%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP023_4 : 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 12:53:53 PM UTC 2026
% Result : Theorem 0.19s 33.31s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 40 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 71 ( 22 ~; 19 |; 24 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 55 !; 0 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
mono_2Etyop_2Emin_2Ebool: $tType ).
tff(decl_sort2,type,
mono_2Etyop_2Enum_2Enum: $tType ).
tff(decl_sort3,type,
mono_2Etyop_2Erealax_2Ereal: $tType ).
tff(decl_sort4,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: $tType ).
tff(decl_sort5,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
tff(decl_27,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
tff(decl_53,type,
mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(decl_54,type,
mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(decl_229,type,
mono_2Ec_2Enum_2E0_2E0: mono_2Etyop_2Enum_2Enum ).
tff(decl_237,type,
mono_2Ec_2Enum_2ESUC_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
tff(decl_554,type,
mono_2Ec_2Eprim__rec_2E_3C_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).
tff(decl_686,type,
mono_2Ec_2Earithmetic_2E_3C_3D_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).
tff(decl_694,type,
mono_2Ec_2Earithmetic_2EBIT1_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
tff(decl_696,type,
mono_2Ec_2Earithmetic_2EBIT2_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
tff(decl_747,type,
mono_2Ec_2Earithmetic_2EZERO_2E0: mono_2Etyop_2Enum_2Enum ).
tff(decl_9625,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_15448,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_15454,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_15456,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_15491,type,
mono_2Ec_2Ereal__topology_2Einterior_2E1: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ).
tff(decl_15667,type,
esk1_0: mono_2Etyop_2Erealax_2Ereal ).
tff(decl_15668,type,
esk2_0: mono_2Etyop_2Erealax_2Ereal ).
tff(thm_2Enumeral_2Enumeral__lte,axiom,
! [X614: mono_2Etyop_2Enum_2Enum,X2669: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT2_2E1(X614),mono_2Ec_2Earithmetic_2EBIT2_2E1(X2669)) = mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X614,X2669) )
& ( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT2_2E1(X614),mono_2Ec_2Earithmetic_2EBIT1_2E1(X2669)))
<=> ~ p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X2669,X614)) )
& ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT1_2E1(X614),mono_2Ec_2Earithmetic_2EBIT2_2E1(X2669)) = mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X614,X2669) )
& ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT1_2E1(X614),mono_2Ec_2Earithmetic_2EBIT1_2E1(X2669)) = mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X614,X2669) )
& ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT2_2E1(X614),mono_2Ec_2Earithmetic_2EZERO_2E0) = mono_2Ec_2Ebool_2EF_2E0 )
& ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT1_2E1(X614),mono_2Ec_2Earithmetic_2EZERO_2E0) = mono_2Ec_2Ebool_2EF_2E0 )
& ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EZERO_2E0,X614) = mono_2Ec_2Ebool_2ET_2E0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP018_4.ax',thm_2Enumeral_2Enumeral__lte) ).
tff(thm_2Earithmetic_2EZERO__LESS__EQ,axiom,
! [X614: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Enum_2E0_2E0,X614)),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP016_4.ax',thm_2Earithmetic_2EZERO__LESS__EQ) ).
tff(thm_2Earithmetic_2EALT__ZERO,axiom,
mono_2Ec_2Earithmetic_2EZERO_2E0 = mono_2Ec_2Enum_2E0_2E0,
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP016_4.ax',thm_2Earithmetic_2EALT__ZERO) ).
tff(thm_2Eprim__rec_2ENOT__LESS__0,axiom,
! [X614: mono_2Etyop_2Enum_2Enum] : ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X614,mono_2Ec_2Enum_2E0_2E0)),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP015_4.ax',thm_2Eprim__rec_2ENOT__LESS__0) ).
tff(reserved_2Eho_2Eboolext,axiom,
! [X6: mono_2Etyop_2Emin_2Ebool,X7: mono_2Etyop_2Emin_2Ebool] :
( ( p(X6)
<=> p(X7) )
=> ( X6 = X7 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP002_4.ax',reserved_2Eho_2Eboolext) ).
