TSTP Solution File: SCT167+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT167+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n020.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 09:02:07 EDT 2024
% Result : ContradictoryAxioms 118.63s 17.41s
% Output : Refutation 118.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of formulae : 95 ( 39 unt; 0 def)
% Number of atoms : 195 ( 61 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 166 ( 66 ~; 53 |; 19 &)
% ( 9 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 4 con; 0-6 aty)
% Number of variables : 238 ( 226 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f153988,plain,
$false,
inference(resolution,[],[f153928,f1891]) ).
fof(f1891,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(cnf_transformation,[],[f247]) ).
fof(f247,axiom,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__indi) ).
fof(f153928,plain,
! [X0] : ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(resolution,[],[f153886,f17057]) ).
fof(f17057,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(resolution,[],[f16944,f2909]) ).
fof(f2909,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(resolution,[],[f1977,f1874]) ).
fof(f1874,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(cnf_transformation,[],[f504]) ).
fof(f504,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(f1977,plain,
! [X0] :
( ~ class_Rings_Olinordered__semidom(X0)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0)),c_Groups_Ozero__class_Ozero(X0))) ),
inference(cnf_transformation,[],[f1042]) ).
fof(f1042,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0)),c_Groups_Ozero__class_Ozero(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(ennf_transformation,[],[f573]) ).
fof(f573,plain,
! [X0] :
( class_Rings_Olinordered__semidom(X0)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0)),c_Groups_Ozero__class_Ozero(X0))) ),
inference(rectify,[],[f331]) ).
fof(f331,axiom,
! [X11] :
( class_Rings_Olinordered__semidom(X11)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X11,c_Groups_Oone__class_Oone(X11)),c_Groups_Ozero__class_Ozero(X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(f16944,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(superposition,[],[f2901,f12592]) ).
fof(f12592,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Finite__Set_Ocard(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(resolution,[],[f12496,f4243]) ).
fof(f4243,plain,
! [X2,X3,X1] : hBOOL(hAPP(hAPP(c_member(X3),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))),
inference(superposition,[],[f4068,f4056]) ).
fof(f4056,plain,
! [X2,X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = c_Set_Oinsert(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(superposition,[],[f3209,f3189]) ).
fof(f3189,plain,
! [X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = c_Set_Oinsert(X0,X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(resolution,[],[f2345,f2069]) ).
fof(f2069,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f602]) ).
fof(f602,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f245]) ).
fof(f245,axiom,
! [X8,X11] : hBOOL(hAPP(hAPP(c_member(X11),X8),c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
fof(f2345,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| c_Set_Oinsert(X2,X1,X0) = X0 ),
inference(cnf_transformation,[],[f1273]) ).
fof(f1273,plain,
! [X0,X1,X2] :
( c_Set_Oinsert(X2,X1,X0) = X0
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0)) ),
inference(ennf_transformation,[],[f808]) ).
fof(f808,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
=> c_Set_Oinsert(X2,X1,X0) = X0 ),
inference(rectify,[],[f276]) ).
fof(f276,axiom,
! [X13,X23,X11] :
( hBOOL(hAPP(hAPP(c_member(X11),X23),X13))
=> c_Set_Oinsert(X11,X23,X13) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(f3209,plain,
! [X2,X3,X0,X1] : c_Set_Oinsert(X2,X1,X3) = c_Set_Oinsert(X0,X1,c_Set_Oinsert(X2,X1,X3)),
inference(resolution,[],[f3186,f2783]) ).
fof(f2783,plain,
! [X2,X3,X1] : hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X2)),
inference(equality_resolution,[],[f2526]) ).
fof(f2526,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0))
| X0 != X2 ),
inference(cnf_transformation,[],[f1783]) ).
fof(f1783,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0))
| ( ~ hBOOL(hAPP(X1,X0))
& X0 != X2 ) )
& ( hBOOL(hAPP(X1,X0))
| X0 = X2
| ~ hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0)) ) ),
inference(flattening,[],[f1782]) ).
