%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP009^2 : 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 : n018.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 08:04:00 AM UTC 2026
% Result : Theorem 199.61s 29.27s
% Output : CNFRefutation 199.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 76 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 377 ( 31 equ; 0 cnn)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 3442 ( 233 ~; 238 |; 22 &;2908 @)
% ( 3 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 16 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 14 con; 0-4 aty)
% Number of variables : 284 ( 0 ^; 284 !; 0 ?; 284 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
del: $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_35,type,
c_2Equotient_2E_2D_2D_3E: del > del > del > del > $i ).
thf(decl_36,type,
c_2Equotient_2E_3D_3D_3D_3E: del > del > $i ).
thf(decl_37,type,
c_2Equotient_2EQUOTIENT: del > del > $i ).
thf(decl_40,type,
c_2Ecombin_2EW: del > del > $i ).
thf(decl_41,type,
c_2Equotient_2Erespects: del > del > $i ).
thf(decl_43,type,
esk1_0: del ).
thf(decl_44,type,
esk2_0: del ).
thf(decl_45,type,
esk3_0: del ).
thf(decl_46,type,
esk4_0: del ).
thf(decl_47,type,
esk5_0: $i ).
thf(decl_48,type,
esk6_0: $i ).
thf(decl_49,type,
esk7_0: $i ).
thf(decl_50,type,
esk8_0: $i ).
thf(decl_51,type,
esk9_0: $i ).
thf(decl_52,type,
esk10_0: $i ).
thf(decl_53,type,
esk11_0: $i ).
thf(decl_54,type,
esk12_0: $i ).
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.hUgaAFsfUm/E---3.1_519170.p',ap_tp) ).
thf(mem_c_2Equotient_2E_3D_3D_3D_3E,axiom,
! [X15: del,X16: del] : ( mem @ ( c_2Equotient_2E_3D_3D_3D_3E @ X15 @ X16 ) @ ( arr @ ( arr @ X15 @ ( arr @ X15 @ bool ) ) @ ( arr @ ( arr @ X16 @ ( arr @ X16 @ bool ) ) @ ( arr @ ( arr @ X15 @ X16 ) @ ( arr @ ( arr @ X15 @ X16 ) @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hUgaAFsfUm/E---3.1_519170.p',mem_c_2Equotient_2E_3D_3D_3D_3E) ).
thf(mem_c_2Equotient_2E_2D_2D_3E,axiom,
! [X15: del,X16: del,X17: del,X18: del] : ( mem @ ( c_2Equotient_2E_2D_2D_3E @ X15 @ X16 @ X17 @ X18 ) @ ( arr @ ( arr @ X15 @ X17 ) @ ( arr @ ( arr @ X16 @ X18 ) @ ( arr @ ( arr @ X17 @ X16 ) @ ( arr @ X15 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hUgaAFsfUm/E---3.1_519170.p',mem_c_2Equotient_2E_2D_2D_3E) ).
thf(conj_thm_2Ecombin_2EW__THM,axiom,
! [X15: del,X16: del,X26: $i] :
( ( mem @ X26 @ ( arr @ X15 @ ( arr @ X15 @ X16 ) ) )
=> ! [X27: $i] :
( ( mem @ X27 @ X15 )
=> ( ( ap @ ( ap @ ( c_2Ecombin_2EW @ X15 @ X16 ) @ X26 ) @ X27 )
= ( ap @ ( ap @ X26 @ X27 ) @ X27 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hUgaAFsfUm/E---3.1_519170.p',conj_thm_2Ecombin_2EW__THM) ).
thf(ax_thm_2Equotient_2Erespects__def,axiom,
! [X15: del,X16: del] :
( ( c_2Equotient_2Erespects @ X15 @ X16 )
= ( c_2Ecombin_2EW @ X15 @ X16 ) ),
file('/export/starexec/sandbox2/tmp/tmp.hUgaAFsfUm/E---3.1_519170.p',ax_thm_2Equotient_2Erespects__def) ).
thf(conj_thm_2Equotient_2EFUN__REL__EQ__REL,conjecture,
! [X15: del,X16: del,X17: del,X18: del,X33: $i] :
( ( mem @ X33 @ ( arr @ X15 @ ( arr @ X15 @ bool ) ) )
=> ! [X34: $i] :
( ( mem @ X34 @ ( arr @ X15 @ X17 ) )
=> ! [X35: $i] :
( ( mem @ X35 @ ( arr @ X17 @ X15 ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X15 @ X17 ) @ X33 ) @ X34 ) @ X35 ) )
=> ! [X36: $i] :
( ( mem @ X36 @ ( arr @ X16 @ ( arr @ X16 @ bool ) ) )
=> ! [X37: $i] :
( ( mem @ X37 @ ( arr @ X16 @ X18 ) )
=> ! [X38: $i] :
( ( mem @ X38 @ ( arr @ X18 @ X16 ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X16 @ X18 ) @ X36 ) @ X37 ) @ X38 ) )
=> ! [X39: $i] :
( ( mem @ X39 @ ( arr @ X15 @ X16 ) )
=> ! [X40: $i] :
( ( mem @ X40 @ ( arr @ X15 @ X16 ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X15 @ X16 ) @ X33 ) @ X36 ) @ X39 ) @ X40 ) )
<=> ( ( p @ ( ap @ ( ap @ ( c_2Equotient_2Erespects @ ( arr @ X15 @ X16 ) @ bool ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X15 @ X16 ) @ X33 ) @ X36 ) ) @ X39 ) )
& ( p @ ( ap @ ( ap @ ( c_2Equotient_2Erespects @ ( arr @ X15 @ X16 ) @ bool ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X15 @ X16 ) @ X33 ) @ X36 ) ) @ X40 ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X17 @ X16 @ X15 @ X18 ) @ X35 ) @ X37 ) @ X39 )
= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X17 @ X16 @ X15 @ X18 ) @ X35 ) @ X37 ) @ X40 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hUgaAFsfUm/E---3.1_519170.p',conj_thm_2Equotient_2EFUN__REL__EQ__REL) ).
thf(conj_thm_2Equotient_2EQUOTIENT__REL,axiom,
! [X15: del,X16: del,X28: $i] :
( ( mem @ X28 @ ( arr @ X15 @ ( arr @ X15 @ bool ) ) )
=> ! [X29: $i] :
( ( mem @ X29 @ ( arr @ X15 @ X16 ) )
=> ! [X30: $i] :
( ( mem @ X30 @ ( arr @ X16 @ X15 ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X15 @ X16 ) @ X28 ) @ X29 ) @ X30 ) )
=> ! [X31: $i] :
( ( mem @ X31 @ X15 )
=> ! [X32: $i] :
( ( mem @ X32 @ X15 )
=> ( ( p @ ( ap @ ( ap @ X28 @ X31 ) @ X32 ) )
<=> ( ( p @ ( ap @ ( ap @ X28 @ X31 ) @ X31 ) )
& ( p @ ( ap @ ( ap @ X28 @ X32 ) @ X32 ) )
& ( ( ap @ X29 @ X31 )
= ( ap @ X29 @ X32 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hUgaAFsfUm/E---3.1_519170.p',conj_thm_2Equotient_2EQUOTIENT__REL) ).
