TSTP Solution File: ITP001+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ITP001+1 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n017.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 : 600s
% DateTime : Sat Jul 16 23:42:33 EDT 2022
% Result : Theorem 0.55s 0.75s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 52
% Syntax : Number of formulae : 402 ( 268 unt; 28 typ; 0 def)
% Number of atoms : 1918 ( 590 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 9812 ( 580 ~; 554 |; 44 &;8598 @)
% ( 28 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 16 con; 0-4 aty)
% Number of variables : 981 ( 0 ^ 979 !; 2 ?; 981 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_app_2E2,type,
app_2E2: $i > $i > $i ).
thf(tp_c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: $i ).
thf(tp_c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: $i ).
thf(tp_c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0: $i ).
thf(tp_c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1: $i > $i ).
thf(tp_c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: $i ).
thf(tp_c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: $i > $i > $i ).
thf(tp_c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0: $i ).
thf(tp_c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1: $i > $i ).
thf(tp_c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: $i ).
thf(tp_c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: $i > $i > $i ).
thf(tp_c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: $i ).
thf(tp_c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: $i > $i ).
thf(tp_c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0: $i ).
thf(tp_c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2: $i > $i > $i ).
thf(tp_c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: $i ).
thf(tp_c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: $i > $i > $i ).
thf(tp_combin_i_2E0,type,
combin_i_2E0: $i ).
thf(tp_combin_k_2E0,type,
combin_k_2E0: $i ).
thf(tp_combin_s_2E0,type,
combin_s_2E0: $i ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_s,type,
s: $i > $i > $i ).
thf(tp_sK1_V0x_2E0,type,
sK1_V0x_2E0: $i ).
thf(tp_sK2_V1x_2E0,type,
sK2_V1x_2E0: $i > $i > $i ).
thf(tp_sK3_V1x_2E0,type,
sK3_V1x_2E0: $i > $i > $i ).
thf(tp_sK4_V2x_2E0,type,
sK4_V2x_2E0: $i > $i > $i > $i > $i ).
thf(tp_tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $i ).
thf(tp_tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $i > $i > $i ).
thf(1,axiom,
( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
<=> ! [V0x_2E0: $i] :
( ( s @ tyop_2Emin_2Ebool @ V0x_2E0 )
= ( s @ tyop_2Emin_2Ebool @ V0x_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ET__DEF) ).
thf(2,axiom,
! [A_27a: $i,X0_2E0: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).
thf(3,axiom,
! [A_27a: $i,X0_2E0: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).
thf(4,axiom,
! [A_27a: $i,X0_2E0: $i,X1_2E0: $i] :
( ( ( s @ A_27a @ X0_2E0 )
= ( s @ A_27a @ X1_2E0 ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
thf(5,axiom,
! [X0_2E0: $i,X1_2E0: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).
thf(6,axiom,
! [X0_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
thf(7,axiom,
! [X0_2E0: $i,X1_2E0: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).
thf(8,axiom,
! [X0_2E0: $i,X1_2E0: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).
thf(9,axiom,
! [A_27a: $i,V0f_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
<=> ? [V1x_2E0: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Equant_2E_3F) ).
thf(10,axiom,
! [A_27a: $i,V0f_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
<=> ! [V1x_2E0: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Equant_2E_21) ).
thf(11,axiom,
! [A_27a: $i,V0_2E0: $i,V1_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
<=> ( ( s @ A_27a @ V0_2E0 )
= ( s @ A_27a @ V1_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D) ).
thf(12,axiom,
! [V0_2E0: $i,V1_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
<=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D_3D_3E) ).
thf(13,axiom,
! [V0_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
<=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_7E) ).
thf(14,axiom,
! [V0_2E0: $i,V1_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
<=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_5C_2F) ).
thf(15,axiom,
! [V0_2E0: $i,V1_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
<=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_2F_5C) ).
thf(16,axiom,
! [A_27a: $i,A_27b: $i,A_27c: $i,V0f_2E0: $i,V1g_2E0: $i,V2x_2E0: $i] :
( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Es__thm) ).
thf(17,axiom,
! [A_27a: $i,A_27b: $i,V0x_2E0: $i,V1y_2E0: $i] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ek__thm) ).
thf(18,axiom,
! [A_27a: $i,V0x_2E0: $i] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ei__thm) ).
thf(19,axiom,
! [V0t_2E0: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ V0t_2E0 )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ V0t_2E0 )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).
thf(20,axiom,
~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
thf(21,axiom,
p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).
thf(22,axiom,
! [V0_2E0: $i,V1_2E0: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) )
=> ( ( s @ tyop_2Emin_2Ebool @ V0_2E0 )
= ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
thf(23,axiom,
! [A_27a: $i,A_27b: $i,V0f_2E0: $i,V1g_2E0: $i] :
( ! [V2x_2E0: $i] :
( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Eeq__ext) ).
thf(24,conjecture,
p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(25,negated_conjecture,
( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[24]) ).
thf(26,plain,
( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $false ),
inference(unfold_def,[status(thm)],[25]) ).