fof(f1782,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0))
| ( ~ hBOOL(hAPP(X1,X0))
& X0 != X2 ) )
& ( hBOOL(hAPP(X1,X0))
| X0 = X2
| ~ hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0)) ) ),
inference(nnf_transformation,[],[f931]) ).
fof(f931,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0))
<=> ( hBOOL(hAPP(X1,X0))
| X0 = X2 ) ),
inference(rectify,[],[f281]) ).
fof(f281,axiom,
! [X8,X13,X7,X11] :
( hBOOL(hAPP(c_Set_Oinsert(X11,X7,X13),X8))
<=> ( hBOOL(hAPP(X13,X8))
| X7 = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
fof(f3186,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Set_Oinsert(X0,X1,X2) = X2 ),
inference(resolution,[],[f2345,f2371]) ).
fof(f2371,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f1730]) ).
fof(f1730,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| ~ hBOOL(hAPP(X0,X1)) )
& ( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0)) ) ),
inference(nnf_transformation,[],[f823]) ).
fof(f823,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
<=> hBOOL(hAPP(X0,X1)) ),
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X13,X8,X11] :
( hBOOL(hAPP(hAPP(c_member(X11),X8),X13))
<=> hBOOL(hAPP(X13,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(f4068,plain,
! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_member(X0),X1),c_Set_Oinsert(X2,X1,X3))),
inference(superposition,[],[f2236,f3209]) ).
fof(f2236,plain,
! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),c_Set_Oinsert(X2,X1,X0))),
inference(cnf_transformation,[],[f720]) ).
fof(f720,plain,
! [X0,X1,X2] : hBOOL(hAPP(hAPP(c_member(X2),X1),c_Set_Oinsert(X2,X1,X0))),
inference(rectify,[],[f280]) ).
fof(f280,axiom,
! [X12,X23,X11] : hBOOL(hAPP(hAPP(c_member(X11),X23),c_Set_Oinsert(X11,X23,X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
fof(f12496,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK34(X0)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Finite__Set_Ocard(tc_Nat_Onat,X0) ),
inference(resolution,[],[f12465,f2087]) ).
fof(f2087,plain,
! [X0,X1] :
( c_Finite__Set_Ofinite(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Finite__Set_Ocard(X1,X0) ),
inference(cnf_transformation,[],[f1060]) ).
fof(f1060,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Finite__Set_Ocard(X1,X0)
| c_Finite__Set_Ofinite(X1,X0) )
& ( c_Finite__Set_Ocard(X1,X0) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Finite__Set_Ofinite(X1,X0) ) ),
inference(ennf_transformation,[],[f619]) ).
fof(f619,plain,
! [X0,X1] :
( ( ~ c_Finite__Set_Ofinite(X1,X0)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Finite__Set_Ocard(X1,X0) )
& ( c_Finite__Set_Ofinite(X1,X0)
=> c_Finite__Set_Ocard(X1,X0) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(rectify,[],[f425]) ).
fof(f425,axiom,
! [X13,X11] :
( ( ~ c_Finite__Set_Ofinite(X11,X13)
=> c_Finite__Set_Ocard(X11,X13) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Finite__Set_Ofinite(X11,X13)
=> c_Finite__Set_Ocard(X11,X13) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X11),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__def) ).
fof(f12465,plain,
! [X0] :
( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK34(X0)),X0)) ),
inference(resolution,[],[f1996,f1957]) ).
fof(f1957,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f551]) ).
fof(f551,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f210]) ).
fof(f210,axiom,
! [X43] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),X43)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(f1996,plain,
! [X0,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK34(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ),
inference(cnf_transformation,[],[f1615]) ).
fof(f1615,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK33(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK33(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK34(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34])],[f1612,f1614,f1613]) ).
fof(f1613,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) )
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK33(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK33(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1614,plain,
! [X0] :
( ? [X3] :
! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
=> ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK34(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1612,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) )
& ( ? [X3] :
! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(rectify,[],[f1611]) ).
fof(f1611,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) )
& ( ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) )
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(nnf_transformation,[],[f1056]) ).
fof(f1056,plain,
! [X0] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) ),
inference(ennf_transformation,[],[f587]) ).
