TSTP Solution File: SWW360+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SWW360+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 : n001.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 01:01:03 EDT 2023
% Result : Theorem 16.46s 3.60s
% Output : Refutation 16.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 69 ( 34 unt; 0 def)
% Number of atoms : 183 ( 84 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 174 ( 60 ~; 47 |; 40 &)
% ( 7 <=>; 20 =>; 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 : 30 ( 30 usr; 12 con; 0-4 aty)
% Number of variables : 210 (; 186 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f55962,plain,
$false,
inference(unit_resulting_resolution,[],[f17887,f19598,f17923,f55628,f22327]) ).
fof(f22327,plain,
! [X2,X3,X0,X1,X7] :
( hAPP(c_Set_Oimage(X1,X2,sK445(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,[],[f16196]) ).
fof(f16196,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,sK444(X0,X1,X2,X3)),X3)),X0))
& c_Fun_Oinj__on(X2,X1,sK444(X0,X1,X2,X3),X3) )
| ! [X5] : hAPP(c_Set_Oimage(X1,X2,X5),X0) != X3 )
& ( hAPP(c_Set_Oimage(X1,X2,sK445(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,[sK444,sK445])],[f16193,f16195,f16194]) ).
fof(f16194,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,sK444(X0,X1,X2,X3)),X3)),X0))
& c_Fun_Oinj__on(X2,X1,sK444(X0,X1,X2,X3),X3) ) ),
introduced(choice_axiom,[]) ).
fof(f16195,plain,
! [X0,X1,X2,X3] :
( ? [X6] : hAPP(c_Set_Oimage(X1,X2,X6),X0) = X3
=> hAPP(c_Set_Oimage(X1,X2,sK445(X0,X1,X2,X3)),X0) = X3 ),
introduced(choice_axiom,[]) ).
fof(f16193,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,[],[f16192]) ).
fof(f16192,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,[],[f13267]) ).
fof(f13267,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,[],[f8921]) ).
fof(f8921,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,[],[f3056]) ).
fof(f3056,axiom,
! [X165,X4,X6,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) != X8
=> ( ? [X74] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X6,X4,X74),X8)),X165))
& c_Fun_Oinj__on(X6,X4,X74,X8) )
<=> ? [X178] : hAPP(c_Set_Oimage(X4,X6,X178),X165) = X8 ) ),
file('/export/starexec/sandbox/tmp/tmp.sOizlA8P7B/Vampire---4.8_12023',fact_inj__on__iff__surj) ).
fof(f55628,plain,
! [X272,X270,X269] : c_Fun_Oinj__on(X270,X272,c_fequal,X269),
inference(subsumption_resolution,[],[f55627,f22626]) ).
fof(f22626,plain,
! [X2,X3,X0,X1] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
| sK486(X0,X1,X3) != sK487(X0,X1,X3) ),
inference(cnf_transformation,[],[f16300]) ).
fof(f16300,plain,
! [X0,X1,X2,X3] :
( ( c_Fun_Oinj__on(X3,X2,X1,X0)
| ( sK486(X0,X1,X3) != sK487(X0,X1,X3)
& hAPP(X1,sK486(X0,X1,X3)) = hAPP(X1,sK487(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),sK487(X0,X1,X3)),X0))
& hBOOL(hAPP(hAPP(c_member(X3),sK486(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,[sK486,sK487])],[f16297,f16299,f16298]) ).
fof(f16298,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] :
( sK486(X0,X1,X3) != X5
& hAPP(X1,X5) = hAPP(X1,sK486(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),sK486(X0,X1,X3)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f16299,plain,
! [X0,X1,X3] :
( ? [X5] :
( sK486(X0,X1,X3) != X5
& hAPP(X1,X5) = hAPP(X1,sK486(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
=> ( sK486(X0,X1,X3) != sK487(X0,X1,X3)
& hAPP(X1,sK486(X0,X1,X3)) = hAPP(X1,sK487(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),sK487(X0,X1,X3)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f16297,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,[],[f16296]) ).
fof(f16296,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,[],[f13560]) ).
fof(f13560,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,[],[f13559]) ).
fof(f13559,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,[],[f9141]) ).
fof(f9141,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,[],[f3042]) ).
fof(f3042,axiom,
! [X8,X1,X4,X6] :
( c_Fun_Oinj__on(X6,X4,X1,X8)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X6),X2),X8))
=> ! [X41] :
( hBOOL(hAPP(hAPP(c_member(X6),X41),X8))
=> ( hAPP(X1,X2) = hAPP(X1,X41)
=> X2 = X41 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sOizlA8P7B/Vampire---4.8_12023',fact_inj__on__def) ).