thf(27,plain,
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
<=> ! [V0x_2E0: $i] :
( ( s @ tyop_2Emin_2Ebool @ V0x_2E0 )
= ( s @ tyop_2Emin_2Ebool @ V0x_2E0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(28,plain,
( ( ! [A_27a: $i,X0_2E0: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(29,plain,
( ( ! [A_27a: $i,X0_2E0: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [A_27a: $i,X0_2E0: $i,X1_2E0: $i] :
( ( ( s @ A_27a @ X0_2E0 )
= ( s @ A_27a @ X1_2E0 ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(31,plain,
( ( ! [X0_2E0: $i,X1_2E0: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(32,plain,
( ( ! [X0_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(33,plain,
( ( ! [X0_2E0: $i,X1_2E0: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(34,plain,
( ( ! [X0_2E0: $i,X1_2E0: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(35,plain,
( ( ! [A_27a: $i,V0f_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
<=> ? [V1x_2E0: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(36,plain,
( ( ! [A_27a: $i,V0f_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
<=> ! [V1x_2E0: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(37,plain,
( ( ! [A_27a: $i,V0_2E0: $i,V1_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
<=> ( ( s @ A_27a @ V0_2E0 )
= ( s @ A_27a @ V1_2E0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(38,plain,
( ( ! [V0_2E0: $i,V1_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
<=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(39,plain,
( ( ! [V0_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
<=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(40,plain,
( ( ! [V0_2E0: $i,V1_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
<=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(41,plain,
( ( ! [V0_2E0: $i,V1_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
<=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(42,plain,
( ( ! [A_27a: $i,A_27b: $i,A_27c: $i,V0f_2E0: $i,V1g_2E0: $i,V2x_2E0: $i] :
( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(43,plain,
( ( ! [A_27a: $i,A_27b: $i,V0x_2E0: $i,V1y_2E0: $i] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(44,plain,
( ( ! [A_27a: $i,V0x_2E0: $i] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(45,plain,
( ( ! [V0t_2E0: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ V0t_2E0 )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ V0t_2E0 )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(46,plain,
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(47,plain,
( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(48,plain,
( ( ! [V0_2E0: $i,V1_2E0: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) )
=> ( ( s @ tyop_2Emin_2Ebool @ V0_2E0 )
= ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(49,plain,
( ( ! [A_27a: $i,A_27b: $i,V0f_2E0: $i,V1g_2E0: $i] :
( ! [V2x_2E0: $i] :
( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(50,plain,
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(51,plain,
( ( ( ~ $true
| ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
& ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ! [V0x_2E0: $i] : $true ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(52,plain,
( ( ! [A_27a: $i] :
( ! [X0_2E0: $i,X1_2E0: $i] :
( ( ( s @ A_27a @ X0_2E0 )
!= ( s @ A_27a @ X1_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) )
& ! [X0_2E0: $i,X1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) )
| ( ( s @ A_27a @ X0_2E0 )
= ( s @ A_27a @ X1_2E0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(53,plain,
( ( ! [X0_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
| ! [X1_2E0: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) ) )
& ! [X0_2E0: $i,X1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) ) )
& ! [X0_2E0: $i,X1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(54,plain,
( ( ! [X0_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) )
& ! [X0_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(55,plain,
( ( ! [X0_2E0: $i,X1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) )
& ! [X0_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
| ! [X1_2E0: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) ) )
& ! [X0_2E0: $i,X1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(56,plain,
( ( ! [X0_2E0: $i,X1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) ) )
& ! [X0_2E0: $i] :
( ! [X1_2E0: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) )
& ! [X0_2E0: $i,X1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(57,plain,
( ( ! [A_27a: $i,V0f_2E0: $i] :
( ! [V1x_2E0: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) ) )
& ! [A_27a: $i,V0f_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ ( sK2_V1x_2E0 @ V0f_2E0 @ A_27a ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(58,plain,
( ( ! [A_27a: $i,V0f_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ ( sK3_V1x_2E0 @ V0f_2E0 @ A_27a ) ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) ) )
& ! [A_27a: $i,V0f_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
| ! [V1x_2E0: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(59,plain,
( ( ! [A_27a: $i] :
( ! [V0_2E0: $i,V1_2E0: $i] :
( ( ( s @ A_27a @ V0_2E0 )
!= ( s @ A_27a @ V1_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) ) )
& ! [V0_2E0: $i,V1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
| ( ( s @ A_27a @ V0_2E0 )
= ( s @ A_27a @ V1_2E0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(60,plain,
( ( ! [V0_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ! [V1_2E0: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) ) )
& ! [V0_2E0: $i,V1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) ) )
& ! [V0_2E0: $i,V1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(61,plain,
( ( ! [V0_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) )
& ! [V0_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(62,plain,
( ( ! [V0_2E0: $i,V1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) )
& ! [V0_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ! [V1_2E0: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) ) )
& ! [V0_2E0: $i,V1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(63,plain,
( ( ! [V0_2E0: $i,V1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) ) )
& ! [V0_2E0: $i] :
( ! [V1_2E0: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) )
& ! [V0_2E0: $i,V1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(64,plain,
( ( ! [V0_2E0: $i,V1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ V0_2E0 )
= ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) )
& ! [V0_2E0: $i,V1_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ V0_2E0 )
= ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(65,plain,
( ( ! [A_27a: $i,A_27b: $i,V0f_2E0: $i,V1g_2E0: $i] :
( ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ ( sK4_V2x_2E0 @ V1g_2E0 @ V0f_2E0 @ A_27b @ A_27a ) ) ) )
!= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ ( sK4_V2x_2E0 @ V1g_2E0 @ V0f_2E0 @ A_27b @ A_27a ) ) ) ) )
| ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(66,plain,
( ( ! [A_27a: $i,A_27b: $i,V0f_2E0: $i,V1g_2E0: $i] :
( ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ ( sK4_V2x_2E0 @ V1g_2E0 @ V0f_2E0 @ A_27b @ A_27a ) ) ) )
!= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ ( sK4_V2x_2E0 @ V1g_2E0 @ V0f_2E0 @ A_27b @ A_27a ) ) ) ) )
| ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(67,plain,
( ( ! [V0_2E0: $i,V1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ V0_2E0 )
= ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) )
& ! [V0_2E0: $i,V1_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ V0_2E0 )
= ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(68,plain,
( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(69,plain,
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(70,plain,
( ( ! [V0t_2E0: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ V0t_2E0 )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ V0t_2E0 )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(71,plain,
( ( ! [A_27a: $i,V0x_2E0: $i] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(72,plain,
( ( ! [A_27a: $i,A_27b: $i,V0x_2E0: $i,V1y_2E0: $i] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(73,plain,
( ( ! [A_27a: $i,A_27b: $i,A_27c: $i,V0f_2E0: $i,V1g_2E0: $i,V2x_2E0: $i] :
( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(74,plain,
( ( ! [V0_2E0: $i,V1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) ) )
& ! [V0_2E0: $i] :
( ! [V1_2E0: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) )
& ! [V0_2E0: $i,V1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(75,plain,
( ( ! [V0_2E0: $i,V1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) )
& ! [V0_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ! [V1_2E0: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) ) )
& ! [V0_2E0: $i,V1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(76,plain,
( ( ! [V0_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) )
& ! [V0_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(77,plain,
( ( ! [V0_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ! [V1_2E0: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) ) )
& ! [V0_2E0: $i,V1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) ) )
& ! [V0_2E0: $i,V1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ V1_2E0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(78,plain,
( ( ! [A_27a: $i] :
( ! [V0_2E0: $i,V1_2E0: $i] :
( ( ( s @ A_27a @ V0_2E0 )
