TSTP Solution File: SWW320+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SWW320+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 : n032.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 01:00:53 EDT 2023
% Result : ContradictoryAxioms 63.20s 10.96s
% Output : Refutation 63.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of formulae : 83 ( 41 unt; 0 def)
% Number of atoms : 219 ( 106 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 208 ( 72 ~; 61 |; 45 &)
% ( 11 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 23 ( 23 usr; 4 con; 0-4 aty)
% Number of variables : 285 (; 260 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f113536,plain,
$false,
inference(unit_resulting_resolution,[],[f17821,f19481,f17857,f113255,f22198]) ).
fof(f22198,plain,
! [X2,X3,X0,X1,X7] :
( hAPP(c_Set_Oimage(X1,X2,sK439(X0,X1,X2,X3)),X0) = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X7),X3)),X0))
| ~ c_Fun_Oinj__on(X2,X1,X7,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X3 ),
inference(cnf_transformation,[],[f16112]) ).
fof(f16112,plain,
! [X0,X1,X2,X3] :
( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,sK438(X0,X1,X2,X3)),X3)),X0))
& c_Fun_Oinj__on(X2,X1,sK438(X0,X1,X2,X3),X3) )
| ! [X5] : hAPP(c_Set_Oimage(X1,X2,X5),X0) != X3 )
& ( hAPP(c_Set_Oimage(X1,X2,sK439(X0,X1,X2,X3)),X0) = X3
| ! [X7] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X7),X3)),X0))
| ~ c_Fun_Oinj__on(X2,X1,X7,X3) ) ) )
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK438,sK439])],[f16109,f16111,f16110]) ).
fof(f16110,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X4),X3)),X0))
& c_Fun_Oinj__on(X2,X1,X4,X3) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,sK438(X0,X1,X2,X3)),X3)),X0))
& c_Fun_Oinj__on(X2,X1,sK438(X0,X1,X2,X3),X3) ) ),
introduced(choice_axiom,[]) ).
fof(f16111,plain,
! [X0,X1,X2,X3] :
( ? [X6] : hAPP(c_Set_Oimage(X1,X2,X6),X0) = X3
=> hAPP(c_Set_Oimage(X1,X2,sK439(X0,X1,X2,X3)),X0) = X3 ),
introduced(choice_axiom,[]) ).
fof(f16109,plain,
! [X0,X1,X2,X3] :
( ( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X4),X3)),X0))
& c_Fun_Oinj__on(X2,X1,X4,X3) )
| ! [X5] : hAPP(c_Set_Oimage(X1,X2,X5),X0) != X3 )
& ( ? [X6] : hAPP(c_Set_Oimage(X1,X2,X6),X0) = X3
| ! [X7] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X7),X3)),X0))
| ~ c_Fun_Oinj__on(X2,X1,X7,X3) ) ) )
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X3 ),
inference(rectify,[],[f16108]) ).
fof(f16108,plain,
! [X0,X1,X2,X3] :
( ( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X4),X3)),X0))
& c_Fun_Oinj__on(X2,X1,X4,X3) )
| ! [X5] : hAPP(c_Set_Oimage(X1,X2,X5),X0) != X3 )
& ( ? [X5] : hAPP(c_Set_Oimage(X1,X2,X5),X0) = X3
| ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X4),X3)),X0))
| ~ c_Fun_Oinj__on(X2,X1,X4,X3) ) ) )
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X3 ),
inference(nnf_transformation,[],[f13206]) ).
fof(f13206,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X4),X3)),X0))
& c_Fun_Oinj__on(X2,X1,X4,X3) )
<=> ? [X5] : hAPP(c_Set_Oimage(X1,X2,X5),X0) = X3 )
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X3 ),
inference(ennf_transformation,[],[f8902]) ).
fof(f8902,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != X3
=> ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X4),X3)),X0))
& c_Fun_Oinj__on(X2,X1,X4,X3) )
<=> ? [X5] : hAPP(c_Set_Oimage(X1,X2,X5),X0) = X3 ) ),
inference(rectify,[],[f237]) ).
