TSTP Solution File: COM128+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM128+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 04:48:31 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 101
% Syntax : Number of formulae : 354 ( 91 unt; 0 def)
% Number of atoms : 1017 ( 593 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1072 ( 409 ~; 290 |; 220 &)
% ( 52 <=>; 101 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 66 ( 64 usr; 53 prp; 0-3 aty)
% Number of functors : 49 ( 49 usr; 7 con; 0-3 aty)
% Number of variables : 981 ( 857 !; 124 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f817,plain,
$false,
inference(avatar_sat_refutation,[],[f593,f598,f603,f607,f611,f615,f619,f623,f627,f631,f635,f639,f645,f649,f653,f657,f661,f665,f669,f673,f677,f681,f685,f689,f694,f698,f702,f706,f710,f714,f718,f722,f726,f730,f734,f739,f743,f747,f751,f755,f759,f770,f774,f778,f782,f789,f793,f797,f801,f805,f809,f813,f816]) ).
fof(f816,plain,
( ~ spl92_12
| spl92_46 ),
inference(avatar_contradiction_clause,[],[f815]) ).
fof(f815,plain,
( $false
| ~ spl92_12
| spl92_46 ),
inference(resolution,[],[f788,f638]) ).
fof(f638,plain,
( ! [X3] : visFreeVar(X3,vvar(X3))
| ~ spl92_12 ),
inference(avatar_component_clause,[],[f637]) ).
fof(f637,plain,
( spl92_12
<=> ! [X3] : visFreeVar(X3,vvar(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_12])]) ).
fof(f788,plain,
( ~ visFreeVar(sK17,vvar(sK17))
| spl92_46 ),
inference(avatar_component_clause,[],[f786]) ).
fof(f786,plain,
( spl92_46
<=> visFreeVar(sK17,vvar(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_46])]) ).
fof(f813,plain,
spl92_52,
inference(avatar_split_clause,[],[f399,f811]) ).
fof(f811,plain,
( spl92_52
<=> ! [X2,X0,X1,X3] :
( X1 = X3
| vapp(X0,X1) != vapp(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_52])]) ).
fof(f399,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| vapp(X0,X1) != vapp(X2,X3) ),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
! [X0,X1,X2,X3] :
( ( vapp(X0,X1) = vapp(X2,X3)
| X1 != X3
| X0 != X2 )
& ( ( X1 = X3
& X0 = X2 )
| vapp(X0,X1) != vapp(X2,X3) ) ),
inference(flattening,[],[f161]) ).
fof(f161,plain,
! [X0,X1,X2,X3] :
( ( vapp(X0,X1) = vapp(X2,X3)
| X1 != X3
| X0 != X2 )
& ( ( X1 = X3
& X0 = X2 )
| vapp(X0,X1) != vapp(X2,X3) ) ),
inference(ennf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2,X3] :
( ( ( X1 = X3
& X0 = X2 )
=> vapp(X0,X1) = vapp(X2,X3) )
& ( vapp(X0,X1) = vapp(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X3,X5,X6,X7] :
( ( ( X5 = X7
& X3 = X6 )
=> vapp(X3,X5) = vapp(X6,X7) )
& ( vapp(X3,X5) = vapp(X6,X7)
=> ( X5 = X7
& X3 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-app') ).
fof(f809,plain,
spl92_51,
inference(avatar_split_clause,[],[f398,f807]) ).
fof(f807,plain,
( spl92_51
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| vapp(X0,X1) != vapp(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_51])]) ).
fof(f398,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| vapp(X0,X1) != vapp(X2,X3) ),
inference(cnf_transformation,[],[f162]) ).
fof(f805,plain,
spl92_50,
inference(avatar_split_clause,[],[f396,f803]) ).
fof(f803,plain,
( spl92_50
<=> ! [X2,X0,X1,X3] :
( X1 = X3
| varrow(X0,X1) != varrow(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_50])]) ).
fof(f396,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| varrow(X0,X1) != varrow(X2,X3) ),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
! [X0,X1,X2,X3] :
( ( varrow(X0,X1) = varrow(X2,X3)
| X1 != X3
| X0 != X2 )
& ( ( X1 = X3
& X0 = X2 )
| varrow(X0,X1) != varrow(X2,X3) ) ),
inference(flattening,[],[f159]) ).
fof(f159,plain,
! [X0,X1,X2,X3] :
( ( varrow(X0,X1) = varrow(X2,X3)
| X1 != X3
| X0 != X2 )
& ( ( X1 = X3
& X0 = X2 )
| varrow(X0,X1) != varrow(X2,X3) ) ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2,X3] :
( ( ( X1 = X3
& X0 = X2 )
=> varrow(X0,X1) = varrow(X2,X3) )
& ( varrow(X0,X1) = varrow(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
inference(rectify,[],[f50]) ).
fof(f50,axiom,
! [X2,X4,X30,X31] :
( ( ( X4 = X31
& X2 = X30 )
=> varrow(X2,X4) = varrow(X30,X31) )
& ( varrow(X2,X4) = varrow(X30,X31)
=> ( X4 = X31
& X2 = X30 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-arrow') ).
fof(f801,plain,
spl92_49,
inference(avatar_split_clause,[],[f395,f799]) ).
fof(f799,plain,
( spl92_49
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| varrow(X0,X1) != varrow(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_49])]) ).
fof(f395,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| varrow(X0,X1) != varrow(X2,X3) ),
inference(cnf_transformation,[],[f160]) ).
fof(f797,plain,
spl92_48,
inference(avatar_split_clause,[],[f383,f795]) ).
fof(f795,plain,
( spl92_48
<=> ! [X2,X0,X1] :
( sK56(X0,X1,X2) = X2
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_48])]) ).
fof(f383,plain,
! [X2,X0,X1] :
( sK56(X0,X1,X2) = X2
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f286]) ).
fof(f286,plain,
! [X0,X1,X2] :
( ( vsomeType(sK58(X0,X1,X2)) = X0
& sK56(X0,X1,X2) = sK57(X0,X1,X2)
& vbind(sK57(X0,X1,X2),sK58(X0,X1,X2),sK55(X0,X1,X2)) = X1
& sK56(X0,X1,X2) = X2 )
| ~ sP7(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55,sK56,sK57,sK58])],[f284,f285]) ).
fof(f285,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vsomeType(X6) = X0
& X4 = X5
& vbind(X5,X6,X3) = X1
& X2 = X4 )
=> ( vsomeType(sK58(X0,X1,X2)) = X0
& sK56(X0,X1,X2) = sK57(X0,X1,X2)
& vbind(sK57(X0,X1,X2),sK58(X0,X1,X2),sK55(X0,X1,X2)) = X1
& sK56(X0,X1,X2) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f284,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vsomeType(X6) = X0
& X4 = X5
& vbind(X5,X6,X3) = X1
& X2 = X4 )
| ~ sP7(X0,X1,X2) ),
inference(rectify,[],[f283]) ).
fof(f283,plain,
! [X2,X1,X0] :
( ? [X7,X8,X9,X10] :
( vsomeType(X10) = X2
& X8 = X9
& vbind(X9,X10,X7) = X1
& X0 = X8 )
| ~ sP7(X2,X1,X0) ),
inference(nnf_transformation,[],[f233]) ).
fof(f233,plain,
! [X2,X1,X0] :
( ? [X7,X8,X9,X10] :
( vsomeType(X10) = X2
& X8 = X9
& vbind(X9,X10,X7) = X1
& X0 = X8 )
| ~ sP7(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f793,plain,
spl92_47,
inference(avatar_split_clause,[],[f379,f791]) ).
