%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW326+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 : Thu Sep 24 03:07:39 PM UTC 2026
% Result : Theorem 159.89s 21.66s
% Output : CNFRefutation 146.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 5 unt; 3 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 128 ( 51 ~; 44 |; 18 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 57 ( 52 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5206,hypothesis,
! [B_s,B_s_H] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),B_s,v_n,B_s_H)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x) )
=> ! [B_Z] :
( v_P(B_Z,B_s)
=> ( ~ hBOOL(hAPP(v_b,B_s_H))
& v_P(B_Z,B_s_H) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5207,conjecture,
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x) )
=> ! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),B_s,v_n,B_s_H)
=> ( ~ hBOOL(hAPP(v_b,B_s_H))
& v_P(B_Z,B_s_H) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5208,negated_conjecture,
~ ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x) )
=> ! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),B_s,v_n,B_s_H)
=> ( ~ hBOOL(hAPP(v_b,B_s_H))
& v_P(B_Z,B_s_H) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5207]) ).
fof(f19789,plain,
! [B_s,B_s_H] :
( ! [B_Z] :
( ( ~ hBOOL(hAPP(v_b,B_s_H))
& v_P(B_Z,B_s_H) )
| ~ v_P(B_Z,B_s) )
| ? [B_x] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) )
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),B_s,v_n,B_s_H) ),
inference(pre_NNF_transformation,[status(thm)],[f5206]) ).
fof(f19790,definition,
! [B_s_H,B_Z] :
( sP41_prd(B_Z,B_s_H)
<=> ( ~ hBOOL(hAPP(v_b,B_s_H))
& v_P(B_Z,B_s_H) ) ),
introduced(definition,[new_symbols(definition,[sP41_prd])],[]) ).
fof(f19791,plain,
! [B_s,B_s_H] :
( ! [B_Z] :
( sP41_prd(B_Z,B_s_H)
| ~ v_P(B_Z,B_s) )
| ? [B_x] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) )
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),B_s,v_n,B_s_H) ),
inference(formula_renaming,[status(thm)],[f19789,f19790]) ).
fof(f19792,plain,
! [B_s,B_s_H] :
( ! [B_Z] :
( sP41_prd(B_Z,B_s_H)
| ~ v_P(B_Z,B_s) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK497_skl(B_s_H,B_s))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK497_skl(B_s_H,B_s)),v_G)) )
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),B_s,v_n,B_s_H) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK497_skl]),skolemize(B_x,sK497_skl(B_s_H,B_s))],[f19791]) ).
fof(f19793,plain,
! [X0,X1,X2] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X2,v_n,X1)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK497_skl(X1,X2)),v_G))
| ~ v_P(X0,X2)
| sP41_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19792]) ).
fof(f19794,plain,
! [X0,X1,X2] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X1,v_n,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK497_skl(X2,X1))
| sP41_prd(X0,X2)
| ~ v_P(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19792]) ).
fof(f19795,plain,
( ? [B_Z,B_s] :
( ? [B_s_H] :
( ( hBOOL(hAPP(v_b,B_s_H))
| ~ v_P(B_Z,B_s_H) )
& c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),B_s,v_n,B_s_H) )
& v_P(B_Z,B_s) )
& ! [B_x] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5208]) ).
fof(f19796,plain,
( ( hBOOL(hAPP(v_b,sK500_skl))
| ~ v_P(sK498_skl,sK500_skl) )
& c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),sK499_skl,v_n,sK500_skl)
& v_P(sK498_skl,sK499_skl)
& ! [B_x] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK498_skl,sK499_skl,sK500_skl]),skolemize(B_Z,sK498_skl),skolemize(B_s,sK499_skl),skolemize(B_s_H,sK500_skl)],[f19795]) ).
fof(f19797,plain,
! [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(cnf_transformation,[status(thm)],[f19796]) ).
fof(f19798,plain,
v_P(sK498_skl,sK499_skl),
inference(cnf_transformation,[status(thm)],[f19796]) ).
fof(f19799,plain,
c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),sK499_skl,v_n,sK500_skl),
inference(cnf_transformation,[status(thm)],[f19796]) ).
fof(f19800,plain,
( hBOOL(hAPP(v_b,sK500_skl))
| ~ v_P(sK498_skl,sK500_skl) ),
inference(cnf_transformation,[status(thm)],[f19796]) ).
