TSTP Solution File: SWW326+1 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SWW326+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n019.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 18:32:03 EDT 2024
% Result : Theorem 0.52s 0.77s
% Output : Refutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 3 unt; 0 def)
% Number of atoms : 185 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 221 ( 88 ~; 74 |; 30 &)
% ( 6 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 7 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 77 ( 62 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5722,plain,
$false,
inference(avatar_sat_refutation,[],[f5431,f5439,f5444,f5448,f5449,f5548,f5666,f5721]) ).
fof(f5721,plain,
( ~ spl13_2
| ~ spl13_4 ),
inference(avatar_contradiction_clause,[],[f5720]) ).
fof(f5720,plain,
( $false
| ~ spl13_2
| ~ spl13_4 ),
inference(subsumption_resolution,[],[f5707,f5320]) ).
fof(f5320,plain,
c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),sK1,v_n,sK2),
inference(cnf_transformation,[],[f5281]) ).
fof(f5281,plain,
( ( hBOOL(hAPP(v_b,sK2))
| ~ v_P(sK0,sK2) )
& c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),sK1,v_n,sK2)
& v_P(sK0,sK1)
& ! [X3] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f5278,f5280,f5279]) ).
fof(f5279,plain,
( ? [X0,X1] :
( ? [X2] :
( ( hBOOL(hAPP(v_b,X2))
| ~ v_P(X0,X2) )
& c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X1,v_n,X2) )
& v_P(X0,X1) )
=> ( ? [X2] :
( ( hBOOL(hAPP(v_b,X2))
| ~ v_P(sK0,X2) )
& c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),sK1,v_n,X2) )
& v_P(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f5280,plain,
( ? [X2] :
( ( hBOOL(hAPP(v_b,X2))
| ~ v_P(sK0,X2) )
& c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),sK1,v_n,X2) )
=> ( ( hBOOL(hAPP(v_b,sK2))
| ~ v_P(sK0,sK2) )
& c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),sK1,v_n,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f5278,plain,
( ? [X0,X1] :
( ? [X2] :
( ( hBOOL(hAPP(v_b,X2))
| ~ v_P(X0,X2) )
& c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X1,v_n,X2) )
& v_P(X0,X1) )
& ! [X3] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G)) ) ),
inference(rectify,[],[f5241]) ).
fof(f5241,plain,
( ? [X1,X2] :
( ? [X3] :
( ( hBOOL(hAPP(v_b,X3))
| ~ v_P(X1,X3) )
& c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X2,v_n,X3) )
& v_P(X1,X2) )
& ! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G)) ) ),
inference(ennf_transformation,[],[f5209]) ).
fof(f5209,plain,
~ ( ! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X0) )
=> ! [X1,X2] :
( v_P(X1,X2)
=> ! [X3] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X2,v_n,X3)
=> ( ~ hBOOL(hAPP(v_b,X3))
& v_P(X1,X3) ) ) ) ),
inference(rectify,[],[f5208]) ).
fof(f5208,negated_conjecture,
~ ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X2) )
=> ! [X26,X27] :
( v_P(X26,X27)
=> ! [X28] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X27,v_n,X28)
=> ( ~ hBOOL(hAPP(v_b,X28))
& v_P(X26,X28) ) ) ) ),
inference(negated_conjecture,[],[f5207]) ).
fof(f5207,conjecture,
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X2) )
=> ! [X26,X27] :
( v_P(X26,X27)
=> ! [X28] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X27,v_n,X28)
=> ( ~ hBOOL(hAPP(v_b,X28))
& v_P(X26,X28) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5707,plain,
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),sK1,v_n,sK2)
| ~ spl13_2
| ~ spl13_4 ),
inference(resolution,[],[f5550,f5430]) ).
fof(f5430,plain,
( hBOOL(hAPP(v_b,sK2))
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f5428]) ).
fof(f5428,plain,
( spl13_2
<=> hBOOL(hAPP(v_b,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).
fof(f5550,plain,
( ! [X0] :
( ~ hBOOL(hAPP(v_b,X0))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),sK1,v_n,X0) )
| ~ spl13_4 ),
inference(resolution,[],[f5438,f5319]) ).
fof(f5319,plain,
v_P(sK0,sK1),
inference(cnf_transformation,[],[f5281]) ).
fof(f5438,plain,
( ! [X2,X0,X1] :
( ~ v_P(X2,X0)
| ~ hBOOL(hAPP(v_b,X1))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X0,v_n,X1) )
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f5437]) ).
