%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW328+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:30:07 PM UTC 2026
% Result : Theorem 1.73s 1.52s
% Output : Refutation 4.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of formulae : 118 ( 20 unt; 15 def)
% Number of atoms : 354 ( 27 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 413 ( 177 ~; 175 |; 34 &)
% ( 11 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 10 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 101 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5205,axiom,
! [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,X3] :
( ( v_P(X2,X3)
& hBOOL(hAPP(v_b,X3)) )
=> ! [X4] :
( c_Natural_Oevaln(v_c,X3,X0,X4)
=> v_P(X2,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f5206,axiom,
hBOOL(hAPP(v_ba,v_s0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f5207,axiom,
c_Natural_Oevaln(v_ca,v_s0,v_na,v_s1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
fof(f5210,axiom,
( c_Com_Ocom_OWhile(v_ba,v_ca) = c_Com_Ocom_OWhile(v_b,v_c)
=> ( ! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X0) )
=> ! [X1] :
( v_P(X1,v_s1)
=> ( v_P(X1,v_s2)
& ~ hBOOL(hAPP(v_b,v_s2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
fof(f5211,conjecture,
( ( v_ba = v_b
& v_ca = v_c )
=> ( ! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X0) )
=> ! [X1] :
( v_P(X1,v_s0)
=> ( v_P(X1,v_s2)
& ~ hBOOL(hAPP(v_b,v_s2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
fof(f5212,negated_conjecture,
~ ( ( v_ba = v_b
& v_ca = v_c )
=> ( ! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X0) )
=> ! [X1] :
( v_P(X1,v_s0)
=> ( v_P(X1,v_s2)
& ~ hBOOL(hAPP(v_b,v_s2)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5211]) ).
fof(f5214,plain,
! [X0] :
( ! [X2,X3] :
( ! [X4] :
( v_P(X2,X4)
| ~ c_Natural_Oevaln(v_c,X3,X0,X4) )
| ~ v_P(X2,X3)
| ~ hBOOL(hAPP(v_b,X3)) )
| ? [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,[],[f5205]) ).
fof(f5215,plain,
! [X0] :
( ! [X2,X3] :
( ! [X4] :
( v_P(X2,X4)
| ~ c_Natural_Oevaln(v_c,X3,X0,X4) )
| ~ v_P(X2,X3)
| ~ hBOOL(hAPP(v_b,X3)) )
| ? [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(flattening,[],[f5214]) ).
fof(f5218,plain,
( ! [X1] :
( ( v_P(X1,v_s2)
& ~ hBOOL(hAPP(v_b,v_s2)) )
| ~ v_P(X1,v_s1) )
| ? [X0] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X0)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G)) )
| c_Com_Ocom_OWhile(v_b,v_c) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(ennf_transformation,[],[f5210]) ).
fof(f5219,plain,
( ! [X1] :
( ( v_P(X1,v_s2)
& ~ hBOOL(hAPP(v_b,v_s2)) )
| ~ v_P(X1,v_s1) )
| ? [X0] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X0)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G)) )
| c_Com_Ocom_OWhile(v_b,v_c) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(flattening,[],[f5218]) ).
fof(f5220,plain,
( ? [X1] :
( ( ~ v_P(X1,v_s2)
| hBOOL(hAPP(v_b,v_s2)) )
& v_P(X1,v_s0) )
& ! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G)) )
& v_ba = v_b
& v_ca = v_c ),
inference(ennf_transformation,[],[f5212]) ).
fof(f5221,plain,
( ? [X1] :
( ( ~ v_P(X1,v_s2)
| hBOOL(hAPP(v_b,v_s2)) )
& v_P(X1,v_s0) )
& ! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G)) )
& v_ba = v_b
& v_ca = v_c ),
inference(flattening,[],[f5220]) ).
fof(f5255,plain,
! [X0] :
( ! [X1,X2] :
( ! [X3] :
( v_P(X1,X3)
| ~ c_Natural_Oevaln(v_c,X2,X0,X3) )
| ~ v_P(X1,X2)
| ~ hBOOL(hAPP(v_b,X2)) )
| ? [X4] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X4)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X4),v_G)) ) ),
inference(rectify,[],[f5215]) ).