fof(f587,plain,
! [X0] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ) ),
inference(rectify,[],[f484]) ).
fof(f484,axiom,
! [X53] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X53)
<=> ? [X4] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X53))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(f2901,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))))
| ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
inference(backward_demodulation,[],[f1986,f2894]) ).
fof(f2894,plain,
hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[],[f1968,f1892]) ).
fof(f1892,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f398]) ).
fof(f398,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
fof(f1968,plain,
! [X0] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0)),
inference(cnf_transformation,[],[f562]) ).
fof(f562,plain,
! [X0] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0)),
inference(rectify,[],[f399]) ).
fof(f399,axiom,
! [X9] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(f1986,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))))
| ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
inference(cnf_transformation,[],[f1051]) ).
fof(f1051,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))))
| ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
inference(ennf_transformation,[],[f582]) ).
fof(f582,plain,
! [X0] :
( c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))) ),
inference(rectify,[],[f344]) ).
fof(f344,axiom,
! [X11] :
( c_Finite__Set_Ofinite(X11,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X11,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
fof(f153886,plain,
! [X0,X1] :
( c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
inference(superposition,[],[f2471,f151069]) ).
fof(f151069,plain,
! [X2,X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) = c_Set_Oimage(X1,X2,c_COMBI(X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(trivial_inequality_removal,[],[f151015]) ).
fof(f151015,plain,
! [X2,X0,X1] :
( sK46(c_COMBI(X0),X2,X1) != sK46(c_COMBI(X0),X2,X1)
| c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) = c_Set_Oimage(X1,X2,c_COMBI(X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(superposition,[],[f2381,f36194]) ).
fof(f36194,plain,
! [X2,X3,X0,X1] : hAPP(c_COMBI(X0),hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_COMBI(X0)),X3)) = X3,
inference(resolution,[],[f2639,f9867]) ).
fof(f9867,plain,
! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),c_Set_Oimage(X3,X2,c_COMBI(X0),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))),
inference(superposition,[],[f2400,f2063]) ).
fof(f2063,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f596]) ).
fof(f596,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(rectify,[],[f525]) ).
fof(f525,axiom,
! [X80,X11] : hAPP(c_COMBI(X11),X80) = X80,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(f2400,plain,
! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_member(X3),hAPP(X2,X1)),c_Set_Oimage(X0,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))),
inference(cnf_transformation,[],[f838]) ).
fof(f838,plain,
! [X0,X1,X2,X3] : hBOOL(hAPP(hAPP(c_member(X3),hAPP(X2,X1)),c_Set_Oimage(X0,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))),
inference(rectify,[],[f467]) ).
fof(f467,axiom,
! [X16,X8,X1,X11] : hBOOL(hAPP(hAPP(c_member(X11),hAPP(X1,X8)),c_Set_Oimage(X16,X11,X1,c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
fof(f2639,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(X4),X3),c_Set_Oimage(X2,X4,X1,X0)))
| hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X4,X0,X1),X3)) = X3 ),
inference(cnf_transformation,[],[f1499]) ).
fof(f1499,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X4,X0,X1),X3)) = X3
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),c_Set_Oimage(X2,X4,X1,X0))) ),
inference(ennf_transformation,[],[f976]) ).
fof(f976,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_member(X4),X3),c_Set_Oimage(X2,X4,X1,X0)))
=> hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X4,X0,X1),X3)) = X3 ),
inference(rectify,[],[f461]) ).
fof(f461,axiom,
! [X13,X1,X16,X7,X11] :
( hBOOL(hAPP(hAPP(c_member(X11),X7),c_Set_Oimage(X16,X11,X1,X13)))
=> hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X16,X11,X13,X1),X7)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
fof(f2381,plain,
! [X2,X0,X1] :
( sK46(X0,X1,X2) != hAPP(X0,hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X0),sK46(X0,X1,X2)))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oimage(X2,X1,X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(cnf_transformation,[],[f1739]) ).
fof(f1739,plain,
! [X0,X1,X2] :
( ( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oimage(X2,X1,X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
| sK46(X0,X1,X2) != hAPP(X0,hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X0),sK46(X0,X1,X2))) )
& ( ! [X4] : hAPP(X0,hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X0),X4)) = X4
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) != c_Set_Oimage(X2,X1,X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f1737,f1738]) ).
