TSTP Solution File: ITP023+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ITP023+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:11:06 EDT 2023
% Result : Theorem 8.24s 8.31s
% Output : CNFRefutation 8.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 47
% Syntax : Number of formulae : 86 ( 13 unt; 37 typ; 0 def)
% Number of atoms : 252 ( 0 equ)
% Maximal formula atoms : 120 ( 5 avg)
% Number of connectives : 309 ( 106 ~; 153 |; 34 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 23 >; 22 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 29 ( 29 usr; 14 con; 0-4 aty)
% Number of variables : 85 ( 8 sgn; 34 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
bool: $i ).
tff(decl_23,type,
ne: $i > $o ).
tff(decl_24,type,
ind: $i ).
tff(decl_25,type,
arr: ( $i * $i ) > $i ).
tff(decl_26,type,
mem: ( $i * $i ) > $o ).
tff(decl_27,type,
ap: ( $i * $i ) > $i ).
tff(decl_28,type,
p: $i > $o ).
tff(decl_29,type,
k: ( $i * $i ) > $i ).
tff(decl_30,type,
i: $i > $i ).
tff(decl_31,type,
c_2Ebool_2ET: $i ).
tff(decl_32,type,
c_2Ebool_2E_3F: $i > $i ).
tff(decl_33,type,
ty_2Erealax_2Ereal: $i ).
tff(decl_34,type,
ty_2Epair_2Eprod: ( $i * $i ) > $i ).
tff(decl_35,type,
c_2Ereal__topology_2Eball: $i ).
tff(decl_36,type,
c_2Epred__set_2ESUBSET: $i > $i ).
tff(decl_37,type,
c_2Epair_2E_2C: ( $i * $i ) > $i ).
tff(decl_38,type,
c_2Ereal__topology_2Ecball: $i ).
tff(decl_39,type,
c_2Ereal__topology_2Ebounded__def: $i ).
tff(decl_40,type,
c_2Ebool_2EF: $i ).
tff(decl_41,type,
c_2Emin_2E_3D_3D_3E: $i ).
tff(decl_42,type,
c_2Ebool_2E_5C_2F: $i ).
tff(decl_43,type,
c_2Ebool_2E_2F_5C: $i ).
tff(decl_44,type,
c_2Ebool_2E_7E: $i ).
tff(decl_45,type,
c_2Emin_2E_3D: $i > $i ).
tff(decl_46,type,
c_2Ebool_2E_21: $i > $i ).
tff(decl_47,type,
epred1_2: ( $i * $i ) > $o ).
tff(decl_48,type,
epred2_3: ( $i * $i * $i ) > $o ).
tff(decl_49,type,
epred3_3: ( $i * $i * $i ) > $o ).
tff(decl_50,type,
epred4_3: ( $i * $i * $i ) > $o ).
tff(decl_51,type,
epred5_3: ( $i * $i * $i ) > $o ).
tff(decl_52,type,
esk1_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_53,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_57,type,
esk6_0: $i ).
tff(decl_58,type,
esk7_0: $i ).
fof(conj_thm_2Ereal__topology_2EBALL__SUBSET__CBALL,axiom,
! [X16] :
( mem(X16,ty_2Erealax_2Ereal)
=> ! [X24] :
( mem(X24,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),X16),X24))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X16),X24)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).
fof(conj_thm_2Ereal__topology_2EBOUNDED__BALL,conjecture,
! [X16] :
( mem(X16,ty_2Erealax_2Ereal)
=> ! [X24] :
( mem(X24,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),X16),X24)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ereal__topology_2EBOUNDED__BALL) ).
fof(conj_thm_2Ereal__topology_2EBOUNDED__CBALL,axiom,
! [X16] :
( mem(X16,ty_2Erealax_2Ereal)
=> ! [X24] :
( mem(X24,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),X16),X24)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ereal__topology_2EBOUNDED__CBALL) ).
fof(conj_thm_2Ereal__topology_2EBOUNDED__SUBSET,axiom,
! [X25] :
( mem(X25,arr(ty_2Erealax_2Ereal,bool))
=> ! [X26] :
( mem(X26,arr(ty_2Erealax_2Ereal,bool))
=> ( ( p(ap(c_2Ereal__topology_2Ebounded__def,X26))
& p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X25),X26)) )
=> p(ap(c_2Ereal__topology_2Ebounded__def,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ereal__topology_2EBOUNDED__SUBSET) ).