fof(f5256,plain,
! [X0] :
( ! [X1,X2] :
( ! [X3] :
( v_P(X1,X3)
| ~ c_Natural_Oevaln(v_c,X2,X0,X3) )
| ~ v_P(X1,X2)
| ~ hBOOL(hAPP(v_b,X2)) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK0(X0))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK0(X0)),v_G)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X4,sK0(X0))],[f5255]) ).
fof(f5259,plain,
( ! [X0] :
( ( v_P(X0,v_s2)
& ~ hBOOL(hAPP(v_b,v_s2)) )
| ~ v_P(X0,v_s1) )
| ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) )
| c_Com_Ocom_OWhile(v_b,v_c) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(rectify,[],[f5219]) ).
fof(f5260,plain,
( ! [X0] :
( ( v_P(X0,v_s2)
& ~ hBOOL(hAPP(v_b,v_s2)) )
| ~ v_P(X0,v_s1) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK2)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),v_G)) )
| c_Com_Ocom_OWhile(v_b,v_c) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2)],[f5259]) ).
fof(f5261,plain,
( ? [X0] :
( ( ~ v_P(X0,v_s2)
| hBOOL(hAPP(v_b,v_s2)) )
& v_P(X0,v_s0) )
& ! [X1] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) )
& v_ba = v_b
& v_ca = v_c ),
inference(rectify,[],[f5221]) ).
fof(f5262,plain,
( ( ~ v_P(sK3,v_s2)
| hBOOL(hAPP(v_b,v_s2)) )
& v_P(sK3,v_s0)
& ! [X1] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) )
& v_ba = v_b
& v_ca = v_c ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f5261]) ).
fof(f5288,plain,
! [X2,X3,X0,X1] :
( v_P(X1,X3)
| ~ c_Natural_Oevaln(v_c,X2,X0,X3)
| ~ v_P(X1,X2)
| ~ hBOOL(hAPP(v_b,X2))
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK0(X0)),v_G)) ),
inference(cnf_transformation,[],[f5256]) ).
fof(f5289,plain,
! [X2,X3,X0,X1] :
( v_P(X1,X3)
| ~ c_Natural_Oevaln(v_c,X2,X0,X3)
| ~ v_P(X1,X2)
| ~ hBOOL(hAPP(v_b,X2))
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK0(X0)) ),
inference(cnf_transformation,[],[f5256]) ).
fof(f5290,plain,
hBOOL(hAPP(v_ba,v_s0)),
inference(cnf_transformation,[],[f5206]) ).
fof(f5291,plain,
c_Natural_Oevaln(v_ca,v_s0,v_na,v_s1),
inference(cnf_transformation,[],[f5207]) ).
fof(f5297,plain,
! [X0] :
( ~ hBOOL(hAPP(v_b,v_s2))
| ~ v_P(X0,v_s1)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),v_G))
| c_Com_Ocom_OWhile(v_b,v_c) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(cnf_transformation,[],[f5260]) ).
fof(f5298,plain,
! [X0] :
( ~ hBOOL(hAPP(v_b,v_s2))
| ~ v_P(X0,v_s1)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK2)
| c_Com_Ocom_OWhile(v_b,v_c) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(cnf_transformation,[],[f5260]) ).
fof(f5299,plain,
! [X0] :
( v_P(X0,v_s2)
| ~ v_P(X0,v_s1)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),v_G))
| c_Com_Ocom_OWhile(v_b,v_c) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(cnf_transformation,[],[f5260]) ).
fof(f5300,plain,
! [X0] :
( v_P(X0,v_s2)
| ~ v_P(X0,v_s1)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK2)
| c_Com_Ocom_OWhile(v_b,v_c) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(cnf_transformation,[],[f5260]) ).
fof(f5301,plain,
v_c = v_ca,
inference(cnf_transformation,[],[f5262]) ).
fof(f5302,plain,
v_b = v_ba,
inference(cnf_transformation,[],[f5262]) ).
fof(f5303,plain,
! [X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X1) ),
inference(cnf_transformation,[],[f5262]) ).
fof(f5304,plain,
v_P(sK3,v_s0),
inference(cnf_transformation,[],[f5262]) ).
fof(f5305,plain,
( ~ v_P(sK3,v_s2)
| hBOOL(hAPP(v_b,v_s2)) ),
inference(cnf_transformation,[],[f5262]) ).