tff(thm_2Ecardinal_2ELT,axiom,
( ! [X29392: mono_2Etyop_2Enum_2Enum,X29393: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X29392,mono_2Ec_2Enum_2ESUC_2E1(X29393)))
<=> ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X29392,X29393))
| ( X29392 = X29393 ) ) )
& ! [X29391: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C_2E2(X29391,mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Ebool_2EF_2E0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP063_4.ax',thm_2Ecardinal_2ELT) ).
tff(thm_2Ereal__topology_2EBOUNDED__CBALL,axiom,
! [X72299: mono_2Etyop_2Erealax_2Ereal,X72300: 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(X72299,X72300)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CBALL) ).
tff(thm_2Ereal__topology_2EBOUNDED__BALL,conjecture,
! [X73613: mono_2Etyop_2Erealax_2Ereal,X73614: 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(X73613,X73614)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__BALL) ).
tff(thm_2Ereal__topology_2EBOUNDED__INTERIOR,axiom,
! [X72296: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
( p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X72296))
=> p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Einterior_2E1(X72296))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__INTERIOR) ).
tff(thm_2Ereal__topology_2EINTERIOR__CBALL,axiom,
! [X72260: mono_2Etyop_2Erealax_2Ereal,X72261: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Einterior_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X72260,X72261))) = mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X72260,X72261)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__CBALL) ).
tff(c_0_10,plain,
! [X614: mono_2Etyop_2Enum_2Enum,X2669: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT2_2E1(X614),mono_2Ec_2Earithmetic_2EBIT2_2E1(X2669)) = mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X614,X2669) )
& ( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT2_2E1(X614),mono_2Ec_2Earithmetic_2EBIT1_2E1(X2669)))
<=> ~ p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X2669,X614)) )
& ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT1_2E1(X614),mono_2Ec_2Earithmetic_2EBIT2_2E1(X2669)) = mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X614,X2669) )
& ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT1_2E1(X614),mono_2Ec_2Earithmetic_2EBIT1_2E1(X2669)) = mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X614,X2669) )
& ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT2_2E1(X614),mono_2Ec_2Earithmetic_2EZERO_2E0) = mono_2Ec_2Ebool_2EF_2E0 )
& ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT1_2E1(X614),mono_2Ec_2Earithmetic_2EZERO_2E0) = mono_2Ec_2Ebool_2EF_2E0 )
& ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EZERO_2E0,X614) = mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(fof_simplification,[status(thm)],[thm_2Enumeral_2Enumeral__lte]) ).
tff(c_0_11,plain,
! [X76908: mono_2Etyop_2Enum_2Enum,X76909: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT2_2E1(X76908),mono_2Ec_2Earithmetic_2EBIT2_2E1(X76909)) = mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X76908,X76909) )
& ( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT2_2E1(X76908),mono_2Ec_2Earithmetic_2EBIT1_2E1(X76909)))
| p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X76909,X76908)) )
& ( ~ p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X76909,X76908))
| ~ p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT2_2E1(X76908),mono_2Ec_2Earithmetic_2EBIT1_2E1(X76909))) )
& ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT1_2E1(X76908),mono_2Ec_2Earithmetic_2EBIT2_2E1(X76909)) = mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X76908,X76909) )
& ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT1_2E1(X76908),mono_2Ec_2Earithmetic_2EBIT1_2E1(X76909)) = mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X76908,X76909) )
& ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT2_2E1(X76908),mono_2Ec_2Earithmetic_2EZERO_2E0) = mono_2Ec_2Ebool_2EF_2E0 )
& ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT1_2E1(X76908),mono_2Ec_2Earithmetic_2EZERO_2E0) = mono_2Ec_2Ebool_2EF_2E0 )
& ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EZERO_2E0,X76908) = mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
tff(c_0_12,plain,
! [X76783: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Enum_2E0_2E0,X76783)),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EZERO__LESS__EQ]) ).
tcf(c_0_13,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EZERO_2E0,X567) = mono_2Ec_2Ebool_2ET_2E0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tcf(c_0_14,plain,
mono_2Ec_2Earithmetic_2EZERO_2E0 = mono_2Ec_2Enum_2E0_2E0,
inference(split_conjunct,[status(thm)],[thm_2Earithmetic_2EALT__ZERO]) ).
