%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW333+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 : n012.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 01:30:08 PM UTC 2026
% Result : Theorem 1.79s 0.81s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 15 unt; 3 def)
% Number of atoms : 142 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 145 ( 59 ~; 61 |; 11 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 11 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 55 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2,X3,X4] :
( c_Hoare__Mirabelle_Otriple__valid(X4,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X0))
<=> c_Hoare__Mirabelle_Otriple__valid(X4,hAPP(c_Nat_OSuc,X3),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X2),hAPP(c_Com_Ocom_OBODY,X1)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Body__triple__valid__Suc) ).
fof(f707,axiom,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
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) )
& ! [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X1),v_Procs))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X1)),hAPP(c_Com_Ocom_OBODY,X1)),v_Q(X1))) ) )
=> ! [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X1),v_Procs))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X1)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),v_Q(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f5206,axiom,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f5207,axiom,
! [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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
fof(f5208,axiom,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Com_Ocom_OBODY,X0)),v_Q(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
fof(f5209,conjecture,
c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(f5210,negated_conjecture,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
inference(negated_conjecture,[status(cth)],[f5209]) ).
fof(f5211,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_Com_Opname),X2),v_Procs))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X2)),hAPP(c_Com_Ocom_OBODY,X2)),v_Q(X2))) ) )
=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X3),v_Procs))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X3)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X3))),v_Q(X3))) ) ),
inference(rectify,[],[f5205]) ).
fof(f5212,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
inference(flattening,[],[f5210]) ).
fof(f5214,plain,
! [X0] :
( ! [X3] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X3)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X3))),v_Q(X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X3),v_Procs)) )
| ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) )
| ? [X2] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X2)),hAPP(c_Com_Ocom_OBODY,X2)),v_Q(X2)))
& hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X2),v_Procs)) ) ),
inference(ennf_transformation,[],[f5211]) ).
fof(f5215,plain,
! [X0] :
( ! [X3] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X3)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X3))),v_Q(X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X3),v_Procs)) )
| ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) )
| ? [X2] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X2)),hAPP(c_Com_Ocom_OBODY,X2)),v_Q(X2)))
& hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X2),v_Procs)) ) ),
inference(flattening,[],[f5214]) ).
fof(f5216,plain,
! [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)) ),
inference(ennf_transformation,[],[f5207]) ).
fof(f5217,plain,
! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Com_Ocom_OBODY,X0)),v_Q(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs)) ),
inference(ennf_transformation,[],[f5208]) ).
fof(f5287,plain,
! [X0] :
( ! [X1] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X1)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),v_Q(X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X1),v_Procs)) )
| ? [X2] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X2)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G)) )
| ? [X3] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X3)),hAPP(c_Com_Ocom_OBODY,X3)),v_Q(X3)))
& hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X3),v_Procs)) ) ),
inference(rectify,[],[f5215]) ).
fof(f5288,plain,
! [X0] :
( ! [X1] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X1)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),v_Q(X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X1),v_Procs)) )
| ( ~ 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)) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(sK1(X0))),hAPP(c_Com_Ocom_OBODY,sK1(X0))),v_Q(sK1(X0))))
& hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),sK1(X0)),v_Procs)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0)),skolemize(X3,sK1(X0))],[f5287]) ).
fof(f5294,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Hoare__Mirabelle_Otriple__valid(X4,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X0))
| ~ c_Hoare__Mirabelle_Otriple__valid(X4,hAPP(c_Nat_OSuc,X3),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X2),hAPP(c_Com_Ocom_OBODY,X1)),X0)) )
& ( c_Hoare__Mirabelle_Otriple__valid(X4,hAPP(c_Nat_OSuc,X3),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X2),hAPP(c_Com_Ocom_OBODY,X1)),X0))
| ~ c_Hoare__Mirabelle_Otriple__valid(X4,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X0)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f5347,plain,
! [X0,X1] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X1)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),v_Q(X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X1),v_Procs))
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK0(X0)),v_G))
| hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),sK1(X0)),v_Procs)) ),
inference(cnf_transformation,[],[f5288]) ).
fof(f5348,plain,
! [X0,X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(sK1(X0))),hAPP(c_Com_Ocom_OBODY,sK1(X0))),v_Q(sK1(X0))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X1),v_Procs))
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK0(X0)),v_G))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X1)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),v_Q(X1))) ),
inference(cnf_transformation,[],[f5288]) ).
fof(f5349,plain,
! [X0,X1] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X1)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),v_Q(X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X1),v_Procs))
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK0(X0))
| hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),sK1(X0)),v_Procs)) ),
inference(cnf_transformation,[],[f5288]) ).
