TSTP Solution File: SWW338+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SWW338+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 : n017.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 01:00:58 EDT 2023
% Result : Theorem 18.13s 3.79s
% Output : Refutation 18.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 21
% Syntax : Number of formulae : 72 ( 35 unt; 0 def)
% Number of atoms : 206 ( 85 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 202 ( 68 ~; 52 |; 48 &)
% ( 7 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 32 ( 32 usr; 13 con; 0-4 aty)
% Number of variables : 227 (; 197 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53014,plain,
$false,
inference(unit_resulting_resolution,[],[f17869,f19518,f17905,f52690,f22204]) ).
fof(f22204,plain,
! [X2,X3,X0,X1,X7] :
( hAPP(c_Set_Oimage(X1,X2,sK458(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,[],[f16140]) ).
fof(f16140,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,sK457(X0,X1,X2,X3)),X3)),X0))
& c_Fun_Oinj__on(X2,X1,sK457(X0,X1,X2,X3),X3) )
| ! [X5] : hAPP(c_Set_Oimage(X1,X2,X5),X0) != X3 )
& ( hAPP(c_Set_Oimage(X1,X2,sK458(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,[sK457,sK458])],[f16137,f16139,f16138]) ).
fof(f16138,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,sK457(X0,X1,X2,X3)),X3)),X0))
& c_Fun_Oinj__on(X2,X1,sK457(X0,X1,X2,X3),X3) ) ),
introduced(choice_axiom,[]) ).
fof(f16139,plain,
! [X0,X1,X2,X3] :
( ? [X6] : hAPP(c_Set_Oimage(X1,X2,X6),X0) = X3
=> hAPP(c_Set_Oimage(X1,X2,sK458(X0,X1,X2,X3)),X0) = X3 ),
introduced(choice_axiom,[]) ).
fof(f16137,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,[],[f16136]) ).
fof(f16136,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,[],[f13202]) ).
fof(f13202,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,[],[f8877]) ).
fof(f8877,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,[],[f3188]) ).
fof(f3188,axiom,
! [X210,X29,X6,X22] :
( c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) != X22
=> ( ? [X207] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29,tc_HOL_Obool)),hAPP(c_Set_Oimage(X6,X29,X207),X22)),X210))
& c_Fun_Oinj__on(X6,X29,X207,X22) )
<=> ? [X223] : hAPP(c_Set_Oimage(X29,X6,X223),X210) = X22 ) ),
file('/export/starexec/sandbox/tmp/tmp.BvqGqdN6bG/Vampire---4.8_13129',fact_inj__on__iff__surj) ).
fof(f52690,plain,
! [X296,X294,X293] : c_Fun_Oinj__on(X294,X296,c_fequal,X293),
inference(subsumption_resolution,[],[f52689,f22512]) ).
fof(f22512,plain,
! [X2,X3,X0,X1] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
| sK501(X0,X1,X3) != sK502(X0,X1,X3) ),
inference(cnf_transformation,[],[f16249]) ).
fof(f16249,plain,
! [X0,X1,X2,X3] :
( ( c_Fun_Oinj__on(X3,X2,X1,X0)
| ( sK501(X0,X1,X3) != sK502(X0,X1,X3)
& hAPP(X1,sK501(X0,X1,X3)) = hAPP(X1,sK502(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),sK502(X0,X1,X3)),X0))
& hBOOL(hAPP(hAPP(c_member(X3),sK501(X0,X1,X3)),X0)) ) )
& ( ! [X6] :
( ! [X7] :
( X6 = X7
| hAPP(X1,X7) != hAPP(X1,X6)
| ~ 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,[sK501,sK502])],[f16246,f16248,f16247]) ).
fof(f16247,plain,
! [X0,X1,X3] :
( ? [X4] :
( ? [X5] :
( X4 != X5
& hAPP(X1,X4) = hAPP(X1,X5)
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) )
=> ( ? [X5] :
( sK501(X0,X1,X3) != X5
& hAPP(X1,X5) = hAPP(X1,sK501(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),sK501(X0,X1,X3)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f16248,plain,
! [X0,X1,X3] :
( ? [X5] :
( sK501(X0,X1,X3) != X5
& hAPP(X1,X5) = hAPP(X1,sK501(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
=> ( sK501(X0,X1,X3) != sK502(X0,X1,X3)
& hAPP(X1,sK501(X0,X1,X3)) = hAPP(X1,sK502(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),sK502(X0,X1,X3)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f16246,plain,
! [X0,X1,X2,X3] :
( ( c_Fun_Oinj__on(X3,X2,X1,X0)
| ? [X4] :
( ? [X5] :
( X4 != X5
& hAPP(X1,X4) = hAPP(X1,X5)
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) ) )
& ( ! [X6] :
( ! [X7] :
( X6 = X7
| hAPP(X1,X7) != hAPP(X1,X6)
| ~ 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,[],[f16245]) ).