tff(c_0_15,plain,
! [X614: mono_2Etyop_2Enum_2Enum] : ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X614,mono_2Ec_2Enum_2E0_2E0)),
inference(fof_simplification,[status(thm)],[thm_2Eprim__rec_2ENOT__LESS__0]) ).
tff(c_0_16,plain,
! [X73617: mono_2Etyop_2Emin_2Ebool,X73618: mono_2Etyop_2Emin_2Ebool] :
( ( ( X73617 = X73618 )
| p(X73618)
| p(X73617) )
& ( ( X73617 = X73618 )
| ~ p(X73618)
| ~ p(X73617) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[reserved_2Eho_2Eboolext])])])]) ).
tcf(c_0_17,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Enum_2E0_2E0,X567)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_18,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Enum_2E0_2E0,X567) = mono_2Ec_2Ebool_2ET_2E0,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
tff(c_0_19,plain,
! [X77525: mono_2Etyop_2Enum_2Enum] : ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X77525,mono_2Ec_2Enum_2E0_2E0)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_15])]) ).
tff(c_0_20,plain,
! [X77147: mono_2Etyop_2Enum_2Enum,X77148: mono_2Etyop_2Enum_2Enum,X77149: mono_2Etyop_2Enum_2Enum] :
( ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X77148,mono_2Ec_2Enum_2ESUC_2E1(X77149)))
| ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X77148,X77149)) )
& ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X77148,mono_2Ec_2Enum_2ESUC_2E1(X77149)))
| ( X77148 != X77149 ) )
& ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X77148,X77149))
| ( X77148 = X77149 )
| ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X77148,mono_2Ec_2Enum_2ESUC_2E1(X77149))) )
& ( mono_2Ec_2Eprim__rec_2E_3C_2E2(X77147,mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Ebool_2EF_2E0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Ecardinal_2ELT])])])])]) ).
tcf(c_0_21,plain,
! [X6: mono_2Etyop_2Emin_2Ebool,X7: mono_2Etyop_2Emin_2Ebool] :
( ~ p(X7)
| ~ p(X6)
| ( X6 = X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
tcf(c_0_22,plain,
p(mono_2Ec_2Ebool_2ET_2E0),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
tff(c_0_23,plain,
! [X74754: mono_2Etyop_2Erealax_2Ereal,X74755: 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(X74754,X74755)))),
inference(variable_rename,[status(thm)],[thm_2Ereal__topology_2EBOUNDED__CBALL]) ).
tff(c_0_24,negated_conjecture,
~ ! [X73613: mono_2Etyop_2Erealax_2Ereal,X73614: 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(X73613,X73614)))),
inference(assume_negation,[status(cth)],[thm_2Ereal__topology_2EBOUNDED__BALL]) ).
tcf(c_0_25,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X567,mono_2Ec_2Enum_2E0_2E0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
tcf(c_0_26,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Eprim__rec_2E_3C_2E2(X567,mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Ebool_2EF_2E0,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
tff(c_0_27,plain,
! [X74751: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
( p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Einterior_2E1(X74751)))
| ~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X74751)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Ereal__topology_2EBOUNDED__INTERIOR])])]) ).
tff(c_0_28,plain,
! [X74787: mono_2Etyop_2Erealax_2Ereal,X74788: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Einterior_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X74787,X74788))) = mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X74787,X74788)) ),
inference(variable_rename,[status(thm)],[thm_2Ereal__topology_2EINTERIOR__CBALL]) ).
tcf(c_0_29,plain,
! [X6: mono_2Etyop_2Emin_2Ebool] :
( ~ p(X6)
| ( X6 = mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
tcf(c_0_30,plain,
! [X45832: mono_2Etyop_2Erealax_2Ereal,X45856: 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(X45832,X45856)))),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
tff(c_0_31,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_24])])])]) ).
