%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW473+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 03:07:58 PM UTC 2026
% Result : Theorem 0.23s 0.56s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 49 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 20 ~; 14 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f372,axiom,
! [A_1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),A_1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f402,axiom,
! [C_6,A_1,B_6] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),C_6))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),C_6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f437,axiom,
! [A_3,C_6,D_1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),D_1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A_3,C_6)),insert_a(A_3,D_1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f441,axiom,
! [F,A_3,B_6] : image_pname_a(F,insert_pname(A_3,B_6)) = insert_a(hAPP_pname_a(F,A_3),image_pname_a(F,B_6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f447,axiom,
! [F,X_3,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
=> insert_a(hAPP_pname_a(F,X_3),image_pname_a(F,A_1)) = image_pname_a(F,A_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f912,hypothesis,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f915,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f917,conjecture,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f918,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
inference(negated_conjecture,[status(cth)],[f917]) ).
fof(f2061,plain,
! [X0] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0)),
inference(cnf_transformation,[status(thm)],[f372]) ).
fof(f2144,plain,
! [C_6,A_1,B_6] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),C_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),C_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ),
inference(pre_NNF_transformation,[status(thm)],[f402]) ).
fof(f2145,plain,
! [A_1,B_6] :
( ! [C_6] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),C_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),C_6)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ),
inference(miniscoping,[status(thm)],[f2144]) ).
fof(f2146,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f2145]) ).
fof(f2248,plain,
! [A_3,C_6,D_1] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A_3,C_6)),insert_a(A_3,D_1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),D_1)) ),
inference(pre_NNF_transformation,[status(thm)],[f437]) ).
fof(f2249,plain,
! [C_6,D_1] :
( ! [A_3] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A_3,C_6)),insert_a(A_3,D_1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),D_1)) ),
inference(miniscoping,[status(thm)],[f2248]) ).
fof(f2250,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X2,X0)),insert_a(X2,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f2249]) ).
fof(f2254,plain,
! [X0,X1,X2] : image_pname_a(X0,insert_pname(X1,X2)) = insert_a(hAPP_pname_a(X0,X1),image_pname_a(X0,X2)),
inference(cnf_transformation,[status(thm)],[f441]) ).
fof(f2270,plain,
! [F,X_3,A_1] :
( insert_a(hAPP_pname_a(F,X_3),image_pname_a(F,A_1)) = image_pname_a(F,A_1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ),
inference(pre_NNF_transformation,[status(thm)],[f447]) ).
fof(f2271,plain,
! [X_3,A_1] :
( ! [F] : insert_a(hAPP_pname_a(F,X_3),image_pname_a(F,A_1)) = image_pname_a(F,A_1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ),
inference(miniscoping,[status(thm)],[f2270]) ).
fof(f2272,plain,
! [X0,X1,X2] :
( insert_a(hAPP_pname_a(X2,X0),image_pname_a(X2,X1)) = image_pname_a(X2,X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f2271]) ).
fof(f3557,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[status(thm)],[f912]) ).
fof(f3560,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(cnf_transformation,[status(thm)],[f915]) ).
fof(f3562,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[status(thm)],[f918]) ).
fof(f3782,plain,
! [X0] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),X0)) ),
inference(resolution,[status(thm)],[f2146,f3562]) ).
fof(f3869,plain,
! [X0,X1,X2] :
( image_pname_a(X2,insert_pname(X0,X1)) = image_pname_a(X2,X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f2254,f2272]) ).
fof(f3870,plain,
! [X0] : image_pname_a(X0,insert_pname(pn,u)) = image_pname_a(X0,u),
inference(resolution,[status(thm)],[f3869,f3560]) ).
fof(f3900,plain,
! [X0] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,g)),insert_a(X0,image_pname_a(mgt_call,u)))),
inference(resolution,[status(thm)],[f3557,f2250]) ).
fof(f4679,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u))),
inference(resolution,[status(thm)],[f3900,f3782]) ).
fof(f4696,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(mgt_call,insert_pname(pn,u))),image_pname_a(mgt_call,u))),
inference(forward_demodulation,[status(thm)],[f2254,f4679]) ).
fof(f4697,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(mgt_call,u)),image_pname_a(mgt_call,u))),
inference(forward_demodulation,[status(thm)],[f3870,f4696]) ).
fof(f4698,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4697,f2061]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW473+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 09:58:20 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.15/0.44 % Drodi V4.1.1
% 0.23/0.56 % Refutation found
% 0.23/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.58 % Elapsed time: 0.209870 seconds
% 0.23/0.58 % CPU time: 0.980487 seconds
% 0.23/0.58 % Total memory used: 195.512 MB
% 0.23/0.58 % Net memory used: 194.517 MB
%------------------------------------------------------------------------------