thf(conj_thm_2Equotient_2EFUN__QUOTIENT,axiom,
! [X15: del,X16: del,X17: del,X18: del,X33: $i] :
( ( mem @ X33 @ ( arr @ X15 @ ( arr @ X15 @ bool ) ) )
=> ! [X34: $i] :
( ( mem @ X34 @ ( arr @ X15 @ X17 ) )
=> ! [X35: $i] :
( ( mem @ X35 @ ( arr @ X17 @ X15 ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X15 @ X17 ) @ X33 ) @ X34 ) @ X35 ) )
=> ! [X36: $i] :
( ( mem @ X36 @ ( arr @ X16 @ ( arr @ X16 @ bool ) ) )
=> ! [X37: $i] :
( ( mem @ X37 @ ( arr @ X16 @ X18 ) )
=> ! [X38: $i] :
( ( mem @ X38 @ ( arr @ X18 @ X16 ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X16 @ X18 ) @ X36 ) @ X37 ) @ X38 ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ ( arr @ X15 @ X16 ) @ ( arr @ X17 @ X18 ) ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X15 @ X16 ) @ X33 ) @ X36 ) ) @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X17 @ X16 @ X15 @ X18 ) @ X35 ) @ X37 ) ) @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X15 @ X18 @ X17 @ X16 ) @ X34 ) @ X38 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hUgaAFsfUm/E---3.1_519170.p',conj_thm_2Equotient_2EFUN__QUOTIENT) ).
thf(c_0_8,plain,
! [X116: del,X117: del,X118: $i,X119: $i] :
( ~ ( mem @ X118 @ ( arr @ X116 @ X117 ) )
| ~ ( mem @ X119 @ X116 )
| ( mem @ ( ap @ X118 @ X119 ) @ X117 ) ),
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_9,plain,
! [X157: del,X158: del] : ( mem @ ( c_2Equotient_2E_3D_3D_3D_3E @ X157 @ X158 ) @ ( arr @ ( arr @ X157 @ ( arr @ X157 @ bool ) ) @ ( arr @ ( arr @ X158 @ ( arr @ X158 @ bool ) ) @ ( arr @ ( arr @ X157 @ X158 ) @ ( arr @ ( arr @ X157 @ X158 ) @ bool ) ) ) ) ),
inference(variable_rename,[status(thm)],[mem_c_2Equotient_2E_3D_3D_3D_3E]) ).
thf(c_0_10,plain,
! [X146: del,X147: del,X148: del,X149: del] : ( mem @ ( c_2Equotient_2E_2D_2D_3E @ X146 @ X147 @ X148 @ X149 ) @ ( arr @ ( arr @ X146 @ X148 ) @ ( arr @ ( arr @ X147 @ X149 ) @ ( arr @ ( arr @ X148 @ X147 ) @ ( arr @ X146 @ X149 ) ) ) ) ),
inference(variable_rename,[status(thm)],[mem_c_2Equotient_2E_2D_2D_3E]) ).
thf(c_0_11,plain,
! [X125: del,X126: del,X127: $i,X128: $i] :
( ~ ( mem @ X127 @ ( arr @ X125 @ ( arr @ X125 @ X126 ) ) )
| ~ ( mem @ X128 @ X125 )
| ( ( ap @ ( ap @ ( c_2Ecombin_2EW @ X125 @ X126 ) @ X127 ) @ X128 )
= ( ap @ ( ap @ X127 @ X128 ) @ X128 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Ecombin_2EW__THM])])])]) ).
thf(c_0_12,plain,
! [X161: del,X162: del] :
( ( c_2Equotient_2Erespects @ X161 @ X162 )
= ( c_2Ecombin_2EW @ X161 @ X162 ) ),
inference(variable_rename,[status(thm)],[ax_thm_2Equotient_2Erespects__def]) ).
thf(c_0_13,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_8]) ).
thf(c_0_14,plain,
! [X3: del,X4: del] : ( mem @ ( c_2Equotient_2E_3D_3D_3D_3E @ X3 @ X4 ) @ ( arr @ ( arr @ X3 @ ( arr @ X3 @ bool ) ) @ ( arr @ ( arr @ X4 @ ( arr @ X4 @ bool ) ) @ ( arr @ ( arr @ X3 @ X4 ) @ ( arr @ ( arr @ X3 @ X4 ) @ bool ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_15,plain,
! [X3: del,X15: del,X4: del,X16: del] : ( mem @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ X4 @ X15 @ X16 ) @ ( arr @ ( arr @ X3 @ X15 ) @ ( arr @ ( arr @ X4 @ X16 ) @ ( arr @ ( arr @ X15 @ X4 ) @ ( arr @ X3 @ X16 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,negated_conjecture,
~ ! [X15: del,X16: del,X17: del,X18: del,X33: $i] :
( ( mem @ X33 @ ( arr @ X15 @ ( arr @ X15 @ bool ) ) )
=> ! [X34: $i] :
( ( mem @ X34 @ ( arr @ X15 @ X17 ) )
=> ! [X35: $i] :
( ( mem @ X35 @ ( arr @ X17 @ X15 ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X15 @ X17 ) @ X33 ) @ X34 ) @ X35 ) )
=> ! [X36: $i] :
( ( mem @ X36 @ ( arr @ X16 @ ( arr @ X16 @ bool ) ) )
=> ! [X37: $i] :
( ( mem @ X37 @ ( arr @ X16 @ X18 ) )
=> ! [X38: $i] :
( ( mem @ X38 @ ( arr @ X18 @ X16 ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X16 @ X18 ) @ X36 ) @ X37 ) @ X38 ) )
=> ! [X39: $i] :
( ( mem @ X39 @ ( arr @ X15 @ X16 ) )
=> ! [X40: $i] :
( ( mem @ X40 @ ( arr @ X15 @ X16 ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X15 @ X16 ) @ X33 ) @ X36 ) @ X39 ) @ X40 ) )
<=> ( ( p @ ( ap @ ( ap @ ( c_2Equotient_2Erespects @ ( arr @ X15 @ X16 ) @ bool ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X15 @ X16 ) @ X33 ) @ X36 ) ) @ X39 ) )
& ( p @ ( ap @ ( ap @ ( c_2Equotient_2Erespects @ ( arr @ X15 @ X16 ) @ bool ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X15 @ X16 ) @ X33 ) @ X36 ) ) @ X40 ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X17 @ X16 @ X15 @ X18 ) @ X35 ) @ X37 ) @ X39 )
= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X17 @ X16 @ X15 @ X18 ) @ X35 ) @ X37 ) @ X40 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Equotient_2EFUN__REL__EQ__REL]) ).
