%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW341+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 : n005.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 : Timeout 291.62s 38.28s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 105 ( 41 ~; 38 |; 14 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-3 aty)
% Number of variables : 76 ( 67 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5224,hypothesis,
! [B_Z,B_s] :
( 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)) )
=> v_Q(B_Z,B_s_H) )
& ! [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_Za,B_sa] :
( hBOOL(hAPP(hAPP(B_P_H,B_Za),B_sa))
=> ! [B_s_H] :
( c_Natural_Oevaln(v_c,B_sa,B_n,B_s_H)
=> hBOOL(hAPP(hAPP(B_Q_H,B_Za),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(f5225,hypothesis,
! [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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5226,conjecture,
! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(v_c,B_s,v_n,B_s_H)
=> v_Q(B_Z,B_s_H) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5227,negated_conjecture,
~ ! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(v_c,B_s,v_n,B_s_H)
=> v_Q(B_Z,B_s_H) ) ),
inference(negated_conjecture,[status(cth)],[f5226]) ).
fof(f20073,plain,
! [B_Z,B_s] :
( ? [B_P_H,B_Q_H] :
( ! [B_s_H] :
( 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)) ) )
& ! [B_n] :
( ! [B_Za,B_sa] :
( ! [B_s_H] :
( hBOOL(hAPP(hAPP(B_Q_H,B_Za),B_s_H))
| ~ c_Natural_Oevaln(v_c,B_sa,B_n,B_s_H) )
| ~ hBOOL(hAPP(hAPP(B_P_H,B_Za),B_sa)) )
| ? [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)) ) )
& 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)))) )
| ~ v_P(B_Z,B_s) ),
inference(pre_NNF_transformation,[status(thm)],[f5224]) ).
fof(f20074,plain,
! [B_Z,B_s] :
( ( ! [B_s_H] :
( v_Q(B_Z,B_s_H)
| ( ~ hBOOL(hAPP(hAPP(sK586_skl(B_s,B_Z),sK588_skl(B_s_H,B_s,B_Z)),B_s_H))
& hBOOL(hAPP(hAPP(sK585_skl(B_s,B_Z),sK588_skl(B_s_H,B_s,B_Z)),B_s)) ) )
& ! [B_n] :
( ! [B_Za,B_sa] :
( ! [B_s_H] :
( hBOOL(hAPP(hAPP(sK586_skl(B_s,B_Z),B_Za),B_s_H))
| ~ c_Natural_Oevaln(v_c,B_sa,B_n,B_s_H) )
| ~ hBOOL(hAPP(hAPP(sK585_skl(B_s,B_Z),B_Za),B_sa)) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,sK587_skl(B_n,B_s,B_Z))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK587_skl(B_n,B_s,B_Z)),v_G)) ) )
& 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),sK585_skl(B_s,B_Z)),v_c),sK586_skl(B_s,B_Z))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) )
| ~ v_P(B_Z,B_s) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK585_skl,sK586_skl,sK587_skl,sK588_skl]),skolemize(B_P_H,sK585_skl(B_s,B_Z)),skolemize(B_Q_H,sK586_skl(B_s,B_Z)),skolemize(B_x,sK587_skl(B_n,B_s,B_Z)),skolemize(B_Z_H,sK588_skl(B_s_H,B_s,B_Z))],[f20073]) ).
fof(f20076,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ v_P(X1,X0)
| hBOOL(hAPP(hAPP(sK586_skl(X0,X1),X2),X5))
| ~ c_Natural_Oevaln(v_c,X3,X4,X5)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK587_skl(X4,X0,X1)),v_G))
| ~ hBOOL(hAPP(hAPP(sK585_skl(X0,X1),X2),X3)) ),
inference(cnf_transformation,[status(thm)],[f20074]) ).
fof(f20077,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ hBOOL(hAPP(hAPP(sK585_skl(X0,X1),X2),X4))
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X5,sK587_skl(X5,X0,X1))
| ~ v_P(X1,X0)
| ~ c_Natural_Oevaln(v_c,X4,X5,X3)
| hBOOL(hAPP(hAPP(sK586_skl(X0,X1),X2),X3)) ),
inference(cnf_transformation,[status(thm)],[f20074]) ).
fof(f20078,plain,
! [X0,X1,X2] :
( v_Q(X0,X2)
| hBOOL(hAPP(hAPP(sK585_skl(X1,X0),sK588_skl(X2,X1,X0)),X1))
| ~ v_P(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f20074]) ).
fof(f20079,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(sK586_skl(X1,X0),sK588_skl(X2,X1,X0)),X2))
| v_Q(X0,X2)
| ~ v_P(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f20074]) ).
fof(f20080,plain,
! [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)],[f5225]) ).
fof(f20081,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)],[f20080]) ).
fof(f20082,plain,
? [B_Z,B_s] :
( ? [B_s_H] :
( ~ v_Q(B_Z,B_s_H)
& c_Natural_Oevaln(v_c,B_s,v_n,B_s_H) )
& v_P(B_Z,B_s) ),
inference(pre_NNF_transformation,[status(thm)],[f5227]) ).