fof(f55627,plain,
! [X272,X270,X269] :
( sK487(X269,c_fequal,X270) = sK486(X269,c_fequal,X270)
| c_Fun_Oinj__on(X270,X272,c_fequal,X269) ),
inference(forward_demodulation,[],[f55597,f53663]) ).
fof(f53663,plain,
! [X0,X1] : c_Set_Othe__elem(X1,hAPP(c_fequal,X0)) = X0,
inference(backward_demodulation,[],[f17948,f53655]) ).
fof(f53655,plain,
! [X286,X285] : hAPP(hAPP(c_Set_Oinsert(X285),X286),c_Orderings_Obot__class_Obot(tc_fun(X285,tc_HOL_Obool))) = hAPP(c_fequal,X286),
inference(forward_demodulation,[],[f51906,f53384]) ).
fof(f53384,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,sF661))),
inference(forward_demodulation,[],[f53383,f17813]) ).
fof(f17813,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(cnf_transformation,[],[f5687]) ).
fof(f5687,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(rectify,[],[f3180]) ).
fof(f3180,axiom,
! [X35,X6] : hAPP(c_Set_OCollect(X6),X35) = X35,
file('/export/starexec/sandbox/tmp/tmp.sOizlA8P7B/Vampire---4.8_12023',fact_Collect__def) ).
fof(f53383,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,sF661))),
inference(forward_demodulation,[],[f48712,f18009]) ).
fof(f18009,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,[],[f5883]) ).
fof(f5883,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,[],[f3203]) ).
fof(f3203,axiom,
! [X7,X6] : hAPP(hAPP(c_Set_Oinsert(X6),X7),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X6),hAPP(c_fequal,X7)),
file('/export/starexec/sandbox/tmp/tmp.sOizlA8P7B/Vampire---4.8_12023',fact_singleton__conv2) ).
fof(f48712,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,sF661))),
inference(unit_resulting_resolution,[],[f25188,f19892]) ).
fof(f19892,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,[],[f11321]) ).
fof(f11321,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,[],[f7216]) ).
fof(f7216,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,[],[f3200]) ).
fof(f3200,axiom,
! [X6,X7,X35] :
( ( ~ hBOOL(hAPP(X35,X7))
=> 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),X7))),X35)) )
& ( hBOOL(hAPP(X35,X7))
=> hAPP(hAPP(c_Set_Oinsert(X6),X7),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),X7))),X35)) ) ),
file('/export/starexec/sandbox/tmp/tmp.sOizlA8P7B/Vampire---4.8_12023',fact_Collect__conv__if) ).
fof(f25188,plain,
! [X0] : hBOOL(hAPP(hAPP(c_fdisj,sF661),X0)),
inference(unit_resulting_resolution,[],[f24819,f18297]) ).
fof(f18297,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6112]) ).
fof(f6112,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5218]) ).
fof(f5218,axiom,
! [X34,X35] :
( hBOOL(hAPP(hAPP(c_fdisj,X35),X34))
| ~ hBOOL(X35) ),
file('/export/starexec/sandbox/tmp/tmp.sOizlA8P7B/Vampire---4.8_12023',help_c__fdisj__1) ).
fof(f24819,plain,
hBOOL(sF661),
inference(definition_folding,[],[f16948,f24818,f24817,f24816]) ).
fof(f24816,plain,
c_member(tc_Com_Opname) = sF659,
introduced(function_definition,[]) ).
fof(f24817,plain,
hAPP(sF659,sK89) = sF660,
introduced(function_definition,[]) ).
fof(f24818,plain,
hAPP(sF660,v_U) = sF661,
introduced(function_definition,[]) ).
fof(f16948,plain,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),sK89),v_U)),
inference(cnf_transformation,[],[f14637]) ).
fof(f14637,plain,
( ~ v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,sK89)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),sK89),v_U)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK89])],[f10310,f14636]) ).
fof(f14636,plain,
( ? [X0] :
( ~ v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,X0)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_U)) )
=> ( ~ v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,sK89)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),sK89),v_U)) ) ),
introduced(choice_axiom,[]) ).
fof(f10310,plain,
? [X0] :
( ~ v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,X0)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_U)) ),
inference(ennf_transformation,[],[f5228]) ).
fof(f5228,plain,
~ ! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_U))
=> v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,X0)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ),
inference(rectify,[],[f5227]) ).
fof(f5227,negated_conjecture,
~ ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X2),v_U))
=> v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,X2)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ),
inference(negated_conjecture,[],[f5226]) ).
fof(f5226,conjecture,
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X2),v_U))
=> v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,X2)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/tmp/tmp.sOizlA8P7B/Vampire---4.8_12023',conj_2) ).