fof(ap_tp,axiom,
! [X1,X2,X3] :
( mem(X3,arr(X1,X2))
=> ! [X4] :
( mem(X4,X1)
=> mem(ap(X3,X4),X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',ap_tp) ).
fof(mem_c_2Epair_2E_2C,axiom,
! [X9] :
( ne(X9)
=> ! [X12] :
( ne(X12)
=> mem(c_2Epair_2E_2C(X9,X12),arr(X9,arr(X12,ty_2Epair_2Eprod(X9,X12)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epair_2E_2C) ).
fof(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/sandbox/benchmark/theBenchmark.p',mem_c_2Ereal__topology_2Ecball) ).
fof(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/sandbox/benchmark/theBenchmark.p',mem_c_2Ereal__topology_2Eball) ).
fof(ne_ty_2Erealax_2Ereal,axiom,
ne(ty_2Erealax_2Ereal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ne_ty_2Erealax_2Ereal) ).
fof(c_0_9,plain,
! [X29,X28,X27] :
( epred2_3(X27,X28,X29)
<=> ( ( p(X27)
| p(X28)
| p(X29) )
& ( p(X27)
| ~ p(X29)
| ~ p(X28) )
& ( p(X28)
| ~ p(X29)
| ~ p(X27) ) ) ),
introduced(definition) ).
fof(c_0_10,plain,
! [X117,X118,X119] :
( ( p(X119)
| p(X118)
| p(X117)
| ~ epred2_3(X119,X118,X117) )
& ( p(X119)
| ~ p(X117)
| ~ p(X118)
| ~ epred2_3(X119,X118,X117) )
& ( p(X118)
| ~ p(X117)
| ~ p(X119)
| ~ epred2_3(X119,X118,X117) )
& ( ~ p(X118)
| ~ p(X119)
| ~ p(X119)
| epred2_3(X119,X118,X117) )
& ( p(X117)
| ~ p(X119)
| ~ p(X119)
| epred2_3(X119,X118,X117) )
& ( p(X119)
| ~ p(X119)
| ~ p(X119)
| epred2_3(X119,X118,X117) )
& ( ~ p(X118)
| p(X117)
| ~ p(X119)
| epred2_3(X119,X118,X117) )
& ( p(X117)
| p(X117)
| ~ p(X119)
| epred2_3(X119,X118,X117) )
& ( p(X119)
| p(X117)
| ~ p(X119)
| epred2_3(X119,X118,X117) )
& ( ~ p(X118)
| p(X118)
| ~ p(X119)
| epred2_3(X119,X118,X117) )
& ( p(X117)
| p(X118)
| ~ p(X119)
| epred2_3(X119,X118,X117) )
& ( p(X119)
| p(X118)
| ~ p(X119)
| epred2_3(X119,X118,X117) )
& ( ~ p(X118)
| ~ p(X119)
| ~ p(X118)
| epred2_3(X119,X118,X117) )
& ( p(X117)
| ~ p(X119)
| ~ p(X118)
| epred2_3(X119,X118,X117) )
& ( p(X119)
| ~ p(X119)
| ~ p(X118)
| epred2_3(X119,X118,X117) )
& ( ~ p(X118)
| p(X117)
| ~ p(X118)
| epred2_3(X119,X118,X117) )
& ( p(X117)
| p(X117)
| ~ p(X118)
| epred2_3(X119,X118,X117) )
& ( p(X119)
| p(X117)
| ~ p(X118)
| epred2_3(X119,X118,X117) )
& ( ~ p(X118)
| p(X118)
| ~ p(X118)
| epred2_3(X119,X118,X117) )
& ( p(X117)
| p(X118)
| ~ p(X118)
| epred2_3(X119,X118,X117) )
& ( p(X119)
| p(X118)
| ~ p(X118)
| epred2_3(X119,X118,X117) )
& ( ~ p(X118)
| ~ p(X119)
| ~ p(X117)
| epred2_3(X119,X118,X117) )
& ( p(X117)
| ~ p(X119)
| ~ p(X117)
| epred2_3(X119,X118,X117) )
& ( p(X119)
| ~ p(X119)
| ~ p(X117)
| epred2_3(X119,X118,X117) )
& ( ~ p(X118)
| p(X117)
| ~ p(X117)
| epred2_3(X119,X118,X117) )
& ( p(X117)
| p(X117)
| ~ p(X117)
| epred2_3(X119,X118,X117) )
& ( p(X119)
| p(X117)
| ~ p(X117)
| epred2_3(X119,X118,X117) )
& ( ~ p(X118)
| p(X118)
| ~ p(X117)
| epred2_3(X119,X118,X117) )
& ( p(X117)
| p(X118)
| ~ p(X117)
| epred2_3(X119,X118,X117) )
& ( p(X119)
| p(X118)
| ~ p(X117)
| epred2_3(X119,X118,X117) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_11,plain,
( p(X1)
| p(X1)
| epred2_3(X2,X3,X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_12,plain,
! [X89,X90] :
( ~ mem(X89,ty_2Erealax_2Ereal)
