TSTP Solution File: SCT164+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT164+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n023.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 : Fri Sep 1 22:00:59 EDT 2023
% Result : ContradictoryAxioms 113.62s 16.72s
% Output : Refutation 113.62s
% 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(f152209,plain,
$false,
inference(resolution,[],[f152149,f1896]) ).
fof(f1896,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,[],[f249]) ).
fof(f249,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/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_finite__indi) ).
fof(f152149,plain,
! [X16] : ~ c_Finite__Set_Ofinite(X16,c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))),
inference(resolution,[],[f152064,f21433]) ).
fof(f21433,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(resolution,[],[f21431,f2762]) ).
fof(f2762,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,[],[f1957,f1879]) ).
fof(f1879,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/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(f1957,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,[],[f1026]) ).
fof(f1026,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,[],[f572]) ).
fof(f572,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,
! [X12] :
( class_Rings_Olinordered__semidom(X12)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Oone__class_Oone(X12)),c_Groups_Ozero__class_Ozero(X12))) ),
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_not__one__le__zero) ).
fof(f21431,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,[],[f2753,f15852]) ).
fof(f15852,plain,
! [X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Finite__Set_Ocard(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(resolution,[],[f15745,f4055]) ).
fof(f4055,plain,
! [X21,X22,X23] : hBOOL(hAPP(hAPP(c_member(X23),X21),c_Orderings_Otop__class_Otop(tc_fun(X22,tc_HOL_Obool)))),
inference(superposition,[],[f3894,f3877]) ).
fof(f3877,plain,
! [X3,X4,X5] : c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)) = c_Set_Oinsert(X5,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),
inference(superposition,[],[f3129,f3063]) ).
fof(f3063,plain,
! [X6,X5] : c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) = c_Set_Oinsert(X5,X6,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),
inference(resolution,[],[f2321,f2024]) ).
fof(f2024,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f600]) ).
fof(f600,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X10,X12] : hBOOL(hAPP(hAPP(c_member(X12),X10),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_iso__tuple__UNIV__I) ).
fof(f2321,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,[],[f806]) ).
fof(f806,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
=> c_Set_Oinsert(X2,X1,X0) = X0 ),
inference(rectify,[],[f282]) ).
fof(f282,axiom,
! [X14,X22,X12] :
( hBOOL(hAPP(hAPP(c_member(X12),X22),X14))
=> c_Set_Oinsert(X12,X22,X14) = X14 ),
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_insert__absorb) ).
fof(f3129,plain,
! [X118,X116,X117,X115] : c_Set_Oinsert(X117,X116,X118) = c_Set_Oinsert(X115,X116,c_Set_Oinsert(X117,X116,X118)),
inference(resolution,[],[f3061,f2769]) ).
fof(f2769,plain,
! [X2,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X1)),
inference(equality_resolution,[],[f2502]) ).
fof(f2502,plain,
! [X2,X3,X0,X1] :
( X0 != X2
| hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0)) ),
inference(cnf_transformation,[],[f1786]) ).
fof(f1786,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,[],[f1785]) ).
fof(f1785,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,[],[f283]) ).
fof(f283,axiom,
! [X10,X14,X9,X12] :
( hBOOL(hAPP(c_Set_Oinsert(X12,X9,X14),X10))
<=> ( hBOOL(hAPP(X14,X10))
| X9 = X10 ) ),
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_insert__code) ).
fof(f3061,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Set_Oinsert(X0,X1,X2) = X2 ),
inference(resolution,[],[f2321,f2347]) ).
fof(f2347,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f1733]) ).
fof(f1733,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,[],[f28]) ).
fof(f28,axiom,
! [X14,X10,X12] :
( hBOOL(hAPP(hAPP(c_member(X12),X10),X14))
<=> hBOOL(hAPP(X14,X10)) ),
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_mem__def) ).
fof(f3894,plain,
! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_member(X0),X1),c_Set_Oinsert(X2,X1,X3))),
inference(superposition,[],[f2210,f3129]) ).
fof(f2210,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,[],[f278]) ).
