%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW473+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 : Sun Sep 27 09:14:20 AM UTC 2026
% Result : Theorem 129.51s 18.09s
% Output : CNFRefutation 129.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 11 unt; 0 def)
% Number of atoms : 19 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_283_insert__mono,axiom,
! [A_1,C,D] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C),D))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A_1,C)),insert_a(A_1,D))) ),
file('theBenchmark.p',fact_283_insert__mono) ).
fof(fact_285_insert__image,axiom,
! [F,X_2,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> insert_a(hAPP_pname_a(F,X_2),image_pname_a(F,A)) = image_pname_a(F,A) ),
file('theBenchmark.p',fact_285_insert__image) ).
fof(conj_6,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('theBenchmark.p',conj_6) ).
fof(conj_6_neg,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(assume_negation,[status(cth)],[conj_6]) ).
cnf(c_853,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(C,A)),insert_a(C,B)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
inference(clausify,[status(thm)],[fact_283_insert__mono]) ).
cnf(c_855,plain,
( insert_a(hAPP_pname_a(C,A),image_pname_a(C,B)) = image_pname_a(C,B)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),B)) ),
inference(clausify,[status(thm)],[fact_285_insert__image]) ).
fof(conj_1,axiom,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
file('theBenchmark.p',conj_1) ).
cnf(c_933,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(clausify,[status(thm)],[conj_1]) ).
fof(conj_4,axiom,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('theBenchmark.p',conj_4) ).
cnf(c_937,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(clausify,[status(thm)],[conj_4]) ).
cnf(c_939,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(clausify,[status(thm)],[conj_6_neg]) ).
cnf(c_3891,plain,
insert_a(hAPP_pname_a(A,pn),image_pname_a(A,u)) = image_pname_a(A,u),
inference(resolve,[status(thm)],[c_855,c_937]) ).
cnf(c_12576,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A,g)),insert_a(A,image_pname_a(mgt_call,u)))),
inference(resolve,[status(thm)],[c_853,c_933]) ).
cnf(c_12586,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(paramod,[status(thm)],[c_3891,c_12576]) ).
cnf(c_12585,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_939,c_12586]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWW473+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.05/0.52 % Computer : n012.cluster.edu
% 0.05/0.52 % Model : x86_64 x86_64
% 0.05/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.52 % Memory : 8046.5625MB
% 0.05/0.52 % OS : Linux 6.8.0-71-generic
% 0.05/0.52 % CPULimit : 300
% 0.05/0.52 % WCLimit : 300
% 0.05/0.52 % DateTime : Sat Sep 26 16:01:05 UTC 2026
% 0.05/0.52 % CPUTime :
% 0.05/0.52 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/0.52 % Process 972336 was started by sandbox2 on n012,
% 0.05/0.52 % Sat Sep 26 16:01:05 2026
% 0.05/0.52 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.60
% 0.11/0.60 % From the command line: assign(max_seconds, 300).
% 0.11/0.60
% 0.11/0.60 % SInE: 322 to sos, 126 to usable, of 448 axioms (tolerance 2.00, depth 0 fixpoint).
% 129.51/18.09
% 129.51/18.09 % given #500 (T,wt=29): 4081 -hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A),g)) | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A),image_pname_a(mgt_call,u))). [resolve(745,a,933,a)].
% 129.51/18.09
% 129.51/18.09 % given #1000 (T,wt=35): 2035 is_fun949378684l_bool(image_112932426a_bool(A,image_a_pname(B,image_pname_a(C,image_pname_pname(D,u))))). [resolve(1115,a,442,a)].
% 129.51/18.09
% 129.51/18.09 % SZS status Theorem for theBenchmark
% 129.51/18.09
% 129.51/18.09 % Proof 1 at 0.90 (+ 0.24) seconds.
% 129.51/18.09 % Length of proof is 11.
% 129.51/18.09 % Level of proof is 3.
% 129.51/18.09 % Maximum clause weight is 37.000.
% 129.51/18.09 % Given clauses 1390.
% 129.51/18.09
% 129.51/18.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------