%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW298+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 : 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 03:07:35 PM UTC 2026
% Result : Theorem 0.48s 0.83s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 5 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 8 ~; 4 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [V_t,V_n,T_a] :
( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
=> c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5224,hypothesis,
! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),B_x) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5225,conjecture,
! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5226,negated_conjecture,
~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x) ),
inference(negated_conjecture,[status(cth)],[f5225]) ).
fof(f5230,plain,
! [V_t,V_n,T_a] :
( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t)
| ~ c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f5231,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Otriple__valid(X0,X1,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(X0,hAPP(c_Nat_OSuc,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f5230]) ).
fof(f20179,plain,
! [B_x] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts)) ),
inference(pre_NNF_transformation,[status(thm)],[f5224]) ).
fof(f20180,plain,
! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts)) ),
inference(cnf_transformation,[status(thm)],[f20179]) ).
fof(f20181,plain,
? [B_x] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts)) ),
inference(pre_NNF_transformation,[status(thm)],[f5226]) ).
fof(f20182,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK557_skl)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK557_skl),v_ts)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK557_skl]),skolemize(B_x,sK557_skl)],[f20181]) ).
fof(f20183,plain,
hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK557_skl),v_ts)),
inference(cnf_transformation,[status(thm)],[f20182]) ).
fof(f20184,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK557_skl),
inference(cnf_transformation,[status(thm)],[f20182]) ).
fof(f20991,plain,
c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),sK557_skl),
inference(resolution,[status(thm)],[f20180,f20183]) ).
fof(f20993,plain,
c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK557_skl),
inference(resolution,[status(thm)],[f20991,f5231]) ).
fof(f20994,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f20993,f20184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW298+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 09:46:53 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.39/0.68 % Drodi V4.1.1
% 0.48/0.83 % Refutation found
% 0.48/0.83 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.48/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.48/0.94 % Elapsed time: 0.556431 seconds
% 0.48/0.94 % CPU time: 1.426628 seconds
% 0.48/0.94 % Total memory used: 667.274 MB
% 0.48/0.94 % Net memory used: 661.316 MB
%------------------------------------------------------------------------------