fof(f5437,plain,
( spl13_4
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(v_b,X1))
| ~ v_P(X2,X0)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X0,v_n,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).
fof(f5666,plain,
( spl13_1
| ~ spl13_6 ),
inference(avatar_contradiction_clause,[],[f5665]) ).
fof(f5665,plain,
( $false
| spl13_1
| ~ spl13_6 ),
inference(subsumption_resolution,[],[f5661,f5320]) ).
fof(f5661,plain,
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),sK1,v_n,sK2)
| spl13_1
| ~ spl13_6 ),
inference(resolution,[],[f5549,f5319]) ).
fof(f5549,plain,
( ! [X0] :
( ~ v_P(sK0,X0)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X0,v_n,sK2) )
| spl13_1
| ~ spl13_6 ),
inference(resolution,[],[f5447,f5426]) ).
fof(f5426,plain,
( ~ v_P(sK0,sK2)
| spl13_1 ),
inference(avatar_component_clause,[],[f5424]) ).
fof(f5424,plain,
( spl13_1
<=> v_P(sK0,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).
fof(f5447,plain,
( ! [X2,X0,X1] :
( v_P(X2,X1)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X0,v_n,X1)
| ~ v_P(X2,X0) )
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f5446]) ).
fof(f5446,plain,
( spl13_6
<=> ! [X2,X0,X1] :
( v_P(X2,X1)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X0,v_n,X1)
| ~ v_P(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).
fof(f5548,plain,
( spl13_3
| ~ spl13_5 ),
inference(avatar_contradiction_clause,[],[f5547]) ).
fof(f5547,plain,
( $false
| spl13_3
| ~ spl13_5 ),
inference(subsumption_resolution,[],[f5544,f5443]) ).
fof(f5443,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK4),v_G))
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f5441]) ).
fof(f5441,plain,
( spl13_5
<=> hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK4),v_G)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).
fof(f5544,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK4),v_G))
| spl13_3 ),
inference(resolution,[],[f5318,f5435]) ).
fof(f5435,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK4)
| spl13_3 ),
inference(avatar_component_clause,[],[f5433]) ).
fof(f5433,plain,
( spl13_3
<=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).
fof(f5318,plain,
! [X3] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G)) ),
inference(cnf_transformation,[],[f5281]) ).
fof(f5449,plain,
( spl13_5
| spl13_6 ),
inference(avatar_split_clause,[],[f5324,f5446,f5441]) ).
fof(f5324,plain,
! [X2,X0,X1] :
( v_P(X2,X1)
| ~ v_P(X2,X0)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK4),v_G))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X0,v_n,X1) ),
inference(cnf_transformation,[],[f5287]) ).
fof(f5287,plain,
! [X0,X1] :
( ! [X2] :
( ( ~ hBOOL(hAPP(v_b,X1))
& v_P(X2,X1) )
| ~ v_P(X2,X0) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK4)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK4),v_G)) )
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X0,v_n,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f5285,f5286]) ).
fof(f5286,plain,
( ? [X3] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X3)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G)) )
=> ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK4)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK4),v_G)) ) ),
introduced(choice_axiom,[]) ).
fof(f5285,plain,
! [X0,X1] :
( ! [X2] :
( ( ~ hBOOL(hAPP(v_b,X1))
& v_P(X2,X1) )
| ~ v_P(X2,X0) )
| ? [X3] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X3)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G)) )
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X0,v_n,X1) ),
inference(rectify,[],[f5245]) ).
fof(f5245,plain,
! [X0,X1] :
( ! [X3] :
( ( ~ hBOOL(hAPP(v_b,X1))
& v_P(X3,X1) )
| ~ v_P(X3,X0) )
| ? [X2] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X2)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G)) )
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X0,v_n,X1) ),
inference(flattening,[],[f5244]) ).
fof(f5244,plain,
! [X0,X1] :
( ! [X3] :
( ( ~ hBOOL(hAPP(v_b,X1))
& v_P(X3,X1) )
| ~ v_P(X3,X0) )
| ? [X2] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X2)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G)) )
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X0,v_n,X1) ),
inference(ennf_transformation,[],[f5211]) ).
fof(f5211,plain,
! [X0,X1] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X0,v_n,X1)
=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X2) )
=> ! [X3] :
( v_P(X3,X0)
=> ( ~ hBOOL(hAPP(v_b,X1))
& v_P(X3,X1) ) ) ) ),
inference(rectify,[],[f5206]) ).