fof(f5377,plain,
! [X2,X3,X0,X1] :
( v_P(X1,X3)
| ~ c_Natural_Oevaln(v_ca,X2,X0,X3)
| ~ v_P(X1,X2)
| ~ hBOOL(hAPP(v_ba,X2))
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK0(X0)) ),
inference(definition_unfolding,[],[f5289,f5301,f5302]) ).
fof(f5378,plain,
! [X2,X3,X0,X1] :
( v_P(X1,X3)
| ~ c_Natural_Oevaln(v_ca,X2,X0,X3)
| ~ v_P(X1,X2)
| ~ hBOOL(hAPP(v_ba,X2))
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK0(X0)),v_G)) ),
inference(definition_unfolding,[],[f5288,f5301,f5302]) ).
fof(f5383,plain,
! [X0] :
( v_P(X0,v_s2)
| ~ v_P(X0,v_s1)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK2)
| c_Com_Ocom_OWhile(v_ba,v_ca) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(definition_unfolding,[],[f5300,f5302,f5301]) ).
fof(f5384,plain,
! [X0] :
( v_P(X0,v_s2)
| ~ v_P(X0,v_s1)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),v_G))
| c_Com_Ocom_OWhile(v_ba,v_ca) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(definition_unfolding,[],[f5299,f5302,f5301]) ).
fof(f5385,plain,
! [X0] :
( ~ hBOOL(hAPP(v_ba,v_s2))
| ~ v_P(X0,v_s1)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK2)
| c_Com_Ocom_OWhile(v_ba,v_ca) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(definition_unfolding,[],[f5298,f5302,f5302,f5301]) ).
fof(f5386,plain,
! [X0] :
( ~ hBOOL(hAPP(v_ba,v_s2))
| ~ v_P(X0,v_s1)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),v_G))
| c_Com_Ocom_OWhile(v_ba,v_ca) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(definition_unfolding,[],[f5297,f5302,f5302,f5301]) ).
fof(f5387,plain,
( ~ v_P(sK3,v_s2)
| hBOOL(hAPP(v_ba,v_s2)) ),
inference(definition_unfolding,[],[f5305,f5302]) ).
fof(f5396,definition,
~ sP16(c_Com_Ocom_OWhile(v_ba,v_ca)),
introduced(definition,[new_symbols(definition,[sP16])],[inequality_splitting_name_introduction]) ).
fof(f5397,plain,
! [X0] :
( v_P(X0,v_s2)
| ~ v_P(X0,v_s1)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK2)
| sP16(c_Com_Ocom_OWhile(v_ba,v_ca)) ),
inference(inequality_splitting,[],[f5383,f5396]) ).
fof(f5398,definition,
~ sP17(c_Com_Ocom_OWhile(v_ba,v_ca)),
introduced(definition,[new_symbols(definition,[sP17])],[inequality_splitting_name_introduction]) ).
fof(f5399,plain,
! [X0] :
( v_P(X0,v_s2)
| ~ v_P(X0,v_s1)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),v_G))
| sP17(c_Com_Ocom_OWhile(v_ba,v_ca)) ),
inference(inequality_splitting,[],[f5384,f5398]) ).
fof(f5400,definition,
~ sP18(c_Com_Ocom_OWhile(v_ba,v_ca)),
introduced(definition,[new_symbols(definition,[sP18])],[inequality_splitting_name_introduction]) ).
fof(f5401,plain,
! [X0] :
( ~ hBOOL(hAPP(v_ba,v_s2))
| ~ v_P(X0,v_s1)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK2)
| sP18(c_Com_Ocom_OWhile(v_ba,v_ca)) ),
inference(inequality_splitting,[],[f5385,f5400]) ).
fof(f5402,definition,
~ sP19(c_Com_Ocom_OWhile(v_ba,v_ca)),
introduced(definition,[new_symbols(definition,[sP19])],[inequality_splitting_name_introduction]) ).
fof(f5403,plain,
! [X0] :
( ~ hBOOL(hAPP(v_ba,v_s2))
| ~ v_P(X0,v_s1)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),v_G))
| sP19(c_Com_Ocom_OWhile(v_ba,v_ca)) ),
inference(inequality_splitting,[],[f5386,f5402]) ).
