%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP023_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 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 : Thu Sep 24 12:53:52 PM UTC 2026
% Result : Theorem 0.10s 0.42s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 7 ~; 4 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
mono_2Etyop_2Emin_2Ebool: $tType ).
tff(decl_sort2,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: $tType ).
tff(decl_sort3,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
tff(decl_sort4,type,
mono_2Etyop_2Erealax_2Ereal: $tType ).
tff(decl_29,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
tff(decl_67,type,
mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
tff(decl_74,type,
mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).
tff(decl_79,type,
mono_2Ec_2Ereal__topology_2Eball_2E1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ).
tff(decl_81,type,
mono_2Ec_2Ereal__topology_2Ebounded__def_2E1: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Emin_2Ebool ).
tff(decl_83,type,
mono_2Ec_2Ereal__topology_2Ecball_2E1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ).
tff(decl_109,type,
esk1_0: mono_2Etyop_2Erealax_2Ereal ).
tff(decl_110,type,
esk2_0: mono_2Etyop_2Erealax_2Ereal ).
tff(thm_2Ereal__topology_2EBOUNDED__BALL,conjecture,
! [X86: mono_2Etyop_2Erealax_2Ereal,X75: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X86,X75)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__BALL) ).
tff(thm_2Ereal__topology_2EBOUNDED__SUBSET,axiom,
! [X76: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,X77: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
( ( p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(X76,X77))
& p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X77)) )
=> p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X76)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__SUBSET) ).
tff(thm_2Ereal__topology_2EBALL__SUBSET__CBALL,axiom,
! [X74: mono_2Etyop_2Erealax_2Ereal,X75: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X74,X75)),mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X74,X75)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).
tff(thm_2Ereal__topology_2EBOUNDED__CBALL,axiom,
! [X78: mono_2Etyop_2Erealax_2Ereal,X75: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X78,X75)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CBALL) ).
tff(c_0_4,negated_conjecture,
~ ! [X86: mono_2Etyop_2Erealax_2Ereal,X75: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X86,X75)))),
inference(assume_negation,[status(cth)],[thm_2Ereal__topology_2EBOUNDED__BALL]) ).
tff(c_0_5,plain,
! [X111: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,X112: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
( p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X111))
| ~ p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(X111,X112))
| ~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X112)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Ereal__topology_2EBOUNDED__SUBSET])])]) ).
tff(c_0_6,plain,
! [X115: mono_2Etyop_2Erealax_2Ereal,X116: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X115,X116)),mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X115,X116)))),
inference(variable_rename,[status(thm)],[thm_2Ereal__topology_2EBALL__SUBSET__CBALL]) ).
tff(c_0_7,plain,
! [X113: mono_2Etyop_2Erealax_2Ereal,X114: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X113,X114)))),
inference(variable_rename,[status(thm)],[thm_2Ereal__topology_2EBOUNDED__CBALL]) ).
tff(c_0_8,negated_conjecture,
~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(esk1_0,esk2_0)))),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
tcf(c_0_9,plain,
! [X44: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,X31: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
( ~ p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(X44,X31))
| ~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X31))
| p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X44)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
tcf(c_0_10,plain,
! [X35: mono_2Etyop_2Erealax_2Ereal,X37: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X35,X37)),mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X35,X37)))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
tcf(c_0_11,plain,
! [X35: mono_2Etyop_2Erealax_2Ereal,X37: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X35,X37)))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
tcf(c_0_12,negated_conjecture,
~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(esk1_0,esk2_0)))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_13,plain,
! [X35: mono_2Etyop_2Erealax_2Ereal,X37: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X35,X37)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]) ).
cnf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP023_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n009.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 21:54:27 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42 % Version: 3.5.1
% 0.10/0.42 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.10/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.42 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.10/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.42 % Starting sh5l with 300s (1) cores
% 0.10/0.42 % new_bool_3 with pid 114866 completed with status 0
% 0.10/0.42 % Result found by new_bool_3
% 0.10/0.42 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.10/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.42 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.10/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.42 % Search class: FGUSS-FFMF21-MFFFFFNN
% 0.10/0.42 % partial match(1): FGUSM-FFMF21-MFFFFFNN
% 0.10/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.42 % SubtermCWHack with pid 114869 completed with status 0
% 0.10/0.42 % Result found by SubtermCWHack
% 0.10/0.42 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.10/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.42 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.10/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.42 % Search class: FGUSS-FFMF21-MFFFFFNN
% 0.10/0.42 % partial match(1): FGUSM-FFMF21-MFFFFFNN
% 0.10/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.42 % Preprocessing time : 0.002 s
% 0.10/0.42
% 0.10/0.42 % Proof found!