!= ( s @ A_27a @ V1_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) ) )
& ! [V0_2E0: $i,V1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
| ( ( s @ A_27a @ V0_2E0 )
= ( s @ A_27a @ V1_2E0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(79,plain,
( ( ! [A_27a: $i,V0f_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ ( sK3_V1x_2E0 @ V0f_2E0 @ A_27a ) ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) ) )
& ! [A_27a: $i,V0f_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
| ! [V1x_2E0: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(80,plain,
( ( ! [A_27a: $i,V0f_2E0: $i] :
( ! [V1x_2E0: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) ) )
& ! [A_27a: $i,V0f_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ ( sK2_V1x_2E0 @ V0f_2E0 @ A_27a ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(81,plain,
( ( ! [X0_2E0: $i,X1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) ) )
& ! [X0_2E0: $i] :
( ! [X1_2E0: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) )
& ! [X0_2E0: $i,X1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(82,plain,
( ( ! [X0_2E0: $i,X1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) )
& ! [X0_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
| ! [X1_2E0: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) ) )
& ! [X0_2E0: $i,X1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(83,plain,
( ( ! [X0_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) )
& ! [X0_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(84,plain,
( ( ! [X0_2E0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
| ! [X1_2E0: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) ) )
& ! [X0_2E0: $i,X1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) ) )
& ! [X0_2E0: $i,X1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ X0_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ X1_2E0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(85,plain,
( ( ! [A_27a: $i] :
( ! [X0_2E0: $i,X1_2E0: $i] :
( ( ( s @ A_27a @ X0_2E0 )
!= ( s @ A_27a @ X1_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) )
& ! [X0_2E0: $i,X1_2E0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) )
| ( ( s @ A_27a @ X0_2E0 )
= ( s @ A_27a @ X1_2E0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(86,plain,
( ( ! [A_27a: $i,X0_2E0: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(87,plain,
( ( ! [A_27a: $i,X0_2E0: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(88,plain,
( ( ( ~ $true
| ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
& ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ! [V0x_2E0: $i] : $true ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(89,plain,
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(90,plain,
( ( ~ ( ~ ( ~ $true
| ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
| ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ! [SX0: $i] : $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(91,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(92,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(93,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(94,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(95,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(96,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( s @ SX0 @ SX1 )
!= ( s @ SX0 @ SX2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SX0 @ SX1 ) ) ) @ ( s @ SX0 @ SX2 ) ) ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SX0 @ SX1 ) ) ) @ ( s @ SX0 @ SX2 ) ) ) )
| ( ( s @ SX0 @ SX1 )
= ( s @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(97,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(98,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(99,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(100,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( s @ SX0 @ SX1 )
!= ( s @ SX0 @ SX2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SX0 @ SX1 ) @ ( s @ SX0 @ SX2 ) ) ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SX0 @ SX1 ) @ ( s @ SX0 @ SX2 ) ) ) )
| ( ( s @ SX0 @ SX1 )
= ( s @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(101,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) @ ( s @ SX0 @ ( sK3_V1x_2E0 @ SX1 @ SX0 ) ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) ) ) )
| ! [SX2: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) @ ( s @ SX0 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(102,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(103,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) @ ( s @ SX0 @ SX2 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) @ ( s @ SX0 @ ( sK2_V1x_2E0 @ SX1 @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(104,plain,
! [SV1: $i] :
( ( ! [SY51: $i,SY52: $i,SY53: $i] :
( ( ( s @ SY51 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV1 @ SY51 ) @ SY52 ) @ ( s @ SV1 @ ( sK4_V2x_2E0 @ SY53 @ SY52 @ SY51 @ SV1 ) ) ) )
!= ( s @ SY51 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV1 @ SY51 ) @ SY53 ) @ ( s @ SV1 @ ( sK4_V2x_2E0 @ SY53 @ SY52 @ SY51 @ SV1 ) ) ) ) )
| ( ( s @ ( tyop_2Emin_2Efun @ SV1 @ SY51 ) @ SY52 )
= ( s @ ( tyop_2Emin_2Efun @ SV1 @ SY51 ) @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(105,plain,
( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(106,plain,
! [SV2: $i] :
( ( ( ( s @ tyop_2Emin_2Ebool @ SV2 )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ SV2 )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(107,plain,
! [SV3: $i] :
( ( ! [SY54: $i] :
( ( s @ SV3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV3 @ SV3 ) @ combin_i_2E0 ) @ ( s @ SV3 @ SY54 ) ) )
= ( s @ SV3 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(108,plain,
! [SV4: $i] :
( ( ! [SY55: $i,SY56: $i,SY57: $i] :
( ( s @ SV4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SY55 @ SV4 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV4 @ ( tyop_2Emin_2Efun @ SY55 @ SV4 ) ) @ combin_k_2E0 ) @ ( s @ SV4 @ SY56 ) ) ) @ ( s @ SY55 @ SY57 ) ) )
= ( s @ SV4 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(109,plain,
! [SV5: $i] :
( ( ! [SY58: $i,SY59: $i,SY60: $i,SY61: $i,SY62: $i] :
( ( s @ SY59 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SY59 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ SY58 ) @ ( tyop_2Emin_2Efun @ SV5 @ SY59 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SY58 @ SY59 ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ SY58 ) @ ( tyop_2Emin_2Efun @ SV5 @ SY59 ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SY58 @ SY59 ) ) @ SY60 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SY58 ) @ SY61 ) ) ) @ ( s @ SV5 @ SY62 ) ) )
= ( s @ SY59 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SY58 @ SY59 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SY58 @ SY59 ) ) @ SY60 ) @ ( s @ SV5 @ SY62 ) ) ) @ ( s @ SY58 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SY58 ) @ SY61 ) @ ( s @ SV5 @ SY62 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(110,plain,
! [SV6: $i] :
( ( ! [SY63: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV6 @ tyop_2Emin_2Ebool ) @ SY63 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV6 @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ SV6 @ tyop_2Emin_2Ebool ) @ SY63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(111,plain,
! [SV7: $i] :
( ( ! [SY64: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV7 @ tyop_2Emin_2Ebool ) @ SY64 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV7 @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ SV7 @ tyop_2Emin_2Ebool ) @ SY64 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(112,plain,
( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(113,plain,
( ( ~ ( ~ $true
| ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
| ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ! [SX0: $i] : $true ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(114,plain,
( ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(115,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(116,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(117,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(118,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(119,plain,
! [SV8: $i] :
( ( ~ ( ~ ! [SY65: $i,SY66: $i] :
( ( ( s @ SV8 @ SY65 )
!= ( s @ SV8 @ SY66 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SV8 @ SY65 ) ) ) @ ( s @ SV8 @ SY66 ) ) ) ) )
| ~ ! [SY67: $i,SY68: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SV8 @ SY67 ) ) ) @ ( s @ SV8 @ SY68 ) ) ) )
| ( ( s @ SV8 @ SY67 )
= ( s @ SV8 @ SY68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(120,plain,
( ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(121,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(122,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(123,plain,
! [SV9: $i] :
( ( ~ ( ~ ! [SY69: $i,SY70: $i] :
( ( ( s @ SV9 @ SY69 )
!= ( s @ SV9 @ SY70 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV9 @ SY69 ) @ ( s @ SV9 @ SY70 ) ) ) ) )
| ~ ! [SY71: $i,SY72: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV9 @ SY71 ) @ ( s @ SV9 @ SY72 ) ) ) )
| ( ( s @ SV9 @ SY71 )
= ( s @ SV9 @ SY72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(124,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) @ ( s @ SX0 @ ( sK3_V1x_2E0 @ SX1 @ SX0 ) ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) ) ) )