fof(f5416,plain,
! [X2,X3,X0] :
( ~ c_Natural_Oevaln(v_ca,X2,X0,X3)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK0(X0))
| sP20(X3,X2) ),
inference(cnf_transformation,[],[f5416_D]) ).
fof(f5416_D,definition,
! [X2,X3] :
( ! [X0] :
( ~ c_Natural_Oevaln(v_ca,X2,X0,X3)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK0(X0)) )
<=> ~ sP20(X3,X2) ),
introduced(definition,[new_symbols(definition,[sP20])],[general_splitting_component_introduction]) ).
fof(f5417,plain,
! [X2,X3,X1] :
( ~ hBOOL(hAPP(v_ba,X2))
| ~ v_P(X1,X2)
| v_P(X1,X3)
| ~ sP20(X3,X2) ),
inference(general_splitting,[],[f5377,f5416_D]) ).
fof(f5418,plain,
! [X2,X3,X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK0(X0)),v_G))
| ~ c_Natural_Oevaln(v_ca,X2,X0,X3)
| sP21(X3,X2) ),
inference(cnf_transformation,[],[f5418_D]) ).
fof(f5418_D,definition,
! [X2,X3] :
( ! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK0(X0)),v_G))
| ~ c_Natural_Oevaln(v_ca,X2,X0,X3) )
<=> ~ sP21(X3,X2) ),
introduced(definition,[new_symbols(definition,[sP21])],[general_splitting_component_introduction]) ).
fof(f5419,plain,
! [X2,X3,X1] :
( ~ hBOOL(hAPP(v_ba,X2))
| ~ v_P(X1,X2)
| v_P(X1,X3)
| ~ sP21(X3,X2) ),
inference(general_splitting,[],[f5378,f5418_D]) ).
fof(f5425,definition,
( spl24_1
<=> hBOOL(hAPP(v_ba,v_s2)) ),
introduced(definition,[new_symbols(definition,[spl24_1])],[avatar_definition]) ).
fof(f5429,definition,
( spl24_2
<=> v_P(sK3,v_s2) ),
introduced(definition,[new_symbols(definition,[spl24_2])],[avatar_definition]) ).
fof(f5431,plain,
( ~ v_P(sK3,v_s2)
| spl24_2 ),
inference(avatar_component_clause,[],[f5429]) ).
fof(f5432,plain,
( spl24_1
| ~ spl24_2 ),
inference(avatar_split_clause,[],[f5387,f5429,f5425]) ).
fof(f5433,plain,
! [X0] :
( ~ hBOOL(hAPP(v_ba,v_s2))
| ~ v_P(X0,v_s1)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),v_G)) ),
inference(forward_subsumption_resolution,[],[f5403,f5402]) ).
fof(f5434,plain,
! [X0] :
( ~ hBOOL(hAPP(v_ba,v_s2))
| ~ v_P(X0,v_s1)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK2) ),
inference(forward_subsumption_resolution,[],[f5401,f5400]) ).
fof(f5435,plain,
! [X0] :
( v_P(X0,v_s2)
| ~ v_P(X0,v_s1)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),v_G)) ),
inference(forward_subsumption_resolution,[],[f5399,f5398]) ).
fof(f5436,plain,
! [X0] :
( v_P(X0,v_s2)
| ~ v_P(X0,v_s1)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK2) ),
inference(forward_subsumption_resolution,[],[f5397,f5396]) ).
fof(f5467,definition,
( spl24_10
<=> ! [X0] :
( v_P(X0,v_s1)
| ~ v_P(X0,v_s0) ) ),
introduced(definition,[new_symbols(definition,[spl24_10])],[avatar_definition]) ).
fof(f5468,plain,
( ! [X0] :
( ~ v_P(X0,v_s0)
| v_P(X0,v_s1) )
| ~ spl24_10 ),
inference(avatar_component_clause,[],[f5467]) ).
fof(f5476,definition,
( spl24_12
<=> hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),v_G)) ),
introduced(definition,[new_symbols(definition,[spl24_12])],[avatar_definition]) ).
fof(f5478,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),v_G))
| ~ spl24_12 ),
inference(avatar_component_clause,[],[f5476]) ).