fof(f791,plain,
( spl92_47
<=> ! [X2,X0,X1] :
( sK53(X0,X1,X2) = X2
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_47])]) ).
fof(f379,plain,
! [X2,X0,X1] :
( sK53(X0,X1,X2) = X2
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f282]) ).
fof(f282,plain,
! [X0,X1,X2] :
( ( vlookup(sK53(X0,X1,X2),sK54(X0,X1,X2)) = X0
& sK52(X0,X1,X2) != sK53(X0,X1,X2)
& vbind(sK52(X0,X1,X2),sK51(X0,X1,X2),sK54(X0,X1,X2)) = X1
& sK53(X0,X1,X2) = X2 )
| ~ sP8(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51,sK52,sK53,sK54])],[f280,f281]) ).
fof(f281,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vlookup(X5,X6) = X0
& X4 != X5
& vbind(X4,X3,X6) = X1
& X2 = X5 )
=> ( vlookup(sK53(X0,X1,X2),sK54(X0,X1,X2)) = X0
& sK52(X0,X1,X2) != sK53(X0,X1,X2)
& vbind(sK52(X0,X1,X2),sK51(X0,X1,X2),sK54(X0,X1,X2)) = X1
& sK53(X0,X1,X2) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f280,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vlookup(X5,X6) = X0
& X4 != X5
& vbind(X4,X3,X6) = X1
& X2 = X5 )
| ~ sP8(X0,X1,X2) ),
inference(rectify,[],[f279]) ).
fof(f279,plain,
! [X2,X1,X0] :
( ? [X3,X4,X5,X6] :
( vlookup(X5,X6) = X2
& X4 != X5
& vbind(X4,X3,X6) = X1
& X0 = X5 )
| ~ sP8(X2,X1,X0) ),
inference(nnf_transformation,[],[f234]) ).
fof(f234,plain,
! [X2,X1,X0] :
( ? [X3,X4,X5,X6] :
( vlookup(X5,X6) = X2
& X4 != X5
& vbind(X4,X3,X6) = X1
& X0 = X5 )
| ~ sP8(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f789,plain,
( ~ spl92_46
| spl92_13
| ~ spl92_40 ),
inference(avatar_split_clause,[],[f764,f753,f642,f786]) ).
fof(f642,plain,
( spl92_13
<=> visFreeVar(sK17,vapp(vapp(sK14,sK15),vvar(sK17))) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_13])]) ).
fof(f753,plain,
( spl92_40
<=> ! [X4,X2,X3] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_40])]) ).
fof(f764,plain,
( ~ visFreeVar(sK17,vvar(sK17))
| spl92_13
| ~ spl92_40 ),
inference(resolution,[],[f754,f644]) ).
fof(f644,plain,
( ~ visFreeVar(sK17,vapp(vapp(sK14,sK15),vvar(sK17)))
| spl92_13 ),
inference(avatar_component_clause,[],[f642]) ).
fof(f754,plain,
( ! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) )
| ~ spl92_40 ),
inference(avatar_component_clause,[],[f753]) ).
fof(f782,plain,
spl92_45,
inference(avatar_split_clause,[],[f568,f780]) ).
fof(f780,plain,
( spl92_45
<=> ! [X6,X0,X3] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_45])]) ).
fof(f568,plain,
! [X3,X0,X6] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0)),
inference(equality_resolution,[],[f567]) ).
fof(f567,plain,
! [X2,X3,X0,X6] :
( vsomeType(X6) = vlookup(X3,vbind(X2,X6,X0))
| X2 != X3 ),
inference(equality_resolution,[],[f566]) ).
fof(f566,plain,
! [X2,X3,X0,X6,X4] :
( vlookup(X3,X4) = vsomeType(X6)
| vbind(X2,X6,X0) != X4
| X2 != X3 ),
inference(equality_resolution,[],[f565]) ).
fof(f565,plain,
! [X2,X3,X0,X1,X6,X4] :
( vlookup(X3,X4) = vsomeType(X6)
| X1 != X2
| vbind(X2,X6,X0) != X4
| X1 != X3 ),
inference(equality_resolution,[],[f469]) ).
fof(f469,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vsomeType(X6) = X5
| vlookup(X3,X4) != X5
| X1 != X2
| vbind(X2,X6,X0) != X4
| X1 != X3 ),
inference(cnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vsomeType(X6) = X5
| vlookup(X3,X4) != X5
| X1 != X2
| vbind(X2,X6,X0) != X4
| X1 != X3 ),
inference(flattening,[],[f210]) ).
fof(f210,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vsomeType(X6) = X5
| vlookup(X3,X4) != X5
| X1 != X2
| vbind(X2,X6,X0) != X4
| X1 != X3 ),
inference(ennf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vbind(X2,X6,X0) = X4
& X1 = X3 )
=> ( X1 = X2
=> ( vlookup(X3,X4) = X5
=> vsomeType(X6) = X5 ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X19,X8,X20,X0,X15,X18,X21] :
( ( vbind(X20,X21,X19) = X15
& X0 = X8 )
=> ( X8 = X20
=> ( vlookup(X0,X15) = X18
=> vsomeType(X21) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lookup1) ).
fof(f778,plain,
spl92_44,
inference(avatar_split_clause,[],[f538,f776]) ).
fof(f776,plain,
( spl92_44
<=> ! [X4,X0,X5,X3] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X4,vabs(X3,X0,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_44])]) ).
fof(f538,plain,
! [X3,X0,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X4,vabs(X3,X0,X5)) ),
inference(equality_resolution,[],[f537]) ).
fof(f537,plain,
! [X3,X0,X1,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X1,vabs(X3,X0,X5))
| X1 != X4 ),
inference(equality_resolution,[],[f461]) ).
fof(f461,plain,
! [X2,X3,X0,X1,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X1,X2)
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(cnf_transformation,[],[f195]) ).
fof(f195,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( ( visFreeVar(X4,X5)
& X3 != X4 )
| ~ visFreeVar(X1,X2) )
& ( visFreeVar(X1,X2)
| ~ visFreeVar(X4,X5)
| X3 = X4 ) )
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(flattening,[],[f194]) ).
fof(f194,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( ( visFreeVar(X4,X5)
& X3 != X4 )
| ~ visFreeVar(X1,X2) )
& ( visFreeVar(X1,X2)
| ~ visFreeVar(X4,X5)
| X3 = X4 ) )
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(ennf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vabs(X3,X0,X5) = X2
& X1 = X4 )
=> ( ( visFreeVar(X1,X2)
=> ( visFreeVar(X4,X5)
& X3 != X4 ) )
& ( ( visFreeVar(X4,X5)
& X3 != X4 )
=> visFreeVar(X1,X2) ) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X14,X0,X3,X8,X13,X10] :
( ( vabs(X8,X14,X10) = X3
& X0 = X13 )
=> ( ( visFreeVar(X0,X3)
=> ( visFreeVar(X13,X10)
& X8 != X13 ) )
& ( ( visFreeVar(X13,X10)
& X8 != X13 )
=> visFreeVar(X0,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar1) ).
fof(f774,plain,
spl92_43,
inference(avatar_split_clause,[],[f393,f772]) ).
fof(f772,plain,
( spl92_43
<=> ! [X2,X0,X1] :
( valphaEquivalent(X1,X2)
| ~ valphaEquivalent(X0,X2)
| ~ valphaEquivalent(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_43])]) ).