fof(f16245,plain,
! [X0,X1,X2,X3] :
( ( c_Fun_Oinj__on(X3,X2,X1,X0)
| ? [X4] :
( ? [X5] :
( X4 != X5
& hAPP(X1,X4) = hAPP(X1,X5)
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) ) )
& ( ! [X4] :
( ! [X5] :
( X4 = X5
| hAPP(X1,X4) != hAPP(X1,X5)
| ~ 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,[],[f13507]) ).
fof(f13507,plain,
! [X0,X1,X2,X3] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
<=> ! [X4] :
( ! [X5] :
( X4 = X5
| hAPP(X1,X4) != hAPP(X1,X5)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) ) ),
inference(flattening,[],[f13506]) ).
fof(f13506,plain,
! [X0,X1,X2,X3] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
<=> ! [X4] :
( ! [X5] :
( X4 = X5
| hAPP(X1,X4) != hAPP(X1,X5)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) ) ),
inference(ennf_transformation,[],[f9104]) ).
fof(f9104,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,X4) = hAPP(X1,X5)
=> X4 = X5 ) ) ) ),
inference(rectify,[],[f3178]) ).
fof(f3178,axiom,
! [X22,X1,X29,X6] :
( c_Fun_Oinj__on(X6,X29,X1,X22)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X6),X2),X22))
=> ! [X86] :
( hBOOL(hAPP(hAPP(c_member(X6),X86),X22))
=> ( hAPP(X1,X2) = hAPP(X1,X86)
=> X2 = X86 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BvqGqdN6bG/Vampire---4.8_13129',fact_inj__on__def) ).
fof(f52689,plain,
! [X296,X294,X293] :
( sK502(X293,c_fequal,X294) = sK501(X293,c_fequal,X294)
| c_Fun_Oinj__on(X294,X296,c_fequal,X293) ),
inference(forward_demodulation,[],[f52660,f52225]) ).
fof(f52225,plain,
! [X0,X1] : c_Set_Othe__elem(X1,hAPP(c_fequal,X0)) = X0,
inference(backward_demodulation,[],[f17930,f52220]) ).
fof(f52220,plain,
! [X246,X245] : hAPP(hAPP(c_Set_Oinsert(X245),X246),c_Orderings_Obot__class_Obot(tc_fun(X245,tc_HOL_Obool))) = hAPP(c_fequal,X246),
inference(forward_demodulation,[],[f49594,f51909]) ).
fof(f51909,plain,
! [X0,X1] : hAPP(c_fequal,X1) = hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),hAPP(c_fdisj,sF668))),
inference(forward_demodulation,[],[f51908,f17793]) ).
fof(f17793,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(cnf_transformation,[],[f5691]) ).
fof(f5691,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(rectify,[],[f3376]) ).
fof(f3376,axiom,
! [X15,X6] : hAPP(c_Set_OCollect(X6),X15) = X15,
file('/export/starexec/sandbox/tmp/tmp.BvqGqdN6bG/Vampire---4.8_13129',fact_Collect__def) ).
fof(f51908,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X0),hAPP(c_fequal,X1)) = hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),hAPP(c_fdisj,sF668))),
inference(forward_demodulation,[],[f45377,f17992]) ).
fof(f17992,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,[],[f5890]) ).
fof(f5890,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,[],[f3386]) ).
fof(f3386,axiom,
! [X12,X6] : hAPP(hAPP(c_Set_Oinsert(X6),X12),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X6),hAPP(c_fequal,X12)),
file('/export/starexec/sandbox/tmp/tmp.BvqGqdN6bG/Vampire---4.8_13129',fact_singleton__conv2) ).
fof(f45377,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),hAPP(c_fdisj,sF668))),
inference(unit_resulting_resolution,[],[f25116,f19820]) ).
fof(f19820,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_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),X2))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(cnf_transformation,[],[f11302]) ).