thf(c_0_17,plain,
! [X2: $i,X5: $i,X4: del,X3: del] :
( ( ( ap @ ( ap @ ( c_2Ecombin_2EW @ X3 @ X4 ) @ X2 ) @ X5 )
= ( ap @ ( ap @ X2 @ X5 ) @ X5 ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ ( arr @ X3 @ X4 ) ) )
| ~ ( mem @ X5 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_18,plain,
! [X3: del,X4: del] :
( ( c_2Equotient_2Erespects @ X3 @ X4 )
= ( c_2Ecombin_2EW @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_19,plain,
! [X2: $i,X4: del,X3: del] :
( ( mem @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X3 @ X4 ) @ X2 ) @ ( arr @ ( arr @ X4 @ ( arr @ X4 @ bool ) ) @ ( arr @ ( arr @ X3 @ X4 ) @ ( arr @ ( arr @ X3 @ X4 ) @ bool ) ) ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ ( arr @ X3 @ bool ) ) ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_20,plain,
! [X129: del,X130: del,X131: $i,X132: $i,X133: $i,X134: $i,X135: $i] :
( ( ( p @ ( ap @ ( ap @ X131 @ X134 ) @ X134 ) )
| ~ ( p @ ( ap @ ( ap @ X131 @ X134 ) @ X135 ) )
| ~ ( mem @ X135 @ X129 )
| ~ ( mem @ X134 @ X129 )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X129 @ X130 ) @ X131 ) @ X132 ) @ X133 ) )
| ~ ( mem @ X133 @ ( arr @ X130 @ X129 ) )
| ~ ( mem @ X132 @ ( arr @ X129 @ X130 ) )
| ~ ( mem @ X131 @ ( arr @ X129 @ ( arr @ X129 @ bool ) ) ) )
& ( ( p @ ( ap @ ( ap @ X131 @ X135 ) @ X135 ) )
| ~ ( p @ ( ap @ ( ap @ X131 @ X134 ) @ X135 ) )
| ~ ( mem @ X135 @ X129 )
| ~ ( mem @ X134 @ X129 )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X129 @ X130 ) @ X131 ) @ X132 ) @ X133 ) )
| ~ ( mem @ X133 @ ( arr @ X130 @ X129 ) )
| ~ ( mem @ X132 @ ( arr @ X129 @ X130 ) )
| ~ ( mem @ X131 @ ( arr @ X129 @ ( arr @ X129 @ bool ) ) ) )
& ( ( ( ap @ X132 @ X134 )
= ( ap @ X132 @ X135 ) )
| ~ ( p @ ( ap @ ( ap @ X131 @ X134 ) @ X135 ) )
| ~ ( mem @ X135 @ X129 )
| ~ ( mem @ X134 @ X129 )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X129 @ X130 ) @ X131 ) @ X132 ) @ X133 ) )
| ~ ( mem @ X133 @ ( arr @ X130 @ X129 ) )
| ~ ( mem @ X132 @ ( arr @ X129 @ X130 ) )
| ~ ( mem @ X131 @ ( arr @ X129 @ ( arr @ X129 @ bool ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ X131 @ X134 ) @ X134 ) )
| ~ ( p @ ( ap @ ( ap @ X131 @ X135 ) @ X135 ) )
| ( ( ap @ X132 @ X134 )
!= ( ap @ X132 @ X135 ) )
| ( p @ ( ap @ ( ap @ X131 @ X134 ) @ X135 ) )
| ~ ( mem @ X135 @ X129 )
| ~ ( mem @ X134 @ X129 )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X129 @ X130 ) @ X131 ) @ X132 ) @ X133 ) )
| ~ ( mem @ X133 @ ( arr @ X130 @ X129 ) )
| ~ ( mem @ X132 @ ( arr @ X129 @ X130 ) )
| ~ ( mem @ X131 @ ( arr @ X129 @ ( arr @ X129 @ bool ) ) ) ) ),
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_2Equotient_2EQUOTIENT__REL])])])])]) ).
thf(c_0_21,plain,
! [X136: del,X137: del,X138: del,X139: del,X140: $i,X141: $i,X142: $i,X143: $i,X144: $i,X145: $i] :
( ~ ( mem @ X140 @ ( arr @ X136 @ ( arr @ X136 @ bool ) ) )
| ~ ( mem @ X141 @ ( arr @ X136 @ X138 ) )
| ~ ( mem @ X142 @ ( arr @ X138 @ X136 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X136 @ X138 ) @ X140 ) @ X141 ) @ X142 ) )
| ~ ( mem @ X143 @ ( arr @ X137 @ ( arr @ X137 @ bool ) ) )
| ~ ( mem @ X144 @ ( arr @ X137 @ X139 ) )
| ~ ( mem @ X145 @ ( arr @ X139 @ X137 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X137 @ X139 ) @ X143 ) @ X144 ) @ X145 ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ ( arr @ X136 @ X137 ) @ ( arr @ X138 @ X139 ) ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X136 @ X137 ) @ X140 ) @ X143 ) ) @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X138 @ X137 @ X136 @ X139 ) @ X142 ) @ X144 ) ) @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X136 @ X139 @ X138 @ X137 ) @ X141 ) @ X145 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Equotient_2EFUN__QUOTIENT])])])]) ).
thf(c_0_22,plain,
! [X2: $i,X3: del,X4: del,X16: del,X15: del] :
( ( mem @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ X4 @ X15 @ X16 ) @ X2 ) @ ( arr @ ( arr @ X4 @ X16 ) @ ( arr @ ( arr @ X15 @ X4 ) @ ( arr @ X3 @ X16 ) ) ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ X15 ) ) ),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
thf(c_0_23,negated_conjecture,
( ( mem @ esk5_0 @ ( arr @ esk1_0 @ ( arr @ esk1_0 @ bool ) ) )
& ( mem @ esk6_0 @ ( arr @ esk1_0 @ esk3_0 ) )
& ( mem @ esk7_0 @ ( arr @ esk3_0 @ esk1_0 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk1_0 @ esk3_0 ) @ esk5_0 ) @ esk6_0 ) @ esk7_0 ) )
& ( mem @ esk8_0 @ ( arr @ esk2_0 @ ( arr @ esk2_0 @ bool ) ) )
& ( mem @ esk9_0 @ ( arr @ esk2_0 @ esk4_0 ) )
& ( mem @ esk10_0 @ ( arr @ esk4_0 @ esk2_0 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk2_0 @ esk4_0 ) @ esk8_0 ) @ esk9_0 ) @ esk10_0 ) )
& ( mem @ esk11_0 @ ( arr @ esk1_0 @ esk2_0 ) )
& ( mem @ esk12_0 @ ( arr @ esk1_0 @ esk2_0 ) )
& ( ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( c_2Equotient_2Erespects @ ( arr @ esk1_0 @ esk2_0 ) @ bool ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) ) @ esk11_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( c_2Equotient_2Erespects @ ( arr @ esk1_0 @ esk2_0 ) @ bool ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) ) @ esk12_0 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ esk3_0 @ esk2_0 @ esk1_0 @ esk4_0 ) @ esk7_0 ) @ esk9_0 ) @ esk11_0 )
!= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ esk3_0 @ esk2_0 @ esk1_0 @ esk4_0 ) @ esk7_0 ) @ esk9_0 ) @ esk12_0 ) ) )
& ( ( p @ ( ap @ ( ap @ ( c_2Equotient_2Erespects @ ( arr @ esk1_0 @ esk2_0 ) @ bool ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) ) @ esk11_0 ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) ) )
& ( ( p @ ( ap @ ( ap @ ( c_2Equotient_2Erespects @ ( arr @ esk1_0 @ esk2_0 ) @ bool ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) ) @ esk12_0 ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) ) )
& ( ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ esk3_0 @ esk2_0 @ esk1_0 @ esk4_0 ) @ esk7_0 ) @ esk9_0 ) @ esk11_0 )
= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ esk3_0 @ esk2_0 @ esk1_0 @ esk4_0 ) @ esk7_0 ) @ esk9_0 ) @ esk12_0 ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_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_16])])])])]) ).
