%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP023^2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 : Wed Sep 30 08:04:07 AM UTC 2026
% Result : Theorem 1.08s 0.47s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 504 ( 23 ~; 20 |; 1 &; 455 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 10 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 58 ( 0 ^; 58 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
del: $tType ).
thf(decl_sort2,type,
tp__ty_2Erealax_2Ereal: $tType ).
thf(decl_23,type,
bool: del ).
thf(decl_25,type,
arr: del > del > del ).
thf(decl_26,type,
mem: $i > del > $o ).
thf(decl_27,type,
ap: $i > $i > $i ).
thf(decl_29,type,
p: $i > $o ).
thf(decl_33,type,
ty_2Erealax_2Ereal: del ).
thf(decl_34,type,
inj__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal > $i ).
thf(decl_36,type,
ty_2Epair_2Eprod: del > del > del ).
thf(decl_39,type,
c_2Ereal__topology_2Eball: $i ).
thf(decl_40,type,
c_2Epred__set_2ESUBSET: del > $i ).
thf(decl_41,type,
c_2Epair_2E_2C: del > del > $i ).
thf(decl_42,type,
c_2Ereal__topology_2Ecball: $i ).
thf(decl_43,type,
c_2Ereal__topology_2Ebounded__def: $i ).
thf(decl_62,type,
esk7_0: tp__ty_2Erealax_2Ereal ).
thf(decl_63,type,
esk8_0: tp__ty_2Erealax_2Ereal ).
thf(conj_thm_2Ereal__topology_2EBOUNDED__SUBSET,axiom,
! [X40: $i] :
( ( mem @ X40 @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
=> ! [X41: $i] :
( ( mem @ X41 @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
=> ( ( ( p @ ( ap @ c_2Ereal__topology_2Ebounded__def @ X41 ) )
& ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ty_2Erealax_2Ereal ) @ X40 ) @ X41 ) ) )
=> ( p @ ( ap @ c_2Ereal__topology_2Ebounded__def @ X40 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btHW3NNXXJ/E---3.1_1076084.p',conj_thm_2Ereal__topology_2EBOUNDED__SUBSET) ).
thf(conj_thm_2Ereal__topology_2EBALL__SUBSET__CBALL,axiom,
! [X38: tp__ty_2Erealax_2Ereal,X39: tp__ty_2Erealax_2Ereal] : ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ty_2Erealax_2Ereal ) @ ( ap @ c_2Ereal__topology_2Eball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X38 ) ) @ ( inj__ty_2Erealax_2Ereal @ X39 ) ) ) ) @ ( ap @ c_2Ereal__topology_2Ecball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X38 ) ) @ ( inj__ty_2Erealax_2Ereal @ X39 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btHW3NNXXJ/E---3.1_1076084.p',conj_thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).
thf(conj_thm_2Ereal__topology_2EBOUNDED__CBALL,axiom,
! [X42: tp__ty_2Erealax_2Ereal,X39: tp__ty_2Erealax_2Ereal] : ( p @ ( ap @ c_2Ereal__topology_2Ebounded__def @ ( ap @ c_2Ereal__topology_2Ecball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X42 ) ) @ ( inj__ty_2Erealax_2Ereal @ X39 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btHW3NNXXJ/E---3.1_1076084.p',conj_thm_2Ereal__topology_2EBOUNDED__CBALL) ).
thf(ap_tp,axiom,
! [X3: del,X4: del,X5: $i] :
( ( mem @ X5 @ ( arr @ X3 @ X4 ) )
=> ! [X6: $i] :
( ( mem @ X6 @ X3 )
=> ( mem @ ( ap @ X5 @ X6 ) @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btHW3NNXXJ/E---3.1_1076084.p',ap_tp) ).
thf(mem_c_2Epair_2E_2C,axiom,
! [X13: del,X22: del] : ( mem @ ( c_2Epair_2E_2C @ X13 @ X22 ) @ ( arr @ X13 @ ( arr @ X22 @ ( ty_2Epair_2Eprod @ X13 @ X22 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btHW3NNXXJ/E---3.1_1076084.p',mem_c_2Epair_2E_2C) ).
thf(mem_c_2Ereal__topology_2Ecball,axiom,
mem @ c_2Ereal__topology_2Ecball @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( arr @ ty_2Erealax_2Ereal @ bool ) ),
file('/export/starexec/sandbox2/tmp/tmp.btHW3NNXXJ/E---3.1_1076084.p',mem_c_2Ereal__topology_2Ecball) ).