% 0.10/0.42 % SZS status Theorem
% 0.10/0.42 % SZS output start CNFRefutation
% See solution above
% 0.10/0.42 % Parsed axioms : 185
% 0.10/0.42 % Removed by relevancy pruning/SinE : 170
% 0.10/0.42 % Initial clauses : 211
% 0.10/0.42 % Removed in clause preprocessing : 181
% 0.10/0.42 % Initial clauses in saturation : 30
% 0.10/0.42 % Processed clauses : 37
% 0.10/0.42 % ...of these trivial : 0
% 0.10/0.42 % ...subsumed : 15
% 0.10/0.42 % ...remaining for further processing : 22
% 0.10/0.42 % Other redundant clauses eliminated : 3
% 0.10/0.42 % Clauses deleted for lack of memory : 0
% 0.10/0.42 % Backward-subsumed : 0
% 0.10/0.42 % Backward-rewritten : 1
% 0.10/0.42 % Generated clauses : 60
% 0.10/0.42 % ...of the previous two non-redundant : 23
% 0.10/0.42 % ...aggressively subsumed : 0
% 0.10/0.42 % Contextual simplify-reflections : 0
% 0.10/0.42 % Paramodulations : 55
% 0.10/0.42 % Factorizations : 2
% 0.10/0.42 % NegExts : 0
% 0.10/0.42 % Equation resolutions : 3
% 0.10/0.42 % Disequality decompositions : 0
% 0.10/0.42 % Total rewrite steps : 6
% 0.10/0.42 % ...of those cached : 3
% 0.10/0.42 % Propositional unsat checks : 0
% 0.10/0.42 % Propositional check models : 0
% 0.10/0.42 % Propositional check unsatisfiable : 0
% 0.10/0.42 % Propositional clauses : 0
% 0.10/0.42 % Propositional clauses after purity: 0
% 0.10/0.42 % Propositional unsat core size : 0
% 0.10/0.42 % Propositional preprocessing time : 0.000
% 0.10/0.42 % Propositional encoding time : 0.000
% 0.10/0.42 % Propositional solver time : 0.000
% 0.10/0.42 % Success case prop preproc time : 0.000
% 0.10/0.42 % Success case prop encoding time : 0.000
% 0.10/0.42 % Success case prop solver time : 0.000
% 0.10/0.42 % Current number of processed clauses : 18
% 0.10/0.42 % Positive orientable unit clauses : 3
% 0.10/0.42 % Positive unorientable unit clauses: 0
% 0.10/0.42 % Negative unit clauses : 0
% 0.10/0.42 % Non-unit-clauses : 15
% 0.10/0.42 % Current number of unprocessed clauses: 16
% 0.10/0.42 % ...number of literals in the above : 50
% 0.10/0.43 % Current number of archived formulas : 0
% 0.10/0.43 % Current number of archived clauses : 1
% 0.10/0.43 % Clause-clause subsumption calls (NU) : 101
% 0.10/0.43 % Rec. Clause-clause subsumption calls : 73
% 0.10/0.43 % Non-unit clause-clause subsumptions : 15
% 0.10/0.43 % Unit Clause-clause subsumption calls : 1
% 0.10/0.43 % Rewrite failures with RHS unbound : 0
% 0.10/0.43 % BW rewrite match attempts : 1
% 0.10/0.43 % BW rewrite match successes : 1
% 0.10/0.43 % Condensation attempts : 0
% 0.10/0.43 % Condensation successes : 0
% 0.10/0.43 % Termbank termtop insertions : 8339
% 0.10/0.43 % Search garbage collected termcells : 1828
% 0.10/0.43
% 0.10/0.43 % -------------------------------------------------
% 0.10/0.43 % User time : 0.009 s
% 0.10/0.43 % System time : 0.003 s
% 0.10/0.43 % Total time : 0.012 s
% 0.10/0.43 % Maximum resident set size: 4120 pages
% 0.10/0.43
% 0.10/0.43 % -------------------------------------------------
% 0.10/0.43 % User time : 0.013 s
% 0.10/0.43 % System time : 0.004 s
% 0.10/0.43 % Total time : 0.018 s
% 0.10/0.43 % Maximum resident set size: 5120 pages
% 0.10/0.43 % E exiting
%------------------------------------------------------------------------------