| ~ mem(X90,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),X89),X90))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X89),X90)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Ereal__topology_2EBALL__SUBSET__CBALL])])]) ).
fof(c_0_13,negated_conjecture,
~ ! [X16] :
( mem(X16,ty_2Erealax_2Ereal)
=> ! [X24] :
( mem(X24,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),X16),X24)))) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Ereal__topology_2EBOUNDED__BALL]) ).
fof(c_0_14,plain,
! [X93,X94] :
( ~ mem(X93,ty_2Erealax_2Ereal)
| ~ mem(X94,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),X93),X94)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Ereal__topology_2EBOUNDED__CBALL])])]) ).
cnf(c_0_15,plain,
( p(X1)
| epred2_3(X2,X3,X1)
| ~ p(X2) ),
inference(cn,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( 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),X1),X2))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X1),X2))))
| ~ mem(X1,ty_2Erealax_2Ereal)
| ~ mem(X2,ty_2Erealax_2Ereal) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,negated_conjecture,
( mem(esk6_0,ty_2Erealax_2Ereal)
& mem(esk7_0,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),esk6_0),esk7_0)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
cnf(c_0_18,plain,
( p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X1),X2))))
| ~ mem(X1,ty_2Erealax_2Ereal)
| ~ mem(X2,ty_2Erealax_2Ereal) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( p(X1)
| p(X2)
| p(X3)
| ~ epred2_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,plain,
( epred2_3(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),X1),X2))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X1),X2))),X3,X4)
| p(X4)
| ~ mem(X2,ty_2Erealax_2Ereal)
| ~ mem(X1,ty_2Erealax_2Ereal) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
mem(esk7_0,ty_2Erealax_2Ereal),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( epred2_3(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X1),X2))),X3,X4)
| p(X4)
| ~ mem(X2,ty_2Erealax_2Ereal)
| ~ mem(X1,ty_2Erealax_2Ereal) ),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_23,plain,
( p(X1)
| p(X2)
| ~ epred2_3(X1,X2,X2) ),
inference(ef,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( epred2_3(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),X1),esk7_0))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X1),esk7_0))),X2,X3)
| p(X3)
| ~ mem(X1,ty_2Erealax_2Ereal) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
mem(esk6_0,ty_2Erealax_2Ereal),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
( epred2_3(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X1),esk7_0))),X2,X3)
| p(X3)
| ~ mem(X1,ty_2Erealax_2Ereal) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
fof(c_0_27,plain,
! [X91,X92] :
( ~ mem(X91,arr(ty_2Erealax_2Ereal,bool))
| ~ mem(X92,arr(ty_2Erealax_2Ereal,bool))
| ~ p(ap(c_2Ereal__topology_2Ebounded__def,X92))
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X91),X92))
| p(ap(c_2Ereal__topology_2Ebounded__def,X91)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Ereal__topology_2EBOUNDED__SUBSET])])]) ).