thf(c_0_24,plain,
! [X2: $i,X5: $i,X4: del,X3: del] :
( ( ( ap @ ( ap @ ( c_2Equotient_2Erespects @ X3 @ X4 ) @ X2 ) @ X5 )
= ( ap @ ( ap @ X2 @ X5 ) @ X5 ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ ( arr @ X3 @ X4 ) ) )
| ~ ( mem @ X5 @ X3 ) ),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_25,plain,
! [X2: $i,X5: $i,X4: del,X3: del] :
( ( mem @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X3 @ X4 ) @ X2 ) @ X5 ) @ ( arr @ ( arr @ X3 @ X4 ) @ ( arr @ ( arr @ X3 @ X4 ) @ bool ) ) )
| ~ ( mem @ X5 @ ( arr @ X4 @ ( arr @ X4 @ bool ) ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ ( arr @ X3 @ bool ) ) ) ),
inference(spm,[status(thm)],[c_0_13,c_0_19]) ).
thf(c_0_26,plain,
! [X8: $i,X2: $i,X5: $i,X9: $i,X6: $i,X4: del,X3: del] :
( ( p @ ( ap @ ( ap @ X2 @ X5 ) @ X5 ) )
| ~ ( p @ ( ap @ ( ap @ X2 @ X5 ) @ X6 ) )
| ~ ( mem @ X6 @ X3 )
| ~ ( mem @ X5 @ X3 )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X3 @ X4 ) @ X2 ) @ X8 ) @ X9 ) )
| ~ ( mem @ X9 @ ( arr @ X4 @ X3 ) )
| ~ ( mem @ X8 @ ( arr @ X3 @ X4 ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ ( arr @ X3 @ bool ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_27,plain,
! [X2: $i,X4: del,X3: del,X6: $i,X5: $i,X8: $i,X9: $i,X16: del,X15: del,X10: $i] :
( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ ( arr @ X3 @ X15 ) @ ( arr @ X4 @ X16 ) ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X3 @ X15 ) @ X2 ) @ X8 ) ) @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X4 @ X15 @ X3 @ X16 ) @ X6 ) @ X9 ) ) @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ X16 @ X4 @ X15 ) @ X5 ) @ X10 ) ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ ( arr @ X3 @ bool ) ) )
| ~ ( mem @ X5 @ ( arr @ X3 @ X4 ) )
| ~ ( mem @ X6 @ ( arr @ X4 @ X3 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X3 @ X4 ) @ X2 ) @ X5 ) @ X6 ) )
| ~ ( mem @ X8 @ ( arr @ X15 @ ( arr @ X15 @ bool ) ) )
| ~ ( mem @ X9 @ ( arr @ X15 @ X16 ) )
| ~ ( mem @ X10 @ ( arr @ X16 @ X15 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X15 @ X16 ) @ X8 ) @ X9 ) @ X10 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_28,plain,
! [X2: $i,X4: del,X3: del,X5: $i,X16: del,X15: del] :
( ( mem @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ X4 @ X15 @ X16 ) @ X2 ) @ X5 ) @ ( arr @ ( arr @ X15 @ X4 ) @ ( arr @ X3 @ X16 ) ) )
| ~ ( mem @ X5 @ ( arr @ X4 @ X16 ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ X15 ) ) ),
inference(spm,[status(thm)],[c_0_13,c_0_22]) ).
thf(c_0_29,negated_conjecture,
( ( p @ ( ap @ ( ap @ ( c_2Equotient_2Erespects @ ( arr @ esk1_0 @ esk2_0 ) @ bool ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) ) @ esk11_0 ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_30,plain,
! [X2: $i,X3: del,X5: $i,X6: $i,X4: del] :
( ( ( ap @ ( ap @ ( c_2Equotient_2Erespects @ ( arr @ X3 @ X4 ) @ bool ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X3 @ X4 ) @ X2 ) @ X5 ) ) @ X6 )
= ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X3 @ X4 ) @ X2 ) @ X5 ) @ X6 ) @ X6 ) )
| ~ ( mem @ X5 @ ( arr @ X4 @ ( arr @ X4 @ bool ) ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ ( arr @ X3 @ bool ) ) )
| ~ ( mem @ X6 @ ( arr @ X3 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_31,negated_conjecture,
mem @ esk8_0 @ ( arr @ esk2_0 @ ( arr @ esk2_0 @ bool ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_32,negated_conjecture,
mem @ esk5_0 @ ( arr @ esk1_0 @ ( arr @ esk1_0 @ bool ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_33,negated_conjecture,
mem @ esk11_0 @ ( arr @ esk1_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_34,plain,
! [X2: $i,X8: $i,X6: $i,X5: $i,X10: $i,X9: $i,X4: del,X3: del,X13: $i,X15: del,X12: $i,X16: del] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X3 @ X4 ) @ X2 ) @ X5 ) @ X6 ) @ X6 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X3 @ X4 ) @ X2 ) @ X5 ) @ X6 ) @ X8 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X4 @ X15 ) @ X5 ) @ X9 ) @ X10 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X3 @ X16 ) @ X2 ) @ X12 ) @ X13 ) )
| ~ ( mem @ X5 @ ( arr @ X4 @ ( arr @ X4 @ bool ) ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ ( arr @ X3 @ bool ) ) )
| ~ ( mem @ X8 @ ( arr @ X3 @ X4 ) )
| ~ ( mem @ X6 @ ( arr @ X3 @ X4 ) )
| ~ ( mem @ X10 @ ( arr @ X15 @ X4 ) )
| ~ ( mem @ X9 @ ( arr @ X4 @ X15 ) )
| ~ ( mem @ X13 @ ( arr @ X16 @ X3 ) )
| ~ ( mem @ X12 @ ( arr @ X3 @ X16 ) ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_28]),c_0_25]) ).
thf(c_0_35,negated_conjecture,
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk11_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]),c_0_33])]) ).
