%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW473+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 03:29:48 PM UTC 2026
% Result : Theorem 18.28s 5.28s
% Output : CNFRefutation 18.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 12 unt; 0 def)
% Number of atoms : 56 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 56 ( 26 ~; 22 |; 5 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 38 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f319,axiom,
! [X0,X1,X2,X3] :
( X1 = hAPP_pname_a(X2,X3)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X0))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_image__eqI) ).
fof(f428,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_insert__subset) ).
fof(f912,axiom,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f915,axiom,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
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/sandbox2/benchmark/theBenchmark.p',conj_6) ).
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(f919,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(flattening,[],[f918]) ).
fof(f1040,plain,
! [X0,X1,X2,X3] :
( hAPP_pname_a(X2,X3) != X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X0))) ),
inference(ennf_transformation,[],[f319]) ).
fof(f1041,plain,
! [X0,X1,X2,X3] :
( hAPP_pname_a(X2,X3) != X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X0))) ),
inference(flattening,[],[f1040]) ).
fof(f1464,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2)) ) ),
inference(nnf_transformation,[],[f428]) ).
fof(f1465,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2)) ) ),
inference(flattening,[],[f1464]) ).
fof(f1658,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f912]) ).
fof(f1661,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(cnf_transformation,[],[f915]) ).
fof(f1663,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,[],[f919]) ).
fof(f1751,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2)) ),
inference(cnf_transformation,[],[f1465]) ).
fof(f1816,plain,
! [X2,X3,X0,X1] :
( hAPP_pname_a(X2,X3) != X1
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X0))) ),
inference(cnf_transformation,[],[f1041]) ).
fof(f2493,plain,
! [X2,X3,X0] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X0))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X2,X3)),image_pname_a(X2,X0))) ),
inference(equality_resolution,[],[f1816]) ).
tcf(c_63,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f1658]) ).
tcf(c_66,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(cnf_transformation,[],[f1661]) ).
tcf(c_68,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(cnf_transformation,[],[f1663]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X2)),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ),
inference(cnf_transformation,[],[f1751]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X2,X0)),image_pname_a(X2,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
inference(cnf_transformation,[],[f2493]) ).
tcf(c_39847,plain,
! [X0: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,pn)),image_pname_a(X0,u)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)) ),
inference(instantiation,[status(thm)],[c_221]) ).
tcf(c_42834,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)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u))) ),
inference(instantiation,[status(thm)],[c_154]) ).
tcf(c_58477,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)) ),
inference(instantiation,[status(thm)],[c_39847]) ).
tcf(c_58478,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_58477,c_42834,c_68,c_63,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW473+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Thu Sep 24 22:31:22 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.40 Running first-order theorem proving
% 0.03/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.42
% 0.03/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.42
% 0.03/0.42 % Detected problem language: tptp
% 0.03/0.43 % Proving...
% 18.28/5.28 % SZS status Started for theBenchmark.p
% 18.28/5.28 % SZS status Theorem for theBenchmark.p
% 18.28/5.28
% 18.28/5.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.28/5.28
% 18.28/5.28 % ------ iProver source info
% 18.28/5.28
% 18.28/5.28 % git: date: 2026-07-19 20:42:38 +0200
% 18.28/5.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.28/5.28 % git: non_committed_changes: false
% 18.28/5.28
% 18.28/5.28 % ------ Parsing...
% 18.28/5.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.28/5.28
% 18.28/5.28 % ------ Preprocessing... sup_sim: 72 sf_s rm: 20 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 18.28/5.28
% 18.28/5.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.28/5.28
% 18.28/5.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 18.28/5.28 % ------ Proving...
% 18.28/5.28 % ------ Problem Properties
% 18.28/5.28
% 18.28/5.28 %
% 18.28/5.28 % clauses 461
% 18.28/5.28 % conjectures 1
% 18.28/5.28 % EPR 5
% 18.28/5.28 % Horn 340
% 18.28/5.28 % unary 86
% 18.28/5.28 % binary 192
% 18.28/5.28 % lits 1150
% 18.28/5.28 % lits eq 196
% 18.28/5.28 % fd_pure 0
% 18.28/5.28 % fd_pseudo 0
% 18.28/5.28 % fd_cond 16
% 18.28/5.28 % fd_pseudo_cond 47
% 18.28/5.28 % AC symbols 0
% 18.28/5.28
% 18.28/5.28 % ------ Schedule dynamic 5 is on
% 18.28/5.28
% 18.28/5.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 18.28/5.28
% 18.28/5.28
% 18.28/5.28 % ------
% 18.28/5.28 % Current options:
% 18.28/5.28 % ------
% 18.28/5.28
% 18.28/5.28
% 18.28/5.28 %
% 18.28/5.28
% 18.28/5.28 % ------ Proving...
% 18.28/5.28 %
% 18.28/5.28
% 18.28/5.28 % SZS status Theorem for theBenchmark.p
% 18.28/5.28
% 18.28/5.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.28/5.28
% 18.28/5.28
%------------------------------------------------------------------------------