%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW306+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 : n019.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 03:07:36 PM UTC 2026
% Result : Theorem 100.34s 14.20s
% Output : CNFRefutation 101.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 86 ( 28 unt; 3 def)
% Number of atoms : 190 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 182 ( 78 ~; 69 |; 17 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 8 con; 0-4 aty)
% Number of variables : 222 ( 215 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,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),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,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),V_ts_2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,axiom,
! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [V_Ga_2,V_ts_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_Ga_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f108,axiom,
! [V_A_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_a_2 = V_b_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f118,axiom,
! [V_Pa_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
<=> hBOOL(hAPP(V_Pa_2,V_a_2)) ),
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(f5212,axiom,
! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Qa_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5229,hypothesis,
! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> 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(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(B_Z)))),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,conjecture,
! [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)) )
=> hBOOL(hAPP(v_Q(B_Z),B_s_H)) )
& 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,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(f5231,negated_conjecture,
~ ! [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)) )
=> hBOOL(hAPP(v_Q(B_Z),B_s_H)) )
& 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,B_P_H,v_c,B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ) ),
inference(negated_conjecture,[status(cth)],[f5230]) ).
fof(f5243,plain,
! [V_Ga_2,V_ts_2,V_G_H_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,V_G_H_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f5244,plain,
! [V_ts_2,V_G_H_2,T_b] :
( ! [V_Ga_2] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2) ),
inference(miniscoping,[status(thm)],[f5243]) ).
fof(f5245,plain,
! [X0,X1,X2,X3] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X3,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5244]) ).
fof(f5246,plain,
! [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)))) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f5247,plain,
! [V_t_2,V_Ga_2,T_b] :
( ! [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),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)))) ),
inference(miniscoping,[status(thm)],[f5246]) ).
fof(f5248,plain,
! [X0,X1,X2,X3] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X3),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)),X3),X2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5247]) ).
fof(f5288,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)) = hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f5311,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X0),hAPP(c_fequal,X1)),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f5325,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X0),X1) = X1,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f5335,plain,
! [T_b,V_B_2,V_A_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| V_A_2 = V_B_2 )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
| V_A_2 != V_B_2 ) ),
inference(NNF_transformation,[status(thm)],[f41]) ).
fof(f5336,plain,
( ! [V_B_2,V_A_2] :
( ! [T_b] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
| V_A_2 = V_B_2 )
& ! [V_B_2,V_A_2] :
( ( ! [T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
& ! [T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
| V_A_2 != V_B_2 ) ),
inference(miniscoping,[status(thm)],[f5335]) ).
fof(f5338,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0))
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f5336]) ).
fof(f5437,plain,
! [X0,X1,X2] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X1))),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f5444,plain,
! [V_Ga_2,V_ts_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_Ga_2)) ),
inference(pre_NNF_transformation,[status(thm)],[f74]) ).
fof(f5445,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_HOL_Obool)),X2),X1))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5444]) ).
fof(f5535,plain,
! [V_A_2,V_b_2,V_a_2,T_b] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
& V_a_2 != V_b_2 )
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_a_2 = V_b_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) ) ),
inference(NNF_transformation,[status(thm)],[f108]) ).
fof(f5536,plain,
( ! [V_A_2,V_b_2,V_a_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
& V_a_2 != V_b_2 )
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) )
& ! [V_A_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_a_2 = V_b_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) ) ),
inference(miniscoping,[status(thm)],[f5535]) ).
fof(f5538,plain,
! [X0,X1,X2,X3] :
( X1 != X2
| hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X3))) ),
inference(cnf_transformation,[status(thm)],[f5536]) ).
fof(f5568,plain,
! [V_Pa_2,V_a_2,T_b] :
( ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) )
& ( hBOOL(hAPP(V_Pa_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ),
inference(NNF_transformation,[status(thm)],[f118]) ).
fof(f5569,plain,
( ! [V_Pa_2,V_a_2] :
( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
| ! [T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) )
& ! [V_Pa_2,V_a_2] :
( hBOOL(hAPP(V_Pa_2,V_a_2))
| ! [T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ),
inference(miniscoping,[status(thm)],[f5568]) ).
fof(f5570,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_Set_OCollect(X2),X0)))
| hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f5569]) ).
fof(f19981,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(c_COMBK(X0,X1),X2),X3) = X2,
inference(cnf_transformation,[status(thm)],[f5210]) ).
fof(f19983,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4),X5) = hAPP(hAPP(X3,X5),X4),
inference(cnf_transformation,[status(thm)],[f5212]) ).