thf(c_0_36,negated_conjecture,
mem @ esk12_0 @ ( arr @ esk1_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_37,negated_conjecture,
! [X2: $i,X8: $i,X3: del,X6: $i,X5: $i,X4: del] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk11_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk2_0 @ X3 ) @ esk8_0 ) @ X2 ) @ X5 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk1_0 @ X4 ) @ esk5_0 ) @ X6 ) @ X8 ) )
| ~ ( mem @ X5 @ ( arr @ X3 @ esk2_0 ) )
| ~ ( mem @ X2 @ ( arr @ esk2_0 @ X3 ) )
| ~ ( mem @ X8 @ ( arr @ X4 @ esk1_0 ) )
| ~ ( mem @ X6 @ ( arr @ esk1_0 @ X4 ) ) ),
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_34,c_0_35]),c_0_31]),c_0_32]),c_0_36]),c_0_33])]) ).
thf(c_0_38,negated_conjecture,
p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk2_0 @ esk4_0 ) @ esk8_0 ) @ esk9_0 ) @ esk10_0 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_39,negated_conjecture,
mem @ esk10_0 @ ( arr @ esk4_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_40,negated_conjecture,
mem @ esk9_0 @ ( arr @ esk2_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_41,plain,
! [X8: $i,X2: $i,X5: $i,X9: $i,X6: $i,X4: del,X3: del] :
( ( p @ ( ap @ ( ap @ X2 @ X5 ) @ X6 ) )
| ~ ( p @ ( ap @ ( ap @ X2 @ X5 ) @ X5 ) )
| ~ ( p @ ( ap @ ( ap @ X2 @ X6 ) @ X6 ) )
| ( ( ap @ X8 @ X5 )
!= ( ap @ X8 @ X6 ) )
| ~ ( mem @ X6 @ X3 )
| ~ ( mem @ X5 @ X3 )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X3 @ X4 ) @ X2 ) @ X8 ) @ X9 ) )
| ~ ( mem @ X9 @ ( arr @ X4 @ X3 ) )
| ~ ( mem @ X8 @ ( arr @ X3 @ X4 ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ ( arr @ X3 @ bool ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_42,negated_conjecture,
! [X2: $i,X5: $i,X3: del] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk11_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk1_0 @ X3 ) @ esk5_0 ) @ X2 ) @ X5 ) )
| ~ ( mem @ X5 @ ( arr @ X3 @ esk1_0 ) )
| ~ ( mem @ X2 @ ( arr @ esk1_0 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40])]) ).
thf(c_0_43,negated_conjecture,
p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk1_0 @ esk3_0 ) @ esk5_0 ) @ esk6_0 ) @ esk7_0 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_44,negated_conjecture,
mem @ esk7_0 @ ( arr @ esk3_0 @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_45,negated_conjecture,
mem @ esk6_0 @ ( arr @ esk1_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_46,plain,
! [X2: $i,X8: $i,X5: $i,X9: $i,X6: $i,X4: del,X3: del] :
( ( ( ap @ X2 @ X5 )
= ( ap @ X2 @ X6 ) )
| ~ ( p @ ( ap @ ( ap @ X8 @ X5 ) @ X6 ) )
| ~ ( mem @ X6 @ X3 )
| ~ ( mem @ X5 @ X3 )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X3 @ X4 ) @ X8 ) @ X2 ) @ X9 ) )
| ~ ( mem @ X9 @ ( arr @ X4 @ X3 ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ X4 ) )
| ~ ( mem @ X8 @ ( arr @ X3 @ ( arr @ X3 @ bool ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_47,plain,
! [X2: $i,X8: $i,X4: del,X6: $i,X9: $i,X5: $i,X3: del,X12: $i,X13: $i,X10: $i,X16: del,X15: del] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X3 @ X4 ) @ X2 ) @ X5 ) @ X6 ) @ X8 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X15 @ X4 @ X3 @ X16 ) @ X9 ) @ X10 ) @ X6 )
!= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X15 @ X4 @ X3 @ X16 ) @ X9 ) @ X10 ) @ X8 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X3 @ X4 ) @ X2 ) @ X5 ) @ X8 ) @ X8 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X3 @ X4 ) @ X2 ) @ X5 ) @ X6 ) @ X6 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X4 @ X16 ) @ X5 ) @ X10 ) @ X12 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X3 @ X15 ) @ X2 ) @ X13 ) @ X9 ) )
| ~ ( mem @ X5 @ ( arr @ X4 @ ( arr @ X4 @ bool ) ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ ( arr @ X3 @ bool ) ) )
| ~ ( mem @ X8 @ ( arr @ X3 @ X4 ) )
| ~ ( mem @ X6 @ ( arr @ X3 @ X4 ) )
| ~ ( mem @ X12 @ ( arr @ X16 @ X4 ) )
| ~ ( mem @ X10 @ ( arr @ X4 @ X16 ) )
| ~ ( mem @ X9 @ ( arr @ X15 @ X3 ) )
| ~ ( mem @ X13 @ ( arr @ X3 @ X15 ) ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_27]),c_0_28]),c_0_28]),c_0_25]) ).
thf(c_0_48,negated_conjecture,
p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk11_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45])]) ).
thf(c_0_49,negated_conjecture,
( ( p @ ( ap @ ( ap @ ( c_2Equotient_2Erespects @ ( arr @ esk1_0 @ esk2_0 ) @ bool ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) ) @ esk12_0 ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_50,plain,
! [X8: $i,X2: $i,X4: del,X6: $i,X10: $i,X12: $i,X9: $i,X5: $i,X16: del,X15: del,X13: $i,X3: del] :
( ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ X4 @ X15 @ X16 ) @ X2 ) @ X5 ) @ X6 )
= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ X4 @ X15 @ X16 ) @ X2 ) @ X5 ) @ X8 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X15 @ X4 ) @ X9 ) @ X10 ) @ X6 ) @ X8 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X4 @ X16 ) @ X10 ) @ X5 ) @ X12 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X15 @ X3 ) @ X9 ) @ X13 ) @ X2 ) )
| ~ ( mem @ X10 @ ( arr @ X4 @ ( arr @ X4 @ bool ) ) )
| ~ ( mem @ X9 @ ( arr @ X15 @ ( arr @ X15 @ bool ) ) )
| ~ ( mem @ X8 @ ( arr @ X15 @ X4 ) )
| ~ ( mem @ X6 @ ( arr @ X15 @ X4 ) )
| ~ ( mem @ X12 @ ( arr @ X16 @ X4 ) )
| ~ ( mem @ X5 @ ( arr @ X4 @ X16 ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ X15 ) )
| ~ ( mem @ X13 @ ( arr @ X15 @ X3 ) ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_27]),c_0_28]),c_0_28]),c_0_25]) ).
