%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW391+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 : n017.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 03:07:46 PM UTC 2026
% Result : Theorem 0.89s 1.44s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 9 unt; 2 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 67 ( 27 ~; 24 |; 8 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 30 ( 23 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5228,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),v_c),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5229,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P_H),v_c),v_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5230,conjecture,
! [B_Z,B_s] :
( ( hBOOL(hAPP(hAPP(v_P_H,B_Z),B_s))
| hBOOL(hAPP(hAPP(v_P,B_Z),B_s)) )
=> ? [B_P_H,B_Q_H] :
( ! [B_s_H] :
( ! [B_Z_H] :
( hBOOL(hAPP(hAPP(B_P_H,B_Z_H),B_s))
=> hBOOL(hAPP(hAPP(B_Q_H,B_Z_H),B_s_H)) )
=> ( hBOOL(hAPP(hAPP(v_Q_H,B_Z),B_s_H))
| hBOOL(hAPP(hAPP(v_Q,B_Z),B_s_H)) ) )
& c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),B_P_H),v_c),B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5231,negated_conjecture,
~ ! [B_Z,B_s] :
( ( hBOOL(hAPP(hAPP(v_P_H,B_Z),B_s))
| hBOOL(hAPP(hAPP(v_P,B_Z),B_s)) )
=> ? [B_P_H,B_Q_H] :
( ! [B_s_H] :
( ! [B_Z_H] :
( hBOOL(hAPP(hAPP(B_P_H,B_Z_H),B_s))
=> hBOOL(hAPP(hAPP(B_Q_H,B_Z_H),B_s_H)) )
=> ( hBOOL(hAPP(hAPP(v_Q_H,B_Z),B_s_H))
| hBOOL(hAPP(hAPP(v_Q,B_Z),B_s_H)) ) )
& c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),B_P_H),v_c),B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ) ),
inference(negated_conjecture,[status(cth)],[f5230]) ).
fof(f20072,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),v_c),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(cnf_transformation,[status(thm)],[f5228]) ).
fof(f20073,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P_H),v_c),v_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(cnf_transformation,[status(thm)],[f5229]) ).
fof(f20074,plain,
? [B_Z,B_s] :
( ! [B_P_H,B_Q_H] :
( ? [B_s_H] :
( ~ hBOOL(hAPP(hAPP(v_Q_H,B_Z),B_s_H))
& ~ hBOOL(hAPP(hAPP(v_Q,B_Z),B_s_H))
& ! [B_Z_H] :
( hBOOL(hAPP(hAPP(B_Q_H,B_Z_H),B_s_H))
| ~ hBOOL(hAPP(hAPP(B_P_H,B_Z_H),B_s)) ) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),B_P_H),v_c),B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) )
& ( hBOOL(hAPP(hAPP(v_P_H,B_Z),B_s))
| hBOOL(hAPP(hAPP(v_P,B_Z),B_s)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5231]) ).
fof(f20075,plain,
( ! [B_P_H,B_Q_H] :
( ( ~ hBOOL(hAPP(hAPP(v_Q_H,sK577_skl),sK579_skl(B_Q_H,B_P_H)))
& ~ hBOOL(hAPP(hAPP(v_Q,sK577_skl),sK579_skl(B_Q_H,B_P_H)))
& ! [B_Z_H] :
( hBOOL(hAPP(hAPP(B_Q_H,B_Z_H),sK579_skl(B_Q_H,B_P_H)))
| ~ hBOOL(hAPP(hAPP(B_P_H,B_Z_H),sK578_skl)) ) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),B_P_H),v_c),B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) )
& ( hBOOL(hAPP(hAPP(v_P_H,sK577_skl),sK578_skl))
| hBOOL(hAPP(hAPP(v_P,sK577_skl),sK578_skl)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK577_skl,sK578_skl,sK579_skl]),skolemize(B_Z,sK577_skl),skolemize(B_s,sK578_skl),skolemize(B_s_H,sK579_skl(B_Q_H,B_P_H))],[f20074]) ).
