TSTP Solution File: ITP021^2 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ITP021^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n024.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 : Sat May 4 08:06:36 EDT 2024
% Result : Theorem 68.59s 9.10s
% Output : CNFRefutation 68.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 39
% Syntax : Number of formulae : 133 ( 42 unt; 21 typ; 0 def)
% Number of atoms : 267 ( 66 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1593 ( 105 ~; 122 |; 10 &;1342 @)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 12 con; 0-2 aty)
% Number of variables : 142 ( 0 ^ 142 !; 0 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
del: $tType ).
thf(decl_sort2,type,
tp__ty_2Eextreal_2Eextreal: $tType ).
thf(decl_22,type,
bool: del ).
thf(decl_24,type,
arr: del > del > del ).
thf(decl_25,type,
mem: $i > del > $o ).
thf(decl_26,type,
ap: $i > $i > $i ).
thf(decl_28,type,
p: $i > $o ).
thf(decl_29,type,
inj__o: $o > $i ).
thf(decl_30,type,
c_2Ebool_2ET: $i ).
thf(decl_31,type,
ty_2Eextreal_2Eextreal: del ).
thf(decl_32,type,
inj__ty_2Eextreal_2Eextreal: tp__ty_2Eextreal_2Eextreal > $i ).
thf(decl_33,type,
surj__ty_2Eextreal_2Eextreal: $i > tp__ty_2Eextreal_2Eextreal ).
thf(decl_34,type,
c_2Eextreal_2Eextreal__le: $i ).
thf(decl_35,type,
c_2Ebool_2ECOND: del > $i ).
thf(decl_36,type,
c_2Eextreal_2Eextreal__max: $i ).
thf(decl_37,type,
fo__c_2Eextreal_2Eextreal__max: tp__ty_2Eextreal_2Eextreal > tp__ty_2Eextreal_2Eextreal > tp__ty_2Eextreal_2Eextreal ).
thf(decl_38,type,
c_2Ebool_2EF: $i ).
thf(decl_42,type,
c_2Ebool_2E_7E: $i ).
thf(decl_53,type,
esk4_0: tp__ty_2Eextreal_2Eextreal ).
thf(decl_54,type,
esk5_0: tp__ty_2Eextreal_2Eextreal ).
thf(decl_55,type,
esk6_0: tp__ty_2Eextreal_2Eextreal ).
thf(stp_iso_mem_o,axiom,
! [X2: $i] :
( ( mem @ X2 @ bool )
=> ( X2
= ( inj__o @ ( p @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',stp_iso_mem_o) ).
thf(ax_false_p,axiom,
~ ( p @ c_2Ebool_2EF ),
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',ax_false_p) ).
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.InFEnsv6KG/E---3.1_14756.p',ap_tp) ).
thf(mem_c_2Ebool_2EF,axiom,
mem @ c_2Ebool_2EF @ bool,
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',mem_c_2Ebool_2EF) ).
thf(mem_c_2Eextreal_2Eextreal__le,axiom,
mem @ c_2Eextreal_2Eextreal__le @ ( arr @ ty_2Eextreal_2Eextreal @ ( arr @ ty_2Eextreal_2Eextreal @ bool ) ),
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',mem_c_2Eextreal_2Eextreal__le) ).
thf(conj_thm_2Eextreal_2Ele__total,axiom,
! [X35: tp__ty_2Eextreal_2Eextreal,X36: tp__ty_2Eextreal_2Eextreal] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X35 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X36 ) ) )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X36 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X35 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',conj_thm_2Eextreal_2Ele__total) ).
thf(stp_inj_surj_ty_2Eextreal_2Eextreal,axiom,
! [X13: tp__ty_2Eextreal_2Eextreal] :
( ( surj__ty_2Eextreal_2Eextreal @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) )
= X13 ),
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',stp_inj_surj_ty_2Eextreal_2Eextreal) ).
thf(stp_eq_fo_c_2Eextreal_2Eextreal__max,axiom,
! [X17: tp__ty_2Eextreal_2Eextreal,X18: tp__ty_2Eextreal_2Eextreal] :
( ( inj__ty_2Eextreal_2Eextreal @ ( fo__c_2Eextreal_2Eextreal__max @ X17 @ X18 ) )
= ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X17 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X18 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',stp_eq_fo_c_2Eextreal_2Eextreal__max) ).
thf(mem_c_2Ebool_2ET,axiom,
mem @ c_2Ebool_2ET @ bool,
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',mem_c_2Ebool_2ET) ).
thf(ax_true_p,axiom,
p @ c_2Ebool_2ET,
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',ax_true_p) ).