| ! [SX2: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) @ ( s @ SX0 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(125,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(126,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) @ ( s @ SX0 @ SX2 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) @ ( s @ SX0 @ ( sK2_V1x_2E0 @ SX1 @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(127,plain,
! [SV1: $i,SV10: $i] :
( ( ! [SY73: $i,SY74: $i] :
( ( ( s @ SV10 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SY73 ) @ ( s @ SV1 @ ( sK4_V2x_2E0 @ SY74 @ SY73 @ SV10 @ SV1 ) ) ) )
!= ( s @ SV10 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SY74 ) @ ( s @ SV1 @ ( sK4_V2x_2E0 @ SY74 @ SY73 @ SV10 @ SV1 ) ) ) ) )
| ( ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SY73 )
= ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(128,plain,
! [SV2: $i] :
( ( ( ( s @ tyop_2Emin_2Ebool @ SV2 )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV2 )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(129,plain,
! [SV11: $i,SV3: $i] :
( ( ( s @ SV3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV3 @ SV3 ) @ combin_i_2E0 ) @ ( s @ SV3 @ SV11 ) ) )
= ( s @ SV3 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(130,plain,
! [SV12: $i,SV4: $i] :
( ( ! [SY75: $i,SY76: $i] :
( ( s @ SV4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV12 @ SV4 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV4 @ ( tyop_2Emin_2Efun @ SV12 @ SV4 ) ) @ combin_k_2E0 ) @ ( s @ SV4 @ SY75 ) ) ) @ ( s @ SV12 @ SY76 ) ) )
= ( s @ SV4 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(131,plain,
! [SV13: $i,SV5: $i] :
( ( ! [SY77: $i,SY78: $i,SY79: $i,SY80: $i] :
( ( s @ SY77 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SY77 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ ( tyop_2Emin_2Efun @ SV5 @ SY77 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SV13 @ SY77 ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ ( tyop_2Emin_2Efun @ SV5 @ SY77 ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SV13 @ SY77 ) ) @ SY78 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ SY79 ) ) ) @ ( s @ SV5 @ SY80 ) ) )
= ( s @ SY77 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV13 @ SY77 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SV13 @ SY77 ) ) @ SY78 ) @ ( s @ SV5 @ SY80 ) ) ) @ ( s @ SV13 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ SY79 ) @ ( s @ SV5 @ SY80 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(132,plain,
! [SV14: $i,SV6: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV6 @ tyop_2Emin_2Ebool ) @ SV14 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV6 @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ SV6 @ tyop_2Emin_2Ebool ) @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(133,plain,
! [SV15: $i,SV7: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV7 @ tyop_2Emin_2Ebool ) @ SV15 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV7 @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ SV7 @ tyop_2Emin_2Ebool ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(134,plain,
( ( ~ ( ~ $true
| ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(135,plain,
( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ! [SX0: $i] : $true ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(136,plain,
( ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(137,plain,
( ( ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(138,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(139,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(140,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(141,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(142,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(143,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(144,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(145,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(146,plain,
! [SV8: $i] :
( ( ~ ! [SY65: $i,SY66: $i] :
( ( ( s @ SV8 @ SY65 )
!= ( s @ SV8 @ SY66 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SV8 @ SY65 ) ) ) @ ( s @ SV8 @ SY66 ) ) ) ) )
| ~ ! [SY67: $i,SY68: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SV8 @ SY67 ) ) ) @ ( s @ SV8 @ SY68 ) ) ) )
| ( ( s @ SV8 @ SY67 )
= ( s @ SV8 @ SY68 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(147,plain,
( ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(148,plain,
( ( ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(149,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(150,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(151,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(152,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(153,plain,
! [SV9: $i] :
( ( ~ ! [SY69: $i,SY70: $i] :
( ( ( s @ SV9 @ SY69 )
!= ( s @ SV9 @ SY70 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV9 @ SY69 ) @ ( s @ SV9 @ SY70 ) ) ) ) )
| ~ ! [SY71: $i,SY72: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV9 @ SY71 ) @ ( s @ SV9 @ SY72 ) ) ) )
| ( ( s @ SV9 @ SY71 )
= ( s @ SV9 @ SY72 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(154,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) @ ( s @ SX0 @ ( sK3_V1x_2E0 @ SX1 @ SX0 ) ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(155,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) ) ) )
| ! [SX2: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) @ ( s @ SX0 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(156,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(157,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(158,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) @ ( s @ SX0 @ SX2 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(159,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) @ ( s @ SX0 @ ( sK2_V1x_2E0 @ SX1 @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(160,plain,
! [SV16: $i,SV1: $i,SV10: $i] :
( ( ! [SY81: $i] :
( ( ( s @ SV10 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SV16 ) @ ( s @ SV1 @ ( sK4_V2x_2E0 @ SY81 @ SV16 @ SV10 @ SV1 ) ) ) )
!= ( s @ SV10 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SY81 ) @ ( s @ SV1 @ ( sK4_V2x_2E0 @ SY81 @ SV16 @ SV10 @ SV1 ) ) ) ) )
| ( ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SV16 )
= ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SY81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(161,plain,
! [SV17: $i,SV12: $i,SV4: $i] :
( ( ! [SY82: $i] :
( ( s @ SV4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV12 @ SV4 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV4 @ ( tyop_2Emin_2Efun @ SV12 @ SV4 ) ) @ combin_k_2E0 ) @ ( s @ SV4 @ SV17 ) ) ) @ ( s @ SV12 @ SY82 ) ) )
= ( s @ SV4 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(162,plain,
! [SV13: $i,SV5: $i,SV18: $i] :
( ( ! [SY83: $i,SY84: $i,SY85: $i] :
( ( s @ SV18 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SV18 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ ( tyop_2Emin_2Efun @ SV5 @ SV18 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SV13 @ SV18 ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ ( tyop_2Emin_2Efun @ SV5 @ SV18 ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SV13 @ SV18 ) ) @ SY83 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ SY84 ) ) ) @ ( s @ SV5 @ SY85 ) ) )
= ( s @ SV18 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV13 @ SV18 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SV13 @ SV18 ) ) @ SY83 ) @ ( s @ SV5 @ SY85 ) ) ) @ ( s @ SV13 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ SY84 ) @ ( s @ SV5 @ SY85 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(163,plain,
( ( ~ $true
| ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(164,plain,
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ! [SX0: $i] : $true )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(165,plain,
( ( ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(166,plain,
( ( ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(167,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(168,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(169,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(170,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(171,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(172,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(173,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(174,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(175,plain,
! [SV8: $i] :
( ( ~ ! [SY65: $i,SY66: $i] :
( ( ( s @ SV8 @ SY65 )
!= ( s @ SV8 @ SY66 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SV8 @ SY65 ) ) ) @ ( s @ SV8 @ SY66 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(176,plain,
! [SV8: $i] :
( ( ~ ! [SY67: $i,SY68: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SV8 @ SY67 ) ) ) @ ( s @ SV8 @ SY68 ) ) ) )
| ( ( s @ SV8 @ SY67 )
= ( s @ SV8 @ SY68 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(177,plain,
( ( ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(178,plain,
( ( ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(179,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(180,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(181,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(182,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(183,plain,
! [SV9: $i] :
( ( ~ ! [SY69: $i,SY70: $i] :
( ( ( s @ SV9 @ SY69 )
!= ( s @ SV9 @ SY70 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV9 @ SY69 ) @ ( s @ SV9 @ SY70 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(184,plain,
! [SV9: $i] :
( ( ~ ! [SY71: $i,SY72: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV9 @ SY71 ) @ ( s @ SV9 @ SY72 ) ) ) )
| ( ( s @ SV9 @ SY71 )