cnf(c_0_28,plain,
( p(X1)
| ~ epred2_3(X1,X1,X1) ),
inference(ef,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( epred2_3(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),esk6_0),esk7_0))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),esk6_0),esk7_0))),X1,X2)
| p(X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( epred2_3(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),esk6_0),esk7_0))),X1,X2)
| p(X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
fof(c_0_31,plain,
! [X32,X33,X34,X35] :
( ~ mem(X34,arr(X32,X33))
| ~ mem(X35,X32)
| mem(ap(X34,X35),X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])]) ).
fof(c_0_32,plain,
! [X56,X57] :
( ~ ne(X56)
| ~ ne(X57)
| mem(c_2Epair_2E_2C(X56,X57),arr(X56,arr(X57,ty_2Epair_2Eprod(X56,X57)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mem_c_2Epair_2E_2C])])]) ).
cnf(c_0_33,plain,
( p(ap(c_2Ereal__topology_2Ebounded__def,X1))
| ~ mem(X1,arr(ty_2Erealax_2Ereal,bool))
| ~ mem(X2,arr(ty_2Erealax_2Ereal,bool))
| ~ p(ap(c_2Ereal__topology_2Ebounded__def,X2))
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
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),esk6_0),esk7_0))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),esk6_0),esk7_0)))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),esk6_0),esk7_0)))),
inference(spm,[status(thm)],[c_0_28,c_0_30]) ).
cnf(c_0_36,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),esk6_0),esk7_0)))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_37,plain,
( mem(ap(X1,X4),X3)
| ~ mem(X1,arr(X2,X3))
| ~ mem(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,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]) ).
cnf(c_0_39,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]) ).
cnf(c_0_40,plain,
( mem(c_2Epair_2E_2C(X1,X2),arr(X1,arr(X2,ty_2Epair_2Eprod(X1,X2))))
| ~ ne(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,plain,
( ~ mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),esk6_0),esk7_0)),arr(ty_2Erealax_2Ereal,bool))
| ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),esk6_0),esk7_0)),arr(ty_2Erealax_2Ereal,bool)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]),c_0_36]) ).
cnf(c_0_42,plain,
( mem(ap(c_2Ereal__topology_2Ecball,X1),arr(ty_2Erealax_2Ereal,bool))
| ~ mem(X1,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
( mem(ap(c_2Ereal__topology_2Eball,X1),arr(ty_2Erealax_2Ereal,bool))
| ~ mem(X1,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(spm,[status(thm)],[c_0_37,c_0_39]) ).
cnf(c_0_44,plain,
( mem(ap(c_2Epair_2E_2C(X1,X2),X3),arr(X2,ty_2Epair_2Eprod(X1,X2)))
| ~ mem(X3,X1)
| ~ ne(X2)
| ~ ne(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_40]) ).
cnf(c_0_45,plain,
~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),esk6_0),esk7_0),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_46,plain,
( mem(ap(ap(c_2Epair_2E_2C(X1,X2),X3),X4),ty_2Epair_2Eprod(X1,X2))
| ~ mem(X4,X2)
| ~ mem(X3,X1)
| ~ ne(X2)
| ~ ne(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_44]) ).
cnf(c_0_47,plain,
ne(ty_2Erealax_2Ereal),
inference(split_conjunct,[status(thm)],[ne_ty_2Erealax_2Ereal]) ).
cnf(c_0_48,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_21]),c_0_25]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP023+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.17/0.36 % Computer : n019.cluster.edu
% 0.17/0.36 % Model : x86_64 x86_64
% 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36 % Memory : 8042.1875MB
% 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36 % CPULimit : 300
% 0.17/0.36 % WCLimit : 300
% 0.17/0.36 % DateTime : Sun Aug 27 10:58:28 EDT 2023
% 0.17/0.36 % CPUTime :
% 0.22/0.56 start to proof: theBenchmark
% 8.24/8.31 % Version : CSE_E---1.5
% 8.24/8.31 % Problem : theBenchmark.p
% 8.24/8.31 % Proof found
% 8.24/8.31 % SZS status Theorem for theBenchmark.p
% 8.24/8.31 % SZS output start Proof
% See solution above
% 8.24/8.31 % Total time : 7.737000 s
% 8.24/8.31 % SZS output end Proof
% 8.24/8.31 % Total time : 7.742000 s
%------------------------------------------------------------------------------