%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW339+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 : n006.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 03:07:40 PM UTC 2026
% Result : Theorem 116.90s 15.71s
% Output : CNFRefutation 116.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 13 unt; 2 def)
% Number of atoms : 89 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 81 ( 33 ~; 28 |; 6 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 55 ( 52 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f93,axiom,
! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OPow(T_b),V_A_2)) = V_A_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f131,axiom,
! [V_A_2,V_C_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5227,hypothesis,
! [B_n] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) )
=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts_H))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5228,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_ts_H)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5229,conjecture,
! [B_n] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) )
=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5230,negated_conjecture,
~ ! [B_n] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) )
=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) ) ),
inference(negated_conjecture,[status(cth)],[f5229]) ).
fof(f5509,plain,
! [X0,X1] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,tc_HOL_Obool),hAPP(c_Set_OPow(X0),X1)) = X1,
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f5560,plain,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(pre_NNF_transformation,[status(thm)],[f113]) ).
fof(f5561,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(c_Set_OPow(X0),X2))) ),
inference(cnf_transformation,[status(thm)],[f5560]) ).
fof(f5613,plain,
! [V_A_2,V_C_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) ),
inference(pre_NNF_transformation,[status(thm)],[f131]) ).
fof(f5614,plain,
! [V_C_2,V_X_2,T_b] :
( ! [V_A_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) ),
inference(miniscoping,[status(thm)],[f5613]) ).
fof(f5615,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),X2),X3))
| hBOOL(hAPP(hAPP(c_member(X0),X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X0,tc_HOL_Obool),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5614]) ).
fof(f20148,plain,
! [B_n] :
( ! [B_x] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts_H)) )
| ? [B_x] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5227]) ).
fof(f20149,plain,
! [B_n] :
( ! [B_x] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts_H)) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,sK587_skl(B_n))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK587_skl(B_n)),v_G)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK587_skl]),skolemize(B_x,sK587_skl(B_n))],[f20148]) ).
fof(f20150,plain,
! [X0,X1] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X0)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK587_skl(X1)),v_G))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts_H)) ),
inference(cnf_transformation,[status(thm)],[f20149]) ).
fof(f20151,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_H))
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK587_skl(X0)) ),
inference(cnf_transformation,[status(thm)],[f20149]) ).
fof(f20152,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_ts_H)),
inference(cnf_transformation,[status(thm)],[f5228]) ).
fof(f20153,plain,
? [B_n] :
( ? [B_x] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts)) )
& ! [B_x] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5230]) ).
fof(f20154,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK588_skl,sK589_skl)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK589_skl),v_ts))
& ! [B_x] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK588_skl,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK588_skl,sK589_skl]),skolemize(B_n,sK588_skl),skolemize(B_x,sK589_skl)],[f20153]) ).
fof(f20155,plain,
! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK588_skl,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G)) ),
inference(cnf_transformation,[status(thm)],[f20154]) ).
fof(f20156,plain,
hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK589_skl),v_ts)),
inference(cnf_transformation,[status(thm)],[f20154]) ).
fof(f20157,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK588_skl,sK589_skl),
inference(cnf_transformation,[status(thm)],[f20154]) ).
fof(f21969,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),hAPP(c_Set_OPow(tc_Hoare__Mirabelle_Otriple(t_a)),v_ts_H))),
inference(resolution,[status(thm)],[f20152,f5561]) ).
fof(f22145,definition,
( sQ47_spl
<=> hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK589_skl),v_ts_H)) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f22147,plain,
( sQ47_spl
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK589_skl),v_ts_H)) ),
inference(component_clause,[status(thm)],[f22145]) ).
fof(f22345,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool),hAPP(c_Set_OPow(tc_Hoare__Mirabelle_Otriple(t_a)),v_ts_H))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts)) ),
inference(resolution,[status(thm)],[f5615,f21969]) ).
fof(f22351,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts))
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts_H)) ),
inference(forward_demodulation,[status(thm)],[f5509,f22345]) ).
fof(f22478,plain,
hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK589_skl),v_ts_H)),
inference(resolution,[status(thm)],[f22351,f20156]) ).
fof(f24374,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK589_skl),v_ts_H))
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK587_skl(sK588_skl)),v_G)) ),
inference(resolution,[status(thm)],[f20150,f20157]) ).
fof(f24376,definition,
( sQ166_spl
<=> hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK587_skl(sK588_skl)),v_G)) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f24377,plain,
( ~ sQ166_spl
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK587_skl(sK588_skl)),v_G)) ),
inference(component_clause,[status(thm)],[f24376]) ).
fof(f24379,plain,
( ~ sQ47_spl
| sQ166_spl ),
inference(split_clause,[status(thm)],[f24374,f24376,f22145]) ).
fof(f27108,plain,
( sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f22147,f22478]) ).
fof(f27109,plain,
sQ47_spl,
inference(contradiction_clause,[status(thm)],[f27108]) ).
fof(f31963,plain,
! [X0] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK587_skl(X0))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK589_skl) ),
inference(resolution,[status(thm)],[f22478,f20151]) ).
fof(f33752,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK588_skl,sK587_skl(sK588_skl)),
inference(resolution,[status(thm)],[f31963,f20157]) ).
fof(f33754,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK587_skl(sK588_skl)),v_G)),
inference(resolution,[status(thm)],[f33752,f20155]) ).
fof(f33758,plain,
( ~ sQ166_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f33754,f24377]) ).
fof(f33759,plain,
~ sQ166_spl,
inference(contradiction_clause,[status(thm)],[f33758]) ).
fof(f33760,plain,
$false,
inference(sat_refutation,[status(thm)],[f24379,f27109,f33759]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW339+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 09:47:45 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.78/1.05 % Drodi V4.1.1
% 116.90/15.71 % Refutation found
% 116.90/15.71 % SZS status Theorem for theBenchmark: Theorem is valid
% 116.90/15.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 78.84/15.89 % Elapsed time: 15.508118 seconds
% 78.84/15.89 % CPU time: 117.793179 seconds
% 78.84/15.89 % Total memory used: 1.333 GB
% 78.84/15.89 % Net memory used: 1.270 GB
%------------------------------------------------------------------------------