fof(f51906,plain,
! [X286,X285] : hAPP(hAPP(c_Set_Oinsert(X285),X286),c_Orderings_Obot__class_Obot(tc_fun(X285,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X285),hAPP(hAPP(c_COMBS(X285,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X285),c_fconj),hAPP(hAPP(c_COMBC(X285,X285,tc_HOL_Obool),c_fequal),X286))),hAPP(c_fdisj,sF661))),
inference(resolution,[],[f25188,f19892]) ).
fof(f17948,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,[],[f5822]) ).
fof(f5822,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,[],[f41]) ).
fof(f41,axiom,
! [X17,X6] : c_Set_Othe__elem(X6,hAPP(hAPP(c_Set_Oinsert(X6),X17),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))) = X17,
file('/export/starexec/sandbox/tmp/tmp.sOizlA8P7B/Vampire---4.8_12023',fact_the__elem__eq) ).
fof(f55597,plain,
! [X271,X272,X270,X269] :
( sK487(X269,c_fequal,X270) = c_Set_Othe__elem(X271,hAPP(c_fequal,sK486(X269,c_fequal,X270)))
| c_Fun_Oinj__on(X270,X272,c_fequal,X269) ),
inference(superposition,[],[f53663,f22625]) ).
fof(f22625,plain,
! [X2,X3,X0,X1] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
| hAPP(X1,sK486(X0,X1,X3)) = hAPP(X1,sK487(X0,X1,X3)) ),
inference(cnf_transformation,[],[f16300]) ).
fof(f17923,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,[],[f5797]) ).
fof(f5797,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,[],[f985]) ).
fof(f985,axiom,
! [X8,X6] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool)),X8),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))),
file('/export/starexec/sandbox/tmp/tmp.sOizlA8P7B/Vampire---4.8_12023',fact_subset__UNIV) ).
fof(f19598,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,[],[f11310]) ).
fof(f11310,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,[],[f11309]) ).
fof(f11309,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,[],[f6930]) ).
fof(f6930,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,[],[f936]) ).
fof(f936,axiom,
! [X8,X6] :
~ ? [X74] : hAPP(c_Set_OPow(X6),X8) = hAPP(c_Set_Oimage(X6,tc_fun(X6,tc_HOL_Obool),X74),X8),
file('/export/starexec/sandbox/tmp/tmp.sOizlA8P7B/Vampire---4.8_12023',fact_Cantors__paradox) ).
fof(f17887,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,[],[f5761]) ).
fof(f5761,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,[],[f821]) ).
fof(f821,axiom,
! [X8,X6] : c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(c_Set_OPow(X6),X8),
file('/export/starexec/sandbox/tmp/tmp.sOizlA8P7B/Vampire---4.8_12023',fact_Pow__not__empty) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.86 % Problem : SWW360+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.88 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.88/1.09 % Computer : n001.cluster.edu
% 0.88/1.09 % Model : x86_64 x86_64
% 0.88/1.09 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.88/1.09 % Memory : 8042.1875MB
% 0.88/1.09 % OS : Linux 3.10.0-693.el7.x86_64
% 0.88/1.09 % CPULimit : 300
% 0.88/1.09 % WCLimit : 300
% 0.88/1.09 % DateTime : Sun Aug 27 19:47:49 EDT 2023
% 0.88/1.09 % CPUTime :
% 0.88/1.09 This is a FOF_CAX_RFO_SEQ problem
% 0.88/1.09 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.sOizlA8P7B/Vampire---4.8_12023
% 0.88/1.10 % (12136)Running in auto input_syntax mode. Trying TPTP
% 0.95/1.38 % (12147)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_394 on Vampire---4 for (394ds/0Mi)
% 0.95/1.40 % (12143)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)
% 0.95/1.40 % (12140)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)
% 0.95/1.40 % (12146)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)
% 0.95/1.41 % (12137)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)
% 0.95/1.41 % (12144)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)
% 0.95/1.41 % (12145)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)
% 16.46/3.59 % (12143)First to succeed.
% 16.46/3.60 % (12143)Refutation found. Thanks to Tanya!
% 16.46/3.60 % SZS status Theorem for Vampire---4
% 16.46/3.60 % SZS output start Proof for Vampire---4
% See solution above
% 16.46/3.61 % (12143)------------------------------
% 16.46/3.61 % (12143)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 16.46/3.61 % (12143)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 16.46/3.61 % (12143)Termination reason: Refutation
% 16.46/3.61
% 16.46/3.61 % (12143)Memory used [KB]: 77909
% 16.46/3.61 % (12143)Time elapsed: 2.188 s
% 16.46/3.61 % (12143)------------------------------
% 16.46/3.61 % (12143)------------------------------
% 16.46/3.61 % (12136)Success in time 2.5 s
% 16.46/3.61 % Vampire---4.8 exiting
%------------------------------------------------------------------------------