thf(c_0_51,negated_conjecture,
( ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ esk3_0 @ esk2_0 @ esk1_0 @ esk4_0 ) @ esk7_0 ) @ esk9_0 ) @ esk11_0 )
= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ esk3_0 @ esk2_0 @ esk1_0 @ esk4_0 ) @ esk7_0 ) @ esk9_0 ) @ esk12_0 ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_52,negated_conjecture,
! [X2: $i,X8: $i,X5: $i,X6: $i,X9: $i,X4: del,X3: del] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ X2 ) @ esk11_0 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ esk2_0 @ esk1_0 @ X4 ) @ X5 ) @ X6 ) @ X2 )
!= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ esk2_0 @ esk1_0 @ X4 ) @ X5 ) @ X6 ) @ esk11_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ X2 ) @ X2 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk2_0 @ X4 ) @ esk8_0 ) @ X6 ) @ X8 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk1_0 @ X3 ) @ esk5_0 ) @ X9 ) @ X5 ) )
| ~ ( mem @ X2 @ ( arr @ esk1_0 @ esk2_0 ) )
| ~ ( mem @ X8 @ ( arr @ X4 @ esk2_0 ) )
| ~ ( mem @ X6 @ ( arr @ esk2_0 @ X4 ) )
| ~ ( mem @ X5 @ ( arr @ X3 @ esk1_0 ) )
| ~ ( mem @ X9 @ ( arr @ esk1_0 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_31]),c_0_32]),c_0_33])]) ).
thf(c_0_53,negated_conjecture,
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk12_0 ) @ esk12_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_30]),c_0_31]),c_0_32]),c_0_36])]) ).
thf(c_0_54,negated_conjecture,
! [X2: $i,X8: $i,X6: $i,X5: $i,X4: del,X3: del] :
( ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ esk3_0 @ esk2_0 @ esk1_0 @ esk4_0 ) @ esk7_0 ) @ esk9_0 ) @ esk12_0 )
= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ esk3_0 @ esk2_0 @ esk1_0 @ esk4_0 ) @ esk7_0 ) @ esk9_0 ) @ esk11_0 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ esk2_0 @ esk1_0 @ X4 ) @ X2 ) @ X5 ) @ esk12_0 )
= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ esk2_0 @ esk1_0 @ X4 ) @ X2 ) @ X5 ) @ esk11_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk2_0 @ X4 ) @ esk8_0 ) @ X5 ) @ X6 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk1_0 @ X3 ) @ esk5_0 ) @ X8 ) @ X2 ) )
| ~ ( mem @ X6 @ ( arr @ X4 @ esk2_0 ) )
| ~ ( mem @ X5 @ ( arr @ esk2_0 @ X4 ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ esk1_0 ) )
| ~ ( mem @ X8 @ ( arr @ esk1_0 @ X3 ) ) ),
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_50,c_0_51]),c_0_31]),c_0_32]),c_0_36]),c_0_33])]) ).
thf(c_0_55,negated_conjecture,
! [X2: $i,X8: $i,X6: $i,X5: $i,X4: del,X3: del] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk12_0 ) @ esk11_0 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ esk2_0 @ esk1_0 @ X4 ) @ X2 ) @ X5 ) @ esk12_0 )
!= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ esk2_0 @ esk1_0 @ X4 ) @ X2 ) @ X5 ) @ esk11_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk2_0 @ X4 ) @ esk8_0 ) @ X5 ) @ X6 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk1_0 @ X3 ) @ esk5_0 ) @ X8 ) @ X2 ) )
| ~ ( mem @ X6 @ ( arr @ X4 @ esk2_0 ) )
| ~ ( mem @ X5 @ ( arr @ esk2_0 @ X4 ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ esk1_0 ) )
| ~ ( mem @ X8 @ ( arr @ esk1_0 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_36])]) ).
thf(c_0_56,negated_conjecture,
! [X2: $i,X5: $i,X3: del] :
( ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ esk3_0 @ esk2_0 @ esk1_0 @ esk4_0 ) @ esk7_0 ) @ esk9_0 ) @ esk12_0 )
= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ esk3_0 @ esk2_0 @ esk1_0 @ esk4_0 ) @ esk7_0 ) @ esk9_0 ) @ esk11_0 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ esk2_0 @ esk1_0 @ esk4_0 ) @ X2 ) @ esk9_0 ) @ esk12_0 )
= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ esk2_0 @ esk1_0 @ esk4_0 ) @ X2 ) @ esk9_0 ) @ esk11_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk1_0 @ X3 ) @ esk5_0 ) @ X5 ) @ X2 ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ esk1_0 ) )
| ~ ( mem @ X5 @ ( arr @ esk1_0 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_38]),c_0_39]),c_0_40])]) ).
thf(c_0_57,negated_conjecture,
! [X2: $i,X5: $i,X3: del] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk12_0 ) @ esk11_0 ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ esk2_0 @ esk1_0 @ esk4_0 ) @ X2 ) @ esk9_0 ) @ esk12_0 )
!= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ esk2_0 @ esk1_0 @ esk4_0 ) @ X2 ) @ esk9_0 ) @ esk11_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk1_0 @ X3 ) @ esk5_0 ) @ X5 ) @ X2 ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ esk1_0 ) )
| ~ ( mem @ X5 @ ( arr @ esk1_0 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_38]),c_0_39]),c_0_40])]) ).
thf(c_0_58,negated_conjecture,
( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ esk3_0 @ esk2_0 @ esk1_0 @ esk4_0 ) @ esk7_0 ) @ esk9_0 ) @ esk12_0 )
= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ esk3_0 @ esk2_0 @ esk1_0 @ esk4_0 ) @ esk7_0 ) @ esk9_0 ) @ esk11_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_43]),c_0_44]),c_0_45])]) ).
thf(c_0_59,negated_conjecture,
( ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( c_2Equotient_2Erespects @ ( arr @ esk1_0 @ esk2_0 ) @ bool ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) ) @ esk11_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( c_2Equotient_2Erespects @ ( arr @ esk1_0 @ esk2_0 ) @ bool ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) ) @ esk12_0 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ esk3_0 @ esk2_0 @ esk1_0 @ esk4_0 ) @ esk7_0 ) @ esk9_0 ) @ esk11_0 )
!= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ esk3_0 @ esk2_0 @ esk1_0 @ esk4_0 ) @ esk7_0 ) @ esk9_0 ) @ esk12_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_60,negated_conjecture,
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk12_0 ) @ esk11_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_43]),c_0_58]),c_0_44]),c_0_45])]) ).
thf(c_0_61,negated_conjecture,
( ~ ( p @ ( ap @ ( ap @ ( c_2Equotient_2Erespects @ ( arr @ esk1_0 @ esk2_0 ) @ bool ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) ) @ esk11_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( c_2Equotient_2Erespects @ ( arr @ esk1_0 @ esk2_0 ) @ bool ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) ) @ esk12_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_58])]) ).