fof(f5480,definition,
( spl24_13
<=> ! [X0] : ~ v_P(X0,v_s1) ),
introduced(definition,[new_symbols(definition,[spl24_13])],[avatar_definition]) ).
fof(f5481,plain,
( ! [X0] : ~ v_P(X0,v_s1)
| ~ spl24_13 ),
inference(avatar_component_clause,[],[f5480]) ).
fof(f5482,plain,
( spl24_12
| spl24_13
| ~ spl24_1 ),
inference(avatar_split_clause,[],[f5433,f5425,f5480,f5476]) ).
fof(f5484,definition,
( spl24_14
<=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK2) ),
introduced(definition,[new_symbols(definition,[spl24_14])],[avatar_definition]) ).
fof(f5486,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK2)
| spl24_14 ),
inference(avatar_component_clause,[],[f5484]) ).
fof(f5487,plain,
( ~ spl24_14
| spl24_13
| ~ spl24_1 ),
inference(avatar_split_clause,[],[f5434,f5425,f5480,f5484]) ).
fof(f5489,definition,
( spl24_15
<=> ! [X0] :
( v_P(X0,v_s2)
| ~ v_P(X0,v_s1) ) ),
introduced(definition,[new_symbols(definition,[spl24_15])],[avatar_definition]) ).
fof(f5490,plain,
( ! [X0] :
( ~ v_P(X0,v_s1)
| v_P(X0,v_s2) )
| ~ spl24_15 ),
inference(avatar_component_clause,[],[f5489]) ).
fof(f5491,plain,
( spl24_12
| spl24_15 ),
inference(avatar_split_clause,[],[f5435,f5489,f5476]) ).
fof(f5492,plain,
( ~ spl24_14
| spl24_15 ),
inference(avatar_split_clause,[],[f5436,f5489,f5484]) ).
fof(f5498,plain,
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK2)
| ~ spl24_12 ),
inference(resolution,[],[f5303,f5478]) ).
fof(f5501,plain,
( $false
| ~ spl24_12
| spl24_14 ),
inference(forward_subsumption_resolution,[],[f5498,f5486]) ).
fof(f5502,plain,
( ~ spl24_12
| spl24_14 ),
inference(avatar_contradiction_clause,[],[f5501]) ).
fof(f5505,plain,
( v_P(sK3,v_s1)
| ~ spl24_10 ),
inference(resolution,[],[f5468,f5304]) ).
fof(f5506,plain,
( v_P(sK3,v_s2)
| ~ spl24_10
| ~ spl24_15 ),
inference(resolution,[],[f5490,f5505]) ).
fof(f5507,plain,
( $false
| spl24_2
| ~ spl24_10
| ~ spl24_15 ),
inference(forward_subsumption_resolution,[],[f5506,f5431]) ).
fof(f5508,plain,
( spl24_2
| ~ spl24_10
| ~ spl24_15 ),
inference(avatar_contradiction_clause,[],[f5507]) ).
fof(f5518,plain,
! [X2,X0,X1] :
( ~ c_Natural_Oevaln(v_ca,X0,X1,X2)
| sP21(X2,X0)
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK0(X1)) ),
inference(resolution,[],[f5418,f5303]) ).
fof(f5521,plain,
! [X0,X1] :
( ~ sP21(X1,v_s0)
| v_P(X0,X1)
| ~ v_P(X0,v_s0) ),
inference(resolution,[],[f5290,f5419]) ).
fof(f5522,plain,
! [X0,X1] :
( ~ sP20(X1,v_s0)
| v_P(X0,X1)
| ~ v_P(X0,v_s0) ),
inference(resolution,[],[f5290,f5417]) ).
fof(f5523,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK0(v_na))
| sP20(v_s1,v_s0) ),
inference(resolution,[],[f5291,f5416]) ).
fof(f5525,definition,
( spl24_16
<=> sP20(v_s1,v_s0) ),
introduced(definition,[new_symbols(definition,[spl24_16])],[avatar_definition]) ).
fof(f5527,plain,
( sP20(v_s1,v_s0)
| ~ spl24_16 ),
inference(avatar_component_clause,[],[f5525]) ).
fof(f5529,definition,
( spl24_17
<=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK0(v_na)) ),
introduced(definition,[new_symbols(definition,[spl24_17])],[avatar_definition]) ).