fof(f278,axiom,
! [X13,X22,X12] : hBOOL(hAPP(hAPP(c_member(X12),X22),c_Set_Oinsert(X12,X22,X13))),
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_insertI1) ).
fof(f15745,plain,
! [X55] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK33(X55)),X55))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Finite__Set_Ocard(tc_Nat_Onat,X55) ),
inference(resolution,[],[f15703,f2042]) ).
fof(f2042,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,[],[f1043]) ).
fof(f1043,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,[],[f617]) ).
fof(f617,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,[],[f428]) ).
fof(f428,axiom,
! [X14,X12] :
( ( ~ c_Finite__Set_Ofinite(X12,X14)
=> c_Finite__Set_Ocard(X12,X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Finite__Set_Ofinite(X12,X14)
=> c_Finite__Set_Ocard(X12,X14) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X12,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X12),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_card__def) ).
fof(f15703,plain,
! [X0] :
( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK33(X0)),X0)) ),
inference(resolution,[],[f1991,f1935]) ).
fof(f1935,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f550]) ).
fof(f550,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f201]) ).
fof(f201,axiom,
! [X42] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X42)),
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_less__not__refl) ).
fof(f1991,plain,
! [X0,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK33(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ),
inference(cnf_transformation,[],[f1620]) ).
fof(f1620,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK32(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK32(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK33(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,[sK32,sK33])],[f1617,f1619,f1618]) ).
fof(f1618,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),sK32(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK32(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1619,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),sK33(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1617,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,[],[f1616]) ).
fof(f1616,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,[],[f1041]) ).
fof(f1041,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,
! [X46] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X46)
<=> ? [X37] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X46))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X37)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_finite__nat__set__iff__bounded) ).
fof(f2753,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,[],[f1966,f2747]) ).
fof(f2747,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,[],[f1946,f1897]) ).
fof(f1897,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f399]) ).
fof(f399,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_One__nat__def) ).
fof(f1946,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,[],[f561]) ).
fof(f561,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,[],[f400]) ).
fof(f400,axiom,
! [X34] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X34)),
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_less__eq__Suc__le__raw) ).
fof(f1966,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,[],[f1035]) ).
fof(f1035,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,[],[f581]) ).
fof(f581,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,[],[f345]) ).
fof(f345,axiom,
! [X12] :
( c_Finite__Set_Ofinite(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,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(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_finite__UNIV__card__ge__0) ).
fof(f152064,plain,
! [X26,X27] :
( c_Finite__Set_Ofinite(X27,c_Orderings_Otop__class_Otop(tc_fun(X27,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X26,c_Orderings_Otop__class_Otop(tc_fun(X26,tc_HOL_Obool))) ),
inference(superposition,[],[f2447,f149385]) ).
fof(f149385,plain,
! [X8,X9,X7] : c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)) = c_Set_Oimage(X8,X9,c_COMBI(X7),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))),
inference(trivial_inequality_removal,[],[f149330]) ).
fof(f149330,plain,
! [X8,X9,X7] :
( sK45(c_COMBI(X7),X9,X8) != sK45(c_COMBI(X7),X9,X8)
| c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)) = c_Set_Oimage(X8,X9,c_COMBI(X7),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) ),
inference(superposition,[],[f2357,f47306]) ).
fof(f47306,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,[],[f2617,f10806]) ).
fof(f10806,plain,
! [X46,X44,X45,X43] : hBOOL(hAPP(hAPP(c_member(X45),X44),c_Set_Oimage(X46,X45,c_COMBI(X43),c_Orderings_Otop__class_Otop(tc_fun(X46,tc_HOL_Obool))))),
inference(superposition,[],[f2376,f2018]) ).
fof(f2018,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f594]) ).
fof(f594,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(rectify,[],[f525]) ).
fof(f525,axiom,
! [X81,X12] : hAPP(c_COMBI(X12),X81) = X81,
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',help_c__COMBI__1) ).
fof(f2376,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,[],[f444]) ).
fof(f444,axiom,
! [X17,X10,X1,X12] : hBOOL(hAPP(hAPP(c_member(X12),hAPP(X1,X10)),c_Set_Oimage(X17,X12,X1,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))))),
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_rangeI) ).