fof(f237,axiom,
! [X66,X16,X4,X18] :
( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) != X18
=> ( ? [X67] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X16,X67),X18)),X66))
& c_Fun_Oinj__on(X4,X16,X67,X18) )
<=> ? [X68] : hAPP(c_Set_Oimage(X16,X4,X68),X66) = X18 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0fyc5dyLNx/Vampire---4.8_19241',fact_inj__on__iff__surj) ).
fof(f113255,plain,
! [X272,X270,X269] : c_Fun_Oinj__on(X270,X272,c_fequal,X269),
inference(subsumption_resolution,[],[f113254,f22500]) ).
fof(f22500,plain,
! [X2,X3,X0,X1] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
| sK480(X0,X1,X3) != sK481(X0,X1,X3) ),
inference(cnf_transformation,[],[f16216]) ).
fof(f16216,plain,
! [X0,X1,X2,X3] :
( ( c_Fun_Oinj__on(X3,X2,X1,X0)
| ( sK480(X0,X1,X3) != sK481(X0,X1,X3)
& hAPP(X1,sK480(X0,X1,X3)) = hAPP(X1,sK481(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),sK481(X0,X1,X3)),X0))
& hBOOL(hAPP(hAPP(c_member(X3),sK480(X0,X1,X3)),X0)) ) )
& ( ! [X6] :
( ! [X7] :
( X6 = X7
| hAPP(X1,X6) != hAPP(X1,X7)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X7),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X0)) )
| ~ c_Fun_Oinj__on(X3,X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK480,sK481])],[f16213,f16215,f16214]) ).
fof(f16214,plain,
! [X0,X1,X3] :
( ? [X4] :
( ? [X5] :
( X4 != X5
& hAPP(X1,X5) = hAPP(X1,X4)
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) )
=> ( ? [X5] :
( sK480(X0,X1,X3) != X5
& hAPP(X1,X5) = hAPP(X1,sK480(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),sK480(X0,X1,X3)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f16215,plain,
! [X0,X1,X3] :
( ? [X5] :
( sK480(X0,X1,X3) != X5
& hAPP(X1,X5) = hAPP(X1,sK480(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
=> ( sK480(X0,X1,X3) != sK481(X0,X1,X3)
& hAPP(X1,sK480(X0,X1,X3)) = hAPP(X1,sK481(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),sK481(X0,X1,X3)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f16213,plain,
! [X0,X1,X2,X3] :
( ( c_Fun_Oinj__on(X3,X2,X1,X0)
| ? [X4] :
( ? [X5] :
( X4 != X5
& hAPP(X1,X5) = hAPP(X1,X4)
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) ) )
& ( ! [X6] :
( ! [X7] :
( X6 = X7
| hAPP(X1,X6) != hAPP(X1,X7)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X7),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X0)) )
| ~ c_Fun_Oinj__on(X3,X2,X1,X0) ) ),
inference(rectify,[],[f16212]) ).
fof(f16212,plain,
! [X0,X1,X2,X3] :
( ( c_Fun_Oinj__on(X3,X2,X1,X0)
| ? [X4] :
( ? [X5] :
( X4 != X5
& hAPP(X1,X5) = hAPP(X1,X4)
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) ) )
& ( ! [X4] :
( ! [X5] :
( X4 = X5
| hAPP(X1,X5) != hAPP(X1,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) )
| ~ c_Fun_Oinj__on(X3,X2,X1,X0) ) ),
inference(nnf_transformation,[],[f13502]) ).
fof(f13502,plain,
! [X0,X1,X2,X3] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
<=> ! [X4] :
( ! [X5] :
( X4 = X5
| hAPP(X1,X5) != hAPP(X1,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) ) ),
inference(flattening,[],[f13501]) ).
fof(f13501,plain,
! [X0,X1,X2,X3] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
<=> ! [X4] :
( ! [X5] :
( X4 = X5
| hAPP(X1,X5) != hAPP(X1,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) ) ),
inference(ennf_transformation,[],[f9124]) ).
fof(f9124,plain,
! [X0,X1,X2,X3] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
<=> ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X3),X4),X0))
=> ! [X5] :
( hBOOL(hAPP(hAPP(c_member(X3),X5),X0))
=> ( hAPP(X1,X5) = hAPP(X1,X4)
=> X4 = X5 ) ) ) ),
inference(rectify,[],[f175]) ).