fof(f393,plain,
! [X2,X0,X1] :
( valphaEquivalent(X1,X2)
| ~ valphaEquivalent(X0,X2)
| ~ valphaEquivalent(X1,X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0,X1,X2] :
( valphaEquivalent(X1,X2)
| ~ valphaEquivalent(X0,X2)
| ~ valphaEquivalent(X1,X0) ),
inference(flattening,[],[f157]) ).
fof(f157,plain,
! [X0,X1,X2] :
( valphaEquivalent(X1,X2)
| ~ valphaEquivalent(X0,X2)
| ~ valphaEquivalent(X1,X0) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( valphaEquivalent(X0,X2)
& valphaEquivalent(X1,X0) )
=> valphaEquivalent(X1,X2) ),
inference(rectify,[],[f57]) ).
fof(f57,axiom,
! [X12,X11,X34] :
( ( valphaEquivalent(X12,X34)
& valphaEquivalent(X11,X12) )
=> valphaEquivalent(X11,X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','alpha-equiv-trans') ).
fof(f770,plain,
spl92_42,
inference(avatar_split_clause,[],[f392,f768]) ).
fof(f768,plain,
( spl92_42
<=> ! [X2,X0,X1] :
( ~ visFreeVar(X1,X2)
| ~ valphaEquivalent(X0,X2)
| visFreeVar(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_42])]) ).
fof(f392,plain,
! [X2,X0,X1] :
( ~ visFreeVar(X1,X2)
| ~ valphaEquivalent(X0,X2)
| visFreeVar(X1,X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0,X1,X2] :
( ~ visFreeVar(X1,X2)
| ~ valphaEquivalent(X0,X2)
| visFreeVar(X1,X0) ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
! [X0,X1,X2] :
( ~ visFreeVar(X1,X2)
| ~ valphaEquivalent(X0,X2)
| visFreeVar(X1,X0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( valphaEquivalent(X0,X2)
& ~ visFreeVar(X1,X0) )
=> ~ visFreeVar(X1,X2) ),
inference(rectify,[],[f60]) ).
fof(f60,axiom,
! [X10,X8,X11] :
( ( valphaEquivalent(X10,X11)
& ~ visFreeVar(X8,X10) )
=> ~ visFreeVar(X8,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','alpha-equiv-FreeVar') ).
fof(f759,plain,
spl92_41,
inference(avatar_split_clause,[],[f524,f757]) ).
fof(f757,plain,
( spl92_41
<=> ! [X4,X2,X3] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_41])]) ).
fof(f524,plain,
! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) ),
inference(equality_resolution,[],[f523]) ).
fof(f523,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X0,vapp(X2,X4))
| ~ visFreeVar(X3,X2)
| X0 != X3 ),
inference(equality_resolution,[],[f444]) ).
fof(f444,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X2)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0,X1,X2,X3,X4] :
( ( ( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
| ( ~ visFreeVar(X3,X4)
& ~ visFreeVar(X3,X2) ) ) )
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(flattening,[],[f180]) ).
fof(f180,plain,
! [X0,X1,X2,X3,X4] :
( ( ( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
| ( ~ visFreeVar(X3,X4)
& ~ visFreeVar(X3,X2) ) ) )
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(ennf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1,X2,X3,X4] :
( ( vapp(X2,X4) = X1
& X0 = X3 )
=> ( ( visFreeVar(X0,X1)
=> ( visFreeVar(X3,X4)
| visFreeVar(X3,X2) ) )
& ( ( visFreeVar(X3,X4)
| visFreeVar(X3,X2) )
=> visFreeVar(X0,X1) ) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X0,X3,X11,X13,X12] :
( ( vapp(X11,X12) = X3
& X0 = X13 )
=> ( ( visFreeVar(X0,X3)
=> ( visFreeVar(X13,X12)
| visFreeVar(X13,X11) ) )
& ( ( visFreeVar(X13,X12)
| visFreeVar(X13,X11) )
=> visFreeVar(X0,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar2) ).
fof(f755,plain,
spl92_40,
inference(avatar_split_clause,[],[f522,f753]) ).
fof(f522,plain,
! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) ),
inference(equality_resolution,[],[f521]) ).
fof(f521,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X0,vapp(X2,X4))
| ~ visFreeVar(X3,X4)
| X0 != X3 ),
inference(equality_resolution,[],[f445]) ).
fof(f445,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X4)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f181]) ).
fof(f751,plain,
spl92_39,
inference(avatar_split_clause,[],[f439,f749]) ).
fof(f749,plain,
( spl92_39
<=> ! [X4,X0,X3,X2,X1] : vapp(X3,X4) != vabs(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_39])]) ).
fof(f439,plain,
! [X2,X3,X0,X1,X4] : vapp(X3,X4) != vabs(X0,X1,X2),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1,X2,X3,X4] : vapp(X3,X4) != vabs(X0,X1,X2),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X0,X2,X3,X5,X6] : vabs(X0,X2,X3) != vapp(X5,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-abs-app') ).
fof(f747,plain,
spl92_38,
inference(avatar_split_clause,[],[f331,f745]) ).
fof(f745,plain,
( spl92_38
<=> ! [X0,X1] :
( X0 = X1
| vvar(X0) != vvar(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_38])]) ).
fof(f331,plain,
! [X0,X1] :
( X0 = X1
| vvar(X0) != vvar(X1) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0,X1] :
( ( vvar(X0) = vvar(X1)
| X0 != X1 )
& ( X0 = X1
| vvar(X0) != vvar(X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ( X0 = X1
=> vvar(X0) = vvar(X1) )
& ( vvar(X0) = vvar(X1)
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-var') ).
fof(f743,plain,
spl92_37,
inference(avatar_split_clause,[],[f329,f741]) ).
fof(f741,plain,
( spl92_37
<=> ! [X0,X1] :
( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_37])]) ).
fof(f329,plain,
! [X0,X1] :
( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0,X1] :
( ( vsomeExp(X0) = vsomeExp(X1)
| X0 != X1 )
& ( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ( X0 = X1
=> vsomeExp(X0) = vsomeExp(X1) )
& ( vsomeExp(X0) = vsomeExp(X1)
=> X0 = X1 ) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X3,X5] :
( ( X3 = X5
=> vsomeExp(X3) = vsomeExp(X5) )
& ( vsomeExp(X3) = vsomeExp(X5)
=> X3 = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-someExp') ).
fof(f739,plain,
spl92_36,
inference(avatar_split_clause,[],[f327,f737]) ).
fof(f737,plain,
( spl92_36
<=> ! [X0,X1] :
( X0 = X1
| vsomeType(X0) != vsomeType(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_36])]) ).
fof(f327,plain,
! [X0,X1] :
( X0 = X1
| vsomeType(X0) != vsomeType(X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0,X1] :
( ( vsomeType(X0) = vsomeType(X1)
| X0 != X1 )
& ( X0 = X1
| vsomeType(X0) != vsomeType(X1) ) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ( X0 = X1
=> vsomeType(X0) = vsomeType(X1) )
& ( vsomeType(X0) = vsomeType(X1)
=> X0 = X1 ) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X2,X4] :
( ( X2 = X4
=> vsomeType(X2) = vsomeType(X4) )
& ( vsomeType(X2) = vsomeType(X4)
=> X2 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-someType') ).
fof(f734,plain,
spl92_35,
inference(avatar_split_clause,[],[f561,f732]) ).
fof(f732,plain,
( spl92_35
<=> ! [X6,X2] : vsubst(X2,X6,vvar(X2)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl92_35])]) ).
