TSTP Solution File: SCT168+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT168+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 : n011.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 Apr 30 14:57:06 EDT 2024
% Result : ContradictoryAxioms 121.77s 17.86s
% Output : Refutation 121.77s
% 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(f152632,plain,
$false,
inference(resolution,[],[f152585,f1861]) ).
fof(f1861,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,[],[f254]) ).
fof(f254,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(f152585,plain,
! [X0] : ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(resolution,[],[f152543,f16927]) ).
fof(f16927,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(resolution,[],[f16925,f2845]) ).
fof(f2845,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,[],[f1928,f1844]) ).
fof(f1844,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(f1928,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,[],[f336]) ).
fof(f336,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(f16925,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,[],[f2837,f12450]) ).
fof(f12450,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,[],[f12356,f4145]) ).
fof(f4145,plain,
! [X2,X3,X1] : hBOOL(hAPP(hAPP(c_member(X3),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))),
inference(superposition,[],[f3969,f3953]) ).
fof(f3953,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,[],[f3143,f3122]) ).
fof(f3122,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,[],[f2291,f2020]) ).
fof(f2020,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,[],[f32]) ).
fof(f32,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(f2291,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| c_Set_Oinsert(X2,X1,X0) = X0 ),
inference(cnf_transformation,[],[f1272]) ).
fof(f1272,plain,
! [X0,X1,X2] :
( c_Set_Oinsert(X2,X1,X0) = X0
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0)) ),
inference(ennf_transformation,[],[f807]) ).
fof(f807,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,
! [X11,X21,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X21),X11))
=> c_Set_Oinsert(X9,X21,X11) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(f3143,plain,
! [X2,X3,X0,X1] : c_Set_Oinsert(X2,X1,X3) = c_Set_Oinsert(X0,X1,c_Set_Oinsert(X2,X1,X3)),
inference(resolution,[],[f3120,f2722]) ).
fof(f2722,plain,
! [X2,X3,X1] : hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X2)),
inference(equality_resolution,[],[f2472]) ).
fof(f2472,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0))
| X0 != X2 ),
inference(cnf_transformation,[],[f1756]) ).
fof(f1756,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,[],[f1755]) ).
fof(f1755,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,[],[f930]) ).
fof(f930,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Set_Oinsert(X3,X2,X1),X0))
<=> ( hBOOL(hAPP(X1,X0))
| X0 = X2 ) ),
inference(rectify,[],[f291]) ).
fof(f291,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(f3120,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X1))
| c_Set_Oinsert(X0,X1,X2) = X2 ),
inference(resolution,[],[f2291,f2317]) ).
fof(f2317,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f1703]) ).
fof(f1703,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,[],[f822]) ).
fof(f822,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
<=> hBOOL(hAPP(X0,X1)) ),
inference(rectify,[],[f41]) ).
fof(f41,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(f3969,plain,
! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_member(X0),X1),c_Set_Oinsert(X2,X1,X3))),
inference(superposition,[],[f2182,f3143]) ).
fof(f2182,plain,
! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),c_Set_Oinsert(X2,X1,X0))),
inference(cnf_transformation,[],[f719]) ).
fof(f719,plain,
! [X0,X1,X2] : hBOOL(hAPP(hAPP(c_member(X2),X1),c_Set_Oinsert(X2,X1,X0))),
inference(rectify,[],[f285]) ).
fof(f285,axiom,
! [X10,X21,X9] : hBOOL(hAPP(hAPP(c_member(X9),X21),c_Set_Oinsert(X9,X21,X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
fof(f12356,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK30(X0)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Finite__Set_Ocard(tc_Nat_Onat,X0) ),
inference(resolution,[],[f12325,f2038]) ).
fof(f2038,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,[],[f432]) ).
fof(f432,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(f12325,plain,
! [X0] :
( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK30(X0)),X0)) ),
inference(resolution,[],[f1947,f1908]) ).
fof(f1908,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,[],[f207]) ).
fof(f207,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(f1947,plain,
! [X0,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK30(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ),
inference(cnf_transformation,[],[f1593]) ).
fof(f1593,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK29(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK29(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK30(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,[sK29,sK30])],[f1590,f1592,f1591]) ).
fof(f1591,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),sK29(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK29(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1592,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),sK30(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1590,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,[],[f1589]) ).
fof(f1589,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,[],[f490]) ).
fof(f490,axiom,
! [X54] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X54)
<=> ? [X19] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X54))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(f2837,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,[],[f1937,f2830]) ).