fof(f175,axiom,
! [X18,X1,X16,X4] :
( c_Fun_Oinj__on(X4,X16,X1,X18)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),X18))
=> ! [X62] :
( hBOOL(hAPP(hAPP(c_member(X4),X62),X18))
=> ( hAPP(X1,X2) = hAPP(X1,X62)
=> X2 = X62 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0fyc5dyLNx/Vampire---4.8_19241',fact_inj__on__def) ).
fof(f113254,plain,
! [X272,X270,X269] :
( sK481(X269,c_fequal,X270) = sK480(X269,c_fequal,X270)
| c_Fun_Oinj__on(X270,X272,c_fequal,X269) ),
inference(forward_demodulation,[],[f113224,f112487]) ).
fof(f112487,plain,
! [X0,X1] : c_Set_Othe__elem(X1,hAPP(c_fequal,X0)) = X0,
inference(backward_demodulation,[],[f17882,f112479]) ).
fof(f112479,plain,
! [X0,X1] : hAPP(c_fequal,X1) = hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(forward_demodulation,[],[f107139,f68076]) ).
fof(f68076,plain,
! [X2,X0,X1] : hAPP(c_fequal,X1) = hAPP(c_Set_Oimage(X2,X0,hAPP(c_COMBK(X0,X2),X1)),c_Finite__Set_Ofinite(t_a)),
inference(forward_demodulation,[],[f68075,f17745]) ).
fof(f17745,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(cnf_transformation,[],[f5696]) ).
fof(f5696,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(rectify,[],[f2492]) ).
fof(f2492,axiom,
! [X29,X4] : hAPP(c_Set_OCollect(X4),X29) = X29,
file('/export/starexec/sandbox2/tmp/tmp.0fyc5dyLNx/Vampire---4.8_19241',fact_Collect__def) ).
fof(f68075,plain,
! [X2,X0,X1] : hAPP(c_Set_OCollect(X0),hAPP(c_fequal,X1)) = hAPP(c_Set_Oimage(X2,X0,hAPP(c_COMBK(X0,X2),X1)),c_Finite__Set_Ofinite(t_a)),
inference(forward_demodulation,[],[f62619,f17944]) ).
fof(f17944,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X0)),
inference(cnf_transformation,[],[f5895]) ).
fof(f5895,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X0)),
inference(rectify,[],[f2503]) ).
fof(f2503,axiom,
! [X5,X4] : hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X4),hAPP(c_fequal,X5)),
file('/export/starexec/sandbox2/tmp/tmp.0fyc5dyLNx/Vampire---4.8_19241',fact_singleton__conv2) ).
fof(f62619,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X2,X0,hAPP(c_COMBK(X0,X2),X1)),c_Finite__Set_Ofinite(t_a)),
inference(unit_resulting_resolution,[],[f30448,f21654]) ).
fof(f21654,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X2,X1,hAPP(c_COMBK(X1,X2),X0)),X3)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X3 ),
inference(cnf_transformation,[],[f12596]) ).
fof(f12596,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X2,X1,hAPP(c_COMBK(X1,X2),X0)),X3)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X3 )
& ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X2,X1,hAPP(c_COMBK(X1,X2),X0)),X3)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != X3 ) ),
inference(ennf_transformation,[],[f8446]) ).
fof(f8446,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != X3
=> hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X2,X1,hAPP(c_COMBK(X1,X2),X0)),X3) )
& ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X3
=> c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X2,X1,hAPP(c_COMBK(X1,X2),X0)),X3) ) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X22,X16,X4,X18] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) != X18
=> hAPP(c_Set_Oimage(X4,X16,hAPP(c_COMBK(X16,X4),X22)),X18) = hAPP(hAPP(c_Set_Oinsert(X16),X22),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))) )
& ( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = X18
=> hAPP(c_Set_Oimage(X4,X16,hAPP(c_COMBK(X16,X4),X22)),X18) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0fyc5dyLNx/Vampire---4.8_19241',fact_image__constant__conv) ).
fof(f30448,plain,
! [X0] : c_Finite__Set_Ofinite(t_a) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),
inference(forward_demodulation,[],[f27338,f17745]) ).
fof(f27338,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(c_Set_OCollect(X0),c_Finite__Set_Ofinite(t_a)),
inference(unit_resulting_resolution,[],[f16875,f19222]) ).
