TSTP Solution File: SCT166+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT166+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 : n016.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 80.14s 11.85s
% Output : Refutation 80.14s
% 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(f152749,plain,
$false,
inference(resolution,[],[f152566,f1892]) ).
fof(f1892,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/sandbox/benchmark/theBenchmark.p',fact_finite__indi) ).
fof(f152566,plain,
! [X0] : ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(resolution,[],[f152524,f16945]) ).
fof(f16945,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(resolution,[],[f16943,f2863]) ).
fof(f2863,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,[],[f1956,f1875]) ).
fof(f1875,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(f1956,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,[],[f1045]) ).
fof(f1045,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,[],[f330]) ).
fof(f330,axiom,
! [X9] :
( class_Rings_Olinordered__semidom(X9)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Oone__class_Oone(X9)),c_Groups_Ozero__class_Ozero(X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(f16943,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,[],[f2855,f12468]) ).
fof(f12468,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,[],[f12374,f4163]) ).
fof(f4163,plain,
! [X2,X3,X1] : hBOOL(hAPP(hAPP(c_member(X3),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))),
inference(superposition,[],[f3987,f3971]) ).
fof(f3971,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,[],[f3161,f3140]) ).
fof(f3140,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,[],[f2300,f2028]) ).
fof(f2028,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,[],[f27]) ).
fof(f27,axiom,
! [X7,X9] : hBOOL(hAPP(hAPP(c_member(X9),X7),c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).
fof(f2300,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| c_Set_Oinsert(X2,X1,X0) = X0 ),
inference(cnf_transformation,[],[f1275]) ).
fof(f1275,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,[],[f274]) ).
fof(f274,axiom,
! [X11,X22,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X22),X11))
=> c_Set_Oinsert(X9,X22,X11) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(f3161,plain,
! [X2,X3,X0,X1] : c_Set_Oinsert(X2,X1,X3) = c_Set_Oinsert(X0,X1,c_Set_Oinsert(X2,X1,X3)),
inference(resolution,[],[f3138,f2736]) ).
fof(f2736,plain,
! [X2,X3,X1] : hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X2)),
inference(equality_resolution,[],[f2481]) ).
fof(f2481,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0))
| X0 != X2 ),
inference(cnf_transformation,[],[f1766]) ).
fof(f1766,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,[],[f1765]) ).
fof(f1765,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,[],[f284]) ).
fof(f284,axiom,
! [X7,X11,X6,X9] :
( hBOOL(hAPP(c_Set_Oinsert(X9,X6,X11),X7))
<=> ( hBOOL(hAPP(X11,X7))
| X6 = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
fof(f3138,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Set_Oinsert(X0,X1,X2) = X2 ),
inference(resolution,[],[f2300,f2326]) ).
fof(f2326,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f1713]) ).
fof(f1713,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,[],[f40]) ).
fof(f40,axiom,
! [X11,X7,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
<=> hBOOL(hAPP(X11,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(f3987,plain,
! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_member(X0),X1),c_Set_Oinsert(X2,X1,X3))),
inference(superposition,[],[f2191,f3161]) ).
fof(f2191,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,
! [X10,X22,X9] : hBOOL(hAPP(hAPP(c_member(X9),X22),c_Set_Oinsert(X9,X22,X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
fof(f12374,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,[],[f12343,f2046]) ).
fof(f2046,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,[],[f1062]) ).
fof(f1062,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,
! [X11,X9] :
( ( ~ c_Finite__Set_Ofinite(X9,X11)
=> c_Finite__Set_Ocard(X9,X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Finite__Set_Ofinite(X9,X11)
=> c_Finite__Set_Ocard(X9,X11) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X9),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__def) ).
fof(f12343,plain,
! [X0] :
( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK31(X0)),X0)) ),
inference(resolution,[],[f1975,f1936]) ).
fof(f1936,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,[],[f214]) ).
fof(f214,axiom,
! [X45] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(f1975,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,[],[f1610]) ).
fof(f1610,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])],[f1607,f1609,f1608]) ).
fof(f1608,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(f1609,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(f1607,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,[],[f1606]) ).
fof(f1606,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,[],[f1059]) ).
fof(f1059,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,[],[f486]) ).