fof(f20076,plain,
( hBOOL(hAPP(hAPP(v_P_H,sK577_skl),sK578_skl))
| hBOOL(hAPP(hAPP(v_P,sK577_skl),sK578_skl)) ),
inference(cnf_transformation,[status(thm)],[f20075]) ).
fof(f20077,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X1,X2),sK579_skl(X1,X0)))
| ~ hBOOL(hAPP(hAPP(X0,X2),sK578_skl))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X0),v_c),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
inference(cnf_transformation,[status(thm)],[f20075]) ).
fof(f20078,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(v_Q,sK577_skl),sK579_skl(X1,X0)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X0),v_c),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
inference(cnf_transformation,[status(thm)],[f20075]) ).
fof(f20079,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(v_Q_H,sK577_skl),sK579_skl(X1,X0)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X0),v_c),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
inference(cnf_transformation,[status(thm)],[f20075]) ).
fof(f20405,definition,
( sQ8_spl
<=> hBOOL(hAPP(hAPP(v_P,sK577_skl),sK578_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f20406,plain,
( ~ sQ8_spl
| hBOOL(hAPP(hAPP(v_P,sK577_skl),sK578_skl)) ),
inference(component_clause,[status(thm)],[f20405]) ).
fof(f20408,definition,
( sQ9_spl
<=> hBOOL(hAPP(hAPP(v_P_H,sK577_skl),sK578_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f20409,plain,
( ~ sQ9_spl
| hBOOL(hAPP(hAPP(v_P_H,sK577_skl),sK578_skl)) ),
inference(component_clause,[status(thm)],[f20408]) ).
fof(f20411,plain,
( sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f20076,f20405,f20408]) ).
fof(f21619,plain,
! [X0] :
( hBOOL(hAPP(hAPP(v_Q,X0),sK579_skl(v_Q,v_P)))
| ~ hBOOL(hAPP(hAPP(v_P,X0),sK578_skl)) ),
inference(resolution,[status(thm)],[f20072,f20077]) ).
fof(f21621,plain,
~ hBOOL(hAPP(hAPP(v_Q,sK577_skl),sK579_skl(v_Q,v_P))),
inference(resolution,[status(thm)],[f20072,f20078]) ).
fof(f21635,plain,
( ~ sQ8_spl
| hBOOL(hAPP(hAPP(v_Q,sK577_skl),sK579_skl(v_Q,v_P))) ),
inference(resolution,[status(thm)],[f21619,f20406]) ).
fof(f21636,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f21635,f21621]) ).
fof(f21637,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f21636]) ).
fof(f21700,plain,
! [X0] :
( hBOOL(hAPP(hAPP(v_Q_H,X0),sK579_skl(v_Q_H,v_P_H)))
| ~ hBOOL(hAPP(hAPP(v_P_H,X0),sK578_skl)) ),
inference(resolution,[status(thm)],[f20073,f20077]) ).
fof(f21701,plain,
~ hBOOL(hAPP(hAPP(v_Q_H,sK577_skl),sK579_skl(v_Q_H,v_P_H))),
inference(resolution,[status(thm)],[f20073,f20079]) ).
fof(f21717,plain,
( ~ sQ9_spl
| hBOOL(hAPP(hAPP(v_Q_H,sK577_skl),sK579_skl(v_Q_H,v_P_H))) ),
inference(resolution,[status(thm)],[f21700,f20409]) ).
fof(f21718,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f21717,f21701]) ).
fof(f21719,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f21718]) ).
fof(f21720,plain,
$false,
inference(sat_refutation,[status(thm)],[f20411,f21637,f21719]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW391+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 09:45:42 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.79/1.03 % Drodi V4.1.1
% 0.89/1.44 % Refutation found
% 0.89/1.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.89/1.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.91/1.55 % Elapsed time: 1.178638 seconds
% 0.91/1.55 % CPU time: 3.997317 seconds
% 0.91/1.55 % Total memory used: 688.723 MB
% 0.91/1.55 % Net memory used: 682.276 MB
%------------------------------------------------------------------------------