fof(f19222,plain,
! [X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X3))
| hAPP(c_Set_OCollect(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(cnf_transformation,[],[f15070]) ).
fof(f15070,plain,
! [X0,X1] :
( ( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(X0,sK201(X0))) )
& ( ! [X3] : ~ hBOOL(hAPP(X0,X3))
| hAPP(c_Set_OCollect(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK201])],[f15068,f15069]) ).
fof(f15069,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP(X0,X2))
=> hBOOL(hAPP(X0,sK201(X0))) ),
introduced(choice_axiom,[]) ).
fof(f15068,plain,
! [X0,X1] :
( ( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ? [X2] : hBOOL(hAPP(X0,X2)) )
& ( ! [X3] : ~ hBOOL(hAPP(X0,X3))
| hAPP(c_Set_OCollect(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ) ),
inference(rectify,[],[f15067]) ).
fof(f15067,plain,
! [X0,X1] :
( ( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ? [X2] : hBOOL(hAPP(X0,X2)) )
& ( ! [X2] : ~ hBOOL(hAPP(X0,X2))
| hAPP(c_Set_OCollect(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ) ),
inference(nnf_transformation,[],[f6819]) ).
fof(f6819,plain,
! [X0,X1] :
( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
<=> ! [X2] : ~ hBOOL(hAPP(X0,X2)) ),
inference(rectify,[],[f2491]) ).
fof(f2491,axiom,
! [X29,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X4),X29)
<=> ! [X2] : ~ hBOOL(hAPP(X29,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.0fyc5dyLNx/Vampire---4.8_19241',fact_Collect__empty__eq) ).
fof(f16875,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_F)),
inference(cnf_transformation,[],[f5229]) ).
fof(f5229,axiom,
hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_F)),
file('/export/starexec/sandbox2/tmp/tmp.0fyc5dyLNx/Vampire---4.8_19241',conj_1) ).
fof(f107139,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X2,X0,hAPP(c_COMBK(X0,X2),X1)),c_Finite__Set_Ofinite(t_a)),
inference(unit_resulting_resolution,[],[f30347,f23196]) ).
fof(f23196,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X4,X1,hAPP(c_COMBK(X1,X4),X0)),X2)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X2)) ),
inference(cnf_transformation,[],[f13852]) ).
fof(f13852,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X4,X1,hAPP(c_COMBK(X1,X4),X0)),X2)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X2)) ),
inference(ennf_transformation,[],[f9572]) ).
fof(f9572,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_member(X4),X3),X2))
=> hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X4,X1,hAPP(c_COMBK(X1,X4),X0)),X2) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X22,X16,X18,X19,X4] :
( hBOOL(hAPP(hAPP(c_member(X4),X19),X18))
=> hAPP(c_Set_Oimage(X4,X16,hAPP(c_COMBK(X16,X4),X22)),X18) = hAPP(hAPP(c_Set_Oinsert(X16),X22),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/tmp/tmp.0fyc5dyLNx/Vampire---4.8_19241',fact_image__constant) ).
fof(f30347,plain,
! [X0] : hBOOL(hAPP(hAPP(c_member(X0),v_F),c_Finite__Set_Ofinite(t_a))),
inference(forward_demodulation,[],[f30346,f17745]) ).
fof(f30346,plain,
! [X0] : hBOOL(hAPP(hAPP(c_member(X0),v_F),hAPP(c_Set_OCollect(X0),c_Finite__Set_Ofinite(t_a)))),
inference(forward_demodulation,[],[f27557,f17881]) ).
fof(f17881,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X0) = X0,
inference(cnf_transformation,[],[f5832]) ).
fof(f5832,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X0) = X0,
inference(rectify,[],[f1030]) ).
fof(f1030,axiom,
! [X21,X4] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X21) = X21,
file('/export/starexec/sandbox2/tmp/tmp.0fyc5dyLNx/Vampire---4.8_19241',fact_Int__UNIV__left) ).
fof(f27557,plain,
! [X0] : hBOOL(hAPP(hAPP(c_member(X0),v_F),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),hAPP(c_Set_OCollect(X0),c_Finite__Set_Ofinite(t_a))))),
inference(unit_resulting_resolution,[],[f17818,f16875,f22669]) ).