thf(conj_thm_2Eextreal_2Ele__trans,axiom,
! [X32: tp__ty_2Eextreal_2Eextreal,X33: tp__ty_2Eextreal_2Eextreal,X34: tp__ty_2Eextreal_2Eextreal] :
( ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X32 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X33 ) ) )
& ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X33 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X34 ) ) ) )
=> ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X32 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X34 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',conj_thm_2Eextreal_2Ele__trans) ).
thf(stp_inj_mem_ty_2Eextreal_2Eextreal,axiom,
! [X14: tp__ty_2Eextreal_2Eextreal] : ( mem @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) @ ty_2Eextreal_2Eextreal ),
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',stp_inj_mem_ty_2Eextreal_2Eextreal) ).
thf(stp_iso_mem_ty_2Eextreal_2Eextreal,axiom,
! [X15: $i] :
( ( mem @ X15 @ ty_2Eextreal_2Eextreal )
=> ( X15
= ( inj__ty_2Eextreal_2Eextreal @ ( surj__ty_2Eextreal_2Eextreal @ X15 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',stp_iso_mem_ty_2Eextreal_2Eextreal) ).
thf(ax_thm_2Eextreal_2Eextreal__max__def,axiom,
! [X37: tp__ty_2Eextreal_2Eextreal,X38: tp__ty_2Eextreal_2Eextreal] :
( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X37 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X38 ) ) )
= ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal ) @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X37 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X38 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X38 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X37 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',ax_thm_2Eextreal_2Eextreal__max__def) ).
thf(conj_thm_2Eextreal_2Emax__le,conjecture,
! [X42: tp__ty_2Eextreal_2Eextreal,X43: tp__ty_2Eextreal_2Eextreal,X44: tp__ty_2Eextreal_2Eextreal] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X43 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X44 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X42 ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X43 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X42 ) ) )
& ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X44 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X42 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',conj_thm_2Eextreal_2Emax__le) ).
thf(mem_c_2Ebool_2E_7E,axiom,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',mem_c_2Ebool_2E_7E) ).
thf(conj_thm_2Ebool_2ECOND__CLAUSES,axiom,
! [X16: del,X24: $i] :
( ( mem @ X24 @ X16 )
=> ! [X25: $i] :
( ( mem @ X25 @ X16 )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X16 ) @ c_2Ebool_2ET ) @ X24 ) @ X25 )
= X24 )
& ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X16 ) @ c_2Ebool_2EF ) @ X24 ) @ X25 )
= X25 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',conj_thm_2Ebool_2ECOND__CLAUSES) ).
thf(ax_neg_p,axiom,
! [X19: $i] :
( ( mem @ X19 @ bool )
=> ( ( p @ ( ap @ c_2Ebool_2E_7E @ X19 ) )
<=> ~ ( p @ X19 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.InFEnsv6KG/E---3.1_14756.p',ax_neg_p) ).
thf(c_0_18,axiom,
! [X2: $i] :
( ( mem @ X2 @ bool )
=> ( ( ~ ( p @ X2 )
| ( X2
= ( inj__o @ $true ) ) )
& ( ( p @ X2 )
| ( X2
= ( inj__o @ $false ) ) ) ) ),
inference(fool_unroll,[status(thm)],[stp_iso_mem_o]) ).
thf(c_0_19,plain,
~ ( p @ c_2Ebool_2EF ),
inference(fof_simplification,[status(thm)],[ax_false_p]) ).
thf(c_0_20,plain,
! [X140: $i] :
( ( ~ ( p @ X140 )
| ( X140
= ( inj__o @ $true ) )
| ~ ( mem @ X140 @ bool ) )
& ( ( p @ X140 )
| ( X140
= ( inj__o @ $false ) )
| ~ ( mem @ X140 @ bool ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
thf(c_0_21,plain,
~ ( p @ c_2Ebool_2EF ),
inference(fof_nnf,[status(thm)],[c_0_19]) ).
thf(c_0_22,plain,
! [X141: del,X142: del,X143: $i,X144: $i] :
( ~ ( mem @ X143 @ ( arr @ X141 @ X142 ) )
| ~ ( mem @ X144 @ X141 )
| ( mem @ ( ap @ X143 @ X144 ) @ X142 ) ),
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_23,plain,
! [X2: $i] :
( ( p @ X2 )
| ( X2
= ( inj__o @ ~ $true ) )
| ~ ( mem @ X2 @ bool ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_24,plain,
mem @ c_2Ebool_2EF @ bool,
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2EF]) ).
thf(c_0_25,plain,
~ ( p @ c_2Ebool_2EF ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_26,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_22]) ).
