%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW387+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 : n002.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 86.88s 17.37s
% Output : CNFRefutation 85.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 13 unt; 0 def)
% Number of atoms : 58 ( 10 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 26 ~; 21 |; 5 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 32 ( 29 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [V_ca_2] :
( c_Hoare__Mirabelle_Ostate__not__singleton
=> ( c_Com_OWT__bodies
=> ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_ts_2,V_t_2,V_G_2,T_a] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2)
& c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [V_a_2] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2)))
<=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5244,hypothesis,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5245,hypothesis,
c_Com_OWT__bodies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5247,hypothesis,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5249,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5250,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
inference(negated_conjecture,[status(cth)],[f5249]) ).
fof(f5256,plain,
! [V_ca_2] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f5257,plain,
( ! [V_ca_2] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) )
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(miniscoping,[status(thm)],[f5256]) ).
fof(f5258,plain,
! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ hBOOL(hAPP(c_Com_OWT,X0)) ),
inference(cnf_transformation,[status(thm)],[f5257]) ).
fof(f5265,plain,
! [V_ts_2,V_t_2,V_G_2,T_a] :
( ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2)
& c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f5266,plain,
! [X0,X1,X2,X3] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X2),X3))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_HOL_Obool)))) ),
inference(cnf_transformation,[status(thm)],[f5265]) ).
fof(f5271,plain,
! [V_a_2] :
( ( ! [B_y] : hAPP(c_Com_Obody,V_a_2) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y)
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) )
& ( ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y)
| ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f5272,plain,
( ! [V_a_2] :
( ! [B_y] : hAPP(c_Com_Obody,V_a_2) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y)
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) )
& ! [V_a_2] :
( ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y)
| ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) ) ),
inference(miniscoping,[status(thm)],[f5271]) ).
fof(f5273,plain,
( ! [V_a_2] :
( ! [B_y] : hAPP(c_Com_Obody,V_a_2) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y)
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) )
& ! [V_a_2] :
( hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK1_skl(V_a_2))
| ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(B_y,sK1_skl(V_a_2))],[f5272]) ).
fof(f5275,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X0)))
| hAPP(c_Com_Obody,X0) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1) ),
inference(cnf_transformation,[status(thm)],[f5273]) ).
fof(f19884,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(cnf_transformation,[status(thm)],[f5244]) ).
fof(f19885,plain,
c_Com_OWT__bodies,
inference(cnf_transformation,[status(thm)],[f5245]) ).
fof(f19887,plain,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
inference(cnf_transformation,[status(thm)],[f5247]) ).
fof(f19889,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
inference(cnf_transformation,[status(thm)],[f5250]) ).
fof(f20878,plain,
! [X0] : ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),X0)),
inference(resolution,[status(thm)],[f5266,f19889]) ).
fof(f22196,plain,
! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,X0))
| ~ c_Com_OWT__bodies ),
inference(forward_subsumption_resolution,[status(thm)],[f5258,f19884]) ).
fof(f22197,plain,
( ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn)))
| ~ c_Com_OWT__bodies ),
inference(resolution,[status(thm)],[f22196,f20878]) ).
fof(f22206,plain,
~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn))),
inference(forward_subsumption_resolution,[status(thm)],[f22197,f19885]) ).
fof(f35021,plain,
hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn))),
inference(resolution,[status(thm)],[f19887,f5275]) ).
fof(f35047,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f35021,f22206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW387+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.40 % Computer : n002.cluster.edu
% 0.12/5.40 % Model : x86_64 x86_64
% 0.12/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.40 % Memory : 8046.5625MB
% 0.12/5.40 % OS : Linux 6.8.0-71-generic
% 0.12/5.40 % CPULimit : 300
% 0.12/5.40 % WCLimit : 300
% 0.12/5.40 % DateTime : Mon Sep 21 09:53:25 UTC 2026
% 0.12/5.41 % CPUTime :
% 1.06/6.43 % Drodi V4.1.1
% 86.88/17.37 % Refutation found
% 86.88/17.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 86.88/17.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 39.58/17.56 % Elapsed time: 12.132774 seconds
% 39.58/17.56 % CPU time: 88.359567 seconds
% 39.58/17.56 % Total memory used: 1.201 GB
% 39.58/17.56 % Net memory used: 1.168 GB
%------------------------------------------------------------------------------