= ( s @ SV9 @ SY72 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(185,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) @ ( s @ SX0 @ ( sK3_V1x_2E0 @ SX1 @ SX0 ) ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(186,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) ) ) )
| ! [SX2: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) @ ( s @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(187,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(188,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(189,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) @ ( s @ SX0 @ SX2 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(190,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SX0 @ tyop_2Emin_2Ebool ) @ SX1 ) @ ( s @ SX0 @ ( sK2_V1x_2E0 @ SX1 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(191,plain,
! [SV19: $i,SV16: $i,SV1: $i,SV10: $i] :
( ( ( ( s @ SV10 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SV16 ) @ ( s @ SV1 @ ( sK4_V2x_2E0 @ SV19 @ SV16 @ SV10 @ SV1 ) ) ) )
!= ( s @ SV10 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SV19 ) @ ( s @ SV1 @ ( sK4_V2x_2E0 @ SV19 @ SV16 @ SV10 @ SV1 ) ) ) ) )
| ( ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SV16 )
= ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(192,plain,
! [SV20: $i,SV17: $i,SV12: $i,SV4: $i] :
( ( ( s @ SV4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV12 @ SV4 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV4 @ ( tyop_2Emin_2Efun @ SV12 @ SV4 ) ) @ combin_k_2E0 ) @ ( s @ SV4 @ SV17 ) ) ) @ ( s @ SV12 @ SV20 ) ) )
= ( s @ SV4 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(193,plain,
! [SV21: $i,SV13: $i,SV5: $i,SV18: $i] :
( ( ! [SY86: $i,SY87: $i] :
( ( s @ SV18 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SV18 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ ( tyop_2Emin_2Efun @ SV5 @ SV18 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SV13 @ SV18 ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ ( tyop_2Emin_2Efun @ SV5 @ SV18 ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SV13 @ SV18 ) ) @ SV21 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ SY86 ) ) ) @ ( s @ SV5 @ SY87 ) ) )
= ( s @ SV18 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV13 @ SV18 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SV13 @ SV18 ) ) @ SV21 ) @ ( s @ SV5 @ SY87 ) ) ) @ ( s @ SV13 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ SY86 ) @ ( s @ SV5 @ SY87 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(194,plain,
( ( ( ~ $true )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(195,plain,
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
= $true )
| ( ( ! [SX0: $i] : $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(196,plain,
! [SV22: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV22 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(197,plain,
! [SV23: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV23 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(198,plain,
! [SV24: $i] :
( ( ! [SY88: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV24 ) @ ( s @ tyop_2Emin_2Ebool @ SY88 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV24 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SY88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(199,plain,
( ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(200,plain,
! [SV25: $i] :
( ( ! [SY89: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV25 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SY89 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV25 ) @ ( s @ tyop_2Emin_2Ebool @ SY89 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(201,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(202,plain,
( ( ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(203,plain,
! [SV26: $i] :
( ( ! [SY90: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV26 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SY90 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV26 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(204,plain,
! [SV27: $i] :
( ( ! [SY91: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV27 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SY91 ) )
| ( ( s @ tyop_2Emin_2Ebool @ SV27 )
= ( s @ tyop_2Emin_2Ebool @ SY91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(205,plain,
! [SV28: $i] :
( ( ! [SY92: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SV28 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SY92 ) )
| ( ( s @ tyop_2Emin_2Ebool @ SV28 )
= ( s @ tyop_2Emin_2Ebool @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(206,plain,
! [SV8: $i] :
( ( ! [SY65: $i,SY66: $i] :
( ( ( s @ SV8 @ SY65 )
!= ( s @ SV8 @ SY66 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SV8 @ SY65 ) ) ) @ ( s @ SV8 @ SY66 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(207,plain,
! [SV8: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SV8 @ SY67 ) ) ) @ ( s @ SV8 @ SY68 ) ) ) )
| ( ( s @ SV8 @ SY67 )
= ( s @ SV8 @ SY68 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(208,plain,
! [SV29: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV29 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(209,plain,
! [SV30: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV30 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(210,plain,
( ( ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(211,plain,
! [SV31: $i] :
( ( ! [SY93: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV31 ) @ ( s @ tyop_2Emin_2Ebool @ SY93 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV31 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(212,plain,
! [SV32: $i] :
( ( ! [SY94: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV32 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SY94 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV32 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SY94 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(213,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(214,plain,
! [SV9: $i] :
( ( ! [SY69: $i,SY70: $i] :
( ( ( s @ SV9 @ SY69 )
!= ( s @ SV9 @ SY70 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV9 @ SY69 ) @ ( s @ SV9 @ SY70 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(215,plain,
! [SV9: $i] :
( ( ! [SY71: $i,SY72: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV9 @ SY71 ) @ ( s @ SV9 @ SY72 ) ) ) )
| ( ( s @ SV9 @ SY71 )
= ( s @ SV9 @ SY72 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(216,plain,
! [SV33: $i] :
( ( ! [SY95: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV33 @ tyop_2Emin_2Ebool ) @ SY95 ) @ ( s @ SV33 @ ( sK3_V1x_2E0 @ SY95 @ SV33 ) ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV33 @ tyop_2Emin_2Ebool ) @ SY95 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(217,plain,
! [SV34: $i] :
( ( ! [SY96: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV34 @ tyop_2Emin_2Ebool ) @ SY96 ) ) ) )
| ! [SY97: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV34 @ tyop_2Emin_2Ebool ) @ SY96 ) @ ( s @ SV34 @ SY97 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(218,plain,
! [SV35: $i] :
( ( ! [SY98: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV35 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SY98 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV35 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SY98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(219,plain,
( ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(220,plain,
! [SV36: $i] :
( ( ! [SY99: $i] :
( ! [SY100: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV36 @ tyop_2Emin_2Ebool ) @ SY99 ) @ ( s @ SV36 @ SY100 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV36 @ tyop_2Emin_2Ebool ) @ SY99 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(221,plain,
! [SV37: $i] :
( ( ! [SY101: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV37 @ tyop_2Emin_2Ebool ) @ SY101 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV37 @ tyop_2Emin_2Ebool ) @ SY101 ) @ ( s @ SV37 @ ( sK2_V1x_2E0 @ SY101 @ SV37 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(222,plain,
! [SV19: $i,SV16: $i,SV1: $i,SV10: $i] :
( ( ( ( ( s @ SV10 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SV16 ) @ ( s @ SV1 @ ( sK4_V2x_2E0 @ SV19 @ SV16 @ SV10 @ SV1 ) ) ) )
!= ( s @ SV10 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SV19 ) @ ( s @ SV1 @ ( sK4_V2x_2E0 @ SV19 @ SV16 @ SV10 @ SV1 ) ) ) ) ) )
= $true )
| ( ( ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SV16 )
= ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(223,plain,
! [SV38: $i,SV21: $i,SV13: $i,SV5: $i,SV18: $i] :
( ( ! [SY102: $i] :
( ( s @ SV18 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SV18 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ ( tyop_2Emin_2Efun @ SV5 @ SV18 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SV13 @ SV18 ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ ( tyop_2Emin_2Efun @ SV5 @ SV18 ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SV13 @ SV18 ) ) @ SV21 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ SV38 ) ) ) @ ( s @ SV5 @ SY102 ) ) )
= ( s @ SV18 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV13 @ SV18 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SV13 @ SV18 ) ) @ SV21 ) @ ( s @ SV5 @ SY102 ) ) ) @ ( s @ SV13 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ SV38 ) @ ( s @ SV5 @ SY102 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(224,plain,
( ( $true = $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(225,plain,
