%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW389+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 : n020.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 0.82s 1.18s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 31 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 9 ~; 5 |; 4 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-5 aty)
% Number of variables : 45 ( 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [V_ts_2,V_t_2,V_Ga_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
& c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [V_Qa_2,V_ca_2,V_Ga_2,T_b,V_P_2] :
( ! [B_Z,B_s] :
( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_ca_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(V_Qa_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) )
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5222,axiom,
! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5228,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5241,conjecture,
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),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),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(f5242,negated_conjecture,
~ 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),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),v_c),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(negated_conjecture,[status(cth)],[f5241]) ).
fof(f5260,plain,
! [V_ts_2,V_t_2,V_Ga_2,T_b] :
( ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
& c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2)) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f5261,plain,
! [X0,X1,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))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X2),X3)) ),
inference(cnf_transformation,[status(thm)],[f5260]) ).
fof(f5284,plain,
! [V_Qa_2,V_ca_2,V_Ga_2,T_b,V_P_2] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
| ? [B_Z,B_s] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_ca_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(V_Qa_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f5285,plain,
! [V_Qa_2,V_ca_2,V_Ga_2,T_b,V_P_2] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
| ( ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK2_skl(V_P_2,T_b,V_Ga_2,V_ca_2,V_Qa_2)))),V_ca_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(V_Qa_2,sK1_skl(V_P_2,T_b,V_Ga_2,V_ca_2,V_Qa_2))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(V_P_2,sK1_skl(V_P_2,T_b,V_Ga_2,V_ca_2,V_Qa_2)),sK2_skl(V_P_2,T_b,V_Ga_2,V_ca_2,V_Qa_2))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(B_Z,sK1_skl(V_P_2,T_b,V_Ga_2,V_ca_2,V_Qa_2)),skolemize(B_s,sK2_skl(V_P_2,T_b,V_Ga_2,V_ca_2,V_Qa_2))],[f5284]) ).
fof(f5286,plain,
! [X0,X1,X2,X3,X4] :
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X0),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(X0,sK1_skl(X0,X1,X2,X3,X4)),sK2_skl(X0,X1,X2,X3,X4))) ),
inference(cnf_transformation,[status(thm)],[f5285]) ).
fof(f19876,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(c_COMBK(X0,X1),X2),X3) = X2,
inference(cnf_transformation,[status(thm)],[f5222]) ).
fof(f19882,plain,
~ hBOOL(c_fFalse),
inference(cnf_transformation,[status(thm)],[f5228]) ).
fof(f19903,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),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),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)],[f5242]) ).
fof(f20696,plain,
! [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),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),v_c),v_Q)),X0)),
inference(resolution,[status(thm)],[f5261,f19903]) ).
fof(f20790,plain,
hBOOL(hAPP(hAPP(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse)),sK1_skl(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse)),t_a,v_G,v_c,v_Q)),sK2_skl(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse)),t_a,v_G,v_c,v_Q))),
inference(resolution,[status(thm)],[f5286,f20696]) ).
fof(f20803,plain,
hBOOL(hAPP(hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse),sK2_skl(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse)),t_a,v_G,v_c,v_Q))),
inference(forward_demodulation,[status(thm)],[f19876,f20790]) ).
fof(f20804,plain,
hBOOL(c_fFalse),
inference(forward_demodulation,[status(thm)],[f19876,f20803]) ).
fof(f20805,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f20804,f19882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW389+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.38 % Computer : n020.cluster.edu
% 0.08/0.38 % Model : x86_64 x86_64
% 0.08/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.38 % Memory : 8046.5625MB
% 0.08/0.38 % OS : Linux 6.8.0-71-generic
% 0.08/0.38 % CPULimit : 300
% 0.08/0.38 % WCLimit : 300
% 0.08/0.38 % DateTime : Mon Sep 21 09:51:34 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.76/1.05 % Drodi V4.1.1
% 0.82/1.18 % Refutation found
% 0.82/1.18 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.82/1.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.84/1.31 % Elapsed time: 0.915537 seconds
% 0.84/1.31 % CPU time: 1.880996 seconds
% 0.84/1.31 % Total memory used: 657.464 MB
% 0.84/1.31 % Net memory used: 651.437 MB
%------------------------------------------------------------------------------