fof(f561,plain,
! [X2,X6] : vsubst(X2,X6,vvar(X2)) = X6,
inference(equality_resolution,[],[f560]) ).
fof(f560,plain,
! [X2,X1,X6] :
( vsubst(X2,X6,vvar(X1)) = X6
| X1 != X2 ),
inference(equality_resolution,[],[f559]) ).
fof(f559,plain,
! [X2,X3,X1,X6] :
( vsubst(X2,X3,vvar(X1)) = X6
| X3 != X6
| X1 != X2 ),
inference(equality_resolution,[],[f558]) ).
fof(f558,plain,
! [X2,X3,X1,X6,X4] :
( vsubst(X2,X3,X4) = X6
| vvar(X1) != X4
| X3 != X6
| X1 != X2 ),
inference(equality_resolution,[],[f557]) ).
fof(f557,plain,
! [X2,X3,X0,X1,X6,X4] :
( vsubst(X2,X3,X4) = X6
| X0 != X1
| vvar(X1) != X4
| X3 != X6
| X0 != X2 ),
inference(equality_resolution,[],[f467]) ).
fof(f467,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( X5 = X6
| vsubst(X2,X3,X4) != X5
| X0 != X1
| vvar(X1) != X4
| X3 != X6
| X0 != X2 ),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X5 = X6
| vsubst(X2,X3,X4) != X5
| X0 != X1
| vvar(X1) != X4
| X3 != X6
| X0 != X2 ),
inference(flattening,[],[f206]) ).
fof(f206,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X5 = X6
| vsubst(X2,X3,X4) != X5
| X0 != X1
| vvar(X1) != X4
| X3 != X6
| X0 != X2 ),
inference(ennf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vvar(X1) = X4
& X3 = X6
& X0 = X2 )
=> ( X0 = X1
=> ( vsubst(X2,X3,X4) = X5
=> X5 = X6 ) ) ),
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X8,X20,X0,X3,X5,X18,X10] :
( ( vvar(X20) = X5
& X3 = X10
& X0 = X8 )
=> ( X8 = X20
=> ( vsubst(X0,X3,X5) = X18
=> X10 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst0) ).
fof(f730,plain,
spl92_34,
inference(avatar_split_clause,[],[f518,f728]) ).
fof(f728,plain,
( spl92_34
<=> ! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_34])]) ).
fof(f518,plain,
! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2)),
inference(equality_resolution,[],[f517]) ).
fof(f517,plain,
! [X2,X3,X0,X1] :
( vnoExp = vreduce(X3)
| vabs(X0,X1,X2) != X3 ),
inference(equality_resolution,[],[f440]) ).
fof(f440,plain,
! [X2,X3,X0,X1,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f174]) ).
fof(f174,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(flattening,[],[f173]) ).
fof(f173,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(ennf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2,X3,X4] :
( vabs(X0,X1,X2) = X3
=> ( vreduce(X3) = X4
=> vnoExp = X4 ) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X8,X9,X10,X3,X18] :
( vabs(X8,X9,X10) = X3
=> ( vreduce(X3) = X18
=> vnoExp = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce1) ).
fof(f726,plain,
spl92_33,
inference(avatar_split_clause,[],[f513,f724]) ).
fof(f724,plain,
( spl92_33
<=> ! [X2,X3] :
( X2 = X3
| ~ visFreeVar(X3,vvar(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_33])]) ).
fof(f513,plain,
! [X2,X3] :
( X2 = X3
| ~ visFreeVar(X3,vvar(X2)) ),
inference(equality_resolution,[],[f512]) ).
fof(f512,plain,
! [X2,X3,X0] :
( X2 = X3
| ~ visFreeVar(X0,vvar(X2))
| X0 != X3 ),
inference(equality_resolution,[],[f437]) ).
fof(f437,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| ~ visFreeVar(X0,X1)
| vvar(X2) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f170]) ).
fof(f170,plain,
! [X0,X1,X2,X3] :
( ( ( X2 = X3
| ~ visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
| X2 != X3 ) )
| vvar(X2) != X1
| X0 != X3 ),
inference(flattening,[],[f169]) ).
fof(f169,plain,
! [X0,X1,X2,X3] :
( ( ( X2 = X3
| ~ visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
| X2 != X3 ) )
| vvar(X2) != X1
| X0 != X3 ),
inference(ennf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2,X3] :
( ( vvar(X2) = X1
& X0 = X3 )
=> ( ( visFreeVar(X0,X1)
=> X2 = X3 )
& ( X2 = X3
=> visFreeVar(X0,X1) ) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X0,X3,X8,X13] :
( ( vvar(X8) = X3
& X0 = X13 )
=> ( ( visFreeVar(X0,X3)
=> X8 = X13 )
& ( X8 = X13
=> visFreeVar(X0,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar0) ).
fof(f722,plain,
spl92_32,
inference(avatar_split_clause,[],[f394,f720]) ).
fof(f720,plain,
( spl92_32
<=> ! [X2,X0,X1,X3] : vvar(X0) != vabs(X1,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_32])]) ).
fof(f394,plain,
! [X2,X3,X0,X1] : vvar(X0) != vabs(X1,X2,X3),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1,X2,X3] : vvar(X0) != vabs(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-var-abs') ).
fof(f718,plain,
spl92_31,
inference(avatar_split_clause,[],[f359,f716]) ).
fof(f716,plain,
( spl92_31
<=> ! [X0,X1] :
( visValue(sK37(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_31])]) ).
fof(f359,plain,
! [X0,X1] :
( visValue(sK37(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f263]) ).
fof(f263,plain,
! [X0,X1] :
( ( vsomeExp(vsubst(sK36(X0,X1),sK37(X0,X1),sK38(X0,X1))) = X0
& visValue(sK37(X0,X1))
& ~ visSomeExp(sK35(X0,X1))
& sK35(X0,X1) = vreduce(sK37(X0,X1))
& vapp(vabs(sK36(X0,X1),sK34(X0,X1),sK38(X0,X1)),sK37(X0,X1)) = X1 )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35,sK36,sK37,sK38])],[f261,f262]) ).
fof(f262,plain,
! [X0,X1] :
( ? [X2,X3,X4,X5,X6] :
( vsomeExp(vsubst(X4,X5,X6)) = X0
& visValue(X5)
& ~ visSomeExp(X3)
& vreduce(X5) = X3
& vapp(vabs(X4,X2,X6),X5) = X1 )
=> ( vsomeExp(vsubst(sK36(X0,X1),sK37(X0,X1),sK38(X0,X1))) = X0
& visValue(sK37(X0,X1))
& ~ visSomeExp(sK35(X0,X1))
& sK35(X0,X1) = vreduce(sK37(X0,X1))
& vapp(vabs(sK36(X0,X1),sK34(X0,X1),sK38(X0,X1)),sK37(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f261,plain,
! [X0,X1] :
( ? [X2,X3,X4,X5,X6] :
( vsomeExp(vsubst(X4,X5,X6)) = X0
& visValue(X5)
& ~ visSomeExp(X3)
& vreduce(X5) = X3
& vapp(vabs(X4,X2,X6),X5) = X1 )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f260]) ).
fof(f260,plain,
! [X1,X0] :
( ? [X19,X20,X21,X22,X23] :
( vsomeExp(vsubst(X21,X22,X23)) = X1
& visValue(X22)
& ~ visSomeExp(X20)
& vreduce(X22) = X20
& vapp(vabs(X21,X19,X23),X22) = X0 )
| ~ sP0(X1,X0) ),
inference(nnf_transformation,[],[f224]) ).
