%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW349+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 03:07:41 PM UTC 2026
% Result : Theorem 15.33s 2.95s
% Output : CNFRefutation 9.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 8 unt; 6 def)
% Number of atoms : 127 ( 55 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 116 ( 39 ~; 62 |; 4 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 54 ( 49 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [V_u,V_t,V_s,V_c] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u))
=> V_u = V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( c_Hoare__Mirabelle_Ostate__not__singleton
<=> ? [B_s,B_t] : B_s != B_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5226,hypothesis,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5227,hypothesis,
! [B_Z_H] :
( ! [B_s1] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),B_s1))
=> B_Z_H = B_s1 )
=> B_Z_H = v_s_H ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5228,conjecture,
hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5229,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H)),
inference(negated_conjecture,[status(cth)],[f5228]) ).
fof(f5233,plain,
! [V_u,V_t,V_s,V_c] :
( V_u = V_t
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f5234,plain,
! [V_t,V_s,V_c] :
( ! [V_u] :
( V_u = V_t
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u)) )
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ),
inference(miniscoping,[status(thm)],[f5233]) ).
fof(f5235,plain,
! [X0,X1,X2,X3] :
( X3 = X2
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X0),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5234]) ).
fof(f5236,plain,
( ( ! [B_s,B_t] : B_s = B_t
| c_Hoare__Mirabelle_Ostate__not__singleton )
& ( ? [B_s,B_t] : B_s != B_t
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5237,plain,
( ( ! [B_s,B_t] : B_s = B_t
| c_Hoare__Mirabelle_Ostate__not__singleton )
& ( sK1_skl != sK2_skl
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(B_s,sK1_skl),skolemize(B_t,sK2_skl)],[f5236]) ).
fof(f5238,plain,
( sK1_skl != sK2_skl
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(cnf_transformation,[status(thm)],[f5237]) ).
fof(f19863,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(cnf_transformation,[status(thm)],[f5226]) ).
fof(f19864,plain,
! [B_Z_H] :
( B_Z_H = v_s_H
| ? [B_s1] :
( B_Z_H != B_s1
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),B_s1)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5227]) ).
fof(f19865,plain,
! [B_Z_H] :
( B_Z_H = v_s_H
| ( B_Z_H != sK523_skl(B_Z_H)
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),sK523_skl(B_Z_H))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK523_skl]),skolemize(B_s1,sK523_skl(B_Z_H))],[f19864]) ).
fof(f19866,plain,
! [X0] :
( X0 = v_s_H
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),sK523_skl(X0))) ),
inference(cnf_transformation,[status(thm)],[f19865]) ).
fof(f19867,plain,
! [X0] :
( X0 = v_s_H
| X0 != sK523_skl(X0) ),
inference(cnf_transformation,[status(thm)],[f19865]) ).
fof(f19868,plain,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H)),
inference(cnf_transformation,[status(thm)],[f5229]) ).
fof(f20164,definition,
( sQ0_spl
<=> c_Hoare__Mirabelle_Ostate__not__singleton ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f20166,plain,
( sQ0_spl
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(component_clause,[status(thm)],[f20164]) ).
fof(f20167,definition,
( sQ1_spl
<=> sK1_skl = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f20169,plain,
( sQ1_spl
| sK1_skl != sK2_skl ),
inference(component_clause,[status(thm)],[f20167]) ).
fof(f20170,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f5238,f20164,f20167]) ).
fof(f20728,plain,
! [X0,X1] :
( X1 = v_s_H
| sK523_skl(X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),X0)) ),
inference(resolution,[status(thm)],[f5235,f19866]) ).
fof(f20729,plain,
! [X0,X1] :
( X1 = v_s_H
| X0 = v_s_H
| sK523_skl(X0) = sK523_skl(X1) ),
inference(resolution,[status(thm)],[f20728,f19866]) ).
fof(f20730,plain,
! [X0,X1,X2] :
( X2 = v_s_H
| X0 = v_s_H
| X1 = v_s_H
| X2 = v_s_H
| sK523_skl(X0) = sK523_skl(X1) ),
inference(paramodulation,[status(thm)],[f20729,f20729]) ).
