TSTP Solution File: SWW336+1 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SWW336+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n027.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 : Mon Jun 24 18:32:05 EDT 2024
% Result : Theorem 0.54s 0.82s
% Output : Refutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 7 unt; 0 def)
% Number of atoms : 176 ( 15 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 180 ( 63 ~; 59 |; 27 &)
% ( 6 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 104 ( 90 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5880,plain,
$false,
inference(avatar_sat_refutation,[],[f5624,f5838,f5877]) ).
fof(f5877,plain,
~ spl16_4,
inference(avatar_contradiction_clause,[],[f5876]) ).
fof(f5876,plain,
( $false
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f5875,f5430]) ).
fof(f5430,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,sK2),
inference(cnf_transformation,[],[f5375]) ).
fof(f5375,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,sK2)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)))
& ! [X2] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f5372,f5374,f5373]) ).
fof(f5373,plain,
( ? [X0] :
( ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),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,sK1,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts))) )
& ! [X2] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f5374,plain,
( ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts))) )
=> ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,sK2)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts))) ) ),
introduced(choice_axiom,[]) ).
fof(f5372,plain,
? [X0] :
( ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),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,[],[f5307]) ).
fof(f5307,plain,
? [X0] :
( ? [X2] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X2)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),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),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X2) ) ),
inference(rectify,[],[f5229]) ).
fof(f5229,negated_conjecture,
~ ! [X9] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X9,X2) )
=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X9,X2) ) ),
inference(negated_conjecture,[],[f5228]) ).
fof(f5228,conjecture,
! [X9] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X9,X2) )
=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X9,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f5875,plain,
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,sK2)
| ~ spl16_4 ),
inference(duplicate_literal_removal,[],[f5873]) ).
fof(f5873,plain,
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,sK2)
| c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,sK2)
| ~ spl16_4 ),
inference(resolution,[],[f5856,f5850]) ).
fof(f5850,plain,
( ! [X0] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK3(X0))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK2) )
| ~ spl16_4 ),
inference(resolution,[],[f5618,f5434]) ).
fof(f5434,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_ts))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK3(X0)) ),
inference(cnf_transformation,[],[f5378]) ).
fof(f5378,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)) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK3(X0))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK3(X0)),v_G)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f5376,f5377]) ).
fof(f5377,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_G)) )
=> ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK3(X0))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK3(X0)),v_G)) ) ),
introduced(choice_axiom,[]) ).
fof(f5376,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,[],[f5308]) ).
fof(f5308,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,[],[f5231]) ).
fof(f5231,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,[],[f5227]) ).
fof(f5227,axiom,
! [X9] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X9,X2) )
=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X9,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f5618,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),v_ts))
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f5616]) ).
fof(f5616,plain,
( spl16_4
<=> hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),v_ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).
fof(f5856,plain,
( ! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,sK3(X0))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK2) )
| ~ spl16_4 ),
inference(resolution,[],[f5701,f5618]) ).
fof(f5701,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X0)
| c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,sK3(X1)) ),
inference(resolution,[],[f5433,f5428]) ).
fof(f5428,plain,
! [X2] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
| c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,X2) ),
inference(cnf_transformation,[],[f5375]) ).
fof(f5433,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK3(X0)),v_G))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_ts))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1) ),
inference(cnf_transformation,[],[f5378]) ).
fof(f5838,plain,
~ spl16_5,
inference(avatar_contradiction_clause,[],[f5837]) ).
fof(f5837,plain,
( $false
| ~ spl16_5 ),
inference(subsumption_resolution,[],[f5836,f5757]) ).
fof(f5757,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,v_t)
| ~ spl16_5 ),
inference(backward_demodulation,[],[f5430,f5622]) ).
fof(f5622,plain,
( v_t = sK2
| ~ spl16_5 ),
inference(avatar_component_clause,[],[f5620]) ).
fof(f5620,plain,
( spl16_5
<=> v_t = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_5])]) ).
fof(f5836,plain,
c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,v_t),
inference(duplicate_literal_removal,[],[f5835]) ).
fof(f5835,plain,
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,v_t)
| c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,v_t) ),
inference(resolution,[],[f5822,f5790]) ).
fof(f5790,plain,
! [X0] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK4(X0))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X0,v_t) ),
inference(resolution,[],[f5436,f5574]) ).
fof(f5574,plain,
! [X2,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),
inference(equality_resolution,[],[f5505]) ).
fof(f5505,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Set_Oinsert(X2),X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))
| X0 != X1 ),
inference(cnf_transformation,[],[f5405]) ).
fof(f5405,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Set_Oinsert(X2),X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))
| X0 != X1 )
& ( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Set_Oinsert(X2),X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))) ) ),
inference(nnf_transformation,[],[f5265]) ).
fof(f5265,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Set_Oinsert(X2),X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))
<=> X0 = X1 ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X5,X14,X4] :
( hBOOL(hAPP(hAPP(c_member(X4),X14),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))
<=> X5 = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f5436,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK4(X0)) ),
inference(cnf_transformation,[],[f5381]) ).
fof(f5381,plain,
! [X0] :
( ! [X1] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK4(X0))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK4(X0)),v_G)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f5379,f5380]) ).
fof(f5380,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_G)) )
=> ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK4(X0))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK4(X0)),v_G)) ) ),
introduced(choice_axiom,[]) ).
fof(f5379,plain,
! [X0] :
( ! [X1] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))) )
| ? [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,[],[f5309]) ).
fof(f5309,plain,
! [X0] :
( ! [X2] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))) )
| ? [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,[],[f5232]) ).
fof(f5232,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),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X2) ) ),
inference(rectify,[],[f5225]) ).