thf(mem_c_2Ereal__topology_2Eball,axiom,
mem @ c_2Ereal__topology_2Eball @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( arr @ ty_2Erealax_2Ereal @ bool ) ),
file('/export/starexec/sandbox2/tmp/tmp.btHW3NNXXJ/E---3.1_1076084.p',mem_c_2Ereal__topology_2Eball) ).
thf(conj_thm_2Ereal__topology_2EBOUNDED__BALL,conjecture,
! [X46: tp__ty_2Erealax_2Ereal,X39: tp__ty_2Erealax_2Ereal] : ( p @ ( ap @ c_2Ereal__topology_2Ebounded__def @ ( ap @ c_2Ereal__topology_2Eball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X46 ) ) @ ( inj__ty_2Erealax_2Ereal @ X39 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btHW3NNXXJ/E---3.1_1076084.p',conj_thm_2Ereal__topology_2EBOUNDED__BALL) ).
thf(stp_inj_mem_ty_2Erealax_2Ereal,axiom,
! [X17: tp__ty_2Erealax_2Ereal] : ( mem @ ( inj__ty_2Erealax_2Ereal @ X17 ) @ ty_2Erealax_2Ereal ),
file('/export/starexec/sandbox2/tmp/tmp.btHW3NNXXJ/E---3.1_1076084.p',stp_inj_mem_ty_2Erealax_2Ereal) ).
thf(c_0_9,plain,
! [X214: $i,X215: $i] :
( ~ ( mem @ X214 @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
| ~ ( mem @ X215 @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
| ~ ( p @ ( ap @ c_2Ereal__topology_2Ebounded__def @ X215 ) )
| ~ ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ty_2Erealax_2Ereal ) @ X214 ) @ X215 ) )
| ( p @ ( ap @ c_2Ereal__topology_2Ebounded__def @ X214 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Ereal__topology_2EBOUNDED__SUBSET])])])]) ).
thf(c_0_10,plain,
! [X212: tp__ty_2Erealax_2Ereal,X213: tp__ty_2Erealax_2Ereal] : ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ty_2Erealax_2Ereal ) @ ( ap @ c_2Ereal__topology_2Eball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X212 ) ) @ ( inj__ty_2Erealax_2Ereal @ X213 ) ) ) ) @ ( ap @ c_2Ereal__topology_2Ecball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X212 ) ) @ ( inj__ty_2Erealax_2Ereal @ X213 ) ) ) ) ),
inference(variable_rename,[status(thm)],[conj_thm_2Ereal__topology_2EBALL__SUBSET__CBALL]) ).
thf(c_0_11,plain,
! [X216: tp__ty_2Erealax_2Ereal,X217: tp__ty_2Erealax_2Ereal] : ( p @ ( ap @ c_2Ereal__topology_2Ebounded__def @ ( ap @ c_2Ereal__topology_2Ecball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X216 ) ) @ ( inj__ty_2Erealax_2Ereal @ X217 ) ) ) ) ),
inference(variable_rename,[status(thm)],[conj_thm_2Ereal__topology_2EBOUNDED__CBALL]) ).
thf(c_0_12,plain,
! [X147: del,X148: del,X149: $i,X150: $i] :
( ~ ( mem @ X149 @ ( arr @ X147 @ X148 ) )
| ~ ( mem @ X150 @ X147 )
| ( mem @ ( ap @ X149 @ X150 ) @ X148 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])])]) ).
thf(c_0_13,plain,
! [X175: del,X176: del] : ( mem @ ( c_2Epair_2E_2C @ X175 @ X176 ) @ ( arr @ X175 @ ( arr @ X176 @ ( ty_2Epair_2Eprod @ X175 @ X176 ) ) ) ),
inference(variable_rename,[status(thm)],[mem_c_2Epair_2E_2C]) ).