fof(f224,plain,
! [X1,X0] :
( ? [X19,X20,X21,X22,X23] :
( vsomeExp(vsubst(X21,X22,X23)) = X1
& visValue(X22)
& ~ visSomeExp(X20)
& vreduce(X22) = X20
& vapp(vabs(X21,X19,X23),X22) = X0 )
| ~ sP0(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f714,plain,
spl92_30,
inference(avatar_split_clause,[],[f358,f712]) ).
fof(f712,plain,
( spl92_30
<=> ! [X0,X1] :
( ~ visSomeExp(sK35(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_30])]) ).
fof(f358,plain,
! [X0,X1] :
( ~ visSomeExp(sK35(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f263]) ).
fof(f710,plain,
spl92_29,
inference(avatar_split_clause,[],[f354,f708]) ).
fof(f708,plain,
( spl92_29
<=> ! [X0,X1] :
( ~ visValue(sK33(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_29])]) ).
fof(f354,plain,
! [X0,X1] :
( ~ visValue(sK33(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f259]) ).
fof(f259,plain,
! [X0,X1] :
( ( vnoExp = X0
& ~ visValue(sK33(X0,X1))
& ~ visSomeExp(sK32(X0,X1))
& sK32(X0,X1) = vreduce(sK33(X0,X1))
& vapp(vabs(sK29(X0,X1),sK30(X0,X1),sK31(X0,X1)),sK33(X0,X1)) = X1 )
| ~ sP1(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31,sK32,sK33])],[f257,f258]) ).
fof(f258,plain,
! [X0,X1] :
( ? [X2,X3,X4,X5,X6] :
( vnoExp = X0
& ~ visValue(X6)
& ~ visSomeExp(X5)
& vreduce(X6) = X5
& vapp(vabs(X2,X3,X4),X6) = X1 )
=> ( vnoExp = X0
& ~ visValue(sK33(X0,X1))
& ~ visSomeExp(sK32(X0,X1))
& sK32(X0,X1) = vreduce(sK33(X0,X1))
& vapp(vabs(sK29(X0,X1),sK30(X0,X1),sK31(X0,X1)),sK33(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f257,plain,
! [X0,X1] :
( ? [X2,X3,X4,X5,X6] :
( vnoExp = X0
& ~ visValue(X6)
& ~ visSomeExp(X5)
& vreduce(X6) = X5
& vapp(vabs(X2,X3,X4),X6) = X1 )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f256]) ).
fof(f256,plain,
! [X1,X0] :
( ? [X14,X15,X16,X17,X18] :
( vnoExp = X1
& ~ visValue(X18)
& ~ visSomeExp(X17)
& vreduce(X18) = X17
& vapp(vabs(X14,X15,X16),X18) = X0 )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f225]) ).
fof(f225,plain,
! [X1,X0] :
( ? [X14,X15,X16,X17,X18] :
( vnoExp = X1
& ~ visValue(X18)
& ~ visSomeExp(X17)
& vreduce(X18) = X17
& vapp(vabs(X14,X15,X16),X18) = X0 )
| ~ sP1(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f706,plain,
spl92_28,
inference(avatar_split_clause,[],[f353,f704]) ).
fof(f704,plain,
( spl92_28
<=> ! [X0,X1] :
( ~ visSomeExp(sK32(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_28])]) ).
fof(f353,plain,
! [X0,X1] :
( ~ visSomeExp(sK32(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f259]) ).
fof(f702,plain,
spl92_27,
inference(avatar_split_clause,[],[f349,f700]) ).
fof(f700,plain,
( spl92_27
<=> ! [X0,X1] :
( visSomeExp(sK27(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_27])]) ).
fof(f349,plain,
! [X0,X1] :
( visSomeExp(sK27(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0,X1] :
( ( vsomeExp(vapp(vgetSomeExp(sK27(X0,X1)),sK28(X0,X1))) = X0
& visSomeExp(sK27(X0,X1))
& sK27(X0,X1) = vreduce(sK26(X0,X1))
& ! [X5,X6,X7] : vabs(X5,X6,X7) != sK26(X0,X1)
& vapp(sK26(X0,X1),sK28(X0,X1)) = X1 )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27,sK28])],[f253,f254]) ).
fof(f254,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( vsomeExp(vapp(vgetSomeExp(X3),X4)) = X0
& visSomeExp(X3)
& vreduce(X2) = X3
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X2
& vapp(X2,X4) = X1 )
=> ( vsomeExp(vapp(vgetSomeExp(sK27(X0,X1)),sK28(X0,X1))) = X0
& visSomeExp(sK27(X0,X1))
& sK27(X0,X1) = vreduce(sK26(X0,X1))
& ! [X7,X6,X5] : vabs(X5,X6,X7) != sK26(X0,X1)
& vapp(sK26(X0,X1),sK28(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f253,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( vsomeExp(vapp(vgetSomeExp(X3),X4)) = X0
& visSomeExp(X3)
& vreduce(X2) = X3
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X2
& vapp(X2,X4) = X1 )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f252]) ).
fof(f252,plain,
! [X1,X0] :
( ? [X8,X9,X10] :
( vsomeExp(vapp(vgetSomeExp(X9),X10)) = X1
& visSomeExp(X9)
& vreduce(X8) = X9
& ! [X11,X12,X13] : vabs(X11,X12,X13) != X8
& vapp(X8,X10) = X0 )
| ~ sP2(X1,X0) ),
inference(nnf_transformation,[],[f226]) ).
fof(f226,plain,
! [X1,X0] :
( ? [X8,X9,X10] :
( vsomeExp(vapp(vgetSomeExp(X9),X10)) = X1
& visSomeExp(X9)
& vreduce(X8) = X9
& ! [X11,X12,X13] : vabs(X11,X12,X13) != X8
& vapp(X8,X10) = X0 )
| ~ sP2(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f698,plain,
spl92_26,
inference(avatar_split_clause,[],[f344,f696]) ).
fof(f696,plain,
( spl92_26
<=> ! [X0,X1] :
( ~ visSomeExp(sK25(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_26])]) ).
fof(f344,plain,
! [X0,X1] :
( ~ visSomeExp(sK25(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f251,plain,
! [X0,X1] :
( ( vnoExp = X0
& ~ visSomeExp(sK25(X0,X1))
& sK25(X0,X1) = vreduce(sK24(X0,X1))
& ! [X5,X6,X7] : vabs(X5,X6,X7) != sK24(X0,X1)
& vapp(sK24(X0,X1),sK23(X0,X1)) = X1 )
| ~ sP3(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24,sK25])],[f249,f250]) ).
fof(f250,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( vnoExp = X0
& ~ visSomeExp(X4)
& vreduce(X3) = X4
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X3
& vapp(X3,X2) = X1 )
=> ( vnoExp = X0
& ~ visSomeExp(sK25(X0,X1))
& sK25(X0,X1) = vreduce(sK24(X0,X1))
& ! [X7,X6,X5] : vabs(X5,X6,X7) != sK24(X0,X1)
& vapp(sK24(X0,X1),sK23(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f249,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( vnoExp = X0
& ~ visSomeExp(X4)
& vreduce(X3) = X4
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X3
& vapp(X3,X2) = X1 )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f248]) ).
fof(f248,plain,
! [X1,X0] :
( ? [X2,X3,X4] :
( vnoExp = X1
& ~ visSomeExp(X4)
& vreduce(X3) = X4
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X3
& vapp(X3,X2) = X0 )
| ~ sP3(X1,X0) ),
inference(nnf_transformation,[],[f227]) ).
