TSTP Solution File: SCT165+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT165+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.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 02:51:44 EDT 2024
% Result : ContradictoryAxioms 120.55s 17.74s
% Output : Refutation 120.55s
% 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(f153136,plain,
$false,
inference(resolution,[],[f153076,f1879]) ).
fof(f1879,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,[],[f244]) ).
fof(f244,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(f153076,plain,
! [X0] : ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(resolution,[],[f153034,f16748]) ).
fof(f16748,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(resolution,[],[f16746,f2877]) ).
fof(f2877,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,[],[f1962,f1862]) ).
fof(f1862,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(f1962,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,[],[f1048]) ).
fof(f1048,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,[],[f326]) ).
fof(f326,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(f16746,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,[],[f2869,f12472]) ).
fof(f12472,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,[],[f12376,f4187]) ).
fof(f4187,plain,
! [X2,X3,X1] : hBOOL(hAPP(hAPP(c_member(X3),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))),
inference(superposition,[],[f4012,f4004]) ).
fof(f4004,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,[],[f3175,f3159]) ).
fof(f3159,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,[],[f2306,f2034]) ).
fof(f2034,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f601]) ).
fof(f601,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f240]) ).
fof(f240,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(f2306,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| c_Set_Oinsert(X2,X1,X0) = X0 ),
inference(cnf_transformation,[],[f1278]) ).
fof(f1278,plain,
! [X0,X1,X2] :
( c_Set_Oinsert(X2,X1,X0) = X0
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0)) ),
inference(ennf_transformation,[],[f806]) ).
fof(f806,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
=> c_Set_Oinsert(X2,X1,X0) = X0 ),
inference(rectify,[],[f281]) ).
fof(f281,axiom,
! [X14,X28,X11] :
( hBOOL(hAPP(hAPP(c_member(X11),X28),X14))
=> c_Set_Oinsert(X11,X28,X14) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(f3175,plain,
! [X2,X3,X0,X1] : c_Set_Oinsert(X2,X1,X3) = c_Set_Oinsert(X0,X1,c_Set_Oinsert(X2,X1,X3)),
inference(resolution,[],[f3152,f2744]) ).
fof(f2744,plain,
! [X2,X3,X1] : hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X2)),
inference(equality_resolution,[],[f2487]) ).
fof(f2487,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0))
| X0 != X2 ),
inference(cnf_transformation,[],[f1771]) ).
fof(f1771,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,[],[f1770]) ).
fof(f1770,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,[],[f929]) ).
fof(f929,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0))
<=> ( hBOOL(hAPP(X1,X0))
| X0 = X2 ) ),
inference(rectify,[],[f276]) ).
fof(f276,axiom,
! [X8,X14,X7,X11] :
( hBOOL(hAPP(c_Set_Oinsert(X11,X7,X14),X8))
<=> ( hBOOL(hAPP(X14,X8))
| X7 = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
fof(f3152,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Set_Oinsert(X0,X1,X2) = X2 ),
inference(resolution,[],[f2306,f2332]) ).
fof(f2332,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f1718]) ).
fof(f1718,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,[],[f821]) ).
fof(f821,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
<=> hBOOL(hAPP(X0,X1)) ),
inference(rectify,[],[f56]) ).
fof(f56,axiom,
! [X14,X8,X11] :
( hBOOL(hAPP(hAPP(c_member(X11),X8),X14))
<=> hBOOL(hAPP(X14,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(f4012,plain,
! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_member(X0),X1),c_Set_Oinsert(X2,X1,X3))),
inference(superposition,[],[f2197,f3175]) ).
fof(f2197,plain,
! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),c_Set_Oinsert(X2,X1,X0))),
inference(cnf_transformation,[],[f718]) ).
fof(f718,plain,
! [X0,X1,X2] : hBOOL(hAPP(hAPP(c_member(X2),X1),c_Set_Oinsert(X2,X1,X0))),
inference(rectify,[],[f277]) ).
fof(f277,axiom,
! [X13,X28,X11] : hBOOL(hAPP(hAPP(c_member(X11),X28),c_Set_Oinsert(X11,X28,X13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
fof(f12376,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK31(X0)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Finite__Set_Ocard(tc_Nat_Onat,X0) ),
inference(resolution,[],[f12345,f2052]) ).
fof(f2052,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,[],[f1065]) ).
fof(f1065,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,[],[f618]) ).
fof(f618,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,[],[f427]) ).
fof(f427,axiom,
! [X14,X11] :
( ( ~ c_Finite__Set_Ofinite(X11,X14)
=> c_Finite__Set_Ocard(X11,X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Finite__Set_Ofinite(X11,X14)
=> c_Finite__Set_Ocard(X11,X14) = 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),X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__def) ).
fof(f12345,plain,
! [X0] :
( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK31(X0)),X0)) ),
inference(resolution,[],[f1981,f1942]) ).
fof(f1942,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,[],[f64]) ).
fof(f64,axiom,
! [X23] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X23)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(f1981,plain,
! [X0,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK31(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),sK30(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK30(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK31(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,[sK30,sK31])],[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),sK30(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK30(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),sK31(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,[],[f1062]) ).
