f334,f337,f336,f339,f338,f341,f340,f344,f343,f342,f346,f353,f352,f351,f435,f349,f348,f360,f359,f358,f357,f356,f355,f364,f363,f362,f368,f367,f366,f365,f370,f436,f377,f376,f375,f374,f373,f372,f378,f386,f385,f384,f383,f437,f381,f380,f379,f389,f438,f439,f390,f391,f394,f393,f392,f396,f395,f400,f399,f398,f397,f401,f402,f403,f404,f405,f440,f409,f408,f411,f418,f417,f416,f415,f414,f413,f419,f420,f422,f423,f425,f424,f254,f257,f275,f276,f281,f289,f290,f291,f294,f297,f300,f326,f327,f278,f279,f283,f284,f325,f304,f447,f328,f288,f293,f296,f299,f302,f321,f322,f354,f361,f277,f282,f292,f295,f298,f301,f323,f245,f270,f451,f271,f274,f453,f330,f331,f347,f454,f303,f246,f247,f371,f434,f464,f253]) ).
fof(f447,plain,
( ~ sP4(sK30)
| spl58_2 ),
inference(avatar_component_clause,[],[f446]) ).
fof(f446,plain,
( spl58_2
<=> sP4(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl58_2])]) ).
fof(f463,plain,
( ~ spl58_3
| ~ spl58_4 ),
inference(avatar_split_clause,[],[f303,f460,f456]) ).
fof(f456,plain,
( spl58_3
<=> sz00 = xa ),
introduced(avatar_definition,[new_symbols(naming,[spl58_3])]) ).
fof(f460,plain,
( spl58_4
<=> sz00 = xb ),
introduced(avatar_definition,[new_symbols(naming,[spl58_4])]) ).
fof(f449,plain,
( ~ spl58_1
| spl58_2 ),
inference(avatar_split_clause,[],[f304,f446,f442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : RNG112+4 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n028.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat May 18 11:58:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (15231)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (15238)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)
% 0.22/0.38 % (15234)WARNING: value z3 for option sas not known
% 0.22/0.38 % (15237)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)
% 0.22/0.38 % (15233)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (15232)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (15235)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (15234)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)
% 0.22/0.38 % (15236)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)
% 0.22/0.40 TRYING [1]
% 0.22/0.40 TRYING [1]
% 0.22/0.40 TRYING [2]
% 0.22/0.40 TRYING [2]
% 0.22/0.42 TRYING [3]
% 0.22/0.42 TRYING [3]
% 0.22/0.48 TRYING [4]
% 0.22/0.49 TRYING [4]
% 1.48/0.58 % (15234)First to succeed.
% 1.48/0.59 % (15234)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-15231"
% 1.48/0.59 % (15234)Refutation found. Thanks to Tanya!
% 1.48/0.59 % SZS status Theorem for theBenchmark
% 1.48/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 1.48/0.60 % (15234)------------------------------
% 1.48/0.60 % (15234)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.48/0.60 % (15234)Termination reason: Refutation
% 1.48/0.60
% 1.48/0.60 % (15234)Memory used [KB]: 5963
% 1.48/0.60 % (15234)Time elapsed: 0.208 s
% 1.48/0.60 % (15234)Instructions burned: 427 (million)
% 1.48/0.60 % (15231)Success in time 0.219 s
%------------------------------------------------------------------------------