fof(f5531,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK0(v_na))
| spl24_17 ),
inference(avatar_component_clause,[],[f5529]) ).
fof(f5532,plain,
( spl24_16
| ~ spl24_17 ),
inference(avatar_split_clause,[],[f5523,f5529,f5525]) ).
fof(f5558,plain,
( sP21(v_s1,v_s0)
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK0(v_na)) ),
inference(resolution,[],[f5518,f5291]) ).
fof(f5566,plain,
( sP21(v_s1,v_s0)
| spl24_17 ),
inference(forward_subsumption_resolution,[],[f5558,f5531]) ).
fof(f5567,plain,
( ! [X0] :
( v_P(X0,v_s1)
| ~ v_P(X0,v_s0) )
| spl24_17 ),
inference(resolution,[],[f5566,f5521]) ).
fof(f5568,plain,
( spl24_10
| spl24_17 ),
inference(avatar_split_clause,[],[f5567,f5529,f5467]) ).
fof(f5569,plain,
( ! [X0] :
( v_P(X0,v_s1)
| ~ v_P(X0,v_s0) )
| ~ spl24_16 ),
inference(resolution,[],[f5527,f5522]) ).
fof(f5570,plain,
( spl24_10
| ~ spl24_16 ),
inference(avatar_split_clause,[],[f5569,f5525,f5467]) ).
fof(f5580,plain,
( $false
| ~ spl24_10
| ~ spl24_13 ),
inference(resolution,[],[f5505,f5481]) ).
fof(f5582,plain,
( ~ spl24_10
| ~ spl24_13 ),
inference(avatar_contradiction_clause,[],[f5580]) ).
cnf(s1,plain,
( spl24_1
| ~ spl24_2 ),
inference(sat_conversion,[],[f5432]) ).
cnf(s6,plain,
( ~ spl24_1
| spl24_12
| spl24_13 ),
inference(sat_conversion,[],[f5482]) ).
cnf(s7,plain,
( ~ spl24_1
| spl24_13
| ~ spl24_14 ),
inference(sat_conversion,[],[f5487]) ).
cnf(s8,plain,
( spl24_12
| spl24_15 ),
inference(sat_conversion,[],[f5491]) ).
cnf(s9,plain,
( ~ spl24_14
| spl24_15 ),
inference(sat_conversion,[],[f5492]) ).
cnf(s10,plain,
( ~ spl24_12
| spl24_14 ),
inference(sat_conversion,[],[f5502]) ).
cnf(s12,plain,
( spl24_2
| ~ spl24_10
| ~ spl24_15 ),
inference(sat_conversion,[],[f5508]) ).
cnf(s13,plain,
( spl24_16
| ~ spl24_17 ),
inference(sat_conversion,[],[f5532]) ).
cnf(s15,plain,
( spl24_10
| spl24_17 ),
inference(sat_conversion,[],[f5568]) ).
cnf(s16,plain,
( spl24_10
| ~ spl24_16 ),
inference(sat_conversion,[],[f5570]) ).
cnf(s19,plain,
( ~ spl24_10
| ~ spl24_13 ),
inference(sat_conversion,[],[f5582]) ).
cnf(s22,plain,
spl24_15,
inference(rat,[],[s10,s8,s9]) ).
cnf(s23,plain,
spl24_10,
inference(rat,[],[s13,s15,s16]) ).
cnf(s24,plain,
~ spl24_13,
inference(rat,[],[s19,s23]) ).
cnf(s25,plain,
spl24_2,
inference(rat,[],[s12,s22,s23]) ).
cnf(s26,plain,
spl24_1,
inference(rat,[],[s1,s25]) ).
cnf(s28,plain,
~ spl24_14,
inference(rat,[],[s7,s24,s26]) ).
cnf(s29,plain,
spl24_12,
inference(rat,[],[s6,s24,s26]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s10,s28,s29]) ).
fof(f5583,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW328+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n010.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 13:36:17 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.73/1.52 % (1926137)Detected formulas, will run a generic FOF schedule.
