%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW310+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 03:07:37 PM UTC 2026
% Result : Theorem 1.27s 1.67s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 11 unt; 0 def)
% Number of atoms : 22 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 6 ~; 3 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 11 con; 0-5 aty)
% Number of variables : 32 ( 30 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [V_Q_2,V_ca_2,V_Ga_2,T_b,V_Pa_2] :
( ! [B_Z,B_s] :
( hBOOL(hAPP(hAPP(V_Pa_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)),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_Q_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)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,V_Q_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(f5210,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(f5216,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5229,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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,hAPP(hAPP(c_COMBC(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),t_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),v_P))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),v_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5230,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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,hAPP(hAPP(c_COMBC(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),t_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),v_P))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),v_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(negated_conjecture,[status(cth)],[f5229]) ).
fof(f5269,plain,
! [V_Q_2,V_ca_2,V_Ga_2,T_b,V_Pa_2] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,V_Q_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)),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_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f5270,plain,
! [V_Q_2,V_ca_2,V_Ga_2,T_b,V_Pa_2] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,V_Q_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)),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_Pa_2,T_b,V_Ga_2,V_ca_2,V_Q_2))),V_ca_2,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(V_Q_2,sK1_skl(V_Pa_2,T_b,V_Ga_2,V_ca_2,V_Q_2))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(V_Pa_2,sK1_skl(V_Pa_2,T_b,V_Ga_2,V_ca_2,V_Q_2)),sK2_skl(V_Pa_2,T_b,V_Ga_2,V_ca_2,V_Q_2))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(B_Z,sK1_skl(V_Pa_2,T_b,V_Ga_2,V_ca_2,V_Q_2)),skolemize(B_s,sK2_skl(V_Pa_2,T_b,V_Ga_2,V_ca_2,V_Q_2))],[f5269]) ).
fof(f5271,plain,
! [X0,X1,X2,X3,X4] :
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),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)],[f5270]) ).
fof(f19981,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(c_COMBK(X0,X1),X2),X3) = X2,
inference(cnf_transformation,[status(thm)],[f5210]) ).
fof(f19987,plain,
~ hBOOL(c_fFalse),
inference(cnf_transformation,[status(thm)],[f5216]) ).
fof(f20008,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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,hAPP(hAPP(c_COMBC(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),t_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),v_P))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),v_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(cnf_transformation,[status(thm)],[f5230]) ).
fof(f20495,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,hAPP(hAPP(c_COMBC(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),t_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),v_P))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),v_b)))),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,hAPP(hAPP(c_COMBC(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),t_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),v_P))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),v_b))))),
inference(resolution,[status(thm)],[f5271,f20008]) ).
fof(f20502,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,hAPP(hAPP(c_COMBC(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),t_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),t_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),v_P))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),v_b))))),
inference(forward_demodulation,[status(thm)],[f19981,f20495]) ).
fof(f20503,plain,
hBOOL(c_fFalse),
inference(forward_demodulation,[status(thm)],[f19981,f20502]) ).
fof(f20504,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f20503,f19987]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW310+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n006.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 09:46:42 UTC 2026
% 0.18/0.45 % CPUTime :
% 1.15/1.49 % Drodi V4.1.1
% 1.27/1.67 % Refutation found
% 1.27/1.67 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.27/1.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.31/1.90 % Elapsed time: 1.426197 seconds
% 1.31/1.90 % CPU time: 2.639215 seconds
% 1.31/1.90 % Total memory used: 578.144 MB
% 1.31/1.90 % Net memory used: 572.892 MB
%------------------------------------------------------------------------------