%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW473+1 : 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 : n011.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 03:29:47 PM UTC 2026
% Result : Theorem 7.55s 17.04s
% Output : CNFRefutation 7.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 17 unt; 0 def)
% Number of atoms : 59 ( 6 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 58 ( 29 ~; 21 |; 5 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 8 ( 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 : 24 ( 24 usr; 9 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 44 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f276,axiom,
! [X0,X1] : insert_a(X0,X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_insert__compr) ).
fof(f344,axiom,
! [X0,X1,X2,X3] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
=> ( X0 = hAPP_pname_a(X1,X2)
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_rev__image__eqI) ).
fof(f356,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_274_insert__subset) ).
fof(f444,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(f447,axiom,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(f449,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(f450,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)],[f449]) ).
fof(f451,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,[],[f450]) ).
fof(f786,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
| hAPP_pname_a(X1,X2) != X0
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3))) ),
inference(ennf_transformation,[],[f344]) ).
fof(f787,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
| hAPP_pname_a(X1,X2) != X0
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3))) ),
inference(flattening,[],[f786]) ).
fof(f883,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,[],[f356]) ).
fof(f884,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,[],[f883]) ).
fof(f1221,plain,
! [X0,X1] : insert_a(X0,X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))),
inference(cnf_transformation,[],[f276]) ).
fof(f1319,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
| hAPP_pname_a(X1,X2) != X0
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3))) ),
inference(cnf_transformation,[],[f787]) ).
fof(f1337,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,[],[f884]) ).
fof(f1443,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f444]) ).
fof(f1446,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(cnf_transformation,[],[f447]) ).
fof(f1448,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,[],[f451]) ).
fof(f1564,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,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))),X2)) ),
inference(definition_unfolding,[],[f1337,f1221]) ).
fof(f1581,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u))),
inference(definition_unfolding,[],[f1448,f1221]) ).
fof(f1618,plain,
! [X2,X3,X1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,X2)),image_pname_a(X1,X3))) ),
inference(equality_resolution,[],[f1319]) ).
tcf(c_460,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,[],[f1618]) ).
tcf(c_470,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
inference(cnf_transformation,[],[f1564]) ).
tcf(c_578,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f1443]) ).
tcf(c_581,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(cnf_transformation,[],[f1446]) ).
tcf(c_583,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f1581]) ).
tcf(c_892,plain,
( ~ 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(superposition,[status(thm)],[c_470,c_583]) ).
tcf(c_1346,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u))),
inference(global_subsumption_just,[status(thm)],[c_892,c_578,c_892]) ).
tcf(c_1348,plain,
~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(superposition,[status(thm)],[c_460,c_1346]) ).
tcf(c_1349,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_581,c_1348]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW473+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.06/15.50 % CPULimit : 300
% 0.06/15.50 % WCLimit : 300
% 0.06/15.50 % DateTime : Thu Sep 24 22:35:19 UTC 2026
% 0.06/15.50 % CPUTime :
% 0.06/15.50 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.06/15.56 Running first-order theorem proving
% 0.06/15.56 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
% 0.06/15.58
% 0.06/15.58 % ======== iProver multi-core TPTP/SMT =========
% 0.06/15.58
% 0.06/15.58 % Detected problem language: tptp
% 0.43/15.60 % Proving...
% 7.55/17.04 % SZS status Started for theBenchmark.p
% 7.55/17.04 % SZS status Theorem for theBenchmark.p
% 7.55/17.04
% 7.55/17.04 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.55/17.04
% 7.55/17.04 % ------ iProver source info
% 7.55/17.04
% 7.55/17.04 % git: date: 2026-07-19 20:42:38 +0200
% 7.55/17.04 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.55/17.04 % git: non_committed_changes: false
% 7.55/17.04
% 7.55/17.04 % ------ Parsing...
% 7.55/17.04 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.55/17.04 % ------ Proving...
% 7.55/17.04 % ------ Problem Properties
% 7.55/17.04
% 7.55/17.04 %
% 7.55/17.04 % clauses 535
% 7.55/17.04 % conjectures 1
% 7.55/17.04 % EPR 5
% 7.55/17.04 % Horn 484
% 7.55/17.04 % unary 144
% 7.55/17.04 % binary 244
% 7.55/17.04 % lits 1131
% 7.55/17.04 % lits eq 139
% 7.55/17.04 % fd_pure 0
% 7.55/17.04 % fd_pseudo 0
% 7.55/17.04 % fd_cond 0
% 7.55/17.04 % fd_pseudo_cond 36
% 7.55/17.04 % AC symbols 0
% 7.55/17.04
% 7.55/17.04 % ------ Input Options Time Limit: Unbounded
% 7.55/17.04
% 7.55/17.04
% 7.55/17.04 % ------
% 7.55/17.04 % Current options:
% 7.55/17.04 % ------
% 7.55/17.04
% 7.55/17.04
% 7.55/17.04 %
% 7.55/17.04
% 7.55/17.04 % ------ Proving...
% 7.55/17.04 %
% 7.55/17.04
% 7.55/17.04 % SZS status Theorem for theBenchmark.p
% 7.55/17.04
% 7.55/17.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.55/17.04
% 7.55/17.04
%------------------------------------------------------------------------------