%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW392+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 : n007.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 0.91s 1.35s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 35 ( 14 ~; 14 |; 3 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-6 aty)
% Number of variables : 62 ( 58 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [V_Pa_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)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OSKIP),V_Pa_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(f17,axiom,
! [V_Qa_2,V_Q_H_2,V_c_2,V_Pa_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)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
=> ( ! [B_Z,B_s] :
( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
=> hBOOL(hAPP(hAPP(V_Qa_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),V_Pa_2),V_c_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(f5223,hypothesis,
! [B_Z,B_s] :
( hBOOL(hAPP(hAPP(v_P,B_Z),B_s))
=> hBOOL(hAPP(hAPP(v_Q,B_Z),B_s)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5224,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),v_P),c_Com_Ocom_OSKIP),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(f5225,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),v_P),c_Com_Ocom_OSKIP),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(negated_conjecture,[status(cth)],[f5224]) ).
fof(f5230,plain,
! [X0,X1,X2] : c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X2),c_Com_Ocom_OSKIP),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_HOL_Obool)))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f5266,plain,
! [V_Qa_2,V_Q_H_2,V_c_2,V_Pa_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)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
| ? [B_Z,B_s] :
( ~ hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s))
& hBOOL(hAPP(hAPP(V_Q_H_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),V_Pa_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f5267,plain,
! [V_Q_H_2,V_c_2,V_Pa_2,V_Ga_2,T_b] :
( ! [V_Qa_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_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
| ? [B_Z,B_s] :
( ~ hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s))
& hBOOL(hAPP(hAPP(V_Q_H_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),V_Pa_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
inference(miniscoping,[status(thm)],[f5266]) ).
fof(f5268,plain,
! [V_Q_H_2,V_c_2,V_Pa_2,V_Ga_2,T_b] :
( ! [V_Qa_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_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
| ( ~ hBOOL(hAPP(hAPP(V_Qa_2,sK1_skl(V_Qa_2,T_b,V_Ga_2,V_Pa_2,V_c_2,V_Q_H_2)),sK2_skl(V_Qa_2,T_b,V_Ga_2,V_Pa_2,V_c_2,V_Q_H_2)))
& hBOOL(hAPP(hAPP(V_Q_H_2,sK1_skl(V_Qa_2,T_b,V_Ga_2,V_Pa_2,V_c_2,V_Q_H_2)),sK2_skl(V_Qa_2,T_b,V_Ga_2,V_Pa_2,V_c_2,V_Q_H_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_Pa_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(B_Z,sK1_skl(V_Qa_2,T_b,V_Ga_2,V_Pa_2,V_c_2,V_Q_H_2)),skolemize(B_s,sK2_skl(V_Qa_2,T_b,V_Ga_2,V_Pa_2,V_c_2,V_Q_H_2))],[f5267]) ).
fof(f5269,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X2),X3),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(X4,sK1_skl(X5,X0,X1,X2,X3,X4)),sK2_skl(X5,X0,X1,X2,X3,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X2),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_HOL_Obool)))) ),
inference(cnf_transformation,[status(thm)],[f5268]) ).
fof(f5270,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X2),X3),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(X5,sK1_skl(X5,X0,X1,X2,X3,X4)),sK2_skl(X5,X0,X1,X2,X3,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X2),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_HOL_Obool)))) ),
inference(cnf_transformation,[status(thm)],[f5268]) ).
fof(f20036,plain,
! [B_Z,B_s] :
( hBOOL(hAPP(hAPP(v_Q,B_Z),B_s))
| ~ hBOOL(hAPP(hAPP(v_P,B_Z),B_s)) ),
inference(pre_NNF_transformation,[status(thm)],[f5223]) ).
fof(f20037,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(v_Q,X0),X1))
| ~ hBOOL(hAPP(hAPP(v_P,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f20036]) ).
fof(f20038,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),c_Com_Ocom_OSKIP),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(cnf_transformation,[status(thm)],[f5225]) ).
fof(f20501,plain,
! [X0,X1,X2,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X0),c_Com_Ocom_OSKIP),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(X0,sK1_skl(X1,X2,X3,X0,c_Com_Ocom_OSKIP,X0)),sK2_skl(X1,X2,X3,X0,c_Com_Ocom_OSKIP,X0))) ),
inference(resolution,[status(thm)],[f5269,f5230]) ).
fof(f20502,plain,
! [X0,X1,X2,X3] :
( 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),X3),c_Com_Ocom_OSKIP),X0)),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,c_Com_Ocom_OSKIP,X3)),sK2_skl(X0,X1,X2,X3,c_Com_Ocom_OSKIP,X3))) ),
inference(resolution,[status(thm)],[f5270,f5230]) ).
fof(f22010,plain,
hBOOL(hAPP(hAPP(v_P,sK1_skl(v_Q,t_a,v_G,v_P,c_Com_Ocom_OSKIP,v_P)),sK2_skl(v_Q,t_a,v_G,v_P,c_Com_Ocom_OSKIP,v_P))),
inference(resolution,[status(thm)],[f20501,f20038]) ).
fof(f22142,plain,
hBOOL(hAPP(hAPP(v_Q,sK1_skl(v_Q,t_a,v_G,v_P,c_Com_Ocom_OSKIP,v_P)),sK2_skl(v_Q,t_a,v_G,v_P,c_Com_Ocom_OSKIP,v_P))),
inference(resolution,[status(thm)],[f22010,f20037]) ).
fof(f22146,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),c_Com_Ocom_OSKIP),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(resolution,[status(thm)],[f22142,f20502]) ).
fof(f22150,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f22146,f20038]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW392+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 09:48:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.80/1.05 % Drodi V4.1.1
% 0.91/1.35 % Refutation found
% 0.91/1.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.91/1.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.92/1.45 % Elapsed time: 1.070631 seconds
% 0.92/1.45 % CPU time: 3.074531 seconds
% 0.92/1.45 % Total memory used: 677.841 MB
% 0.92/1.45 % Net memory used: 671.345 MB
%------------------------------------------------------------------------------