thf(c_0_27,plain,
mem @ c_2Eextreal_2Eextreal__le @ ( arr @ ty_2Eextreal_2Eextreal @ ( arr @ ty_2Eextreal_2Eextreal @ bool ) ),
inference(split_conjunct,[status(thm)],[mem_c_2Eextreal_2Eextreal__le]) ).
thf(c_0_28,plain,
( ( inj__o @ ~ $true )
= c_2Ebool_2EF ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
thf(c_0_29,plain,
! [X2: $i] :
( ( mem @ ( ap @ c_2Eextreal_2Eextreal__le @ X2 ) @ ( arr @ ty_2Eextreal_2Eextreal @ bool ) )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal ) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_30,plain,
! [X200: tp__ty_2Eextreal_2Eextreal,X201: tp__ty_2Eextreal_2Eextreal] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X200 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X201 ) ) )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X201 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X200 ) ) ) ),
inference(variable_rename,[status(thm)],[conj_thm_2Eextreal_2Ele__total]) ).
thf(c_0_31,plain,
! [X157: tp__ty_2Eextreal_2Eextreal] :
( ( surj__ty_2Eextreal_2Eextreal @ ( inj__ty_2Eextreal_2Eextreal @ X157 ) )
= X157 ),
inference(variable_rename,[status(thm)],[stp_inj_surj_ty_2Eextreal_2Eextreal]) ).
thf(c_0_32,plain,
! [X161: tp__ty_2Eextreal_2Eextreal,X162: tp__ty_2Eextreal_2Eextreal] :
( ( inj__ty_2Eextreal_2Eextreal @ ( fo__c_2Eextreal_2Eextreal__max @ X161 @ X162 ) )
= ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X161 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X162 ) ) ),
inference(variable_rename,[status(thm)],[stp_eq_fo_c_2Eextreal_2Eextreal__max]) ).
thf(c_0_33,plain,
! [X2: $i] :
( ( X2
= ( inj__o @ $true ) )
| ~ ( p @ X2 )
| ~ ( mem @ X2 @ bool ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_34,plain,
mem @ c_2Ebool_2ET @ bool,
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2ET]) ).
thf(c_0_35,plain,
p @ c_2Ebool_2ET,
inference(split_conjunct,[status(thm)],[ax_true_p]) ).
thf(c_0_36,plain,
! [X197: tp__ty_2Eextreal_2Eextreal,X198: tp__ty_2Eextreal_2Eextreal,X199: tp__ty_2Eextreal_2Eextreal] :
( ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X197 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X198 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X198 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X199 ) ) )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X197 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X199 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Eextreal_2Ele__trans])])]) ).
thf(c_0_37,plain,
! [X2: $i] :
( ( X2 = c_2Ebool_2EF )
| ( p @ X2 )
| ~ ( mem @ X2 @ bool ) ),
inference(rw,[status(thm)],[c_0_23,c_0_28]) ).
thf(c_0_38,plain,
! [X5: $i,X2: $i] :
( ( mem @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ X2 ) @ X5 ) @ bool )
| ~ ( mem @ X5 @ ty_2Eextreal_2Eextreal )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal ) ),
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
thf(c_0_39,plain,
! [X158: tp__ty_2Eextreal_2Eextreal] : ( mem @ ( inj__ty_2Eextreal_2Eextreal @ X158 ) @ ty_2Eextreal_2Eextreal ),
inference(variable_rename,[status(thm)],[stp_inj_mem_ty_2Eextreal_2Eextreal]) ).
thf(c_0_40,plain,
! [X14: tp__ty_2Eextreal_2Eextreal,X13: tp__ty_2Eextreal_2Eextreal] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_41,plain,
! [X159: $i] :
( ~ ( mem @ X159 @ ty_2Eextreal_2Eextreal )
| ( X159
= ( inj__ty_2Eextreal_2Eextreal @ ( surj__ty_2Eextreal_2Eextreal @ X159 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[stp_iso_mem_ty_2Eextreal_2Eextreal])])]) ).
thf(c_0_42,plain,
! [X202: tp__ty_2Eextreal_2Eextreal,X203: tp__ty_2Eextreal_2Eextreal] :
( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X202 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X203 ) ) )
= ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal ) @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X202 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X203 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X203 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X202 ) ) ) ),
inference(variable_rename,[status(thm)],[ax_thm_2Eextreal_2Eextreal__max__def]) ).