thf(c_0_14,plain,
! [X2: $i,X5: $i] :
( ( p @ ( ap @ c_2Ereal__topology_2Ebounded__def @ X2 ) )
| ~ ( mem @ X2 @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
| ~ ( mem @ X5 @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
| ~ ( p @ ( ap @ c_2Ereal__topology_2Ebounded__def @ X5 ) )
| ~ ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ty_2Erealax_2Ereal ) @ X2 ) @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_15,plain,
! [X16: tp__ty_2Erealax_2Ereal,X17: tp__ty_2Erealax_2Ereal] : ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ty_2Erealax_2Ereal ) @ ( ap @ c_2Ereal__topology_2Eball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X16 ) ) @ ( inj__ty_2Erealax_2Ereal @ X17 ) ) ) ) @ ( ap @ c_2Ereal__topology_2Ecball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X16 ) ) @ ( inj__ty_2Erealax_2Ereal @ X17 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,plain,
! [X16: tp__ty_2Erealax_2Ereal,X17: tp__ty_2Erealax_2Ereal] : ( p @ ( ap @ c_2Ereal__topology_2Ebounded__def @ ( ap @ c_2Ereal__topology_2Ecball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X16 ) ) @ ( inj__ty_2Erealax_2Ereal @ X17 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_17,plain,
! [X2: $i,X5: $i,X4: del,X3: del] :
( ( mem @ ( ap @ X2 @ X5 ) @ X4 )
| ~ ( mem @ X2 @ ( arr @ X3 @ X4 ) )
| ~ ( mem @ X5 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,plain,
mem @ c_2Ereal__topology_2Ecball @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( arr @ ty_2Erealax_2Ereal @ bool ) ),
inference(split_conjunct,[status(thm)],[mem_c_2Ereal__topology_2Ecball]) ).
thf(c_0_19,plain,
mem @ c_2Ereal__topology_2Eball @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( arr @ ty_2Erealax_2Ereal @ bool ) ),
inference(split_conjunct,[status(thm)],[mem_c_2Ereal__topology_2Eball]) ).
thf(c_0_20,plain,
! [X3: del,X4: del] : ( mem @ ( c_2Epair_2E_2C @ X3 @ X4 ) @ ( arr @ X3 @ ( arr @ X4 @ ( ty_2Epair_2Eprod @ X3 @ X4 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_21,negated_conjecture,
~ ! [X46: tp__ty_2Erealax_2Ereal,X39: tp__ty_2Erealax_2Ereal] : ( p @ ( ap @ c_2Ereal__topology_2Ebounded__def @ ( ap @ c_2Ereal__topology_2Eball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X46 ) ) @ ( inj__ty_2Erealax_2Ereal @ X39 ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Ereal__topology_2EBOUNDED__BALL]) ).
thf(c_0_22,plain,
! [X16: tp__ty_2Erealax_2Ereal,X17: tp__ty_2Erealax_2Ereal] :
( ( p @ ( ap @ c_2Ereal__topology_2Ebounded__def @ ( ap @ c_2Ereal__topology_2Eball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X16 ) ) @ ( inj__ty_2Erealax_2Ereal @ X17 ) ) ) ) )
| ~ ( mem @ ( ap @ c_2Ereal__topology_2Ecball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X16 ) ) @ ( inj__ty_2Erealax_2Ereal @ X17 ) ) ) @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
| ~ ( mem @ ( ap @ c_2Ereal__topology_2Eball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X16 ) ) @ ( inj__ty_2Erealax_2Ereal @ X17 ) ) ) @ ( arr @ ty_2Erealax_2Ereal @ bool ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
thf(c_0_23,plain,
! [X2: $i] :
( ( mem @ ( ap @ c_2Ereal__topology_2Ecball @ X2 ) @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
| ~ ( mem @ X2 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_24,plain,
! [X2: $i] :
( ( mem @ ( ap @ c_2Ereal__topology_2Eball @ X2 ) @ ( arr @ ty_2Erealax_2Ereal @ bool ) )
| ~ ( mem @ X2 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ) ),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
thf(c_0_25,plain,
! [X2: $i,X4: del,X3: del] :
( ( mem @ ( ap @ ( c_2Epair_2E_2C @ X3 @ X4 ) @ X2 ) @ ( arr @ X4 @ ( ty_2Epair_2Eprod @ X3 @ X4 ) ) )
| ~ ( mem @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
thf(c_0_26,plain,
! [X169: tp__ty_2Erealax_2Ereal] : ( mem @ ( inj__ty_2Erealax_2Ereal @ X169 ) @ ty_2Erealax_2Ereal ),
inference(variable_rename,[status(thm)],[stp_inj_mem_ty_2Erealax_2Ereal]) ).