thf(c_0_62,negated_conjecture,
! [X2: $i,X8: $i,X5: $i,X6: $i,X9: $i,X4: del,X3: del] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ X2 ) @ esk12_0 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ esk2_0 @ esk1_0 @ X4 ) @ X5 ) @ X6 ) @ X2 )
!= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ esk2_0 @ esk1_0 @ X4 ) @ X5 ) @ X6 ) @ esk12_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ X2 ) @ X2 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk2_0 @ X4 ) @ esk8_0 ) @ X6 ) @ X8 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk1_0 @ X3 ) @ esk5_0 ) @ X9 ) @ X5 ) )
| ~ ( mem @ X2 @ ( arr @ esk1_0 @ esk2_0 ) )
| ~ ( mem @ X8 @ ( arr @ X4 @ esk2_0 ) )
| ~ ( mem @ X6 @ ( arr @ esk2_0 @ X4 ) )
| ~ ( mem @ X5 @ ( arr @ X3 @ esk1_0 ) )
| ~ ( mem @ X9 @ ( arr @ esk1_0 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_53]),c_0_31]),c_0_32]),c_0_36])]) ).
thf(c_0_63,negated_conjecture,
! [X2: $i,X8: $i,X6: $i,X5: $i,X4: del,X3: del] :
( ( ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ esk2_0 @ esk1_0 @ X4 ) @ X2 ) @ X5 ) @ esk12_0 )
= ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ X3 @ esk2_0 @ esk1_0 @ X4 ) @ X2 ) @ X5 ) @ esk11_0 ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk2_0 @ X4 ) @ esk8_0 ) @ X5 ) @ X6 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk1_0 @ X3 ) @ esk5_0 ) @ X8 ) @ X2 ) )
| ~ ( mem @ X6 @ ( arr @ X4 @ esk2_0 ) )
| ~ ( mem @ X5 @ ( arr @ esk2_0 @ X4 ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ esk1_0 ) )
| ~ ( mem @ X8 @ ( arr @ esk1_0 @ X3 ) ) ),
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_50,c_0_60]),c_0_31]),c_0_32]),c_0_33]),c_0_36])]) ).
thf(c_0_64,negated_conjecture,
( ~ ( p @ ( ap @ ( ap @ ( c_2Equotient_2Erespects @ ( arr @ esk1_0 @ esk2_0 ) @ bool ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) ) @ esk11_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk12_0 ) @ esk12_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_30]),c_0_31]),c_0_32]),c_0_36])]) ).
thf(c_0_65,negated_conjecture,
! [X2: $i,X8: $i,X3: del,X6: $i,X5: $i,X4: del] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk2_0 @ X3 ) @ esk8_0 ) @ X2 ) @ X5 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk1_0 @ X4 ) @ esk5_0 ) @ X6 ) @ X8 ) )
| ~ ( mem @ X5 @ ( arr @ X3 @ esk2_0 ) )
| ~ ( mem @ X2 @ ( arr @ esk2_0 @ X3 ) )
| ~ ( mem @ X8 @ ( arr @ X4 @ esk1_0 ) )
| ~ ( mem @ X6 @ ( arr @ esk1_0 @ X4 ) ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_48]),c_0_33])]),c_0_63]) ).
thf(c_0_66,negated_conjecture,
( ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk11_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk12_0 ) @ esk12_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_30]),c_0_31]),c_0_32]),c_0_33])]) ).
thf(c_0_67,negated_conjecture,
! [X2: $i,X5: $i,X3: del] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk1_0 @ X3 ) @ esk5_0 ) @ X2 ) @ X5 ) )
| ~ ( mem @ X5 @ ( arr @ X3 @ esk1_0 ) )
| ~ ( mem @ X2 @ ( arr @ esk1_0 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_38]),c_0_39]),c_0_40])]) ).
thf(c_0_68,plain,
! [X8: $i,X2: $i,X5: $i,X9: $i,X6: $i,X4: del,X3: del] :
( ( p @ ( ap @ ( ap @ X2 @ X5 ) @ X5 ) )
| ~ ( p @ ( ap @ ( ap @ X2 @ X6 ) @ X5 ) )
| ~ ( mem @ X5 @ X3 )
| ~ ( mem @ X6 @ X3 )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X3 @ X4 ) @ X2 ) @ X8 ) @ X9 ) )
| ~ ( mem @ X9 @ ( arr @ X4 @ X3 ) )
| ~ ( mem @ X8 @ ( arr @ X3 @ X4 ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ ( arr @ X3 @ bool ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_69,negated_conjecture,
( ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk12_0 ) @ esk12_0 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_48])]) ).
thf(c_0_70,negated_conjecture,
p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk11_0 ) @ esk12_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_43]),c_0_44]),c_0_45])]) ).
thf(c_0_71,plain,
! [X2: $i,X8: $i,X6: $i,X5: $i,X10: $i,X9: $i,X4: del,X3: del,X13: $i,X15: del,X12: $i,X16: del] :
( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X3 @ X4 ) @ X2 ) @ X5 ) @ X6 ) @ X6 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ X3 @ X4 ) @ X2 ) @ X5 ) @ X8 ) @ X6 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X4 @ X15 ) @ X5 ) @ X9 ) @ X10 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ X3 @ X16 ) @ X2 ) @ X12 ) @ X13 ) )
| ~ ( mem @ X5 @ ( arr @ X4 @ ( arr @ X4 @ bool ) ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ ( arr @ X3 @ bool ) ) )
| ~ ( mem @ X8 @ ( arr @ X3 @ X4 ) )
| ~ ( mem @ X6 @ ( arr @ X3 @ X4 ) )
| ~ ( mem @ X10 @ ( arr @ X15 @ X4 ) )
| ~ ( mem @ X9 @ ( arr @ X4 @ X15 ) )
| ~ ( mem @ X13 @ ( arr @ X16 @ X3 ) )
| ~ ( mem @ X12 @ ( arr @ X3 @ X16 ) ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_27]),c_0_28]),c_0_28]),c_0_25]) ).
thf(c_0_72,negated_conjecture,
~ ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ esk1_0 @ esk2_0 ) @ esk5_0 ) @ esk8_0 ) @ esk12_0 ) @ esk12_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
thf(c_0_73,negated_conjecture,
! [X2: $i,X8: $i,X3: del,X6: $i,X5: $i,X4: del] :
( ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk2_0 @ X3 ) @ esk8_0 ) @ X2 ) @ X5 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk1_0 @ X4 ) @ esk5_0 ) @ X6 ) @ X8 ) )
| ~ ( mem @ X5 @ ( arr @ X3 @ esk2_0 ) )
| ~ ( mem @ X2 @ ( arr @ esk2_0 @ X3 ) )
| ~ ( mem @ X8 @ ( arr @ X4 @ esk1_0 ) )
| ~ ( mem @ X6 @ ( arr @ esk1_0 @ X4 ) ) ),
inference(sr,[status(thm)],[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_71,c_0_70]),c_0_31]),c_0_32]),c_0_33]),c_0_36])]),c_0_72]) ).
thf(c_0_74,negated_conjecture,
! [X2: $i,X5: $i,X3: del] :
( ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ esk1_0 @ X3 ) @ esk5_0 ) @ X2 ) @ X5 ) )
| ~ ( mem @ X5 @ ( arr @ X3 @ esk1_0 ) )
| ~ ( mem @ X2 @ ( arr @ esk1_0 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_38]),c_0_39]),c_0_40])]) ).
thf(c_0_75,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_43]),c_0_44]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP009^2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n018.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 19:26:56 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 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.hUgaAFsfUm/E---3.1_519170.p
% 199.61/29.27 % Version: 3.5.1-ho
% 199.61/29.27 % Preprocessing class: HSLSSMSSSSSNSFA.