thf(c_0_43,plain,
! [X13: tp__ty_2Eextreal_2Eextreal] :
( ( surj__ty_2Eextreal_2Eextreal @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) )
= X13 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_44,plain,
! [X13: tp__ty_2Eextreal_2Eextreal,X14: tp__ty_2Eextreal_2Eextreal] :
( ( inj__ty_2Eextreal_2Eextreal @ ( fo__c_2Eextreal_2Eextreal__max @ X13 @ X14 ) )
= ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_45,plain,
( ( inj__o @ $true )
= c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
thf(c_0_46,plain,
! [X13: tp__ty_2Eextreal_2Eextreal,X14: tp__ty_2Eextreal_2Eextreal,X17: tp__ty_2Eextreal_2Eextreal] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X17 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X17 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_47,plain,
! [X5: $i,X2: $i] :
( ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ X2 ) @ X5 )
= c_2Ebool_2EF )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ X2 ) @ X5 ) )
| ~ ( mem @ X5 @ ty_2Eextreal_2Eextreal )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal ) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_48,plain,
! [X13: tp__ty_2Eextreal_2Eextreal] : ( mem @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) @ ty_2Eextreal_2Eextreal ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_49,plain,
! [X13: tp__ty_2Eextreal_2Eextreal] : ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) ),
inference(ef,[status(thm)],[c_0_40]) ).
thf(c_0_50,plain,
! [X2: $i] :
( ( X2
= ( inj__ty_2Eextreal_2Eextreal @ ( surj__ty_2Eextreal_2Eextreal @ X2 ) ) )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_51,plain,
! [X14: tp__ty_2Eextreal_2Eextreal,X13: tp__ty_2Eextreal_2Eextreal] :
( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) )
= ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal ) @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_52,plain,
! [X13: tp__ty_2Eextreal_2Eextreal,X14: tp__ty_2Eextreal_2Eextreal] :
( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) )
= ( fo__c_2Eextreal_2Eextreal__max @ X13 @ X14 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_53,plain,
! [X2: $i] :
( ( X2 = c_2Ebool_2ET )
| ~ ( mem @ X2 @ bool )
| ~ ( p @ X2 ) ),
inference(rw,[status(thm)],[c_0_33,c_0_45]) ).
thf(c_0_54,plain,
! [X17: tp__ty_2Eextreal_2Eextreal,X14: tp__ty_2Eextreal_2Eextreal,X13: tp__ty_2Eextreal_2Eextreal] :
( ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) )
= c_2Ebool_2EF )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X17 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X17 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_48])]) ).
thf(c_0_55,plain,
! [X2: $i] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ X2 ) @ X2 ) )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal ) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_56,negated_conjecture,
~ ! [X42: tp__ty_2Eextreal_2Eextreal,X43: tp__ty_2Eextreal_2Eextreal,X44: tp__ty_2Eextreal_2Eextreal] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X43 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X44 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X42 ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X43 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X42 ) ) )
& ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X44 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X42 ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Eextreal_2Emax__le]) ).
thf(c_0_57,plain,
! [X13: tp__ty_2Eextreal_2Eextreal,X14: tp__ty_2Eextreal_2Eextreal] :
( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal ) @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) )
= ( fo__c_2Eextreal_2Eextreal__max @ X13 @ X14 ) ),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
thf(c_0_58,plain,
! [X5: $i,X2: $i] :
( ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ X2 ) @ X5 )
= c_2Ebool_2ET )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ X2 ) @ X5 ) )
| ~ ( mem @ X5 @ ty_2Eextreal_2Eextreal )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal ) ),
inference(spm,[status(thm)],[c_0_53,c_0_38]) ).
thf(c_0_59,plain,
! [X13: tp__ty_2Eextreal_2Eextreal,X14: tp__ty_2Eextreal_2Eextreal] :
( ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) )
= c_2Ebool_2EF )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_48])]) ).
thf(c_0_60,plain,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2E_7E]) ).
thf(c_0_61,negated_conjecture,
( ( ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])])])])]) ).
thf(c_0_62,plain,
! [X14: tp__ty_2Eextreal_2Eextreal,X13: tp__ty_2Eextreal_2Eextreal] :
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal ) @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) )
= ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) )
| ~ ( mem @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal ) @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ty_2Eextreal_2Eextreal ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_57]),c_0_44]) ).
thf(c_0_63,plain,
! [X13: tp__ty_2Eextreal_2Eextreal,X14: tp__ty_2Eextreal_2Eextreal] :
( ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) )
= c_2Ebool_2EF )
| ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) )
= c_2Ebool_2ET ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_48]),c_0_48])]) ).