thf(c_0_27,negated_conjecture,
~ ( p @ ( ap @ c_2Ereal__topology_2Ebounded__def @ ( ap @ c_2Ereal__topology_2Eball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ esk7_0 ) ) @ ( inj__ty_2Erealax_2Ereal @ esk8_0 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
thf(c_0_28,plain,
! [X16: tp__ty_2Erealax_2Ereal,X17: tp__ty_2Erealax_2Ereal] :
( ( p @ ( ap @ c_2Ereal__topology_2Ebounded__def @ ( ap @ c_2Ereal__topology_2Eball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X16 ) ) @ ( inj__ty_2Erealax_2Ereal @ X17 ) ) ) ) )
| ~ ( mem @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X16 ) ) @ ( inj__ty_2Erealax_2Ereal @ X17 ) ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
thf(c_0_29,plain,
! [X2: $i,X5: $i,X4: del,X3: del] :
( ( mem @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ X3 @ X4 ) @ X2 ) @ X5 ) @ ( ty_2Epair_2Eprod @ X3 @ X4 ) )
| ~ ( mem @ X5 @ X4 )
| ~ ( mem @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
thf(c_0_30,plain,
! [X16: tp__ty_2Erealax_2Ereal] : ( mem @ ( inj__ty_2Erealax_2Ereal @ X16 ) @ ty_2Erealax_2Ereal ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_31,negated_conjecture,
~ ( p @ ( ap @ c_2Ereal__topology_2Ebounded__def @ ( ap @ c_2Ereal__topology_2Eball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ esk7_0 ) ) @ ( inj__ty_2Erealax_2Ereal @ esk8_0 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_32,plain,
! [X16: tp__ty_2Erealax_2Ereal,X17: tp__ty_2Erealax_2Ereal] : ( p @ ( ap @ c_2Ereal__topology_2Ebounded__def @ ( ap @ c_2Ereal__topology_2Eball @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( inj__ty_2Erealax_2Ereal @ X16 ) ) @ ( inj__ty_2Erealax_2Ereal @ X17 ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_30])]) ).
thf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP023^2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n026.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 19:38:12 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.24 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.btHW3NNXXJ/E---3.1_1076084.p
% 1.08/0.47 % Version: 3.5.1-ho
% 1.08/0.47 % Preprocessing class: HSLSSMSMSSSNSFA.
% 1.08/0.47 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 1.08/0.47 % Starting new_ho_10 with 900s (3) cores
% 1.08/0.47 % Starting sh2lt with 300s (1) cores
% 1.08/0.47 % Starting new_ho_5 with 300s (1) cores
% 1.08/0.47 % Starting full_lambda_5 with 300s (1) cores
% 1.08/0.47 % Starting sh9 with 300s (1) cores
% 1.08/0.47 % Starting ehoh_best8_lambda with 300s (1) cores
% 1.08/0.47 % new_ho_10 with pid 1076097 completed with status 0
% 1.08/0.47 % Result found by new_ho_10
% 1.08/0.47 % Preprocessing class: HSLSSMSMSSSNSFA.
% 1.08/0.47 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 1.08/0.47 % Starting new_ho_10 with 900s (3) cores
% 1.08/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.08/0.47 % No SInE strategy applied
% 1.08/0.47 % Search class: HGHSM-FFMM31-DSFFFFBN
% 1.08/0.47 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 1.08/0.47 % Starting SubtermCWHack with 82s (1) cores
% 1.08/0.47 % Starting new_ho_10 with 91s (1) cores
% 1.08/0.47 % Starting pre_casc_8 with 82s (1) cores
% 1.08/0.47 % new_ho_10 with pid 1076106 completed with status 0
% 1.08/0.47 % Result found by new_ho_10
% 1.08/0.47 % Preprocessing class: HSLSSMSMSSSNSFA.
% 1.08/0.47 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 1.08/0.47 % Starting new_ho_10 with 900s (3) cores
% 1.08/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.08/0.47 % No SInE strategy applied
% 1.08/0.47 % Search class: HGHSM-FFMM31-DSFFFFBN
% 1.08/0.47 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 1.08/0.47 % Starting SubtermCWHack with 82s (1) cores
% 1.08/0.47 % Starting new_ho_10 with 91s (1) cores
% 1.08/0.47 % Preprocessing time : 0.003 s
% 1.08/0.47 % Presaturation interreduction done
% 1.08/0.47
% 1.08/0.47 % Proof found!