fof(f227,plain,
! [X1,X0] :
( ? [X2,X3,X4] :
( vnoExp = X1
& ~ visSomeExp(X4)
& vreduce(X3) = X4
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X3
& vapp(X3,X2) = X0 )
| ~ sP3(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f694,plain,
spl92_25,
inference(avatar_split_clause,[],[f339,f692]) ).
fof(f692,plain,
( spl92_25
<=> ! [X0,X1] :
( visSomeExp(sK22(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_25])]) ).
fof(f339,plain,
! [X0,X1] :
( visSomeExp(sK22(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f247,plain,
! [X0,X1] :
( ( vsomeExp(vapp(vabs(sK19(X0,X1),sK20(X0,X1),sK21(X0,X1)),vgetSomeExp(sK22(X0,X1)))) = X0
& visSomeExp(sK22(X0,X1))
& sK22(X0,X1) = vreduce(sK18(X0,X1))
& vapp(vabs(sK19(X0,X1),sK20(X0,X1),sK21(X0,X1)),sK18(X0,X1)) = X1 )
| ~ sP4(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22])],[f245,f246]) ).
fof(f246,plain,
! [X0,X1] :
( ? [X2,X3,X4,X5,X6] :
( vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(X6))) = X0
& visSomeExp(X6)
& vreduce(X2) = X6
& vapp(vabs(X3,X4,X5),X2) = X1 )
=> ( vsomeExp(vapp(vabs(sK19(X0,X1),sK20(X0,X1),sK21(X0,X1)),vgetSomeExp(sK22(X0,X1)))) = X0
& visSomeExp(sK22(X0,X1))
& sK22(X0,X1) = vreduce(sK18(X0,X1))
& vapp(vabs(sK19(X0,X1),sK20(X0,X1),sK21(X0,X1)),sK18(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f245,plain,
! [X0,X1] :
( ? [X2,X3,X4,X5,X6] :
( vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(X6))) = X0
& visSomeExp(X6)
& vreduce(X2) = X6
& vapp(vabs(X3,X4,X5),X2) = X1 )
| ~ sP4(X0,X1) ),
inference(rectify,[],[f244]) ).
fof(f244,plain,
! [X1,X0] :
( ? [X24,X25,X26,X27,X28] :
( vsomeExp(vapp(vabs(X25,X26,X27),vgetSomeExp(X28))) = X1
& visSomeExp(X28)
& vreduce(X24) = X28
& vapp(vabs(X25,X26,X27),X24) = X0 )
| ~ sP4(X1,X0) ),
inference(nnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X1,X0] :
( ? [X24,X25,X26,X27,X28] :
( vsomeExp(vapp(vabs(X25,X26,X27),vgetSomeExp(X28))) = X1
& visSomeExp(X28)
& vreduce(X24) = X28
& vapp(vabs(X25,X26,X27),X24) = X0 )
| ~ sP4(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f689,plain,
spl92_24,
inference(avatar_split_clause,[],[f541,f687]) ).
fof(f687,plain,
( spl92_24
<=> ! [X4,X5,X0] : ~ visFreeVar(X4,vabs(X4,X0,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_24])]) ).
fof(f541,plain,
! [X0,X4,X5] : ~ visFreeVar(X4,vabs(X4,X0,X5)),
inference(equality_resolution,[],[f540]) ).
fof(f540,plain,
! [X0,X1,X4,X5] :
( ~ visFreeVar(X1,vabs(X4,X0,X5))
| X1 != X4 ),
inference(equality_resolution,[],[f539]) ).
fof(f539,plain,
! [X2,X0,X1,X4,X5] :
( ~ visFreeVar(X1,X2)
| vabs(X4,X0,X5) != X2
| X1 != X4 ),
inference(equality_resolution,[],[f460]) ).
fof(f460,plain,
! [X2,X3,X0,X1,X4,X5] :
( X3 != X4
| ~ visFreeVar(X1,X2)
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(cnf_transformation,[],[f195]) ).
fof(f685,plain,
spl92_23,
inference(avatar_split_clause,[],[f367,f683]) ).
fof(f683,plain,
( spl92_23
<=> ! [X2,X0,X1] : vvar(X0) != vapp(X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_23])]) ).
fof(f367,plain,
! [X2,X0,X1] : vvar(X0) != vapp(X1,X2),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2] : vvar(X0) != vapp(X1,X2),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X3,X5] : vvar(X0) != vapp(X3,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-var-app') ).
fof(f681,plain,
spl92_22,
inference(avatar_split_clause,[],[f366,f679]) ).
fof(f679,plain,
( spl92_22
<=> ! [X2,X0,X1] : vempty != vbind(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_22])]) ).
fof(f366,plain,
! [X2,X0,X1] : vempty != vbind(X0,X1,X2),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2] : vempty != vbind(X0,X1,X2),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X0,X2,X15] : vempty != vbind(X0,X2,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-empty-bind') ).
fof(f677,plain,
spl92_21,
inference(avatar_split_clause,[],[f355,f675]) ).
fof(f675,plain,
( spl92_21
<=> ! [X0,X1] :
( vnoExp = X0
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_21])]) ).
fof(f355,plain,
! [X0,X1] :
( vnoExp = X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f259]) ).
fof(f673,plain,
spl92_20,
inference(avatar_split_clause,[],[f345,f671]) ).
fof(f671,plain,
( spl92_20
<=> ! [X0,X1] :
( vnoExp = X0
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_20])]) ).
fof(f345,plain,
! [X0,X1] :
( vnoExp = X0
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f669,plain,
spl92_19,
inference(avatar_split_clause,[],[f333,f667]) ).
fof(f667,plain,
( spl92_19
<=> ! [X0,X1] :
( valphaEquivalent(X0,X1)
| ~ valphaEquivalent(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_19])]) ).
fof(f333,plain,
! [X0,X1] :
( valphaEquivalent(X0,X1)
| ~ valphaEquivalent(X1,X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0,X1] :
( valphaEquivalent(X0,X1)
| ~ valphaEquivalent(X1,X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( valphaEquivalent(X1,X0)
=> valphaEquivalent(X0,X1) ),
inference(rectify,[],[f56]) ).
fof(f56,axiom,
! [X12,X11] :
( valphaEquivalent(X11,X12)
=> valphaEquivalent(X12,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','alpha-equiv-sym') ).
fof(f665,plain,
spl92_18,
inference(avatar_split_clause,[],[f511,f663]) ).
fof(f663,plain,
( spl92_18
<=> ! [X1] : vnoType = vlookup(X1,vempty) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_18])]) ).
fof(f511,plain,
! [X1] : vnoType = vlookup(X1,vempty),
inference(equality_resolution,[],[f510]) ).
fof(f510,plain,
! [X0,X1] :
( vnoType = vlookup(X1,vempty)
| X0 != X1 ),
inference(equality_resolution,[],[f509]) ).
fof(f509,plain,
! [X2,X0,X1] :
( vnoType = vlookup(X1,X2)
| vempty != X2
| X0 != X1 ),
inference(equality_resolution,[],[f435]) ).
fof(f435,plain,
! [X2,X3,X0,X1] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(cnf_transformation,[],[f168]) ).
fof(f168,plain,
! [X0,X1,X2,X3] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(flattening,[],[f167]) ).