thf(c_0_64,plain,
! [X190: del,X191: $i,X192: $i] :
( ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X190 ) @ c_2Ebool_2ET ) @ X191 ) @ X192 )
= X191 )
| ~ ( mem @ X192 @ X190 )
| ~ ( mem @ X191 @ X190 ) )
& ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X190 ) @ c_2Ebool_2EF ) @ X191 ) @ X192 )
= X192 )
| ~ ( mem @ X192 @ X190 )
| ~ ( mem @ X191 @ X190 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Ebool_2ECOND__CLAUSES])])])])]) ).
thf(c_0_65,plain,
! [X2: $i] :
( ( mem @ ( ap @ c_2Ebool_2E_7E @ X2 ) @ bool )
| ~ ( mem @ X2 @ bool ) ),
inference(spm,[status(thm)],[c_0_26,c_0_60]) ).
thf(c_0_66,plain,
! [X14: tp__ty_2Eextreal_2Eextreal,X13: tp__ty_2Eextreal_2Eextreal,X2: $i] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ X2 ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) @ X2 ) )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal ) ),
inference(spm,[status(thm)],[c_0_46,c_0_50]) ).
thf(c_0_67,negated_conjecture,
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_68,plain,
! [X13: tp__ty_2Eextreal_2Eextreal,X14: tp__ty_2Eextreal_2Eextreal] : ( mem @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) @ ty_2Eextreal_2Eextreal ),
inference(spm,[status(thm)],[c_0_48,c_0_44]) ).
thf(c_0_69,plain,
! [X13: tp__ty_2Eextreal_2Eextreal,X14: tp__ty_2Eextreal_2Eextreal] :
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal ) @ c_2Ebool_2EF ) @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) )
= ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) )
| ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) )
= c_2Ebool_2ET )
| ~ ( mem @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal ) @ c_2Ebool_2EF ) @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) @ ty_2Eextreal_2Eextreal ) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
thf(c_0_70,plain,
! [X2: $i,X5: $i,X3: del] :
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X3 ) @ c_2Ebool_2EF ) @ X2 ) @ X5 )
= X5 )
| ~ ( mem @ X5 @ X3 )
| ~ ( mem @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_71,plain,
! [X19: $i] :
( ( mem @ X19 @ bool )
=> ( ( p @ ( ap @ c_2Ebool_2E_7E @ X19 ) )
<=> ~ ( p @ X19 ) ) ),
inference(fof_simplification,[status(thm)],[ax_neg_p]) ).
thf(c_0_72,plain,
! [X2: $i] :
( ( ( ap @ c_2Ebool_2E_7E @ X2 )
= c_2Ebool_2ET )
| ~ ( p @ ( ap @ c_2Ebool_2E_7E @ X2 ) )
| ~ ( mem @ X2 @ bool ) ),
inference(spm,[status(thm)],[c_0_53,c_0_65]) ).
thf(c_0_73,plain,
! [X2: $i] :
( ( ( ap @ c_2Ebool_2E_7E @ X2 )
= c_2Ebool_2EF )
| ( p @ ( ap @ c_2Ebool_2E_7E @ X2 ) )
| ~ ( mem @ X2 @ bool ) ),
inference(spm,[status(thm)],[c_0_37,c_0_65]) ).
thf(c_0_74,plain,
! [X13: tp__ty_2Eextreal_2Eextreal,X17: tp__ty_2Eextreal_2Eextreal,X14: tp__ty_2Eextreal_2Eextreal,X2: $i] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) ) @ X2 ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X17 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X17 ) ) @ X2 ) )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal ) ),
inference(spm,[status(thm)],[c_0_66,c_0_44]) ).
thf(c_0_75,negated_conjecture,
( ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) )
= c_2Ebool_2ET )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_67]),c_0_48]),c_0_68])]) ).
thf(c_0_76,negated_conjecture,
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_77,plain,
! [X13: tp__ty_2Eextreal_2Eextreal,X14: tp__ty_2Eextreal_2Eextreal] :
( ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) )
= ( inj__ty_2Eextreal_2Eextreal @ X13 ) )
| ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) )
= c_2Ebool_2ET ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_48]),c_0_48])]) ).
thf(c_0_78,plain,
! [X169: $i] :
( ( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ X169 ) )
| ~ ( p @ X169 )
| ~ ( mem @ X169 @ bool ) )
& ( ( p @ X169 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ X169 ) )
| ~ ( mem @ X169 @ bool ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_71])])])]) ).
thf(c_0_79,plain,
! [X2: $i] :
( ( ( ap @ c_2Ebool_2E_7E @ X2 )
= c_2Ebool_2EF )
| ( ( ap @ c_2Ebool_2E_7E @ X2 )
= c_2Ebool_2ET )
| ~ ( mem @ X2 @ bool ) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
thf(c_0_80,negated_conjecture,
! [X2: $i] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) @ X2 ) )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) @ X2 ) )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_35])]) ).