fof(f2830,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,[],[f1919,f1862]) ).
fof(f1862,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f404]) ).
fof(f404,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(f1919,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,[],[f405]) ).
fof(f405,axiom,
! [X18] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(f1937,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,[],[f350]) ).
fof(f350,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(f152543,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,[],[f2417,f149758]) ).
fof(f149758,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,[],[f149704]) ).
fof(f149704,plain,
! [X2,X0,X1] :
( sK40(c_COMBI(X0),X2,X1) != sK40(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,[],[f2327,f35877]) ).
fof(f35877,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,[],[f2578,f9844]) ).
fof(f9844,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,[],[f2346,f2014]) ).
fof(f2014,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,
! [X79,X9] : hAPP(c_COMBI(X9),X79) = X79,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(f2346,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,[],[f837]) ).
fof(f837,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,[],[f443]) ).
fof(f443,axiom,
! [X14,X7,X1,X9] : hBOOL(hAPP(hAPP(c_member(X9),hAPP(X1,X7)),c_Set_Oimage(X14,X9,X1,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
fof(f2578,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,[],[f1490]) ).
fof(f1490,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,[],[f971]) ).
fof(f971,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,
! [X11,X1,X14,X6,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X6),c_Set_Oimage(X14,X9,X1,X11)))
=> hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X14,X9,X11,X1),X6)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
fof(f2327,plain,
! [X2,X0,X1] :
( sK40(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),sK40(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,[],[f1712]) ).
fof(f1712,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)))
| sK40(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),sK40(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,[sK40])],[f1710,f1711]) ).
fof(f1711,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
=> sK40(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),sK40(X0,X1,X2))) ),
introduced(choice_axiom,[]) ).
fof(f1710,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,[],[f1709]) ).
fof(f1709,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,[],[f826]) ).
fof(f826,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,X9,X14] :
( c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)) = c_Set_Oimage(X14,X9,X1,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool)))
<=> ! [X2] : hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X14,X9,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool)),X1),X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff__all) ).
fof(f2417,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,[],[f1377]) ).
fof(f1377,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,[],[f889]) ).
fof(f889,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,[],[f437]) ).
fof(f437,axiom,
! [X64,X14,X26,X9] :
( c_Finite__Set_Ofinite(X9,X26)
=> c_Finite__Set_Ofinite(X14,c_Set_Oimage(X9,X14,X64,X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SCT168+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.37 % Computer : n011.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Mon Apr 29 22:26:01 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.14/0.37 % (16616)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.44 % (16619)WARNING: value z3 for option sas not known
% 0.21/0.44 % (16622)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)
% 0.21/0.44 % (16618)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.44 % (16619)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)
% 0.21/0.44 % (16623)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)
% 0.21/0.44 % (16621)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)
% 0.21/0.44 % (16620)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.44 % (16617)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 4.24/1.03 TRYING [1]
% 4.69/1.10 TRYING [2]
% 9.02/1.74 TRYING [3]
% 12.70/2.23 TRYING [1]
% 13.20/2.31 TRYING [2]
% 17.66/2.99 TRYING [3]
% 19.65/3.22 TRYING [1]
% 20.86/3.40 TRYING [2]
% 27.69/4.36 TRYING [4]
% 34.09/5.33 TRYING [4]
% 36.18/5.61 TRYING [3]
% 102.48/15.12 TRYING [5]
% 110.53/16.25 TRYING [5]
% 114.25/16.83 TRYING [4]
% 121.77/17.84 % (16622)First to succeed.
% 121.77/17.86 % (16622)Refutation found. Thanks to Tanya!
% 121.77/17.86 % SZS status ContradictoryAxioms for theBenchmark
% 121.77/17.86 % SZS output start Proof for theBenchmark
% See solution above
% 121.77/17.86 % (16622)------------------------------
% 121.77/17.86 % (16622)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 121.77/17.86 % (16622)Termination reason: Refutation
% 121.77/17.86
% 121.77/17.86 % (16622)Memory used [KB]: 134221
% 121.77/17.86 % (16622)Time elapsed: 17.406 s
% 121.77/17.86 % (16622)Instructions burned: 28854 (million)
% 121.77/17.86 % (16622)------------------------------
% 121.77/17.86 % (16622)------------------------------
% 121.77/17.86 % (16616)Success in time 17.357 s
%------------------------------------------------------------------------------