% 1.73/1.52 % (1926142)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=308179735:i=141193_2995 on theBenchmark for (2995ds/141193Mi)
% 1.73/1.52 % (1926143)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2717145446:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2995 on theBenchmark for (2995ds/134677Mi)
% 1.73/1.52 % (1926146)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1060661683:i=119:av=off:ss=axioms_2995 on theBenchmark for (2995ds/119Mi)
% 1.73/1.52 % (1926144)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=452894063:i=141695:sd=1:nm=32:gsp=on:ss=included_2995 on theBenchmark for (2995ds/141695Mi)
% 1.73/1.52 % (1926145)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=591011726:i=109:sd=1:ins=1:gsp=on:ss=axioms_2995 on theBenchmark for (2995ds/109Mi)
% 1.73/1.52 % (1926148)dis-21_1_sil=8000:lcm=predicate:random_seed=2736407969:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2995 on theBenchmark for (2995ds/129Mi)
% 1.73/1.52 % (1926147)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2855388270:s2a=on:i=139:gtg=position_2995 on theBenchmark for (2995ds/139Mi)
% 1.73/1.52 % (1926145)First to succeed.
% 1.73/1.52 % (1926145)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1926137"
% 1.73/1.52 % (1926147)Instruction limit reached!
% 1.73/1.52 % (1926147)------------------------------
% 1.73/1.52 % (1926147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.73/1.52 % (1926147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/1.52 % (1926147)CaDiCaL version: 2.1.3
% 1.73/1.52 % (1926147)Termination reason: Instruction limit
% 1.73/1.52 % (1926147)Termination phase: SInE selection
% 1.73/1.52 % (1926147)Time elapsed: 0.059 s
% 1.73/1.52 % (1926147)Peak memory usage: 90 MB
% 1.73/1.52 % (1926147)Instructions burned: 140 (million)
% 1.73/1.52 % (1926146)Instruction limit reached!
% 1.73/1.52 % (1926146)------------------------------
% 1.73/1.52 % (1926146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.73/1.52 % (1926146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/1.52 % (1926146)CaDiCaL version: 2.1.3
% 1.73/1.52 % (1926146)Termination reason: Instruction limit
% 1.73/1.52 % (1926146)Termination phase: Property scanning
% 1.73/1.52 % (1926146)Time elapsed: 0.072 s
% 1.73/1.52 % (1926146)Peak memory usage: 92 MB
% 1.73/1.52 % (1926146)Instructions burned: 120 (million)
% 1.73/1.52 % (1926148)Instruction limit reached!
% 1.73/1.52 % (1926148)------------------------------
% 1.73/1.52 % (1926148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.73/1.52 % (1926148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/1.52 % (1926148)CaDiCaL version: 2.1.3
% 1.73/1.52 % (1926148)Termination reason: Instruction limit
% 1.73/1.52 % (1926148)Termination phase: Preprocessing 3
% 1.73/1.52 % (1926148)Time elapsed: 0.082 s
% 1.73/1.52 % (1926148)Peak memory usage: 93 MB
% 1.73/1.52 % (1926148)Instructions burned: 130 (million)
% 1.73/1.52 % (1926156)lrs+10_1_sil=8000:sp=occurrence:random_seed=2355090948:i=285:sd=3:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/285Mi)
% 1.73/1.52 % (1926157)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2758087464:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/157Mi)
% 1.73/1.52 % (1926158)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1806879666:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 1.73/1.52 % (1926158)Also succeeded, but the first one will report.
% 1.73/1.52 % (1926145)Refutation found. Thanks to Tanya!
% 1.73/1.52 % SZS status Theorem for theBenchmark
% 1.73/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 4.35/1.72 % (1926145)------------------------------
% 4.35/1.72 % (1926145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.72 % (1926145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.72 % (1926145)CaDiCaL version: 2.1.3
% 4.35/1.72 % (1926145)Termination reason: Refutation
% 4.35/1.72 % (1926145)Time elapsed: 0.035 s
% 4.35/1.72 % (1926145)Peak memory usage: 95 MB
% 4.35/1.72 % (1926145)Instructions burned: 48 (million)
% 4.35/1.72 % (1926145)------------------------------
% 4.35/1.72 % (1926145)------------------------------
% 4.35/1.72 % (1926137)Success in time 0.863 s
% 4.35/1.72 % Vampire exiting
%------------------------------------------------------------------------------