fof(f5350,plain,
! [X0,X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(sK1(X0))),hAPP(c_Com_Ocom_OBODY,sK1(X0))),v_Q(sK1(X0))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X1),v_Procs))
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK0(X0))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X0,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X1)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),v_Q(X1))) ),
inference(cnf_transformation,[],[f5288]) ).
fof(f5351,plain,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs)),
inference(cnf_transformation,[],[f5206]) ).
fof(f5352,plain,
! [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) ),
inference(cnf_transformation,[],[f5216]) ).
fof(f5353,plain,
! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Com_Ocom_OBODY,X0)),v_Q(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs)) ),
inference(cnf_transformation,[],[f5217]) ).
fof(f5354,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
inference(cnf_transformation,[],[f5212]) ).
fof(f5363,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Hoare__Mirabelle_Otriple__valid(X4,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X0))
| c_Hoare__Mirabelle_Otriple__valid(X4,hAPP(c_Nat_OSuc,X3),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X2),hAPP(c_Com_Ocom_OBODY,X1)),X0)) ),
inference(cnf_transformation,[],[f5294]) ).
fof(f5425,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(cnf_transformation,[],[f707]) ).
fof(f5607,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
inference(forward_demodulation,[],[f5354,f5425]) ).
fof(f5689,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs))
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK0(v_na))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X0))),v_Q(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),sK1(v_na)),v_Procs)) ),
inference(resolution,[],[f5350,f5353]) ).
fof(f5699,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs))
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK0(v_na))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X0))),v_Q(X0))) ),
inference(forward_subsumption_resolution,[],[f5689,f5349]) ).
fof(f5701,definition,
( spl46_14
<=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK0(v_na)) ),
introduced(definition,[new_symbols(definition,[spl46_14])],[avatar_definition]) ).
fof(f5703,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK0(v_na))
| spl46_14 ),
inference(avatar_component_clause,[],[f5701]) ).
fof(f5705,definition,
( spl46_15
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X0))),v_Q(X0))) ) ),
introduced(definition,[new_symbols(definition,[spl46_15])],[avatar_definition]) ).
fof(f5706,plain,
( ! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X0))),v_Q(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs)) )
| ~ spl46_15 ),
inference(avatar_component_clause,[],[f5705]) ).
fof(f5707,plain,
( ~ spl46_14
| spl46_15 ),
inference(avatar_split_clause,[],[f5699,f5705,f5701]) ).
fof(f5708,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs))
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK0(v_na)),v_G))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X0))),v_Q(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),sK1(v_na)),v_Procs)) ),
inference(resolution,[],[f5348,f5353]) ).
fof(f5715,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs))
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK0(v_na)),v_G))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X0))),v_Q(X0))) ),
inference(forward_subsumption_resolution,[],[f5708,f5347]) ).
fof(f5717,definition,
( spl46_17
<=> hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK0(v_na)),v_G)) ),
introduced(definition,[new_symbols(definition,[spl46_17])],[avatar_definition]) ).
fof(f5719,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK0(v_na)),v_G))
| ~ spl46_17 ),
inference(avatar_component_clause,[],[f5717]) ).
fof(f5720,plain,
( spl46_17
| spl46_15 ),
inference(avatar_split_clause,[],[f5715,f5705,f5717]) ).
fof(f5748,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Com_Ocom_OBODY,X0)),v_Q(X0))) )
| ~ spl46_15 ),
inference(resolution,[],[f5706,f5363]) ).
fof(f5750,plain,
( ! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Com_Ocom_OBODY,X0)),v_Q(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs)) )
| ~ spl46_15 ),
inference(forward_demodulation,[],[f5748,f5425]) ).
fof(f5803,plain,
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK0(v_na))
| ~ spl46_17 ),
inference(resolution,[],[f5719,f5352]) ).
fof(f5805,plain,
( $false
| spl46_14
| ~ spl46_17 ),
inference(forward_subsumption_resolution,[],[f5803,f5703]) ).
fof(f5806,plain,
( spl46_14
| ~ spl46_17 ),
inference(avatar_contradiction_clause,[],[f5805]) ).
fof(f6054,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs))
| ~ spl46_15 ),
inference(resolution,[],[f5750,f5607]) ).
fof(f6065,plain,
( $false
| ~ spl46_15 ),
inference(forward_subsumption_resolution,[],[f6054,f5351]) ).
fof(f6066,plain,
~ spl46_15,
inference(avatar_contradiction_clause,[],[f6065]) ).
cnf(s9,plain,
( ~ spl46_14
| spl46_15 ),
inference(sat_conversion,[],[f5707]) ).
cnf(s11,plain,
( spl46_15
| spl46_17 ),
inference(sat_conversion,[],[f5720]) ).
cnf(s14,plain,
( spl46_14
| ~ spl46_17 ),
inference(sat_conversion,[],[f5806]) ).
cnf(s35,plain,
~ spl46_15,
inference(sat_conversion,[],[f6066]) ).
cnf(s38,plain,
spl46_17,
inference(rat,[],[s11,s35]) ).
cnf(s40,plain,
spl46_14,
inference(rat,[],[s14,s38]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s9,s35,s40]) ).
fof(f6080,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWW333+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Mon Sep 28 13:36:34 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.13 Running first-order theorem proving
% 0.09/0.13 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
% 1.79/0.81 % (3379798)Detected formulas, will run a generic FOF schedule.