% 199.61/29.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 199.61/29.27 % Starting new_ho_11 with 1500s (5) cores
% 199.61/29.27 % Starting post_as_ho6 with 300s (1) cores
% 199.61/29.27 % Starting sh9 with 300s (1) cores
% 199.61/29.27 % Starting sh5l with 300s (1) cores
% 199.61/29.27 % sh5l with pid 519207 completed with status 0
% 199.61/29.27 % Result found by sh5l
% 199.61/29.27 % Preprocessing class: HSLSSMSSSSSNSFA.
% 199.61/29.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 199.61/29.27 % Starting new_ho_11 with 1500s (5) cores
% 199.61/29.27 % Starting post_as_ho6 with 300s (1) cores
% 199.61/29.27 % Starting sh9 with 300s (1) cores
% 199.61/29.27 % Starting sh5l with 300s (1) cores
% 199.61/29.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 199.61/29.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 199.61/29.27 % Search class: HGHSM-FFMM32-DSFFFFNN
% 199.61/29.27 % partial match(2): HGHSM-FFMM31-DSFFFFBN
% 199.61/29.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 199.61/29.27 % Starting SubtermCWHack with 28s (1) cores
% 199.61/29.27 % SubtermCWHack with pid 519215 completed with status 8
% 199.61/29.27 % Starting sh5l with 31s (1) cores
% 199.61/29.27 % sh5l with pid 519826 completed with status 0
% 199.61/29.27 % Result found by sh5l
% 199.61/29.27 % Preprocessing class: HSLSSMSSSSSNSFA.
% 199.61/29.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 199.61/29.27 % Starting new_ho_11 with 1500s (5) cores
% 199.61/29.27 % Starting post_as_ho6 with 300s (1) cores
% 199.61/29.27 % Starting sh9 with 300s (1) cores
% 199.61/29.27 % Starting sh5l with 300s (1) cores
% 199.61/29.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 199.61/29.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 199.61/29.27 % Search class: HGHSM-FFMM32-DSFFFFNN
% 199.61/29.27 % partial match(2): HGHSM-FFMM31-DSFFFFBN
% 199.61/29.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 199.61/29.27 % Starting SubtermCWHack with 28s (1) cores
% 199.61/29.27 % SubtermCWHack with pid 519215 completed with status 8
% 199.61/29.27 % Starting sh5l with 31s (1) cores
% 199.61/29.27 % Preprocessing time : 0.002 s
% 199.61/29.27 % Presaturation interreduction done
% 199.61/29.27
% 199.61/29.27 % Proof found!
% 199.61/29.27 % SZS status Theorem
% 199.61/29.27 % SZS output start CNFRefutation
% See solution above
% 199.61/29.27 % Parsed axioms : 57
% 199.61/29.27 % Removed by relevancy pruning/SinE : 41
% 199.61/29.27 % Initial clauses : 71
% 199.61/29.27 % Removed in clause preprocessing : 42
% 199.61/29.27 % Initial clauses in saturation : 29
% 199.61/29.27 % Processed clauses : 577
% 199.61/29.27 % ...of these trivial : 3
% 199.61/29.27 % ...subsumed : 160
% 199.61/29.27 % ...remaining for further processing : 414
% 199.61/29.27 % Other redundant clauses eliminated : 0
% 199.61/29.27 % Clauses deleted for lack of memory : 0
% 199.61/29.27 % Backward-subsumed : 17
% 199.61/29.27 % Backward-rewritten : 18
% 199.61/29.27 % Generated clauses : 3739
% 199.61/29.27 % ...of the previous two non-redundant : 3724
% 199.61/29.27 % ...aggressively subsumed : 0
% 199.61/29.27 % Contextual simplify-reflections : 21
% 199.61/29.27 % Paramodulations : 3732
% 199.61/29.27 % Factorizations : 0
% 199.61/29.27 % NegExts : 0
% 199.61/29.27 % Equation resolutions : 1
% 199.61/29.27 % Disequality decompositions : 0
% 199.61/29.27 % Total rewrite steps : 348
% 199.61/29.27 % ...of those cached : 330
% 199.61/29.27 % Propositional unsat checks : 0
% 199.61/29.27 % Propositional check models : 0
% 199.61/29.27 % Propositional check unsatisfiable : 0
% 199.61/29.27 % Propositional clauses : 0
% 199.61/29.27 % Propositional clauses after purity: 0
% 199.61/29.27 % Propositional unsat core size : 0
% 199.61/29.27 % Propositional preprocessing time : 0.000
% 199.61/29.27 % Propositional encoding time : 0.000
% 199.61/29.27 % Propositional solver time : 0.000
% 199.61/29.27 % Success case prop preproc time : 0.000
% 199.61/29.27 % Success case prop encoding time : 0.000
% 199.61/29.27 % Success case prop solver time : 0.000
% 199.61/29.27 % Current number of processed clauses : 351
% 199.61/29.27 % Positive orientable unit clauses : 21
% 199.61/29.27 % Positive unorientable unit clauses: 0
% 199.61/29.27 % Negative unit clauses : 1
% 199.61/29.27 % Non-unit-clauses : 329
% 199.61/29.27 % Current number of unprocessed clauses: 3189
% 199.61/29.27 % ...number of literals in the above : 22406
% 199.61/29.27 % Current number of archived formulas : 0
% 199.61/29.27 % Current number of archived clauses : 63
% 199.61/29.27 % Clause-clause subsumption calls (NU) : 52899
% 199.61/29.27 % Rec. Clause-clause subsumption calls : 11005
% 199.61/29.27 % Non-unit clause-clause subsumptions : 197
% 199.61/29.27 % Unit Clause-clause subsumption calls : 11
% 199.61/29.27 % Rewrite failures with RHS unbound : 0
% 199.61/29.27 % BW rewrite match attempts : 8
% 199.61/29.27 % BW rewrite match successes : 3
% 199.61/29.27 % Condensation attempts : 577
% 199.61/29.27 % Condensation successes : 0
% 199.61/29.27 % Termbank termtop insertions : 1324576
% 199.61/29.27 % Search garbage collected termcells : 1810
% 199.61/29.27
% 199.61/29.27 % -------------------------------------------------
% 199.61/29.27 % User time : 27.973 s
% 199.61/29.27 % System time : 0.567 s
% 199.61/29.27 % Total time : 28.540 s
% 199.61/29.27 % Maximum resident set size: 3984 pages
% 199.61/29.27
% 199.61/29.27 % -------------------------------------------------
% 199.61/29.27 % User time : 27.978 s
% 199.61/29.27 % System time : 0.574 s
% 199.61/29.27 % Total time : 28.552 s
% 199.61/29.27 % Maximum resident set size: 4864 pages
% 199.61/29.27 % E exiting
%------------------------------------------------------------------------------