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $false )
| ( ( ! [SX0: $i] : $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(226,plain,
! [SV22: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV22 ) ) ) ) )
= $true )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(227,plain,
! [SV23: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV23 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(228,plain,
! [SV39: $i,SV24: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV24 ) @ ( s @ tyop_2Emin_2Ebool @ SV39 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV24 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(229,plain,
( ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(230,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(231,plain,
! [SV40: $i,SV25: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV25 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV40 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV25 ) @ ( s @ tyop_2Emin_2Ebool @ SV40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(232,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(233,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(234,plain,
( ( ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(235,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(236,plain,
! [SV41: $i,SV26: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV26 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV41 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV26 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(237,plain,
! [SV42: $i,SV27: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV27 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV42 ) )
| ( ( s @ tyop_2Emin_2Ebool @ SV27 )
= ( s @ tyop_2Emin_2Ebool @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(238,plain,
! [SV43: $i,SV28: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV28 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV43 ) )
| ( ( s @ tyop_2Emin_2Ebool @ SV28 )
= ( s @ tyop_2Emin_2Ebool @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(239,plain,
! [SV44: $i,SV8: $i] :
( ( ! [SY103: $i] :
( ( ( s @ SV8 @ SV44 )
!= ( s @ SV8 @ SY103 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SV8 @ SV44 ) ) ) @ ( s @ SV8 @ SY103 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(240,plain,
! [SV45: $i,SV8: $i] :
( ( ! [SY104: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SV8 @ SV45 ) ) ) @ ( s @ SV8 @ SY104 ) ) ) )
| ( ( s @ SV8 @ SV45 )
= ( s @ SV8 @ SY104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(241,plain,
! [SV29: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV29 ) ) ) ) )
= $true )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(242,plain,
! [SV30: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV30 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(243,plain,
( ( ~ ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(244,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(245,plain,
! [SV46: $i,SV31: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV31 ) @ ( s @ tyop_2Emin_2Ebool @ SV46 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV31 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(246,plain,
! [SV47: $i,SV32: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV32 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV47 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV32 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(247,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(248,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(249,plain,
! [SV48: $i,SV9: $i] :
( ( ! [SY105: $i] :
( ( ( s @ SV9 @ SV48 )
!= ( s @ SV9 @ SY105 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV9 @ SV48 ) @ ( s @ SV9 @ SY105 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(250,plain,
! [SV49: $i,SV9: $i] :
( ( ! [SY106: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV9 @ SV49 ) @ ( s @ SV9 @ SY106 ) ) ) )
| ( ( s @ SV9 @ SV49 )
= ( s @ SV9 @ SY106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(251,plain,
! [SV50: $i,SV33: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV33 @ tyop_2Emin_2Ebool ) @ SV50 ) @ ( s @ SV33 @ ( sK3_V1x_2E0 @ SV50 @ SV33 ) ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV33 @ tyop_2Emin_2Ebool ) @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(252,plain,
! [SV51: $i,SV34: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV34 @ tyop_2Emin_2Ebool ) @ SV51 ) ) ) )
| ! [SY107: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV34 @ tyop_2Emin_2Ebool ) @ SV51 ) @ ( s @ SV34 @ SY107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(253,plain,
! [SV52: $i,SV35: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV35 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV52 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV35 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(254,plain,
( ( ~ ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(255,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(256,plain,
! [SV53: $i,SV36: $i] :
( ( ! [SY108: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV36 @ tyop_2Emin_2Ebool ) @ SV53 ) @ ( s @ SV36 @ SY108 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV36 @ tyop_2Emin_2Ebool ) @ SV53 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(257,plain,
! [SV54: $i,SV37: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV37 @ tyop_2Emin_2Ebool ) @ SV54 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV37 @ tyop_2Emin_2Ebool ) @ SV54 ) @ ( s @ SV37 @ ( sK2_V1x_2E0 @ SV54 @ SV37 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(258,plain,
! [SV19: $i,SV16: $i,SV1: $i,SV10: $i] :
( ( ( ( s @ SV10 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SV16 ) @ ( s @ SV1 @ ( sK4_V2x_2E0 @ SV19 @ SV16 @ SV10 @ SV1 ) ) ) )
= ( s @ SV10 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SV19 ) @ ( s @ SV1 @ ( sK4_V2x_2E0 @ SV19 @ SV16 @ SV10 @ SV1 ) ) ) ) )
= $false )
| ( ( ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SV16 )
= ( s @ ( tyop_2Emin_2Efun @ SV1 @ SV10 ) @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(259,plain,
! [SV55: $i,SV38: $i,SV21: $i,SV13: $i,SV5: $i,SV18: $i] :
( ( ( s @ SV18 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SV18 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ ( tyop_2Emin_2Efun @ SV5 @ SV18 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SV13 @ SV18 ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ ( tyop_2Emin_2Efun @ SV5 @ SV18 ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SV13 @ SV18 ) ) @ SV21 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ SV38 ) ) ) @ ( s @ SV5 @ SV55 ) ) )
= ( s @ SV18 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV13 @ SV18 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ ( tyop_2Emin_2Efun @ SV13 @ SV18 ) ) @ SV21 ) @ ( s @ SV5 @ SV55 ) ) ) @ ( s @ SV13 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV5 @ SV13 ) @ SV38 ) @ ( s @ SV5 @ SV55 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(260,plain,
( ( $true = $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(261,plain,
! [SV22: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV22 ) ) ) )
= $false )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(262,plain,
! [SV39: $i,SV24: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV24 ) @ ( s @ tyop_2Emin_2Ebool @ SV39 ) ) ) ) )
= $true )
| ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV24 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(263,plain,
( ( ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(264,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(265,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV25 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV40 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV25 ) @ ( s @ tyop_2Emin_2Ebool @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(266,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(267,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(268,plain,
( ( ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(269,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(270,plain,
! [SV41: $i,SV26: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV26 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV41 ) ) ) ) )
= $true )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV26 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(271,plain,
! [SV42: $i,SV27: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV27 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV42 ) ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV27 )
= ( s @ tyop_2Emin_2Ebool @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(272,plain,
! [SV43: $i,SV28: $i] :
( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV28 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV43 ) ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV28 )
= ( s @ tyop_2Emin_2Ebool @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(273,plain,
! [SV57: $i,SV44: $i,SV8: $i] :
( ( ( ( s @ SV8 @ SV44 )
!= ( s @ SV8 @ SV57 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SV8 @ SV44 ) ) ) @ ( s @ SV8 @ SV57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(274,plain,
! [SV58: $i,SV45: $i,SV8: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SV8 @ SV45 ) ) ) @ ( s @ SV8 @ SV58 ) ) ) )
| ( ( s @ SV8 @ SV45 )
= ( s @ SV8 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(275,plain,
! [SV29: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV29 ) ) ) )
