%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW337+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 03:07:40 PM UTC 2026
% Result : Theorem 0.83s 6.33s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 7 unt; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 24 ~; 18 |; 6 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 50 ( 48 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f639,axiom,
! [V_c_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_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f666,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/sandbox/benchmark/theBenchmark.p') ).
fof(f5225,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5226,conjecture,
! [B_n] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) )
=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5227,negated_conjecture,
~ ! [B_n] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) )
=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) ) ),
inference(negated_conjecture,[status(cth)],[f5226]) ).
fof(f7125,plain,
! [V_c_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_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)) ),
inference(pre_NNF_transformation,[status(thm)],[f639]) ).
fof(f7126,plain,
! [V_B_2,V_A_2,T_b] :
( ! [V_c_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_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)) ),
inference(miniscoping,[status(thm)],[f7125]) ).
fof(f7127,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_member(X0),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f7126]) ).
fof(f7198,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)],[f666]) ).
fof(f7199,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)],[f7198]) ).
fof(f7200,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f7199]) ).
fof(f7201,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f7199]) ).
fof(f20136,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G)),
inference(cnf_transformation,[status(thm)],[f5225]) ).
fof(f20137,plain,
? [B_n] :
( ? [B_x] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts)) )
& ! [B_x] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5227]) ).
fof(f20138,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK579_skl,sK580_skl)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK580_skl),v_ts))
& ! [B_x] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK579_skl,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK579_skl,sK580_skl]),skolemize(B_n,sK579_skl),skolemize(B_x,sK580_skl)],[f20137]) ).
fof(f20139,plain,
! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK579_skl,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G)) ),
inference(cnf_transformation,[status(thm)],[f20138]) ).
fof(f20140,plain,
hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK580_skl),v_ts)),
inference(cnf_transformation,[status(thm)],[f20138]) ).
fof(f20141,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK579_skl,sK580_skl),
inference(cnf_transformation,[status(thm)],[f20138]) ).
fof(f20949,plain,
! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK579_skl,X0)
| ~ hBOOL(hAPP(v_G,X0)) ),
inference(resolution,[status(thm)],[f7201,f20139]) ).
fof(f20950,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X0),v_G))
| c_Hoare__Mirabelle_Otriple__valid(t_a,sK579_skl,X0) ),
inference(resolution,[status(thm)],[f20949,f7200]) ).
fof(f20954,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_member(X0),sK580_skl),v_G)),
inference(resolution,[status(thm)],[f20950,f20141]) ).
fof(f20962,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts)) ),
inference(resolution,[status(thm)],[f20136,f7127]) ).
fof(f20972,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK580_skl),v_ts)),
inference(resolution,[status(thm)],[f20962,f20954]) ).
fof(f20973,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f20972,f20140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW337+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.59 % Computer : n007.cluster.edu
% 0.10/5.59 % Model : x86_64 x86_64
% 0.10/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.59 % Memory : 8046.5625MB
% 0.10/5.59 % OS : Linux 6.8.0-71-generic
% 0.10/5.59 % CPULimit : 300
% 0.10/5.59 % WCLimit : 300
% 0.10/5.59 % DateTime : Mon Sep 21 09:45:57 UTC 2026
% 0.10/5.59 % CPUTime :
% 0.73/6.27 % Drodi V4.1.1
% 0.83/6.33 % Refutation found
% 0.83/6.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.83/6.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.96/6.49 % Elapsed time: 0.890182 seconds
% 0.96/6.49 % CPU time: 1.248010 seconds
% 0.96/6.49 % Total memory used: 290.434 MB
% 0.96/6.49 % Net memory used: 287.743 MB
%------------------------------------------------------------------------------