fof(f5206,axiom,
! [X27,X28] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X27,v_n,X28)
=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X2) )
=> ! [X26] :
( v_P(X26,X27)
=> ( ~ hBOOL(hAPP(v_b,X28))
& v_P(X26,X28) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5448,plain,
( ~ spl13_3
| spl13_6 ),
inference(avatar_split_clause,[],[f5325,f5446,f5433]) ).
fof(f5325,plain,
! [X2,X0,X1] :
( v_P(X2,X1)
| ~ v_P(X2,X0)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK4)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X0,v_n,X1) ),
inference(cnf_transformation,[],[f5287]) ).
fof(f5444,plain,
( spl13_5
| spl13_4 ),
inference(avatar_split_clause,[],[f5326,f5437,f5441]) ).
fof(f5326,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(v_b,X1))
| ~ v_P(X2,X0)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK4),v_G))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X0,v_n,X1) ),
inference(cnf_transformation,[],[f5287]) ).
fof(f5439,plain,
( ~ spl13_3
| spl13_4 ),
inference(avatar_split_clause,[],[f5327,f5437,f5433]) ).
fof(f5327,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(v_b,X1))
| ~ v_P(X2,X0)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK4)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X0,v_n,X1) ),
inference(cnf_transformation,[],[f5287]) ).
fof(f5431,plain,
( ~ spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f5321,f5428,f5424]) ).
fof(f5321,plain,
( hBOOL(hAPP(v_b,sK2))
| ~ v_P(sK0,sK2) ),
inference(cnf_transformation,[],[f5281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW326+1 : TPTP v8.2.0. Released v5.2.0.
% 0.11/0.12 % Command : run_vampire %s %d THM
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jun 19 07:51:24 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.36 This is a FOF_CAX_RFO_SEQ problem
% 0.13/0.36 Running first-order theorem proving
% 0.13/0.36 Running /export/starexec/sandbox/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.52/0.73 % (21402)Running in auto input_syntax mode. Trying TPTP
% 0.52/0.73 % (21560)dis+2_1:50_sil=256000:flr=on:sac=on:i=218245:fsr=off:uhcvi=on_0 on theBenchmark for (2999ds/218245Mi)
% 0.52/0.73 % (21402)Running in auto input_syntax mode. Trying TPTP
% 0.52/0.73 % (21562)lrs-1011_8:1_sil=16000:sos=all:i=346:sd=1:ep=R:ss=axioms_0 on theBenchmark for (2999ds/346Mi)
% 0.52/0.73 % (21402)Running in auto input_syntax mode. Trying TPTP
% 0.52/0.73 % (21558)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)
% 0.52/0.73 % (21402)Running in auto input_syntax mode. Trying TPTP
% 0.52/0.73 % (21561)lrs-1010_1:1_sil=2000:i=250:sd=1:ss=axioms:sgt=32:sos=on_0 on theBenchmark for (2999ds/250Mi)
% 0.52/0.73 % (21402)Running in auto input_syntax mode. Trying TPTP
% 0.52/0.73 % (21559)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)
% 0.52/0.73 % (21402)Running in auto input_syntax mode. Trying TPTP
% 0.52/0.73 % (21563)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)
% 0.52/0.73 % (21402)Running in auto input_syntax mode. Trying TPTP
% 0.52/0.73 % (21556)lrs+10_1:628_anc=all_dependent:bsr=unit_only:sil=256000:sp=frequency:i=136310:newcnf=on_0 on theBenchmark for (2999ds/136310Mi)
% 0.52/0.77 % (21562)First to succeed.
% 0.52/0.77 % (21562)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-21402"
% 0.52/0.77 % (21402)Running in auto input_syntax mode. Trying TPTP
% 0.52/0.77 % (21562)Refutation found. Thanks to Tanya!
% 0.52/0.77 % SZS status Theorem for theBenchmark
% 0.52/0.77 % SZS output start Proof for theBenchmark
% See solution above
% 0.52/0.77 % (21562)------------------------------
% 0.52/0.77 % (21562)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.52/0.77 % (21562)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.52/0.77 % (21562)Termination reason: Refutation
% 0.52/0.77
% 0.52/0.77 % (21562)Memory used [KB]: 6159
% 0.52/0.77 % (21562)Time elapsed: 0.040 s
% 0.52/0.77 % (21562)Instructions burned: 55 (million)
% 0.52/0.77 % (21562)------------------------------
% 0.52/0.77 % (21562)------------------------------
% 0.52/0.77 % (21402)Success in time 0.116 s
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