= $false )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(276,plain,
( ( ! [SX0: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(277,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(278,plain,
! [SV46: $i,SV31: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV31 ) @ ( s @ tyop_2Emin_2Ebool @ SV46 ) ) ) ) )
= $true )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV31 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(279,plain,
! [SV47: $i,SV32: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV32 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV47 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV32 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV47 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(280,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(281,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(282,plain,
! [SV59: $i,SV48: $i,SV9: $i] :
( ( ( ( s @ SV9 @ SV48 )
!= ( s @ SV9 @ SV59 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV9 @ SV48 ) @ ( s @ SV9 @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(283,plain,
! [SV60: $i,SV49: $i,SV9: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV9 @ SV49 ) @ ( s @ SV9 @ SV60 ) ) ) )
| ( ( s @ SV9 @ SV49 )
= ( s @ SV9 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(284,plain,
! [SV50: $i,SV33: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV33 @ tyop_2Emin_2Ebool ) @ SV50 ) @ ( s @ SV33 @ ( sK3_V1x_2E0 @ SV50 @ SV33 ) ) ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV33 @ tyop_2Emin_2Ebool ) @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(285,plain,
! [SV51: $i,SV34: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV34 @ tyop_2Emin_2Ebool ) @ SV51 ) ) ) ) )
= $true )
| ( ( ! [SY107: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV34 @ tyop_2Emin_2Ebool ) @ SV51 ) @ ( s @ SV34 @ SY107 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(286,plain,
! [SV52: $i,SV35: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV35 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV52 ) ) ) ) )
= $true )
| ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV35 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(287,plain,
( ( ! [SX0: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ! [SX1: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(288,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(289,plain,
! [SV53: $i,SV36: $i] :
( ( ( ! [SY108: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV36 @ tyop_2Emin_2Ebool ) @ SV53 ) @ ( s @ SV36 @ SY108 ) ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV36 @ tyop_2Emin_2Ebool ) @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(290,plain,
! [SV54: $i,SV37: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV37 @ tyop_2Emin_2Ebool ) @ SV54 ) ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV37 @ tyop_2Emin_2Ebool ) @ SV54 ) @ ( s @ SV37 @ ( sK2_V1x_2E0 @ SV54 @ SV37 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(291,plain,
! [SV22: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV22 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV22 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(292,plain,
! [SV39: $i,SV24: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV24 ) @ ( s @ tyop_2Emin_2Ebool @ SV39 ) ) ) )
= $false )
| ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV24 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(293,plain,
! [SV61: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV61 ) )
| ! [SY109: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV61 ) @ ( s @ tyop_2Emin_2Ebool @ SY109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(294,plain,
! [SV62: $i] :
( ( ! [SY110: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SY110 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV62 ) @ ( s @ tyop_2Emin_2Ebool @ SY110 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(295,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV25 ) ) )
= $true )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV40 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV25 ) @ ( s @ tyop_2Emin_2Ebool @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(296,plain,
! [SV63: $i] :
( ( ! [SY111: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV63 ) @ ( s @ tyop_2Emin_2Ebool @ SY111 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(297,plain,
! [SV64: $i] :
( ( ! [SY112: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV64 ) @ ( s @ tyop_2Emin_2Ebool @ SY112 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SY112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(298,plain,
! [SV65: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV65 ) )
| ! [SY113: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV65 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SY113 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(299,plain,
! [SV66: $i] :
( ( ! [SY114: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SY114 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV66 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SY114 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(300,plain,
! [SV41: $i,SV26: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV26 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV41 ) ) ) )
= $false )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV26 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(301,plain,
! [SV42: $i,SV27: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV27 ) ) )
= $true )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV42 ) ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV27 )
= ( s @ tyop_2Emin_2Ebool @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(302,plain,
! [SV43: $i,SV28: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV28 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV43 ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV28 )
= ( s @ tyop_2Emin_2Ebool @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(303,plain,
! [SV57: $i,SV44: $i,SV8: $i] :
( ( ( ( ( s @ SV8 @ SV44 )
!= ( s @ SV8 @ SV57 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SV8 @ SV44 ) ) ) @ ( s @ SV8 @ SV57 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(304,plain,
! [SV58: $i,SV45: $i,SV8: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SV8 @ SV45 ) ) ) @ ( s @ SV8 @ SV58 ) ) ) ) )
= $true )
| ( ( ( s @ SV8 @ SV45 )
= ( s @ SV8 @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(305,plain,
! [SV29: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV29 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV29 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(306,plain,
! [SV67: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV67 ) )
| ! [SY115: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV67 ) @ ( s @ tyop_2Emin_2Ebool @ SY115 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(307,plain,
! [SV68: $i] :
( ( ! [SY116: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SY116 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV68 ) @ ( s @ tyop_2Emin_2Ebool @ SY116 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(308,plain,
! [SV46: $i,SV31: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV31 ) @ ( s @ tyop_2Emin_2Ebool @ SV46 ) ) ) )
= $false )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV31 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(309,plain,
! [SV47: $i,SV32: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV32 ) ) )
= $true )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV47 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV32 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV47 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(310,plain,
! [SV69: $i] :
( ( ! [SY117: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV69 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SY117 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(311,plain,
! [SV70: $i] :
( ( ! [SY118: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV70 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SY118 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SY118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(312,plain,
! [SV59: $i,SV48: $i,SV9: $i] :
( ( ( ( ( s @ SV9 @ SV48 )
!= ( s @ SV9 @ SV59 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV9 @ SV48 ) @ ( s @ SV9 @ SV59 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(313,plain,
! [SV60: $i,SV49: $i,SV9: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV9 @ SV49 ) @ ( s @ SV9 @ SV60 ) ) ) ) )
= $true )
| ( ( ( s @ SV9 @ SV49 )
= ( s @ SV9 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(314,plain,
! [SV50: $i,SV33: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV33 @ tyop_2Emin_2Ebool ) @ SV50 ) @ ( s @ SV33 @ ( sK3_V1x_2E0 @ SV50 @ SV33 ) ) ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV33 @ tyop_2Emin_2Ebool ) @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(315,plain,
! [SV51: $i,SV34: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV34 @ tyop_2Emin_2Ebool ) @ SV51 ) ) ) )
= $false )
| ( ( ! [SY107: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV34 @ tyop_2Emin_2Ebool ) @ SV51 ) @ ( s @ SV34 @ SY107 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(316,plain,
! [SV52: $i,SV35: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV35 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV52 ) ) ) )
= $false )
| ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV35 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(317,plain,