fof(f1738,plain,
! [X0,X1,X2] :
( ? [X3] : hAPP(X0,hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X0),X3)) != X3
=> sK46(X0,X1,X2) != hAPP(X0,hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X0),sK46(X0,X1,X2))) ),
introduced(choice_axiom,[]) ).
fof(f1737,plain,
! [X0,X1,X2] :
( ( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oimage(X2,X1,X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
| ? [X3] : hAPP(X0,hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X0),X3)) != X3 )
& ( ! [X4] : hAPP(X0,hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X0),X4)) = X4
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) != c_Set_Oimage(X2,X1,X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ) ),
inference(rectify,[],[f1736]) ).
fof(f1736,plain,
! [X0,X1,X2] :
( ( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oimage(X2,X1,X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
| ? [X3] : hAPP(X0,hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X0),X3)) != X3 )
& ( ! [X3] : hAPP(X0,hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X0),X3)) = X3
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) != c_Set_Oimage(X2,X1,X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ) ),
inference(nnf_transformation,[],[f827]) ).
fof(f827,plain,
! [X0,X1,X2] :
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oimage(X2,X1,X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
<=> ! [X3] : hAPP(X0,hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X0),X3)) = X3 ),
inference(rectify,[],[f457]) ).
fof(f457,axiom,
! [X1,X11,X16] :
( c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)) = c_Set_Oimage(X16,X11,X1,c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)))
<=> ! [X2] : hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X16,X11,c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)),X1),X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff__all) ).
fof(f2471,plain,
! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(cnf_transformation,[],[f1378]) ).
fof(f1378,plain,
! [X0,X1,X2,X3] :
( c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(ennf_transformation,[],[f890]) ).
fof(f890,plain,
! [X0,X1,X2,X3] :
( c_Finite__Set_Ofinite(X3,X2)
=> c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2)) ),
inference(rectify,[],[f431]) ).
fof(f431,axiom,
! [X64,X16,X39,X11] :
( c_Finite__Set_Ofinite(X11,X39)
=> c_Finite__Set_Ofinite(X16,c_Set_Oimage(X11,X16,X64,X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SCT167+1 : TPTP v8.1.2. Released v5.2.0.
% 0.13/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 13:02:01 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (28009)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.43 % (28012)WARNING: value z3 for option sas not known
% 0.14/0.43 % (28012)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.43 % (28010)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.43 % (28011)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.43 % (28013)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.43 % (28014)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.43 % (28015)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.43 % (28016)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)
% 5.60/1.22 TRYING [1]
% 5.93/1.26 TRYING [2]
% 9.96/1.89 TRYING [3]
% 12.76/2.29 TRYING [1]
% 13.31/2.37 TRYING [2]
% 18.62/3.09 TRYING [3]
% 23.51/3.79 TRYING [1]
% 25.01/3.97 TRYING [2]
% 28.54/4.54 TRYING [4]
% 35.90/5.55 TRYING [4]
% 43.30/6.63 TRYING [3]
% 100.42/14.83 TRYING [5]
% 104.62/15.38 TRYING [5]
% 118.63/17.38 % (28015)First to succeed.
% 118.63/17.39 % (28015)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28009"
% 118.63/17.41 % (28015)Refutation found. Thanks to Tanya!
% 118.63/17.41 % SZS status ContradictoryAxioms for theBenchmark
% 118.63/17.41 % SZS output start Proof for theBenchmark
% See solution above
% 118.63/17.41 % (28015)------------------------------
% 118.63/17.41 % (28015)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 118.63/17.41 % (28015)Termination reason: Refutation
% 118.63/17.41
% 118.63/17.41 % (28015)Memory used [KB]: 130438
% 118.63/17.41 % (28015)Time elapsed: 16.949 s
% 118.63/17.41 % (28015)Instructions burned: 27766 (million)
% 118.63/17.41 % (28009)Success in time 17.013 s
%------------------------------------------------------------------------------