thf(c_0_81,negated_conjecture,
( ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_82,negated_conjecture,
( ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) )
= c_2Ebool_2ET )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
thf(c_0_83,plain,
! [X2: $i] :
( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ X2 ) )
| ~ ( p @ X2 )
| ~ ( mem @ X2 @ bool ) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
thf(c_0_84,plain,
! [X2: $i] :
( ( ( ap @ c_2Ebool_2E_7E @ X2 )
= c_2Ebool_2ET )
| ( c_2Ebool_2EF != c_2Ebool_2ET )
| ~ ( mem @ X2 @ bool ) ),
inference(ef,[status(thm)],[c_0_79]) ).
thf(c_0_85,negated_conjecture,
! [X13: tp__ty_2Eextreal_2Eextreal,X2: $i] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) @ X2 ) )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ X2 ) )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_80]),c_0_48])]) ).
thf(c_0_86,plain,
! [X13: tp__ty_2Eextreal_2Eextreal,X2: $i] :
( ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ X2 )
= c_2Ebool_2EF )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ X2 ) )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal ) ),
inference(spm,[status(thm)],[c_0_59,c_0_50]) ).
thf(c_0_87,negated_conjecture,
( ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) )
= c_2Ebool_2ET )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_77]),c_0_82]) ).
thf(c_0_88,plain,
! [X2: $i] :
( ( c_2Ebool_2EF != c_2Ebool_2ET )
| ~ ( mem @ X2 @ bool )
| ~ ( p @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_35])]) ).
thf(c_0_89,negated_conjecture,
! [X13: tp__ty_2Eextreal_2Eextreal,X2: $i] :
( ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) )
= c_2Ebool_2EF )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) @ X2 ) )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ X2 ) )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_48])]) ).
thf(c_0_90,negated_conjecture,
( ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) )
= c_2Ebool_2ET )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_87,c_0_40]) ).
thf(c_0_91,plain,
! [X13: tp__ty_2Eextreal_2Eextreal] :
( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) )
= c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_49]),c_0_48])]) ).
thf(c_0_92,plain,
c_2Ebool_2EF != c_2Ebool_2ET,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_34]),c_0_35])]) ).
thf(c_0_93,negated_conjecture,
( ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) )
= c_2Ebool_2ET )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_48])]),c_0_92]),c_0_87]) ).
thf(c_0_94,plain,
! [X13: tp__ty_2Eextreal_2Eextreal,X2: $i] :
( ( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal ) @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ X2 ) @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ X2 ) )
= ( fo__c_2Eextreal_2Eextreal__max @ ( surj__ty_2Eextreal_2Eextreal @ X2 ) @ X13 ) )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal ) ),
inference(spm,[status(thm)],[c_0_57,c_0_50]) ).
thf(c_0_95,negated_conjecture,
( ( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) )
= c_2Ebool_2ET )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_93,c_0_77]) ).
thf(c_0_96,plain,
! [X14: tp__ty_2Eextreal_2Eextreal,X13: tp__ty_2Eextreal_2Eextreal,X2: $i] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ X2 ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ X2 ) )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal ) ),
inference(spm,[status(thm)],[c_0_46,c_0_50]) ).
thf(c_0_97,plain,
! [X2: $i,X5: $i] :
( ( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal ) @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ X2 ) @ X5 ) ) @ X5 ) @ X2 ) )
= ( fo__c_2Eextreal_2Eextreal__max @ ( surj__ty_2Eextreal_2Eextreal @ X2 ) @ ( surj__ty_2Eextreal_2Eextreal @ X5 ) ) )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal )
| ~ ( mem @ X5 @ ty_2Eextreal_2Eextreal ) ),
inference(spm,[status(thm)],[c_0_94,c_0_50]) ).
thf(c_0_98,negated_conjecture,
( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) )
= c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_95]),c_0_48]),c_0_48])]) ).
thf(c_0_99,negated_conjecture,
! [X13: tp__ty_2Eextreal_2Eextreal] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_67]),c_0_68])]) ).
thf(c_0_100,negated_conjecture,
( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Eextreal_2Eextreal ) @ c_2Ebool_2ET ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) )
= ( fo__c_2Eextreal_2Eextreal__max @ esk5_0 @ esk6_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_43]),c_0_43]),c_0_48]),c_0_48])]) ).