fof(f167,plain,
! [X0,X1,X2,X3] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(ennf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1,X2,X3] :
( ( vempty = X2
& X0 = X1 )
=> ( vlookup(X1,X2) = X3
=> vnoType = X3 ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X8,X0,X15,X18] :
( ( vempty = X15
& X0 = X8 )
=> ( vlookup(X0,X15) = X18
=> vnoType = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lookup0) ).
fof(f661,plain,
spl92_17,
inference(avatar_split_clause,[],[f508,f659]) ).
fof(f659,plain,
( spl92_17
<=> ! [X2,X0,X1] : visValue(vabs(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_17])]) ).
fof(f508,plain,
! [X2,X0,X1] : visValue(vabs(X0,X1,X2)),
inference(equality_resolution,[],[f434]) ).
fof(f434,plain,
! [X2,X3,X0,X1] :
( visValue(X3)
| vabs(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
! [X0,X1,X2,X3] :
( visValue(X3)
| vabs(X0,X1,X2) != X3 ),
inference(ennf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1,X2,X3] :
( vabs(X0,X1,X2) = X3
=> visValue(X3) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X8,X9,X10,X3] :
( vabs(X8,X9,X10) = X3
=> visValue(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue0) ).
fof(f657,plain,
spl92_16,
inference(avatar_split_clause,[],[f495,f655]) ).
fof(f655,plain,
( spl92_16
<=> ! [X0] : vnoExp = vreduce(vvar(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_16])]) ).
fof(f495,plain,
! [X0] : vnoExp = vreduce(vvar(X0)),
inference(equality_resolution,[],[f494]) ).
fof(f494,plain,
! [X0,X1] :
( vnoExp = vreduce(X1)
| vvar(X0) != X1 ),
inference(equality_resolution,[],[f370]) ).
fof(f370,plain,
! [X2,X0,X1] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0,X1,X2] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(flattening,[],[f147]) ).
fof(f147,plain,
! [X0,X1,X2] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2] :
( vvar(X0) = X1
=> ( vreduce(X1) = X2
=> vnoExp = X2 ) ),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X8,X3,X18] :
( vvar(X8) = X3
=> ( vreduce(X3) = X18
=> vnoExp = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce0) ).
fof(f653,plain,
spl92_15,
inference(avatar_split_clause,[],[f493,f651]) ).
fof(f651,plain,
( spl92_15
<=> ! [X2] : vgetSomeExp(vsomeExp(X2)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl92_15])]) ).
fof(f493,plain,
! [X2] : vgetSomeExp(vsomeExp(X2)) = X2,
inference(equality_resolution,[],[f492]) ).
fof(f492,plain,
! [X2,X0] :
( vgetSomeExp(X0) = X2
| vsomeExp(X2) != X0 ),
inference(equality_resolution,[],[f369]) ).
fof(f369,plain,
! [X2,X0,X1] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(flattening,[],[f145]) ).
fof(f145,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2] :
( vsomeExp(X2) = X0
=> ( vgetSomeExp(X0) = X1
=> X1 = X2 ) ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X24,X18,X10] :
( vsomeExp(X10) = X24
=> ( vgetSomeExp(X24) = X18
=> X10 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',getSomeExp0) ).
fof(f649,plain,
spl92_14,
inference(avatar_split_clause,[],[f491,f647]) ).
fof(f647,plain,
( spl92_14
<=> ! [X2] : vgetSomeType(vsomeType(X2)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl92_14])]) ).
fof(f491,plain,
! [X2] : vgetSomeType(vsomeType(X2)) = X2,
inference(equality_resolution,[],[f490]) ).
fof(f490,plain,
! [X2,X0] :
( vgetSomeType(X0) = X2
| vsomeType(X2) != X0 ),
inference(equality_resolution,[],[f368]) ).
fof(f368,plain,
! [X2,X0,X1] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(flattening,[],[f143]) ).
fof(f143,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2] :
( vsomeType(X2) = X0
=> ( vgetSomeType(X0) = X1
=> X1 = X2 ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X17,X18,X10] :
( vsomeType(X10) = X17
=> ( vgetSomeType(X17) = X18
=> X10 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',getSomeType0) ).
fof(f645,plain,
( ~ spl92_13
| ~ spl92_3
| ~ spl92_10 ),
inference(avatar_split_clause,[],[f640,f629,f600,f642]) ).
fof(f600,plain,
( spl92_3
<=> sK17 = vgensym(vapp(vapp(sK14,sK15),vvar(sK17))) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_3])]) ).
fof(f629,plain,
( spl92_10
<=> ! [X1] : ~ visFreeVar(vgensym(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_10])]) ).
fof(f640,plain,
( ~ visFreeVar(sK17,vapp(vapp(sK14,sK15),vvar(sK17)))
| ~ spl92_3
| ~ spl92_10 ),
inference(superposition,[],[f630,f602]) ).
fof(f602,plain,
( sK17 = vgensym(vapp(vapp(sK14,sK15),vvar(sK17)))
| ~ spl92_3 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f630,plain,
( ! [X1] : ~ visFreeVar(vgensym(X1),X1)
| ~ spl92_10 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f639,plain,
spl92_12,
inference(avatar_split_clause,[],[f516,f637]) ).
fof(f516,plain,
! [X3] : visFreeVar(X3,vvar(X3)),
inference(equality_resolution,[],[f515]) ).
fof(f515,plain,
! [X3,X0] :
( visFreeVar(X0,vvar(X3))
| X0 != X3 ),
inference(equality_resolution,[],[f514]) ).
fof(f514,plain,
! [X3,X0,X1] :
( visFreeVar(X0,X1)
| vvar(X3) != X1
| X0 != X3 ),
inference(equality_resolution,[],[f436]) ).
fof(f436,plain,
! [X2,X3,X0,X1] :
( visFreeVar(X0,X1)
| X2 != X3
| vvar(X2) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f170]) ).
fof(f635,plain,
spl92_11,
inference(avatar_split_clause,[],[f499,f633]) ).
fof(f633,plain,
( spl92_11
<=> ! [X0,X1] : ~ visValue(vapp(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_11])]) ).
fof(f499,plain,
! [X0,X1] : ~ visValue(vapp(X0,X1)),
inference(equality_resolution,[],[f390]) ).
fof(f390,plain,
! [X2,X0,X1] :
( ~ visValue(X2)
| vapp(X0,X1) != X2 ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0,X1,X2] :
( ~ visValue(X2)
| vapp(X0,X1) != X2 ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( vapp(X0,X1) = X2
=> ~ visValue(X2) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X11,X12,X3] :
( vapp(X11,X12) = X3
=> ~ visValue(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue2) ).
fof(f631,plain,
spl92_10,
inference(avatar_split_clause,[],[f482,f629]) ).
fof(f482,plain,
! [X1] : ~ visFreeVar(vgensym(X1),X1),
inference(equality_resolution,[],[f334]) ).
fof(f334,plain,
! [X0,X1] :
( ~ visFreeVar(X0,X1)
| vgensym(X1) != X0 ),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0,X1] :
( ~ visFreeVar(X0,X1)
| vgensym(X1) != X0 ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( vgensym(X1) = X0
=> ~ visFreeVar(X0,X1) ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X13,X10] :
( vgensym(X10) = X13
=> ~ visFreeVar(X13,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','gensym-is-fresh') ).
fof(f627,plain,
spl92_9,
inference(avatar_split_clause,[],[f324,f625]) ).
fof(f625,plain,
( spl92_9
<=> ! [X0] : vnoExp != vsomeExp(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_9])]) ).
fof(f324,plain,
! [X0] : vnoExp != vsomeExp(X0),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0] : vnoExp != vsomeExp(X0),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X3] : vnoExp != vsomeExp(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-noExp-someExp') ).