fof(f5225,axiom,
! [X9] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X9,X2) )
=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X9,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f5822,plain,
! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK1,sK4(X0))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X0,v_t) ),
inference(resolution,[],[f5805,f5428]) ).
fof(f5805,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK4(X0)),v_G))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X0,v_t) ),
inference(resolution,[],[f5435,f5574]) ).
fof(f5435,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK4(X0)),v_G)) ),
inference(cnf_transformation,[],[f5381]) ).
fof(f5624,plain,
( spl16_4
| spl16_5 ),
inference(avatar_split_clause,[],[f5611,f5620,f5616]) ).
fof(f5611,plain,
( v_t = sK2
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),v_ts)) ),
inference(resolution,[],[f5429,f5476]) ).
fof(f5476,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),X0)))
| X1 = X2
| hBOOL(hAPP(hAPP(c_member(X3),X2),X0)) ),
inference(cnf_transformation,[],[f5398]) ).
fof(f5398,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),X0)))
| ( ~ hBOOL(hAPP(hAPP(c_member(X3),X2),X0))
& X1 != X2 ) )
& ( hBOOL(hAPP(hAPP(c_member(X3),X2),X0))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),X0))) ) ),
inference(flattening,[],[f5397]) ).
fof(f5397,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),X0)))
| ( ~ hBOOL(hAPP(hAPP(c_member(X3),X2),X0))
& X1 != X2 ) )
& ( hBOOL(hAPP(hAPP(c_member(X3),X2),X0))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),X0))) ) ),
inference(nnf_transformation,[],[f5249]) ).
fof(f5249,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),X0)))
<=> ( hBOOL(hAPP(hAPP(c_member(X3),X2),X0))
| X1 = X2 ) ),
inference(rectify,[],[f126]) ).
fof(f126,axiom,
! [X11,X14,X5,X4] :
( hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X14),X11)))
<=> ( hBOOL(hAPP(hAPP(c_member(X4),X5),X11))
| X5 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f5429,plain,
hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts))),
inference(cnf_transformation,[],[f5375]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWW336+1 : TPTP v8.2.0. Released v5.2.0.
% 0.08/0.14 % Command : run_vampire %s %d THM
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Jun 19 05:09:09 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.38 This is a FOF_CAX_RFO_SEQ problem
% 0.14/0.38 Running first-order theorem proving
% 0.14/0.38 Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.54/0.73 % (26872)Running in auto input_syntax mode. Trying TPTP
% 0.54/0.73 % (26879)lrs-1011_8:1_sil=16000:sos=all:i=346:sd=1:ep=R:ss=axioms_0 on theBenchmark for (2999ds/346Mi)
% 0.54/0.75 % (26872)Running in auto input_syntax mode. Trying TPTP
% 0.54/0.75 % (26875)lrs+2_3:1_to=lpo:sil=256000:irw=on:fde=unused:sp=unary_first:bce=on:nwc=6.0:s2agt=30:newcnf=on:s2a=on:i=140573:nm=2_0 on theBenchmark for (2999ds/140573Mi)
% 0.54/0.75 % (26872)Running in auto input_syntax mode. Trying TPTP
% 0.54/0.75 % (26874)lrs+10_1:628_anc=all_dependent:bsr=unit_only:sil=256000:sp=frequency:i=136310:newcnf=on_0 on theBenchmark for (2999ds/136310Mi)
% 0.54/0.75 % (26872)Running in auto input_syntax mode. Trying TPTP
% 0.54/0.75 % (26877)dis+2_1:50_sil=256000:flr=on:sac=on:i=218245:fsr=off:uhcvi=on_0 on theBenchmark for (2999ds/218245Mi)
% 0.54/0.75 % (26872)Running in auto input_syntax mode. Trying TPTP
% 0.54/0.75 % (26876)lrs+11_1:12_to=lpo:sil=128000:sp=const_min:i=103397:ss=included:sgt=16:av=off:fsd=on:nm=16_0 on theBenchmark for (2999ds/103397Mi)
% 0.54/0.76 % (26872)Running in auto input_syntax mode. Trying TPTP
% 0.54/0.76 % (26880)lrs+1002_1:1_to=lpo:sil=2000:sp=frequency:sos=on:st=3.0:i=282:sd=2:ss=axioms_0 on theBenchmark for (2999ds/282Mi)
% 0.54/0.76 % (26872)Running in auto input_syntax mode. Trying TPTP
% 0.54/0.76 % (26878)lrs-1010_1:1_sil=2000:i=250:sd=1:ss=axioms:sgt=32:sos=on_0 on theBenchmark for (2999ds/250Mi)
% 0.54/0.81 % (26878)First to succeed.
% 0.54/0.81 % (26878)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26872"
% 0.54/0.82 % (26872)Running in auto input_syntax mode. Trying TPTP
% 0.54/0.82 % (26878)Refutation found. Thanks to Tanya!
% 0.54/0.82 % SZS status Theorem for theBenchmark
% 0.54/0.82 % SZS output start Proof for theBenchmark
% See solution above
% 0.54/0.82 % (26878)------------------------------
% 0.54/0.82 % (26878)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.54/0.82 % (26878)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.54/0.82 % (26878)Termination reason: Refutation
% 0.54/0.82
% 0.54/0.82 % (26878)Memory used [KB]: 6440
% 0.54/0.82 % (26878)Time elapsed: 0.060 s
% 0.54/0.82 % (26878)Instructions burned: 86 (million)
% 0.54/0.82 % (26878)------------------------------
% 0.54/0.82 % (26878)------------------------------
% 0.54/0.82 % (26872)Success in time 0.146 s
%------------------------------------------------------------------------------