thf(c_0_101,plain,
! [X2: $i,X5: $i,X3: del] :
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X3 ) @ c_2Ebool_2ET ) @ X2 ) @ X5 )
= X2 )
| ~ ( mem @ X5 @ X3 )
| ~ ( mem @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_102,negated_conjecture,
! [X13: tp__ty_2Eextreal_2Eextreal,X14: tp__ty_2Eextreal_2Eextreal] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X14 ) ) ) @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_99,c_0_44]) ).
thf(c_0_103,negated_conjecture,
( ( fo__c_2Eextreal_2Eextreal__max @ esk5_0 @ esk6_0 )
= esk6_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_43]),c_0_48]),c_0_48])]) ).
thf(c_0_104,negated_conjecture,
! [X13: tp__ty_2Eextreal_2Eextreal,X2: $i] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ X2 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ X2 ) ) @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) ) )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal ) ),
inference(spm,[status(thm)],[c_0_102,c_0_50]) ).
thf(c_0_105,negated_conjecture,
( ( ap @ ( ap @ c_2Eextreal_2Eextreal__max @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) )
= ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_103]) ).
thf(c_0_106,plain,
! [X2: $i,X13: tp__ty_2Eextreal_2Eextreal,X5: $i] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ X2 ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ X13 ) ) @ X5 ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ X5 ) @ X2 ) )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal )
| ~ ( mem @ X5 @ ty_2Eextreal_2Eextreal ) ),
inference(spm,[status(thm)],[c_0_66,c_0_50]) ).
thf(c_0_107,negated_conjecture,
p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_105]),c_0_91]),c_0_35]),c_0_48])]) ).
thf(c_0_108,negated_conjecture,
! [X2: $i] :
( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ X2 ) )
| ~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) @ X2 ) )
| ~ ( mem @ X2 @ ty_2Eextreal_2Eextreal ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_98]),c_0_35]),c_0_48])]) ).
thf(c_0_109,negated_conjecture,
( ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk6_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) )
= c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_107]),c_0_48]),c_0_48])]) ).
thf(c_0_110,negated_conjecture,
~ ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ esk5_0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ esk4_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_105]),c_0_107]),c_0_107])]) ).
thf(c_0_111,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_35]),c_0_48])]),c_0_110]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ITP021^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n024.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri May 3 12:39:20 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.17/0.45 Running higher-order theorem proving
% 0.17/0.45 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.InFEnsv6KG/E---3.1_14756.p
% 68.59/9.10 # Version: 3.1.0-ho
% 68.59/9.10 # Preprocessing class: HSLSSMSMSSSNSFA.
% 68.59/9.10 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 68.59/9.10 # Starting new_ho_10 with 900s (3) cores
% 68.59/9.10 # Starting sh2lt with 300s (1) cores
% 68.59/9.10 # Starting new_ho_5 with 300s (1) cores
% 68.59/9.10 # Starting full_lambda_5 with 300s (1) cores
% 68.59/9.10 # Starting sh9 with 300s (1) cores
% 68.59/9.10 # Starting ehoh_best8_lambda with 300s (1) cores
% 68.59/9.10 # full_lambda_5 with pid 14838 completed with status 0
% 68.59/9.10 # Result found by full_lambda_5
% 68.59/9.10 # Preprocessing class: HSLSSMSMSSSNSFA.
% 68.59/9.10 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 68.59/9.10 # Starting new_ho_10 with 900s (3) cores
% 68.59/9.10 # Starting sh2lt with 300s (1) cores
% 68.59/9.10 # Starting new_ho_5 with 300s (1) cores
% 68.59/9.10 # Starting full_lambda_5 with 300s (1) cores
% 68.59/9.10 # No SInE strategy applied
% 68.59/9.10 # Search class: HGHSM-FFMM31-DSFFFFBN
% 68.59/9.10 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 68.59/9.10 # Starting sh5 with 163s (1) cores
% 68.59/9.10 # sh5 with pid 14843 completed with status 0
% 68.59/9.10 # Result found by sh5
% 68.59/9.10 # Preprocessing class: HSLSSMSMSSSNSFA.
% 68.59/9.10 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 68.59/9.10 # Starting new_ho_10 with 900s (3) cores
% 68.59/9.10 # Starting sh2lt with 300s (1) cores
% 68.59/9.10 # Starting new_ho_5 with 300s (1) cores
% 68.59/9.10 # Starting full_lambda_5 with 300s (1) cores
% 68.59/9.10 # No SInE strategy applied
% 68.59/9.10 # Search class: HGHSM-FFMM31-DSFFFFBN
% 68.59/9.10 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 68.59/9.10 # Starting sh5 with 163s (1) cores
% 68.59/9.10 # Preprocessing time : 0.002 s
% 68.59/9.10 # Presaturation interreduction done
% 68.59/9.10
% 68.59/9.10 # Proof found!