fof(f20070,plain,
! [B_s_H,B_Z] :
( ( hBOOL(hAPP(v_b,B_s_H))
| ~ v_P(B_Z,B_s_H)
| sP41_prd(B_Z,B_s_H) )
& ( ( ~ hBOOL(hAPP(v_b,B_s_H))
& v_P(B_Z,B_s_H) )
| ~ sP41_prd(B_Z,B_s_H) ) ),
inference(NNF_transformation,[status(thm)],[f19790]) ).
fof(f20071,plain,
( ! [B_s_H,B_Z] :
( hBOOL(hAPP(v_b,B_s_H))
| ~ v_P(B_Z,B_s_H)
| sP41_prd(B_Z,B_s_H) )
& ! [B_s_H,B_Z] :
( ( ~ hBOOL(hAPP(v_b,B_s_H))
& v_P(B_Z,B_s_H) )
| ~ sP41_prd(B_Z,B_s_H) ) ),
inference(miniscoping,[status(thm)],[f20070]) ).
fof(f20072,plain,
! [X0,X1] :
( ~ sP41_prd(X0,X1)
| v_P(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f20071]) ).
fof(f20073,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(v_b,X1))
| ~ sP41_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f20071]) ).
fof(f20138,definition,
( sQ13_spl
<=> v_P(sK498_skl,sK500_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f20140,plain,
( sQ13_spl
| ~ v_P(sK498_skl,sK500_skl) ),
inference(component_clause,[status(thm)],[f20138]) ).
fof(f20141,definition,
( sQ14_spl
<=> hBOOL(hAPP(v_b,sK500_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f20142,plain,
( ~ sQ14_spl
| hBOOL(hAPP(v_b,sK500_skl)) ),
inference(component_clause,[status(thm)],[f20141]) ).
fof(f20144,plain,
( sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f19800,f20138,f20141]) ).
fof(f24863,plain,
! [X0] :
( ~ sQ14_spl
| ~ sP41_prd(X0,sK500_skl) ),
inference(resolution,[status(thm)],[f20073,f20142]) ).
fof(f25535,plain,
! [X0,X1,X2] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X1,v_n,X2)
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK497_skl(X2,X1))
| sP41_prd(X0,X2)
| ~ v_P(X0,X1) ),
inference(resolution,[status(thm)],[f19793,f19797]) ).
fof(f29693,plain,
! [X0,X1,X2] :
( ~ v_P(X2,X0)
| sP41_prd(X2,X1)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X0,v_n,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f19794,f25535]) ).
fof(f29694,plain,
! [X0] :
( sP41_prd(X0,sK500_skl)
| ~ v_P(X0,sK499_skl) ),
inference(resolution,[status(thm)],[f29693,f19799]) ).
fof(f29710,plain,
! [X0] :
( ~ sQ14_spl
| ~ v_P(X0,sK499_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f29694,f24863]) ).
fof(f29742,plain,
( ~ sQ14_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f19798,f29710]) ).
fof(f29743,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f29742]) ).
fof(f29985,plain,
! [X0] :
( v_P(X0,sK500_skl)
| ~ v_P(X0,sK499_skl) ),
inference(resolution,[status(thm)],[f29694,f20072]) ).
fof(f30012,plain,
( sQ13_spl
| ~ v_P(sK498_skl,sK499_skl) ),
inference(resolution,[status(thm)],[f29985,f20140]) ).
fof(f30013,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f30012,f19798]) ).
fof(f30014,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f30013]) ).
fof(f30015,plain,
$false,
inference(sat_refutation,[status(thm)],[f20144,f29743,f30014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW326+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49 % Computer : n013.cluster.edu
% 0.19/0.49 % Model : x86_64 x86_64
% 0.19/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.49 % Memory : 8046.5625MB
% 0.19/0.49 % OS : Linux 6.8.0-71-generic
% 0.19/0.49 % CPULimit : 300
% 0.19/0.49 % WCLimit : 300
% 0.19/0.49 % DateTime : Mon Sep 21 09:47:07 UTC 2026
% 0.19/0.50 % CPUTime :
% 1.20/1.56 % Drodi V4.1.1
% 159.89/21.66 % Refutation found
% 159.89/21.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 159.89/21.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 84.09/22.92 % Elapsed time: 22.180573 seconds
% 84.09/22.92 % CPU time: 157.108794 seconds
% 84.09/22.92 % Total memory used: 1.281 GB
% 84.09/22.92 % Net memory used: 1.197 GB
%------------------------------------------------------------------------------