fof(f11302,plain,
! [X0,X1,X2] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),X2))
| hBOOL(hAPP(X2,X1)) )
& ( hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),X2))
| ~ hBOOL(hAPP(X2,X1)) ) ),
inference(ennf_transformation,[],[f7200]) ).
fof(f7200,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(X2,X1))
=> c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),X2)) )
& ( hBOOL(hAPP(X2,X1))
=> hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBS(X0,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X0),c_fconj),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1))),X2)) ) ),
inference(rectify,[],[f3383]) ).
fof(f3383,axiom,
! [X6,X12,X15] :
( ( ~ hBOOL(hAPP(X15,X12))
=> c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6),hAPP(hAPP(c_COMBS(X6,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6),c_fconj),hAPP(hAPP(c_COMBC(X6,X6,tc_HOL_Obool),c_fequal),X12))),X15)) )
& ( hBOOL(hAPP(X15,X12))
=> hAPP(hAPP(c_Set_Oinsert(X6),X12),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X6),hAPP(hAPP(c_COMBS(X6,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6),c_fconj),hAPP(hAPP(c_COMBC(X6,X6,tc_HOL_Obool),c_fequal),X12))),X15)) ) ),
file('/export/starexec/sandbox/tmp/tmp.BvqGqdN6bG/Vampire---4.8_13129',fact_Collect__conv__if) ).
fof(f25116,plain,
! [X0] : hBOOL(hAPP(hAPP(c_fdisj,sF668),X0)),
inference(unit_resulting_resolution,[],[f24747,f18284]) ).
fof(f18284,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6123]) ).
fof(f6123,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5218]) ).
fof(f5218,axiom,
! [X14,X15] :
( hBOOL(hAPP(hAPP(c_fdisj,X15),X14))
| ~ hBOOL(X15) ),
file('/export/starexec/sandbox/tmp/tmp.BvqGqdN6bG/Vampire---4.8_13129',help_c__fdisj__1) ).
fof(f24747,plain,
hBOOL(sF668),
inference(definition_folding,[],[f16926,f24746,f24745,f24744,f24743]) ).
fof(f24743,plain,
tc_Hoare__Mirabelle_Otriple(t_a) = sF665,
introduced(function_definition,[]) ).
fof(f24744,plain,
c_member(sF665) = sF666,
introduced(function_definition,[]) ).
fof(f24745,plain,
hAPP(sF666,sK93) = sF667,
introduced(function_definition,[]) ).
fof(f24746,plain,
hAPP(sF667,v_ts) = sF668,
introduced(function_definition,[]) ).
fof(f16926,plain,
hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK93),v_ts)),
inference(cnf_transformation,[],[f14614]) ).
fof(f14614,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK92,sK93)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK93),v_ts))
& ! [X2] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK92,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK92,sK93])],[f14611,f14613,f14612]) ).
fof(f14612,plain,
( ? [X0] :
( ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_ts)) )
& ! [X2] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G)) ) )
=> ( ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK92,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_ts)) )
& ! [X2] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK92,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f14613,plain,
( ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK92,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_ts)) )
=> ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK92,sK93)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK93),v_ts)) ) ),
introduced(choice_axiom,[]) ).
fof(f14611,plain,
? [X0] :
( ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_ts)) )
& ! [X2] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G)) ) ),
inference(rectify,[],[f10324]) ).
fof(f10324,plain,
? [X0] :
( ? [X2] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X2)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts)) )
& ! [X1] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) ) ),
inference(ennf_transformation,[],[f5230]) ).
fof(f5230,plain,
~ ! [X0] :
( ! [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1) )
=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X2) ) ),
inference(rectify,[],[f5229]) ).
fof(f5229,negated_conjecture,
~ ! [X7] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X7,X2) )
=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X7,X2) ) ),
inference(negated_conjecture,[],[f5228]) ).
fof(f5228,conjecture,
! [X7] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X7,X2) )
=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X7,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.BvqGqdN6bG/Vampire---4.8_13129',conj_4) ).
fof(f49594,plain,
! [X246,X245] : hAPP(hAPP(c_Set_Oinsert(X245),X246),c_Orderings_Obot__class_Obot(tc_fun(X245,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X245),hAPP(hAPP(c_COMBS(X245,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X245),c_fconj),hAPP(hAPP(c_COMBC(X245,X245,tc_HOL_Obool),c_fequal),X246))),hAPP(c_fdisj,sF668))),
inference(resolution,[],[f25116,f19820]) ).
fof(f17930,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,[],[f5828]) ).
