%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW319+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 : n008.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 03:07:38 PM UTC 2026
% Result : Theorem 8.60s 2.27s
% Output : CNFRefutation 9.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 17 unt; 0 def)
% Number of atoms : 122 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 116 ( 50 ~; 45 |; 11 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 161 ( 159 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_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_tsa_2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [V_x_2,V_A_2,V_y_2,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
<=> ( hBOOL(hAPP(V_A_2,V_x_2))
| V_y_2 = V_x_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
<=> hBOOL(hAPP(V_A_2,V_x_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [V_A_2,T_b] :
( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,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(f86,axiom,
! [V_a_2,V_D_2,V_C_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f87,axiom,
! [V_Ga_2,V_tsa_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_Ga_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f88,axiom,
! [V_tsa_2,V_ts_H_2,V_Ga_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5226,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5227,conjecture,
( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts)
& c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5228,negated_conjecture,
~ ( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts)
& c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
inference(negated_conjecture,[status(cth)],[f5227]) ).
fof(f5234,plain,
! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_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_tsa_2) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f5235,plain,
! [V_tsa_2,V_G_H_2,T_b] :
( ! [V_Ga_2] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_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_tsa_2) ),
inference(miniscoping,[status(thm)],[f5234]) ).
fof(f5236,plain,
! [X0,X1,X2,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X3,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X3,X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5235]) ).
fof(f5259,plain,
! [V_x_2,V_A_2,V_y_2,T_b] :
( ( ( ~ hBOOL(hAPP(V_A_2,V_x_2))
& V_y_2 != V_x_2 )
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) )
& ( hBOOL(hAPP(V_A_2,V_x_2))
| V_y_2 = V_x_2
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f5260,plain,
( ! [V_x_2,V_A_2,V_y_2] :
( ( ~ hBOOL(hAPP(V_A_2,V_x_2))
& V_y_2 != V_x_2 )
| ! [T_b] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) )
& ! [V_x_2,V_A_2,V_y_2] :
( hBOOL(hAPP(V_A_2,V_x_2))
| V_y_2 = V_x_2
| ! [T_b] : ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) ) ),
inference(miniscoping,[status(thm)],[f5259]) ).
fof(f5262,plain,
! [X0,X1,X2,X3] :
( X1 != X3
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X3)) ),
inference(cnf_transformation,[status(thm)],[f5260]) ).
fof(f5340,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),X1)),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f5348,plain,
! [V_A_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(V_A_2,V_x_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ( hBOOL(hAPP(V_A_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
inference(NNF_transformation,[status(thm)],[f44]) ).
fof(f5349,plain,
( ! [V_A_2,V_x_2] :
( ~ hBOOL(hAPP(V_A_2,V_x_2))
| ! [T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ! [V_A_2,V_x_2] :
( hBOOL(hAPP(V_A_2,V_x_2))
| ! [T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
inference(miniscoping,[status(thm)],[f5348]) ).
fof(f5351,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5349]) ).
fof(f5455,plain,
! [V_A_2,T_b] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
inference(NNF_transformation,[status(thm)],[f74]) ).
fof(f5456,plain,
( ! [V_A_2,T_b] :
( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
& ! [V_A_2,T_b] :
( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
inference(miniscoping,[status(thm)],[f5455]) ).
fof(f5457,plain,
( ! [V_A_2,T_b] :
( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
& ! [V_A_2,T_b] :
( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),sK9_skl(T_b,V_A_2)),V_A_2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(B_x,sK9_skl(T_b,V_A_2))],[f5456]) ).
fof(f5458,plain,
! [X0,X1] :
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X0),sK9_skl(X0,X1)),X1)) ),
inference(cnf_transformation,[status(thm)],[f5457]) ).
fof(f5459,plain,
! [X0,X1,X2] :
( X2 != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5457]) ).
fof(f5487,plain,
! [V_A_2,V_a_2,T_b] :
( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f5488,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5487]) ).
fof(f5489,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)],[f84]) ).
fof(f5493,plain,
! [V_a_2,V_D_2,V_C_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)) ),
inference(pre_NNF_transformation,[status(thm)],[f86]) ).
fof(f5494,plain,
! [V_D_2,V_C_2,T_b] :
( ! [V_a_2] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)) ),
inference(miniscoping,[status(thm)],[f5493]) ).
fof(f5495,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X1)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5494]) ).
fof(f5496,plain,
! [V_Ga_2,V_tsa_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_Ga_2)) ),
inference(pre_NNF_transformation,[status(thm)],[f87]) ).
fof(f5497,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_HOL_Obool)),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5496]) ).
fof(f5498,plain,
! [V_tsa_2,V_ts_H_2,V_Ga_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2) ),
inference(pre_NNF_transformation,[status(thm)],[f88]) ).
fof(f5499,plain,
! [V_ts_H_2,V_Ga_2,T_b] :
( ! [V_tsa_2] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2)) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2) ),
inference(miniscoping,[status(thm)],[f5498]) ).
fof(f5500,plain,
! [X0,X1,X2,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_HOL_Obool)),X3),X2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5499]) ).
fof(f20072,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)),
inference(cnf_transformation,[status(thm)],[f5226]) ).
fof(f20073,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
inference(pre_NNF_transformation,[status(thm)],[f5228]) ).
fof(f20074,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
inference(cnf_transformation,[status(thm)],[f20073]) ).
fof(f20372,plain,
! [X0,X1,X2] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X1)),
inference(destructive_equality_resolution,[status(thm)],[f5262]) ).
fof(f20580,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)],[f5489,f5497]) ).
fof(f20587,plain,
! [X0,X1,X2,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X2),X3)) ),
inference(resolution,[status(thm)],[f20580,f5236]) ).
fof(f20591,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts),
inference(resolution,[status(thm)],[f20587,f20072]) ).
fof(f20597,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(backward_subsumption_resolution,[status(thm)],[f20074,f20591]) ).
fof(f20776,plain,
! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),X0),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts))) ),
inference(resolution,[status(thm)],[f5500,f20072]) ).
fof(f20852,plain,
! [X0,X1,X2] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2))),
inference(resolution,[status(thm)],[f5495,f5340]) ).
fof(f21072,plain,
! [X0,X1,X2,X3] : hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(hAPP(c_Set_Oinsert(X2),X1),X3))),
inference(resolution,[status(thm)],[f5351,f20372]) ).
fof(f21085,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),
inference(resolution,[status(thm)],[f21072,f5459]) ).
fof(f22112,plain,
! [X0,X1] :
( hAPP(hAPP(c_Set_Oinsert(X1),sK9_skl(X1,X0)),X0) = X0
| X0 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(resolution,[status(thm)],[f5458,f5488]) ).
fof(f22171,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(resolution,[status(thm)],[f22112,f21085]) ).
fof(f22308,plain,
! [X0] : ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
inference(paramodulation,[status(thm)],[f22171,f20597]) ).
fof(f23998,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(resolution,[status(thm)],[f20852,f20776]) ).
fof(f24042,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f23998,f22308]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW319+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 09:47:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.96/1.25 % Drodi V4.1.1
% 8.60/2.27 % Refutation found
% 8.60/2.27 % SZS status Theorem for theBenchmark: Theorem is valid
% 8.60/2.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.06/2.36 % Elapsed time: 1.986373 seconds
% 9.06/2.36 % CPU time: 9.072319 seconds
% 9.06/2.36 % Total memory used: 725.400 MB
% 9.06/2.36 % Net memory used: 716.682 MB
%------------------------------------------------------------------------------