tcf(c_0_32,plain,
~ p(mono_2Ec_2Ebool_2EF_2E0),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
tcf(c_0_33,plain,
! [X6: mono_2Etyop_2Emin_2Ebool,X7: mono_2Etyop_2Emin_2Ebool] :
( ( X6 = X7 )
| p(X7)
| p(X6) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
tcf(c_0_34,plain,
! [X45823: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
( ~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X45823))
| p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Einterior_2E1(X45823))) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
tcf(c_0_35,plain,
! [X45832: mono_2Etyop_2Erealax_2Ereal,X45856: mono_2Etyop_2Erealax_2Ereal] : mono_2Ec_2Ereal__topology_2Einterior_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X45832,X45856))) = mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X45832,X45856)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
tcf(c_0_36,plain,
! [X45832: mono_2Etyop_2Erealax_2Ereal,X45856: mono_2Etyop_2Erealax_2Ereal] : 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(X45832,X45856))) = mono_2Ec_2Ebool_2ET_2E0,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
tcf(c_0_37,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_31]) ).
tcf(c_0_38,plain,
! [X6: mono_2Etyop_2Emin_2Ebool] :
( p(X6)
| ( X6 = mono_2Ec_2Ebool_2EF_2E0 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
tcf(c_0_39,plain,
! [X45832: mono_2Etyop_2Erealax_2Ereal,X45856: 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(X45832,X45856)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_22])]) ).
tcf(c_0_40,negated_conjecture,
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))) = mono_2Ec_2Ebool_2EF_2E0,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP023_4 : 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 21:54:48 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.19/33.31 % Version: 3.5.1
% 0.19/33.31 % Preprocessing class: FMLLSMLLSSSNFFN.
% 0.19/33.31 % Scheduled 4 strats onto 8 cores with 275 seconds (2200 total)
% 0.19/33.31 % Starting new_bool_3 with 825s (3) cores
% 0.19/33.31 % Starting new_bool_1 with 825s (3) cores
% 0.19/33.31 % Starting sh5l with 275s (1) cores
% 0.19/33.31 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 275s (1) cores
% 0.19/33.31 % new_bool_1 with pid 117417 completed with status 0
% 0.19/33.31 % Result found by new_bool_1
% 0.19/33.31 % Preprocessing class: FMLLSMLLSSSNFFN.
% 0.19/33.31 % Scheduled 4 strats onto 8 cores with 275 seconds (2200 total)
% 0.19/33.31 % Starting new_bool_3 with 825s (3) cores
% 0.19/33.31 % Starting new_bool_1 with 825s (3) cores
% 0.19/33.31 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/33.31 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/33.31 % Search class: FGHSM-SMLM32-DFFFFFNN
% 0.19/33.31 % Scheduled 13 strats onto 3 cores with 821 seconds (821 total)
% 0.19/33.31 % Starting SubtermCWHack with 74s (1) cores
% 0.19/33.31 % Starting new_bool_1 with 83s (1) cores
% 0.19/33.31 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 62s (1) cores
% 0.19/33.31 % SubtermCWHack with pid 117424 completed with status 0
% 0.19/33.31 % Result found by SubtermCWHack
% 0.19/33.31 % Preprocessing class: FMLLSMLLSSSNFFN.
% 0.19/33.31 % Scheduled 4 strats onto 8 cores with 275 seconds (2200 total)
% 0.19/33.31 % Starting new_bool_3 with 825s (3) cores
% 0.19/33.31 % Starting new_bool_1 with 825s (3) cores
% 0.19/33.31 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/33.31 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/33.31 % Search class: FGHSM-SMLM32-DFFFFFNN
% 0.19/33.31 % Scheduled 13 strats onto 3 cores with 821 seconds (821 total)
% 0.19/33.31 % Starting SubtermCWHack with 74s (1) cores
% 0.19/33.31 % Preprocessing time : 0.253 s
% 0.19/33.31
% 0.19/33.31 % Proof found!