% 68.59/9.10 # SZS status Theorem
% 68.59/9.10 # SZS output start CNFRefutation
% See solution above
% 68.59/9.10 # Parsed axioms : 83
% 68.59/9.10 # Removed by relevancy pruning/SinE : 0
% 68.59/9.10 # Initial clauses : 359
% 68.59/9.10 # Removed in clause preprocessing : 278
% 68.59/9.10 # Initial clauses in saturation : 81
% 68.59/9.10 # Processed clauses : 22188
% 68.59/9.10 # ...of these trivial : 202
% 68.59/9.10 # ...subsumed : 18335
% 68.59/9.10 # ...remaining for further processing : 3651
% 68.59/9.10 # Other redundant clauses eliminated : 158
% 68.59/9.10 # Clauses deleted for lack of memory : 0
% 68.59/9.10 # Backward-subsumed : 366
% 68.59/9.10 # Backward-rewritten : 530
% 68.59/9.10 # Generated clauses : 290567
% 68.59/9.10 # ...of the previous two non-redundant : 258698
% 68.59/9.10 # ...aggressively subsumed : 0
% 68.59/9.10 # Contextual simplify-reflections : 99
% 68.59/9.10 # Paramodulations : 290236
% 68.59/9.10 # Factorizations : 94
% 68.59/9.10 # NegExts : 0
% 68.59/9.10 # Equation resolutions : 159
% 68.59/9.10 # Disequality decompositions : 0
% 68.59/9.10 # Total rewrite steps : 177984
% 68.59/9.10 # ...of those cached : 176883
% 68.59/9.10 # Propositional unsat checks : 0
% 68.59/9.10 # Propositional check models : 0
% 68.59/9.10 # Propositional check unsatisfiable : 0
% 68.59/9.10 # Propositional clauses : 0
% 68.59/9.10 # Propositional clauses after purity: 0
% 68.59/9.10 # Propositional unsat core size : 0
% 68.59/9.10 # Propositional preprocessing time : 0.000
% 68.59/9.10 # Propositional encoding time : 0.000
% 68.59/9.10 # Propositional solver time : 0.000
% 68.59/9.10 # Success case prop preproc time : 0.000
% 68.59/9.10 # Success case prop encoding time : 0.000
% 68.59/9.10 # Success case prop solver time : 0.000
% 68.59/9.10 # Current number of processed clauses : 2654
% 68.59/9.10 # Positive orientable unit clauses : 97
% 68.59/9.10 # Positive unorientable unit clauses: 0
% 68.59/9.10 # Negative unit clauses : 3
% 68.59/9.10 # Non-unit-clauses : 2554
% 68.59/9.10 # Current number of unprocessed clauses: 235322
% 68.59/9.10 # ...number of literals in the above : 1154404
% 68.59/9.10 # Current number of archived formulas : 0
% 68.59/9.10 # Current number of archived clauses : 996
% 68.59/9.10 # Clause-clause subsumption calls (NU) : 1425678
% 68.59/9.10 # Rec. Clause-clause subsumption calls : 395259
% 68.59/9.10 # Non-unit clause-clause subsumptions : 16705
% 68.59/9.10 # Unit Clause-clause subsumption calls : 25899
% 68.59/9.10 # Rewrite failures with RHS unbound : 0
% 68.59/9.10 # BW rewrite match attempts : 1622
% 68.59/9.10 # BW rewrite match successes : 46
% 68.59/9.10 # Condensation attempts : 22189
% 68.59/9.10 # Condensation successes : 656
% 68.59/9.10 # Termbank termtop insertions : 10406723
% 68.59/9.10 # Search garbage collected termcells : 4218
% 68.59/9.10
% 68.59/9.10 # -------------------------------------------------
% 68.59/9.10 # User time : 8.360 s
% 68.59/9.10 # System time : 0.190 s
% 68.59/9.10 # Total time : 8.550 s
% 68.59/9.10 # Maximum resident set size: 2568 pages
% 68.59/9.10
% 68.59/9.10 # -------------------------------------------------
% 68.59/9.10 # User time : 8.364 s
% 68.59/9.10 # System time : 0.191 s
% 68.59/9.10 # Total time : 8.555 s
% 68.59/9.10 # Maximum resident set size: 1836 pages
% 68.59/9.10 % E---3.1 exiting
% 68.59/9.10 % E exiting
%------------------------------------------------------------------------------