% 1.08/0.47 % SZS status Theorem
% 1.08/0.47 % SZS output start CNFRefutation
% See solution above
% 1.08/0.47 % Parsed axioms : 93
% 1.08/0.47 % Removed by relevancy pruning/SinE : 0
% 1.08/0.47 % Initial clauses : 371
% 1.08/0.47 % Removed in clause preprocessing : 282
% 1.08/0.47 % Initial clauses in saturation : 89
% 1.08/0.47 % Processed clauses : 574
% 1.08/0.47 % ...of these trivial : 7
% 1.08/0.47 % ...subsumed : 109
% 1.08/0.47 % ...remaining for further processing : 458
% 1.08/0.47 % Other redundant clauses eliminated : 1
% 1.08/0.47 % Clauses deleted for lack of memory : 0
% 1.08/0.47 % Backward-subsumed : 9
% 1.08/0.47 % Backward-rewritten : 32
% 1.08/0.47 % Generated clauses : 2752
% 1.08/0.47 % ...of the previous two non-redundant : 2528
% 1.08/0.47 % ...aggressively subsumed : 0
% 1.08/0.47 % Contextual simplify-reflections : 10
% 1.08/0.47 % Paramodulations : 2741
% 1.08/0.47 % Factorizations : 9
% 1.08/0.47 % NegExts : 0
% 1.08/0.47 % Equation resolutions : 2
% 1.08/0.47 % Disequality decompositions : 0
% 1.08/0.47 % Total rewrite steps : 731
% 1.08/0.47 % ...of those cached : 703
% 1.08/0.47 % Propositional unsat checks : 0
% 1.08/0.47 % Propositional check models : 0
% 1.08/0.47 % Propositional check unsatisfiable : 0
% 1.08/0.47 % Propositional clauses : 0
% 1.08/0.47 % Propositional clauses after purity: 0
% 1.08/0.47 % Propositional unsat core size : 0
% 1.08/0.47 % Propositional preprocessing time : 0.000
% 1.08/0.47 % Propositional encoding time : 0.000
% 1.08/0.47 % Propositional solver time : 0.000
% 1.08/0.47 % Success case prop preproc time : 0.000
% 1.08/0.47 % Success case prop encoding time : 0.000
% 1.08/0.47 % Success case prop solver time : 0.000
% 1.08/0.47 % Current number of processed clauses : 345
% 1.08/0.47 % Positive orientable unit clauses : 37
% 1.08/0.47 % Positive unorientable unit clauses: 0
% 1.08/0.47 % Negative unit clauses : 2
% 1.08/0.47 % Non-unit-clauses : 306
% 1.08/0.47 % Current number of unprocessed clauses: 2043
% 1.08/0.47 % ...number of literals in the above : 9834
% 1.08/0.47 % Current number of archived formulas : 0
% 1.08/0.47 % Current number of archived clauses : 112
% 1.08/0.47 % Clause-clause subsumption calls (NU) : 16865
% 1.08/0.47 % Rec. Clause-clause subsumption calls : 5560
% 1.08/0.47 % Non-unit clause-clause subsumptions : 73
% 1.08/0.47 % Unit Clause-clause subsumption calls : 649
% 1.08/0.47 % Rewrite failures with RHS unbound : 0
% 1.08/0.47 % BW rewrite match attempts : 34
% 1.08/0.47 % BW rewrite match successes : 18
% 1.08/0.47 % Condensation attempts : 574
% 1.08/0.47 % Condensation successes : 0
% 1.08/0.47 % Termbank termtop insertions : 102650
% 1.08/0.47 % Search garbage collected termcells : 4327
% 1.08/0.47
% 1.08/0.47 % -------------------------------------------------
% 1.08/0.47 % User time : 0.155 s
% 1.08/0.47 % System time : 0.007 s
% 1.08/0.47 % Total time : 0.162 s
% 1.08/0.47 % Maximum resident set size: 4532 pages
% 1.08/0.47
% 1.08/0.47 % -------------------------------------------------
% 1.08/0.47 % User time : 0.471 s
% 1.08/0.47 % System time : 0.030 s
% 1.08/0.47 % Total time : 0.501 s
% 1.08/0.47 % Maximum resident set size: 4608 pages
% 1.08/0.47 % E exiting
%------------------------------------------------------------------------------