fof(f20008,plain,
! [B_Z,B_s] :
( 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(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(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(pre_NNF_transformation,[status(thm)],[f5229]) ).
fof(f20009,plain,
! [X0,X1] :
( 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(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),X1)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(X0)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
| ~ v_P(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f20008]) ).
fof(f20010,plain,
? [B_Z,B_s] :
( ! [B_P_H,B_Q_H] :
( ? [B_s_H] :
( ~ hBOOL(hAPP(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)) ) )
| ~ 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,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)],[f5231]) ).
fof(f20011,plain,
( ! [B_P_H,B_Q_H] :
( ( ~ hBOOL(hAPP(v_Q(sK578_skl),sK580_skl(B_Q_H,B_P_H)))
& ! [B_Z_H] :
( hBOOL(hAPP(hAPP(B_Q_H,B_Z_H),sK580_skl(B_Q_H,B_P_H)))
| ~ hBOOL(hAPP(hAPP(B_P_H,B_Z_H),sK579_skl)) ) )
| ~ 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,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(sK578_skl,sK579_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK578_skl,sK579_skl,sK580_skl]),skolemize(B_Z,sK578_skl),skolemize(B_s,sK579_skl),skolemize(B_s_H,sK580_skl(B_Q_H,B_P_H))],[f20010]) ).
fof(f20012,plain,
v_P(sK578_skl,sK579_skl),
inference(cnf_transformation,[status(thm)],[f20011]) ).
fof(f20013,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X2,X1),sK580_skl(X2,X0)))
| ~ 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,X0,v_c,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(X0,X1),sK579_skl)) ),
inference(cnf_transformation,[status(thm)],[f20011]) ).
fof(f20014,plain,
! [X0,X1] :
( ~ 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,X1,v_c,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
| ~ hBOOL(hAPP(v_Q(sK578_skl),sK580_skl(X0,X1))) ),
inference(cnf_transformation,[status(thm)],[f20011]) ).
fof(f20347,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X1)),
inference(destructive_equality_resolution,[status(thm)],[f5338]) ).
fof(f20353,plain,
! [X0,X1,X2] : hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2))),
inference(destructive_equality_resolution,[status(thm)],[f5538]) ).
fof(f20879,plain,
! [X0,X1,X2] : c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X1),X2),X2),
inference(resolution,[status(thm)],[f5437,f5445]) ).
fof(f20928,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X2,X1),sK580_skl(X2,X0)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,X0,v_c,X2))))
| ~ hBOOL(hAPP(hAPP(X0,X1),sK579_skl)) ),
inference(backward_demodulation,[status(thm)],[f5311,f20013]) ).
fof(f20929,plain,
! [X0,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,X1,v_c,X0))))
| ~ hBOOL(hAPP(v_Q(sK578_skl),sK580_skl(X0,X1))) ),
inference(backward_demodulation,[status(thm)],[f5311,f20014]) ).
fof(f20931,plain,
! [X0,X1,X2,X3] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(c_fequal,X2)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X2),X3)) ),
inference(backward_demodulation,[status(thm)],[f5311,f5248]) ).
fof(f20944,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(c_Set_OCollect(X0),hAPP(c_fequal,X1)))),
inference(paramodulation,[status(thm)],[f5311,f20353]) ).
fof(f20972,plain,
! [X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),X1)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(X0))))))
| ~ v_P(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f5311,f20009]) ).
fof(f20973,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl)))))),
inference(resolution,[status(thm)],[f20972,f20012]) ).
fof(f20988,plain,
! [X0] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,X0,v_G)
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,X0,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl)))))) ),
inference(resolution,[status(thm)],[f20973,f5245]) ).
fof(f20989,plain,
! [X0] : c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G),hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl)))))),
inference(resolution,[status(thm)],[f20988,f20879]) ).
fof(f20994,plain,
! [X0,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,X0,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G))
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,X0,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl)))))) ),
inference(resolution,[status(thm)],[f20989,f5245]) ).
fof(f21094,plain,
! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X0),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)),hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl)))))),
inference(resolution,[status(thm)],[f20994,f20879]) ).
fof(f21115,plain,
! [X0,X1,X2] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,X0,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X1),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G)))
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,X0,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl)))))) ),
inference(resolution,[status(thm)],[f21094,f5245]) ).
fof(f21121,plain,
! [X0,X1,X2] : c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X0),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X1),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))),hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl)))))),
inference(resolution,[status(thm)],[f21115,f20879]) ).
fof(f21125,plain,
! [X0,X1,X2,X3] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,X0,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X1),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G))))
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,X0,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl)))))) ),
inference(resolution,[status(thm)],[f21121,f5245]) ).