fof(f20734,plain,
! [X0,X1] :
( X0 = v_s_H
| X1 = v_s_H
| X1 = v_s_H
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),sK523_skl(X0))) ),
inference(paramodulation,[status(thm)],[f20729,f19866]) ).
fof(f20736,definition,
! [X0,X1] :
( sQ17_spl
<=> ( X0 = v_s_H
| X1 = v_s_H
| sK523_skl(X0) = sK523_skl(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f20737,plain,
! [X0,X1] :
( ~ sQ17_spl
| X0 = v_s_H
| X1 = v_s_H
| sK523_skl(X0) = sK523_skl(X1) ),
inference(component_clause,[status(thm)],[f20736]) ).
fof(f20739,definition,
! [X2] :
( sQ18_spl
<=> ( X2 = v_s_H
| X2 = v_s_H ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f20740,plain,
! [X0] :
( ~ sQ18_spl
| X0 = v_s_H
| X0 = v_s_H ),
inference(component_clause,[status(thm)],[f20739]) ).
fof(f20742,plain,
( sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f20730,f20736,f20739]) ).
fof(f20746,definition,
! [X0] :
( sQ19_spl
<=> ( X0 = v_s_H
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),sK523_skl(X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f20747,plain,
! [X0] :
( ~ sQ19_spl
| X0 = v_s_H
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),sK523_skl(X0))) ),
inference(component_clause,[status(thm)],[f20746]) ).
fof(f20749,plain,
( sQ18_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f20734,f20746,f20739]) ).
fof(f20751,plain,
! [X0] :
( ~ sQ18_spl
| X0 = v_s_H ),
inference(duplicate_literals_removal,[status(thm)],[f20740]) ).
fof(f20752,plain,
! [X0,X1] :
( ~ sQ18_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f20751,f20751]) ).
fof(f20764,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f20166,f19863]) ).
fof(f20765,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f20764]) ).
fof(f20766,plain,
( sQ1_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f20169,f20752]) ).
fof(f20767,plain,
( sQ1_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f20766]) ).
fof(f27166,plain,
! [X0] :
( ~ sQ17_spl
| X0 = v_s_H
| sK523_skl(X0) = v_s_H
| sK523_skl(X0) = v_s_H ),
inference(resolution,[status(thm)],[f19867,f20737]) ).
fof(f27174,plain,
! [X0] :
( ~ sQ17_spl
| X0 = v_s_H
| sK523_skl(X0) = v_s_H ),
inference(duplicate_literals_removal,[status(thm)],[f27166]) ).
fof(f27292,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ19_spl
| X0 = v_s_H
| X0 = v_s_H
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H)) ),
inference(paramodulation,[status(thm)],[f27174,f20747]) ).
fof(f27624,definition,
( sQ574_spl
<=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H)) ),
introduced(definition,[new_symbols(definition,[sQ574_spl])],[split_symbol_definition]) ).
fof(f27625,plain,
( ~ sQ574_spl
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H)) ),
inference(component_clause,[status(thm)],[f27624]) ).
fof(f27627,plain,
( ~ sQ17_spl
| ~ sQ19_spl
| sQ18_spl
| sQ574_spl ),
inference(split_clause,[status(thm)],[f27292,f27624,f20739,f20746,f20736]) ).
fof(f27760,plain,
( ~ sQ574_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27625,f19868]) ).
fof(f27761,plain,
~ sQ574_spl,
inference(contradiction_clause,[status(thm)],[f27760]) ).
fof(f27762,plain,
$false,
inference(sat_refutation,[status(thm)],[f20170,f20742,f20749,f20765,f20767,f27627,f27761]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW349+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 09:46:21 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.78/1.04 % Drodi V4.1.1
% 15.33/2.95 % Refutation found
% 15.33/2.95 % SZS status Theorem for theBenchmark: Theorem is valid
% 15.33/2.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.36/3.05 % Elapsed time: 2.678331 seconds
% 9.36/3.05 % CPU time: 15.963806 seconds
% 9.36/3.05 % Total memory used: 795.723 MB
% 9.36/3.05 % Net memory used: 778.355 MB
%------------------------------------------------------------------------------