fof(f623,plain,
spl92_8,
inference(avatar_split_clause,[],[f323,f621]) ).
fof(f621,plain,
( spl92_8
<=> ! [X0] : vnoType != vsomeType(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_8])]) ).
fof(f323,plain,
! [X0] : vnoType != vsomeType(X0),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] : vnoType != vsomeType(X0),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X2] : vnoType != vsomeType(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-noType-someType') ).
fof(f619,plain,
spl92_7,
inference(avatar_split_clause,[],[f489,f617]) ).
fof(f617,plain,
( spl92_7
<=> ! [X0] : ~ visValue(vvar(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_7])]) ).
fof(f489,plain,
! [X0] : ~ visValue(vvar(X0)),
inference(equality_resolution,[],[f365]) ).
fof(f365,plain,
! [X0,X1] :
( ~ visValue(X1)
| vvar(X0) != X1 ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0,X1] :
( ~ visValue(X1)
| vvar(X0) != X1 ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( vvar(X0) = X1
=> ~ visValue(X1) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X8,X3] :
( vvar(X8) = X3
=> ~ visValue(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue1) ).
fof(f615,plain,
spl92_6,
inference(avatar_split_clause,[],[f484,f613]) ).
fof(f613,plain,
( spl92_6
<=> ! [X0] : visSomeExp(vsomeExp(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_6])]) ).
fof(f484,plain,
! [X0] : visSomeExp(vsomeExp(X0)),
inference(equality_resolution,[],[f336]) ).
fof(f336,plain,
! [X0,X1] :
( visSomeExp(X1)
| vsomeExp(X0) != X1 ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
! [X0,X1] :
( visSomeExp(X1)
| vsomeExp(X0) != X1 ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( vsomeExp(X0) = X1
=> visSomeExp(X1) ),
inference(rectify,[],[f40]) ).
fof(f40,axiom,
! [X10,X24] :
( vsomeExp(X10) = X24
=> visSomeExp(X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeExp1) ).
fof(f611,plain,
spl92_5,
inference(avatar_split_clause,[],[f483,f609]) ).
fof(f609,plain,
( spl92_5
<=> ! [X0] : visSomeType(vsomeType(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_5])]) ).
fof(f483,plain,
! [X0] : visSomeType(vsomeType(X0)),
inference(equality_resolution,[],[f335]) ).
fof(f335,plain,
! [X0,X1] :
( visSomeType(X1)
| vsomeType(X0) != X1 ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
! [X0,X1] :
( visSomeType(X1)
| vsomeType(X0) != X1 ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( vsomeType(X0) = X1
=> visSomeType(X1) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X10,X17] :
( vsomeType(X10) = X17
=> visSomeType(X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeType1) ).
fof(f607,plain,
spl92_4,
inference(avatar_split_clause,[],[f322,f605]) ).
fof(f605,plain,
( spl92_4
<=> ! [X0] : valphaEquivalent(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_4])]) ).
fof(f322,plain,
! [X0] : valphaEquivalent(X0,X0),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] : valphaEquivalent(X0,X0),
inference(rectify,[],[f55]) ).
fof(f55,axiom,
! [X10] : valphaEquivalent(X10,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','alpha-equiv-refl') ).
fof(f603,plain,
spl92_3,
inference(avatar_split_clause,[],[f476,f600]) ).
fof(f476,plain,
sK17 = vgensym(vapp(vapp(sK14,sK15),vvar(sK17))),
inference(definition_unfolding,[],[f317,f318]) ).
fof(f318,plain,
sK16 = sK17,
inference(cnf_transformation,[],[f243]) ).
fof(f243,plain,
( sK16 = sK17
& sK17 = vgensym(vapp(vapp(sK14,sK15),vvar(sK16))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17])],[f130,f242]) ).
fof(f242,plain,
( ? [X0,X1,X2,X3] :
( X2 = X3
& vgensym(vapp(vapp(X0,X1),vvar(X2))) = X3 )
=> ( sK16 = sK17
& sK17 = vgensym(vapp(vapp(sK14,sK15),vvar(sK16))) ) ),
introduced(choice_axiom,[]) ).
fof(f130,plain,
? [X0,X1,X2,X3] :
( X2 = X3
& vgensym(vapp(vapp(X0,X1),vvar(X2))) = X3 ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,plain,
~ ! [X0,X1,X2,X3] :
( vgensym(vapp(vapp(X0,X1),vvar(X2))) = X3
=> X2 != X3 ),
inference(rectify,[],[f66]) ).
fof(f66,negated_conjecture,
~ ! [X10,X11,X8,X23] :
( vgensym(vapp(vapp(X10,X11),vvar(X8))) = X23
=> X8 != X23 ),
inference(negated_conjecture,[],[f65]) ).
fof(f65,conjecture,
! [X10,X11,X8,X23] :
( vgensym(vapp(vapp(X10,X11),vvar(X8))) = X23
=> X8 != X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','fresh-unequal-var-3') ).
fof(f317,plain,
sK17 = vgensym(vapp(vapp(sK14,sK15),vvar(sK16))),
inference(cnf_transformation,[],[f243]) ).
fof(f598,plain,
~ spl92_2,
inference(avatar_split_clause,[],[f478,f595]) ).
fof(f595,plain,
( spl92_2
<=> visSomeExp(vnoExp) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_2])]) ).
fof(f478,plain,
~ visSomeExp(vnoExp),
inference(equality_resolution,[],[f326]) ).
fof(f326,plain,
! [X0] :
( ~ visSomeExp(X0)
| vnoExp != X0 ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ~ visSomeExp(X0)
| vnoExp != X0 ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( vnoExp = X0
=> ~ visSomeExp(X0) ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X24] :
( vnoExp = X24
=> ~ visSomeExp(X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeExp0) ).
fof(f593,plain,
~ spl92_1,
inference(avatar_split_clause,[],[f477,f590]) ).
fof(f590,plain,
( spl92_1
<=> visSomeType(vnoType) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_1])]) ).
fof(f477,plain,
~ visSomeType(vnoType),
inference(equality_resolution,[],[f325]) ).
fof(f325,plain,
! [X0] :
( ~ visSomeType(X0)
| vnoType != X0 ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0] :
( ~ visSomeType(X0)
| vnoType != X0 ),
inference(ennf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( vnoType = X0
=> ~ visSomeType(X0) ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X17] :
( vnoType = X17
=> ~ visSomeType(X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeType0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM128+1 : TPTP v8.1.2. Released v6.4.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n013.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 21:25:08 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (6082)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (6087)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)
% 0.15/0.37 % (6085)WARNING: value z3 for option sas not known
% 0.15/0.37 % (6083)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (6084)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37 % (6086)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % (6085)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)
% 0.15/0.37 % (6088)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)
% 0.15/0.37 % (6089)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)
% 0.15/0.38 % (6087)First to succeed.
% 0.15/0.38 % (6085)Also succeeded, but the first one will report.
% 0.15/0.38 % (6088)Also succeeded, but the first one will report.
% 0.15/0.38 % (6087)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-6082"
% 0.15/0.39 % (6087)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39 % (6087)------------------------------
% 0.15/0.39 % (6087)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39 % (6087)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (6087)Memory used [KB]: 1243
% 0.15/0.39 % (6087)Time elapsed: 0.017 s
% 0.15/0.39 % (6087)Instructions burned: 31 (million)
% 0.15/0.39 % (6082)Success in time 0.033 s
%------------------------------------------------------------------------------