fof(f20083,plain,
( ~ v_Q(sK589_skl,sK591_skl)
& c_Natural_Oevaln(v_c,sK590_skl,v_n,sK591_skl)
& v_P(sK589_skl,sK590_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK589_skl,sK590_skl,sK591_skl]),skolemize(B_Z,sK589_skl),skolemize(B_s,sK590_skl),skolemize(B_s_H,sK591_skl)],[f20082]) ).
fof(f20084,plain,
v_P(sK589_skl,sK590_skl),
inference(cnf_transformation,[status(thm)],[f20083]) ).
fof(f20085,plain,
c_Natural_Oevaln(v_c,sK590_skl,v_n,sK591_skl),
inference(cnf_transformation,[status(thm)],[f20083]) ).
fof(f20086,plain,
~ v_Q(sK589_skl,sK591_skl),
inference(cnf_transformation,[status(thm)],[f20083]) ).
fof(f20821,plain,
! [X0] :
( ~ v_P(sK589_skl,X0)
| ~ hBOOL(hAPP(hAPP(sK586_skl(X0,sK589_skl),sK588_skl(sK591_skl,X0,sK589_skl)),sK591_skl)) ),
inference(resolution,[status(thm)],[f20079,f20086]) ).
fof(f20824,plain,
~ hBOOL(hAPP(hAPP(sK586_skl(sK590_skl,sK589_skl),sK588_skl(sK591_skl,sK590_skl,sK589_skl)),sK591_skl)),
inference(resolution,[status(thm)],[f20821,f20084]) ).
fof(f22620,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(sK586_skl(sK590_skl,sK589_skl),X0),X3))
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK587_skl(X2,sK590_skl,sK589_skl)),v_G))
| ~ c_Natural_Oevaln(v_c,X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(sK585_skl(sK590_skl,sK589_skl),X0),X1)) ),
inference(resolution,[status(thm)],[f20076,f20084]) ).
fof(f23690,plain,
! [X0,X1,X2,X3] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X3,sK587_skl(X3,sK590_skl,sK589_skl))
| ~ hBOOL(hAPP(hAPP(sK585_skl(sK590_skl,sK589_skl),X0),X2))
| ~ c_Natural_Oevaln(v_c,X2,X3,X1)
| hBOOL(hAPP(hAPP(sK586_skl(sK590_skl,sK589_skl),X0),X1)) ),
inference(resolution,[status(thm)],[f20077,f20084]) ).
fof(f23695,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK587_skl(v_n,sK590_skl,sK589_skl)),v_G))
| ~ hBOOL(hAPP(hAPP(sK585_skl(sK590_skl,sK589_skl),X0),X2))
| ~ c_Natural_Oevaln(v_c,X2,v_n,X1)
| hBOOL(hAPP(hAPP(sK586_skl(sK590_skl,sK589_skl),X0),X1)) ),
inference(resolution,[status(thm)],[f23690,f20081]) ).
fof(f23697,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(sK585_skl(sK590_skl,sK589_skl),X0),X2))
| ~ c_Natural_Oevaln(v_c,X2,v_n,X1)
| hBOOL(hAPP(hAPP(sK586_skl(sK590_skl,sK589_skl),X0),X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f23695,f22620]) ).
fof(f27176,plain,
! [X0] :
( ~ v_P(sK589_skl,X0)
| hBOOL(hAPP(hAPP(sK585_skl(X0,sK589_skl),sK588_skl(sK591_skl,X0,sK589_skl)),X0)) ),
inference(resolution,[status(thm)],[f20078,f20086]) ).
fof(f27219,plain,
hBOOL(hAPP(hAPP(sK585_skl(sK590_skl,sK589_skl),sK588_skl(sK591_skl,sK590_skl,sK589_skl)),sK590_skl)),
inference(resolution,[status(thm)],[f27176,f20084]) ).
fof(f27239,plain,
! [X0] :
( hBOOL(hAPP(hAPP(sK586_skl(sK590_skl,sK589_skl),sK588_skl(sK591_skl,sK590_skl,sK589_skl)),X0))
| ~ c_Natural_Oevaln(v_c,sK590_skl,v_n,X0) ),
inference(resolution,[status(thm)],[f27219,f23697]) ).
fof(f27295,plain,
hBOOL(hAPP(hAPP(sK586_skl(sK590_skl,sK589_skl),sK588_skl(sK591_skl,sK590_skl,sK589_skl)),sK591_skl)),
inference(resolution,[status(thm)],[f27239,f20085]) ).
fof(f27299,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f27295,f20824]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW341+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.47 % Computer : n005.cluster.edu
% 0.18/0.47 % Model : x86_64 x86_64
% 0.18/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.47 % Memory : 8046.5625MB
% 0.18/0.47 % OS : Linux 6.8.0-71-generic
% 0.18/0.47 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.47 % DateTime : Mon Sep 21 09:48:18 UTC 2026
% 0.18/0.47 % CPUTime :
% 1.24/1.55 % Drodi V4.1.1
% 291.62/38.28 % Refutation found
% 291.62/38.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 291.62/38.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.55/39.33 % Elapsed time: 38.830245 seconds
% 15.55/39.33 % CPU time: 293.767916 seconds
% 15.55/39.33 % Total memory used: 1.396 GB
% 15.55/39.33 % Net memory used: 1.303 GB
%------------------------------------------------------------------------------