fof(f1062,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,[],[f485]) ).
fof(f485,axiom,
! [X50] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X50)
<=> ? [X4] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X50))
=> 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(f2869,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,[],[f1971,f2862]) ).
fof(f2862,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,[],[f1953,f1880]) ).
fof(f1880,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f394]) ).
fof(f394,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(f1953,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,[],[f395]) ).
fof(f395,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(f1971,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,[],[f1057]) ).
fof(f1057,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,[],[f340]) ).
fof(f340,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(f153034,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,[],[f2432,f150217]) ).
fof(f150217,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,[],[f150163]) ).
fof(f150163,plain,
! [X2,X0,X1] :
( sK41(c_COMBI(X0),X2,X1) != sK41(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,[],[f2342,f35672]) ).
fof(f35672,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,[],[f2600,f9812]) ).
fof(f9812,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,[],[f2361,f2028]) ).
fof(f2028,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f595]) ).
fof(f595,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(f2361,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,[],[f836]) ).
fof(f836,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,[],[f469]) ).
fof(f469,axiom,
! [X17,X8,X1,X11] : hBOOL(hAPP(hAPP(c_member(X11),hAPP(X1,X8)),c_Set_Oimage(X17,X11,X1,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
fof(f2600,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,[],[f1504]) ).
fof(f1504,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,[],[f974]) ).
fof(f974,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,[],[f467]) ).
fof(f467,axiom,
! [X14,X1,X17,X7,X11] :
( hBOOL(hAPP(hAPP(c_member(X11),X7),c_Set_Oimage(X17,X11,X1,X14)))
=> hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X17,X11,X14,X1),X7)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
fof(f2342,plain,
! [X2,X0,X1] :
( sK41(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),sK41(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,[],[f1727]) ).
fof(f1727,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)))
| sK41(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),sK41(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,[sK41])],[f1725,f1726]) ).
fof(f1726,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
=> sK41(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),sK41(X0,X1,X2))) ),
introduced(choice_axiom,[]) ).
fof(f1725,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,[],[f1724]) ).
fof(f1724,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,[],[f825]) ).
fof(f825,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,[],[f441]) ).
fof(f441,axiom,
! [X1,X11,X17] :
( c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)) = c_Set_Oimage(X17,X11,X1,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
<=> ! [X2] : hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X17,X11,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)),X1),X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff__all) ).
fof(f2432,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,[],[f1383]) ).
fof(f1383,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,[],[f888]) ).
fof(f888,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,[],[f432]) ).
fof(f432,axiom,
! [X64,X17,X45,X11] :
( c_Finite__Set_Ofinite(X11,X45)
=> c_Finite__Set_Ofinite(X17,c_Set_Oimage(X11,X17,X64,X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SCT165+1 : TPTP v8.2.0. Released v5.2.0.
% 0.09/0.17 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.17/0.39 % Computer : n006.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.40 % WCLimit : 300
% 0.17/0.40 % DateTime : Sun May 19 23:49:08 EDT 2024
% 0.17/0.40 % CPUTime :
% 0.26/0.40 % (13784)Running in auto input_syntax mode. Trying TPTP
% 0.26/0.47 % (13788)WARNING: value z3 for option sas not known
% 0.26/0.47 % (13792)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)
% 0.26/0.47 % (13790)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)
% 0.26/0.47 % (13791)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)
% 0.26/0.47 % (13787)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.26/0.47 % (13789)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.26/0.47 % (13788)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)
% 0.26/0.47 % (13786)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 3.56/0.95 TRYING [1]
% 3.56/0.99 TRYING [2]
% 6.73/1.44 TRYING [3]
% 10.84/2.05 TRYING [1]
% 11.60/2.09 TRYING [2]
% 15.01/2.59 TRYING [3]
% 17.24/2.96 TRYING [1]
% 18.08/3.08 TRYING [2]
% 18.73/3.13 TRYING [4]
% 27.29/4.38 TRYING [4]
% 32.65/5.13 TRYING [3]
% 83.59/12.49 TRYING [5]
% 85.69/12.76 TRYING [5]
% 107.28/15.85 TRYING [4]
% 120.55/17.72 % (13791)First to succeed.
% 120.55/17.72 % (13791)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-13784"
% 120.55/17.74 % (13791)Refutation found. Thanks to Tanya!
% 120.55/17.74 % SZS status ContradictoryAxioms for theBenchmark
% 120.55/17.74 % SZS output start Proof for theBenchmark
% See solution above
% 120.55/17.74 % (13791)------------------------------
% 120.55/17.74 % (13791)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 120.55/17.74 % (13791)Termination reason: Refutation
% 120.55/17.74
% 120.55/17.74 % (13791)Memory used [KB]: 133370
% 120.55/17.74 % (13791)Time elapsed: 17.257 s
% 120.55/17.74 % (13791)Instructions burned: 28573 (million)
% 120.55/17.74 % (13784)Success in time 17.245 s
%------------------------------------------------------------------------------