fof(f5828,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,[],[f158]) ).
fof(f158,axiom,
! [X36,X6] : c_Set_Othe__elem(X6,hAPP(hAPP(c_Set_Oinsert(X6),X36),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))) = X36,
file('/export/starexec/sandbox/tmp/tmp.BvqGqdN6bG/Vampire---4.8_13129',fact_the__elem__eq) ).
fof(f52660,plain,
! [X295,X294,X296,X293] :
( sK502(X293,c_fequal,X294) = c_Set_Othe__elem(X295,hAPP(c_fequal,sK501(X293,c_fequal,X294)))
| c_Fun_Oinj__on(X294,X296,c_fequal,X293) ),
inference(superposition,[],[f52225,f22511]) ).
fof(f22511,plain,
! [X2,X3,X0,X1] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
| hAPP(X1,sK501(X0,X1,X3)) = hAPP(X1,sK502(X0,X1,X3)) ),
inference(cnf_transformation,[],[f16249]) ).
fof(f17905,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,[],[f5803]) ).
fof(f5803,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,[],[f150]) ).
fof(f150,axiom,
! [X22,X6] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool)),X22),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))),
file('/export/starexec/sandbox/tmp/tmp.BvqGqdN6bG/Vampire---4.8_13129',fact_subset__UNIV) ).
fof(f19518,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,[],[f11291]) ).
fof(f11291,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,[],[f11290]) ).
fof(f11290,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,[],[f6906]) ).
fof(f6906,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,[],[f3007]) ).
fof(f3007,axiom,
! [X22,X6] :
~ ? [X207] : hAPP(c_Set_OPow(X6),X22) = hAPP(c_Set_Oimage(X6,tc_fun(X6,tc_HOL_Obool),X207),X22),
file('/export/starexec/sandbox/tmp/tmp.BvqGqdN6bG/Vampire---4.8_13129',fact_Cantors__paradox) ).
fof(f17869,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,[],[f5767]) ).
fof(f5767,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,[],[f82]) ).
fof(f82,axiom,
! [X22,X6] : hAPP(c_Set_OPow(X6),X22) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool)),
file('/export/starexec/sandbox/tmp/tmp.BvqGqdN6bG/Vampire---4.8_13129',fact_Pow__not__empty) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.79/0.87 % Problem : SWW338+1 : TPTP v8.1.2. Released v5.2.0.
% 0.79/0.88 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.89/1.09 % Computer : n017.cluster.edu
% 0.89/1.09 % Model : x86_64 x86_64
% 0.89/1.09 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.89/1.09 % Memory : 8042.1875MB
% 0.89/1.09 % OS : Linux 3.10.0-693.el7.x86_64
% 0.89/1.09 % CPULimit : 300
% 0.89/1.09 % WCLimit : 300
% 0.89/1.09 % DateTime : Sun Aug 27 21:10:12 EDT 2023
% 0.89/1.10 % CPUTime :
% 0.89/1.10 This is a FOF_CAX_RFO_SEQ problem
% 0.89/1.10 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.BvqGqdN6bG/Vampire---4.8_13129
% 0.89/1.10 % (13240)Running in auto input_syntax mode. Trying TPTP
% 0.95/1.38 % (13246)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)
% 0.95/1.39 % (13247)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_394 on Vampire---4 for (394ds/0Mi)
% 1.18/1.40 % (13244)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)
% 1.18/1.41 % (13243)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)
% 1.18/1.41 % (13242)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)
% 1.18/1.41 % (13241)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)
% 1.18/1.41 % (13245)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)
% 18.13/3.78 % (13243)First to succeed.
% 18.13/3.79 % (13243)Refutation found. Thanks to Tanya!
% 18.13/3.79 % SZS status Theorem for Vampire---4
% 18.13/3.79 % SZS output start Proof for Vampire---4
% See solution above
% 18.13/3.80 % (13243)------------------------------
% 18.13/3.80 % (13243)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 18.13/3.80 % (13243)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 18.13/3.80 % (13243)Termination reason: Refutation
% 18.13/3.80
% 18.13/3.80 % (13243)Memory used [KB]: 73175
% 18.13/3.80 % (13243)Time elapsed: 2.370 s
% 18.13/3.80 % (13243)------------------------------
% 18.13/3.80 % (13243)------------------------------
% 18.13/3.80 % (13240)Success in time 2.679 s
% 18.13/3.80 % Vampire---4.8 exiting
%------------------------------------------------------------------------------