fof(f2617,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,[],[f975]) ).
fof(f975,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,[],[f450]) ).
fof(f450,axiom,
! [X14,X1,X17,X9,X12] :
( hBOOL(hAPP(hAPP(c_member(X12),X9),c_Set_Oimage(X17,X12,X1,X14)))
=> hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X17,X12,X14,X1),X9)) = X9 ),
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_f__inv__into__f) ).
fof(f2357,plain,
! [X2,X0,X1] :
( sK45(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),sK45(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,[],[f1742]) ).
fof(f1742,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)))
| sK45(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),sK45(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,[sK45])],[f1740,f1741]) ).
fof(f1741,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
=> sK45(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),sK45(X0,X1,X2))) ),
introduced(choice_axiom,[]) ).
fof(f1740,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,[],[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)))
| ? [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,[],[f454]) ).
fof(f454,axiom,
! [X1,X12,X17] :
( c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)) = c_Set_Oimage(X17,X12,X1,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
<=> ! [X2] : hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X17,X12,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)),X1),X2)) = X2 ),
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_surj__iff__all) ).
fof(f2447,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,[],[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,
! [X65,X17,X27,X12] :
( c_Finite__Set_Ofinite(X12,X27)
=> c_Finite__Set_Ofinite(X17,c_Set_Oimage(X12,X17,X65,X27)) ),
file('/export/starexec/sandbox2/tmp/tmp.iHBYupnizO/Vampire---4.8_30665',fact_finite__imageI) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.17/0.18 % Problem : SCT164+1 : TPTP v8.1.2. Released v5.2.0.
% 0.17/0.19 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.18/0.38 % Computer : n023.cluster.edu
% 0.18/0.38 % Model : x86_64 x86_64
% 0.18/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.38 % Memory : 8042.1875MB
% 0.18/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.38 % CPULimit : 300
% 0.18/0.38 % WCLimit : 300
% 0.18/0.38 % DateTime : Wed Aug 30 14:59:54 EDT 2023
% 0.18/0.38 % CPUTime :
% 0.18/0.44 % (30772)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.47 % (30773)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.22/0.47 % (30776)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.47 % (30775)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 Vampire---4 for (569ds/0Mi)
% 0.22/0.47 % (30774)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.22/0.47 % (30779)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 Vampire---4 for (497ds/0Mi)
% 0.22/0.47 % (30778)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 Vampire---4 for (522ds/0Mi)
% 0.22/0.47 % (30777)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 Vampire---4 for (531ds/0Mi)
% 3.46/0.96 TRYING [1]
% 3.80/1.02 TRYING [2]
% 7.79/1.63 TRYING [3]
% 10.81/2.04 TRYING [1]
% 11.47/2.09 TRYING [2]
% 14.69/2.54 TRYING [1]
% 15.55/2.72 TRYING [3]
% 15.55/2.72 TRYING [2]
% 22.61/3.69 TRYING [4]
% 33.97/5.34 TRYING [4]
% 34.95/5.52 TRYING [3]
% 92.26/13.77 TRYING [5]
% 107.24/15.87 TRYING [5]
% 113.17/16.69 % (30778)First to succeed.
% 113.62/16.72 % (30778)Refutation found. Thanks to Tanya!
% 113.62/16.72 % SZS status ContradictoryAxioms for Vampire---4
% 113.62/16.72 % SZS output start Proof for Vampire---4
% See solution above
% 113.62/16.72 % (30778)------------------------------
% 113.62/16.72 % (30778)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 113.62/16.72 % (30778)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 113.62/16.72 % (30778)Termination reason: Refutation
% 113.62/16.72
% 113.62/16.72 % (30778)Memory used [KB]: 231424
% 113.62/16.72 % (30778)Time elapsed: 16.227 s
% 113.62/16.72 % (30778)------------------------------
% 113.62/16.72 % (30778)------------------------------
% 113.62/16.72 % (30772)Success in time 16.284 s
% 113.62/16.72 % Vampire---4.8 exiting
%------------------------------------------------------------------------------