% 0.19/33.31 % SZS status Theorem
% 0.19/33.31 % SZS output start CNFRefutation
% See solution above
% 0.19/33.31 % Parsed axioms : 90685
% 0.19/33.31 % Removed by relevancy pruning/SinE : 88466
% 0.19/33.31 % Initial clauses : 4638
% 0.19/33.31 % Removed in clause preprocessing : 893
% 0.19/33.31 % Initial clauses in saturation : 3745
% 0.19/33.31 % Processed clauses : 4379
% 0.19/33.31 % ...of these trivial : 436
% 0.19/33.31 % ...subsumed : 2562
% 0.19/33.31 % ...remaining for further processing : 1381
% 0.19/33.31 % Other redundant clauses eliminated : 249
% 0.19/33.31 % Clauses deleted for lack of memory : 0
% 0.19/33.31 % Backward-subsumed : 54
% 0.19/33.31 % Backward-rewritten : 288
% 0.19/33.31 % Generated clauses : 17186
% 0.19/33.31 % ...of the previous two non-redundant : 12253
% 0.19/33.31 % ...aggressively subsumed : 0
% 0.19/33.31 % Contextual simplify-reflections : 0
% 0.19/33.31 % Paramodulations : 16888
% 0.19/33.31 % Factorizations : 42
% 0.19/33.31 % NegExts : 0
% 0.19/33.31 % Equation resolutions : 260
% 0.19/33.31 % Disequality decompositions : 0
% 0.19/33.31 % Total rewrite steps : 11810
% 0.19/33.31 % ...of those cached : 10232
% 0.19/33.31 % Propositional unsat checks : 0
% 0.19/33.31 % Propositional check models : 0
% 0.19/33.31 % Propositional check unsatisfiable : 0
% 0.19/33.31 % Propositional clauses : 0
% 0.19/33.31 % Propositional clauses after purity: 0
% 0.19/33.31 % Propositional unsat core size : 0
% 0.19/33.31 % Propositional preprocessing time : 0.000
% 0.19/33.31 % Propositional encoding time : 0.000
% 0.19/33.31 % Propositional solver time : 0.000
% 0.19/33.31 % Success case prop preproc time : 0.000
% 0.19/33.31 % Success case prop encoding time : 0.000
% 0.19/33.31 % Success case prop solver time : 0.000
% 0.19/33.31 % Current number of processed clauses : 945
% 0.19/33.31 % Positive orientable unit clauses : 500
% 0.19/33.31 % Positive unorientable unit clauses: 14
% 0.19/33.31 % Negative unit clauses : 168
% 0.19/33.31 % Non-unit-clauses : 263
% 0.19/33.31 % Current number of unprocessed clauses: 11206
% 0.19/33.31 % ...number of literals in the above : 27887
% 0.19/33.31 % Current number of archived formulas : 0
% 0.19/33.31 % Current number of archived clauses : 342
% 0.19/33.31 % Clause-clause subsumption calls (NU) : 43388
% 0.19/33.31 % Rec. Clause-clause subsumption calls : 15534
% 0.19/33.31 % Non-unit clause-clause subsumptions : 1117
% 0.19/33.31 % Unit Clause-clause subsumption calls : 23147
% 0.19/33.31 % Rewrite failures with RHS unbound : 0
% 0.19/33.31 % BW rewrite match attempts : 1245
% 0.19/33.31 % BW rewrite match successes : 397
% 0.19/33.31 % Condensation attempts : 0
% 0.19/33.31 % Condensation successes : 0
% 0.19/33.31 % Termbank termtop insertions : 2258937
% 0.19/33.31 % Search garbage collected termcells : 666892
% 0.19/33.31
% 0.19/33.31 % -------------------------------------------------
% 0.19/33.31 % User time : 6.662 s
% 0.19/33.31 % System time : 0.413 s
% 0.19/33.31 % Total time : 7.075 s
% 0.19/33.31 % Maximum resident set size: 176232 pages
% 0.19/33.31
% 0.19/33.31 % -------------------------------------------------
% 0.19/33.31 % User time : 37.300 s
% 0.19/33.31 % System time : 1.199 s
% 0.19/33.31 % Total time : 38.500 s
% 0.19/33.31 % Maximum resident set size: 149276 pages
% 0.19/33.31 % E exiting
%------------------------------------------------------------------------------