fof(f22669,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_Set_OCollect(X3),X0))))
| ~ hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),X1)) ),
inference(cnf_transformation,[],[f16335]) ).
fof(f16335,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_Set_OCollect(X3),X0))))
| ~ hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),X1)) )
& ( ( hBOOL(hAPP(X0,X2))
& hBOOL(hAPP(hAPP(c_member(X3),X2),X1)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_Set_OCollect(X3),X0)))) ) ),
inference(flattening,[],[f16334]) ).
fof(f16334,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_Set_OCollect(X3),X0))))
| ~ hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),X1)) )
& ( ( hBOOL(hAPP(X0,X2))
& hBOOL(hAPP(hAPP(c_member(X3),X2),X1)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_Set_OCollect(X3),X0)))) ) ),
inference(nnf_transformation,[],[f9180]) ).
fof(f9180,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_Set_OCollect(X3),X0))))
<=> ( hBOOL(hAPP(X0,X2))
& hBOOL(hAPP(hAPP(c_member(X3),X2),X1)) ) ),
inference(rectify,[],[f2502]) ).
fof(f2502,axiom,
! [X29,X18,X19,X4] :
( hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X18),hAPP(c_Set_OCollect(X4),X29))))
<=> ( hBOOL(hAPP(X29,X19))
& hBOOL(hAPP(hAPP(c_member(X4),X19),X18)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0fyc5dyLNx/Vampire---4.8_19241',fact_Int__Collect) ).
fof(f17818,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5769]) ).
fof(f5769,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f607]) ).
fof(f607,axiom,
! [X19,X4] : hBOOL(hAPP(hAPP(c_member(X4),X19),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/tmp/tmp.0fyc5dyLNx/Vampire---4.8_19241',fact_UNIV__I) ).
fof(f17882,plain,
! [X0,X1] : c_Set_Othe__elem(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0,
inference(cnf_transformation,[],[f5833]) ).
fof(f5833,plain,
! [X0,X1] : c_Set_Othe__elem(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0,
inference(rectify,[],[f53]) ).
fof(f53,axiom,
! [X19,X4] : c_Set_Othe__elem(X4,hAPP(hAPP(c_Set_Oinsert(X4),X19),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X19,
file('/export/starexec/sandbox2/tmp/tmp.0fyc5dyLNx/Vampire---4.8_19241',fact_the__elem__eq) ).
fof(f113224,plain,
! [X271,X272,X270,X269] :
( sK481(X269,c_fequal,X270) = c_Set_Othe__elem(X271,hAPP(c_fequal,sK480(X269,c_fequal,X270)))
| c_Fun_Oinj__on(X270,X272,c_fequal,X269) ),
inference(superposition,[],[f112487,f22499]) ).
fof(f22499,plain,
! [X2,X3,X0,X1] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
| hAPP(X1,sK480(X0,X1,X3)) = hAPP(X1,sK481(X0,X1,X3)) ),
inference(cnf_transformation,[],[f16216]) ).
fof(f17857,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5808]) ).
fof(f5808,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f693]) ).
fof(f693,axiom,
! [X18,X4] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X18),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/tmp/tmp.0fyc5dyLNx/Vampire---4.8_19241',fact_subset__UNIV) ).
fof(f19481,plain,
! [X2,X0,X1] : hAPP(c_Set_OPow(X1),X0) != hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),X2),X0),
inference(cnf_transformation,[],[f11282]) ).
fof(f11282,plain,
! [X0,X1,X2] : hAPP(c_Set_OPow(X1),X0) != hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),X2),X0),
inference(flattening,[],[f11281]) ).
fof(f11281,plain,
! [X0,X1,X2] : hAPP(c_Set_OPow(X1),X0) != hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),X2),X0),
inference(ennf_transformation,[],[f6915]) ).
fof(f6915,plain,
! [X0,X1] :
~ ? [X2] : hAPP(c_Set_OPow(X1),X0) = hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),X2),X0),
inference(rectify,[],[f2221]) ).
fof(f2221,axiom,
! [X18,X4] :
~ ? [X67] : hAPP(c_Set_OPow(X4),X18) = hAPP(c_Set_Oimage(X4,tc_fun(X4,tc_HOL_Obool),X67),X18),
file('/export/starexec/sandbox2/tmp/tmp.0fyc5dyLNx/Vampire---4.8_19241',fact_Cantors__paradox) ).
