%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP023+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 01:48:00 PM UTC 2026
% Result : Theorem 3.84s 1.17s
% Output : CNFRefutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 14 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 9 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 30 !; 2 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f40,axiom,
! [X0,X1] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1))))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1)))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).
fof(f41,axiom,
! [X0,X1] :
( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1))))
& p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__SUBSET) ).
fof(f42,axiom,
! [X0,X1] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1)))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CBALL) ).
fof(f53,conjecture,
! [X0,X1] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1)))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__BALL) ).
fof(f54,negated_conjecture,
~ ! [X0,X1] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1)))))))),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
? [X0,X1] : ~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1)))))))),
inference(ennf_transformation,[],[f54]) ).
fof(f60,plain,
! [X0,X1] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1))))
| p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0)))) ),
inference(ennf_transformation,[],[f41]) ).
fof(f61,plain,
! [X0,X1] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1))))
| p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0)))) ),
inference(flattening,[],[f60]) ).
fof(f81,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,sK11),s(tyop_2Erealax_2Ereal,sK12)))))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f55]) ).
fof(f134,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,sK11),s(tyop_2Erealax_2Ereal,sK12)))))))),
inference(cnf_transformation,[],[f81]) ).
fof(f219,plain,
! [X0,X1] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1)))))))),
inference(cnf_transformation,[],[f42]) ).
fof(f220,plain,
! [X0,X1] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1))))
| p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0)))) ),
inference(cnf_transformation,[],[f61]) ).
fof(f221,plain,
! [X0,X1] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1))))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1)))))))),
inference(cnf_transformation,[],[f40]) ).
tcf(c_49,negated_conjecture,
~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,sK11),s(tyop_2Erealax_2Ereal,sK12)))))))),
inference(cnf_transformation,[],[f134]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1)))))))),
inference(cnf_transformation,[],[f219]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1)))) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1))))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1)))))))),
inference(cnf_transformation,[],[f221]) ).
tcf(c_2775,plain,
! [X0: $i,X1: $i] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1))))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1)))))))) ),
inference(superposition,[status(thm)],[c_114,c_113]) ).
tcf(c_2776,plain,
! [X0: $i,X1: $i] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1)))))))),
inference(forward_subsumption_resolution,[status(thm)],[c_2775,c_112]) ).
tcf(c_2784,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_2776]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP023+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 17:49:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 3.84/1.17 % SZS status Started for theBenchmark.p
% 3.84/1.17 % SZS status Theorem for theBenchmark.p
% 3.84/1.17
% 3.84/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.84/1.17
% 3.84/1.17 % ------ iProver source info
% 3.84/1.17
% 3.84/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 3.84/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.84/1.17 % git: non_committed_changes: false
% 3.84/1.17
% 3.84/1.17 % ------ Parsing...
% 3.84/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.84/1.17
% 3.84/1.17 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.84/1.17
% 3.84/1.17 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.84/1.17
% 3.84/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.84/1.17 % ------ Proving...
% 3.84/1.17 % ------ Problem Properties
% 3.84/1.17
% 3.84/1.17 %
% 3.84/1.17 % clauses 14
% 3.84/1.17 % conjectures 1
% 3.84/1.17 % EPR 1
% 3.84/1.17 % Horn 12
% 3.84/1.17 % unary 3
% 3.84/1.17 % binary 5
% 3.84/1.17 % lits 31
% 3.84/1.17 % lits eq 8
% 3.84/1.17 % fd_pure 0
% 3.84/1.17 % fd_pseudo 0
% 3.84/1.17 % fd_cond 0
% 3.84/1.17 % fd_pseudo_cond 0
% 3.84/1.17 % AC symbols 0
% 3.84/1.17
% 3.84/1.17 % ------ Schedule dynamic 5 is on
% 3.84/1.17
% 3.84/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.84/1.17
% 3.84/1.17
% 3.84/1.17 % ------
% 3.84/1.17 % Current options:
% 3.84/1.17 % ------
% 3.84/1.17
% 3.84/1.17
% 3.84/1.17 %
% 3.84/1.17
% 3.84/1.17 % ------ Proving...
% 3.84/1.17 %
% 3.84/1.17
% 3.84/1.17 % SZS status Theorem for theBenchmark.p
% 3.84/1.17
% 3.84/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.84/1.17
% 3.84/1.17
%------------------------------------------------------------------------------