% 1.79/0.81 % (3379803)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=4219655144:i=141193_2998 on theBenchmark for (2998ds/141193Mi)
% 1.79/0.81 % (3379807)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1007865226:i=119:av=off:ss=axioms_2998 on theBenchmark for (2998ds/119Mi)
% 1.79/0.81 % (3379806)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3412976855:i=109:sd=1:ins=1:gsp=on:ss=axioms_2998 on theBenchmark for (2998ds/109Mi)
% 1.79/0.81 % (3379809)dis-21_1_sil=8000:lcm=predicate:random_seed=2619899637:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2998 on theBenchmark for (2998ds/129Mi)
% 1.79/0.81 % (3379805)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=4010787720:i=141695:sd=1:nm=32:gsp=on:ss=included_2998 on theBenchmark for (2998ds/141695Mi)
% 1.79/0.81 % (3379804)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=284712704:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2998 on theBenchmark for (2998ds/134677Mi)
% 1.79/0.81 % (3379808)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2041946722:s2a=on:i=139:gtg=position_2998 on theBenchmark for (2998ds/139Mi)
% 1.79/0.81 % (3379806)First to succeed.
% 1.79/0.81 % (3379806)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3379798"
% 1.79/0.81 % (3379808)Instruction limit reached!
% 1.79/0.81 % (3379808)------------------------------
% 1.79/0.81 % (3379808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.79/0.81 % (3379808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.81 % (3379808)CaDiCaL version: 2.1.3
% 1.79/0.81 % (3379808)Termination reason: Instruction limit
% 1.79/0.81 % (3379808)Termination phase: SInE selection
% 1.79/0.81 % (3379808)Time elapsed: 0.031 s
% 1.79/0.81 % (3379808)Peak memory usage: 90 MB
% 1.79/0.81 % (3379808)Instructions burned: 141 (million)
% 1.79/0.81 % (3379807)Instruction limit reached!
% 1.79/0.81 % (3379807)------------------------------
% 1.79/0.81 % (3379807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.79/0.81 % (3379807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.81 % (3379807)CaDiCaL version: 2.1.3
% 1.79/0.81 % (3379807)Termination reason: Instruction limit
% 1.79/0.81 % (3379807)Termination phase: Property scanning
% 1.79/0.81 % (3379807)Time elapsed: 0.041 s
% 1.79/0.81 % (3379807)Peak memory usage: 92 MB
% 1.79/0.81 % (3379807)Instructions burned: 124 (million)
% 1.79/0.81 % (3379809)Instruction limit reached!
% 1.79/0.81 % (3379809)------------------------------
% 1.79/0.81 % (3379809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.79/0.81 % (3379809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.81 % (3379809)CaDiCaL version: 2.1.3
% 1.79/0.81 % (3379809)Termination reason: Instruction limit
% 1.79/0.81 % (3379809)Termination phase: Preprocessing 3
% 1.79/0.81 % (3379809)Time elapsed: 0.048 s
% 1.79/0.81 % (3379809)Peak memory usage: 93 MB
% 1.79/0.81 % (3379809)Instructions burned: 132 (million)
% 1.79/0.81 % (3379817)lrs+10_1_sil=8000:sp=occurrence:random_seed=466584049:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 1.79/0.81 % (3379818)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2587390790:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 1.79/0.81 % (3379819)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3348543558:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 1.79/0.81 % (3379806)Refutation found. Thanks to Tanya!
% 1.79/0.81 % SZS status Theorem for theBenchmark
% 1.79/0.81 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.90 % (3379806)------------------------------
% 0.09/0.90 % (3379806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.09/0.90 % (3379806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.90 % (3379806)CaDiCaL version: 2.1.3
% 0.09/0.90 % (3379806)Termination reason: Refutation
% 0.09/0.90 % (3379806)Time elapsed: 0.028 s
% 0.09/0.90 % (3379806)Peak memory usage: 95 MB
% 0.09/0.90 % (3379806)Instructions burned: 76 (million)
% 0.09/0.90 % (3379806)------------------------------
% 0.09/0.90 % (3379806)------------------------------
% 0.09/0.90 % (3379798)Success in time 0.483 s
% 0.09/0.90 % Vampire exiting
%------------------------------------------------------------------------------