fof(f21132,plain,
! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X1),
inference(resolution,[status(thm)],[f20347,f5445]) ).
fof(f21161,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(v_Q(sK578_skl),sK580_skl(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl)),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl)))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X0),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X1),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G)))) ),
inference(resolution,[status(thm)],[f21125,f20929]) ).
fof(f21164,definition,
! [X0,X1,X2] :
( sQ10_spl
<=> ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X0),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X1),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G)))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f21165,plain,
! [X0,X1,X2] :
( ~ sQ10_spl
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X0),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X1),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G)))) ),
inference(component_clause,[status(thm)],[f21164]) ).
fof(f21179,definition,
( sQ14_spl
<=> hBOOL(hAPP(v_Q(sK578_skl),sK580_skl(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl)),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f21182,plain,
( ~ sQ14_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f21161,f21164,f21179]) ).
fof(f21215,plain,
! [X0,X1] :
( ~ sQ10_spl
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X0),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G))) ),
inference(paramodulation,[status(thm)],[f5288,f21165]) ).
fof(f21222,plain,
! [X0] :
( ~ sQ10_spl
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G)) ),
inference(paramodulation,[status(thm)],[f5288,f21215]) ).
fof(f21512,plain,
! [X0] :
( 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(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl)))),X0))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,X0) ),
inference(resolution,[status(thm)],[f20931,f20973]) ).
fof(f21533,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(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl)))),v_G)),
inference(resolution,[status(thm)],[f21512,f21132]) ).
fof(f21540,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f21533,f21222]) ).
fof(f21541,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f21540]) ).
fof(f21870,plain,
! [X0] : hBOOL(hAPP(hAPP(c_fequal,X0),X0)),
inference(resolution,[status(thm)],[f5570,f20944]) ).
fof(f23901,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl))))),
inference(backward_demodulation,[status(thm)],[f5325,f20973]) ).
fof(f23973,plain,
! [X0,X1,X2] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X0)))
| ~ hBOOL(hAPP(hAPP(X2,X1),sK579_skl))
| hBOOL(hAPP(hAPP(X0,X1),sK580_skl(X0,X2))) ),
inference(forward_demodulation,[status(thm)],[f5325,f20928]) ).
fof(f24107,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl)),X0),sK579_skl))
| hBOOL(hAPP(hAPP(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl)),X0),sK580_skl(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl)),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl))))) ),
inference(resolution,[status(thm)],[f23901,f23973]) ).
fof(f28277,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl)),X0),sK579_skl))
| hBOOL(hAPP(v_Q(sK578_skl),sK580_skl(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl)),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl))))) ),
inference(forward_demodulation,[status(thm)],[f19981,f24107]) ).
fof(f28278,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl),sK579_skl))
| hBOOL(hAPP(v_Q(sK578_skl),sK580_skl(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK578_skl)),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl))))) ),
inference(forward_demodulation,[status(thm)],[f19981,f28277]) ).
fof(f28796,definition,
( sQ117_spl
<=> hBOOL(hAPP(hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl),sK579_skl)) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f28798,plain,
( sQ117_spl
| ~ hBOOL(hAPP(hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK579_skl),sK579_skl)) ),
inference(component_clause,[status(thm)],[f28796]) ).
fof(f28799,plain,
( ~ sQ117_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f28278,f21179,f28796]) ).
fof(f28804,plain,
( sQ117_spl
| ~ hBOOL(hAPP(hAPP(c_fequal,sK579_skl),sK579_skl)) ),
inference(forward_demodulation,[status(thm)],[f19983,f28798]) ).
fof(f28805,plain,
( sQ117_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f28804,f21870]) ).
fof(f28806,plain,
sQ117_spl,
inference(contradiction_clause,[status(thm)],[f28805]) ).
fof(f28807,plain,
$false,
inference(sat_refutation,[status(thm)],[f21182,f21541,f28799,f28806]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW306+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n019.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 09:47:05 UTC 2026
% 0.19/0.46 % CPUTime :
% 1.21/1.56 % Drodi V4.1.1
% 100.34/14.20 % Refutation found
% 100.34/14.20 % SZS status Theorem for theBenchmark: Theorem is valid
% 100.34/14.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 41.27/14.39 % Elapsed time: 13.889685 seconds
% 41.27/14.39 % CPU time: 101.672177 seconds
% 41.27/14.39 % Total memory used: 1.283 GB
% 41.27/14.39 % Net memory used: 1.223 GB
%------------------------------------------------------------------------------