fof(f486,axiom,
! [X55] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X55)
<=> ? [X16] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X55))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(f2855,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,[],[f1965,f2848]) ).
fof(f2848,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,[],[f1947,f1893]) ).
fof(f1893,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f400]) ).
fof(f400,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(f1947,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,[],[f401]) ).
fof(f401,axiom,
! [X17] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(f1965,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,[],[f1054]) ).
fof(f1054,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,
! [X9] :
( c_Finite__Set_Ofinite(X9,c_Orderings_Otop__class_Otop(tc_fun(X9,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(X9,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
fof(f152524,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,[],[f2426,f149769]) ).
fof(f149769,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,[],[f149715]) ).
fof(f149715,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,[],[f2336,f35895]) ).
fof(f35895,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,[],[f2592,f9862]) ).
fof(f9862,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,[],[f2355,f2022]) ).
fof(f2022,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,X9] : hAPP(c_COMBI(X9),X80) = X80,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(f2355,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,[],[f447]) ).
fof(f447,axiom,
! [X13,X7,X1,X9] : hBOOL(hAPP(hAPP(c_member(X9),hAPP(X1,X7)),c_Set_Oimage(X13,X9,X1,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
fof(f2592,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,[],[f973]) ).
fof(f973,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,[],[f454]) ).
fof(f454,axiom,
! [X11,X1,X13,X6,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X6),c_Set_Oimage(X13,X9,X1,X11)))
=> hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X13,X9,X11,X1),X6)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
fof(f2336,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,[],[f1722]) ).
fof(f1722,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])],[f1720,f1721]) ).
fof(f1721,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(f1720,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,[],[f1719]) ).
fof(f1719,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,[],[f458]) ).
fof(f458,axiom,
! [X1,X9,X13] :
( c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)) = c_Set_Oimage(X13,X9,X1,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
<=> ! [X2] : hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X13,X9,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)),X1),X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff__all) ).
fof(f2426,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,[],[f1380]) ).
fof(f1380,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,[],[f433]) ).
fof(f433,axiom,
! [X64,X13,X39,X9] :
( c_Finite__Set_Ofinite(X9,X39)
=> c_Finite__Set_Ofinite(X13,c_Set_Oimage(X9,X13,X64,X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SCT166+1 : TPTP v8.2.0. Released v5.2.0.
% 0.14/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n016.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 : Mon May 20 00:02:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.36 % (31875)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (31878)WARNING: value z3 for option sas not known
% 0.21/0.43 % (31877)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.43 % (31876)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.43 % (31880)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)
% 0.21/0.43 % (31878)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)
% 0.21/0.43 % (31881)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)
% 0.21/0.43 % (31882)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)
% 0.21/0.43 % (31879)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 3.47/0.92 TRYING [1]
% 4.04/0.98 TRYING [2]
% 6.69/1.42 TRYING [3]
% 10.18/1.90 TRYING [1]
% 10.60/1.93 TRYING [2]
% 13.22/2.29 TRYING [3]
% 13.77/2.37 TRYING [1]
% 14.40/2.47 TRYING [2]
% 17.44/2.92 TRYING [4]
% 24.46/3.90 TRYING [4]
% 26.15/4.17 TRYING [3]
% 63.53/9.46 TRYING [5]
% 71.99/10.69 TRYING [5]
% 80.14/11.83 % (31881)First to succeed.
% 80.14/11.83 % (31881)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-31875"
% 80.14/11.85 % (31881)Refutation found. Thanks to Tanya!
% 80.14/11.85 % SZS status ContradictoryAxioms for theBenchmark
% 80.14/11.85 % SZS output start Proof for theBenchmark
% See solution above
% 80.14/11.85 % (31881)------------------------------
% 80.14/11.85 % (31881)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 80.14/11.85 % (31881)Termination reason: Refutation
% 80.14/11.85
% 80.14/11.85 % (31881)Memory used [KB]: 133076
% 80.14/11.85 % (31881)Time elapsed: 11.404 s
% 80.14/11.85 % (31881)Instructions burned: 28595 (million)
% 80.14/11.85 % (31875)Success in time 11.448 s
%------------------------------------------------------------------------------