fof(f17821,plain,
! [X0,X1] : hAPP(c_Set_OPow(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),
inference(cnf_transformation,[],[f5772]) ).
fof(f5772,plain,
! [X0,X1] : hAPP(c_Set_OPow(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),
inference(rectify,[],[f2222]) ).
fof(f2222,axiom,
! [X18,X4] : c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(c_Set_OPow(X4),X18),
file('/export/starexec/sandbox2/tmp/tmp.0fyc5dyLNx/Vampire---4.8_19241',fact_Pow__not__empty) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 1.04/1.08 % Problem : SWW320+1 : TPTP v8.1.2. Released v5.2.0.
% 1.04/1.10 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 1.09/1.33 % Computer : n032.cluster.edu
% 1.09/1.33 % Model : x86_64 x86_64
% 1.09/1.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 1.09/1.33 % Memory : 8042.1875MB
% 1.09/1.33 % OS : Linux 3.10.0-693.el7.x86_64
% 1.09/1.33 % CPULimit : 300
% 1.09/1.33 % WCLimit : 300
% 1.09/1.33 % DateTime : Sun Aug 27 22:15:16 EDT 2023
% 1.09/1.33 % CPUTime :
% 1.09/1.33 This is a FOF_CAX_RFO_SEQ problem
% 1.18/1.33 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.0fyc5dyLNx/Vampire---4.8_19241
% 1.18/1.33 % (19680)Running in auto input_syntax mode. Trying TPTP
% 1.68/1.90 % (19687)dis+3_3:2_aac=none:fsd=off:fde=none:lcm=reverse:nm=32:nicw=on:sos=on:sac=on:sp=occurrence_419 on Vampire---4 for (419ds/0Mi)
% 1.68/1.90 % (19685)ott+1010_3_aac=none:bs=unit_only:bce=on:ep=R:er=filter:fsd=off:fde=none:gsp=on:irw=on:lcm=predicate:nwc=10.0:sos=all:sp=occurrence_449 on Vampire---4 for (449ds/0Mi)
% 1.68/1.90 % (19681)dis+1011_3_av=off:bd=off:er=known:fsd=off:fde=unused:irw=on:nm=64:nwc=1.3:sos=on:sp=reverse_arity_577 on Vampire---4 for (577ds/0Mi)
% 1.68/1.90 % (19688)dis+1011_2:1_add=off:afr=on:er=known:fde=unused:nwc=1.3:nicw=on:sas=z3:sims=off:sos=on:sac=on:tgt=full_398 on Vampire---4 for (398ds/0Mi)
% 1.68/1.90 % (19682)dis-1002_1_bd=off:fsd=off:fsr=off:fde=none:nwc=1.3:sims=off:sos=all_501 on Vampire---4 for (501ds/0Mi)
% 1.68/1.90 % (19683)ott-11_3:1_afr=on:anc=all_dependent:bd=preordered:bce=on:er=filter:fsd=off:fde=unused:nm=4:sos=all:sac=on:tgt=full:urr=on_476 on Vampire---4 for (476ds/0Mi)
% 1.68/1.91 % (19689)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_394 on Vampire---4 for (394ds/0Mi)
% 63.20/10.94 % (19683)First to succeed.
% 63.20/10.96 % (19683)Refutation found. Thanks to Tanya!
% 63.20/10.96 % SZS status ContradictoryAxioms for Vampire---4
% 63.20/10.96 % SZS output start Proof for Vampire---4
% See solution above
% 63.20/10.96 % (19683)------------------------------
% 63.20/10.96 % (19683)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 63.20/10.96 % (19683)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 63.20/10.96 % (19683)Termination reason: Refutation
% 63.20/10.96
% 63.20/10.96 % (19683)Memory used [KB]: 122556
% 63.20/10.96 % (19683)Time elapsed: 9.053 s
% 63.20/10.96 % (19683)------------------------------
% 63.20/10.96 % (19683)------------------------------
% 63.20/10.96 % (19680)Success in time 9.616 s
% 64.46/10.97 % Vampire---4.8 exiting
%------------------------------------------------------------------------------