! [SV71: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV71 ) )
| ! [SY119: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV71 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SY119 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(318,plain,
! [SV72: $i] :
( ( ! [SY120: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SY120 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV72 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SY120 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(319,plain,
! [SV73: $i,SV53: $i,SV36: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV36 @ tyop_2Emin_2Ebool ) @ SV53 ) @ ( s @ SV36 @ SV73 ) ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV36 @ tyop_2Emin_2Ebool ) @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(320,plain,
! [SV54: $i,SV37: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV37 @ tyop_2Emin_2Ebool ) @ SV54 ) ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV37 @ tyop_2Emin_2Ebool ) @ SV54 ) @ ( s @ SV37 @ ( sK2_V1x_2E0 @ SV54 @ SV37 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(321,plain,
! [SV39: $i,SV24: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV24 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV39 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV24 ) @ ( s @ tyop_2Emin_2Ebool @ SV39 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(322,plain,
! [SV61: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV61 ) ) )
= $true )
| ( ( ! [SY109: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV61 ) @ ( s @ tyop_2Emin_2Ebool @ SY109 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(323,plain,
! [SV62: $i,SV74: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV74 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV62 ) @ ( s @ tyop_2Emin_2Ebool @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(324,plain,
! [SV40: $i,SV25: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV25 ) )
= $false )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV40 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV25 ) @ ( s @ tyop_2Emin_2Ebool @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(325,plain,
! [SV63: $i] :
( ( ( ! [SY111: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV63 ) @ ( s @ tyop_2Emin_2Ebool @ SY111 ) ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(326,plain,
! [SV75: $i,SV64: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV64 ) @ ( s @ tyop_2Emin_2Ebool @ SV75 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(327,plain,
! [SV65: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV65 ) )
= $true )
| ( ( ! [SY113: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV65 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SY113 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(328,plain,
! [SV66: $i,SV76: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV76 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV66 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(329,plain,
! [SV41: $i,SV26: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV26 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV41 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV26 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV41 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(330,plain,
! [SV42: $i,SV27: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV27 ) )
= $false )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV42 ) ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV27 )
= ( s @ tyop_2Emin_2Ebool @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(331,plain,
! [SV57: $i,SV44: $i,SV8: $i] :
( ( ( ( s @ SV8 @ SV44 )
= ( s @ SV8 @ SV57 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SV8 @ SV44 ) ) ) @ ( s @ SV8 @ SV57 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(332,plain,
! [SV58: $i,SV45: $i,SV8: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV8 @ ( tyop_2Emin_2Efun @ SV8 @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ SV8 @ SV45 ) ) ) @ ( s @ SV8 @ SV58 ) ) ) )
= $false )
| ( ( ( s @ SV8 @ SV45 )
= ( s @ SV8 @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(333,plain,
! [SV67: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV67 ) )
= $true )
| ( ( ! [SY115: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV67 ) @ ( s @ tyop_2Emin_2Ebool @ SY115 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(334,plain,
! [SV68: $i,SV77: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV77 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV68 ) @ ( s @ tyop_2Emin_2Ebool @ SV77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(335,plain,
! [SV46: $i,SV31: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV31 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV46 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV31 ) @ ( s @ tyop_2Emin_2Ebool @ SV46 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(336,plain,
! [SV47: $i,SV32: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV32 ) )
= $false )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV47 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV32 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV47 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(337,plain,
! [SV69: $i] :
( ( ( ! [SY117: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV69 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SY117 ) ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(338,plain,
! [SV78: $i,SV70: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV70 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV78 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(339,plain,
! [SV59: $i,SV48: $i,SV9: $i] :
( ( ( ( s @ SV9 @ SV48 )
= ( s @ SV9 @ SV59 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV9 @ SV48 ) @ ( s @ SV9 @ SV59 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(340,plain,
! [SV60: $i,SV49: $i,SV9: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV9 @ SV49 ) @ ( s @ SV9 @ SV60 ) ) ) )
= $false )
| ( ( ( s @ SV9 @ SV49 )
= ( s @ SV9 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(341,plain,
! [SV79: $i,SV51: $i,SV34: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV34 @ tyop_2Emin_2Ebool ) @ SV51 ) @ ( s @ SV34 @ SV79 ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV34 @ tyop_2Emin_2Ebool ) @ SV51 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(342,plain,
! [SV52: $i,SV35: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV35 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV52 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV35 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV52 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(343,plain,
! [SV71: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV71 ) ) )
= $true )
| ( ( ! [SY119: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV71 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SY119 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(344,plain,
! [SV72: $i,SV80: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV80 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV72 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(345,plain,
! [SV73: $i,SV53: $i,SV36: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ SV36 @ tyop_2Emin_2Ebool ) @ SV53 ) @ ( s @ SV36 @ SV73 ) ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ SV36 @ tyop_2Emin_2Ebool ) @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(346,plain,
! [SV61: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV61 ) )
= $false )
| ( ( ! [SY109: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV61 ) @ ( s @ tyop_2Emin_2Ebool @ SY109 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(347,plain,
! [SV62: $i,SV74: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV74 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV62 ) @ ( s @ tyop_2Emin_2Ebool @ SV74 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(348,plain,
! [SV25: $i,SV40: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV40 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV25 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV25 ) @ ( s @ tyop_2Emin_2Ebool @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(349,plain,
! [SV81: $i,SV63: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV63 ) @ ( s @ tyop_2Emin_2Ebool @ SV81 ) ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV63 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(350,plain,
! [SV75: $i,SV64: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV64 ) @ ( s @ tyop_2Emin_2Ebool @ SV75 ) ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(351,plain,
! [SV82: $i,SV65: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV65 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV82 ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV65 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(352,plain,
! [SV66: $i,SV76: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV76 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV66 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV76 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(353,plain,
! [SV41: $i,SV26: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV26 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV41 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV26 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV41 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(354,plain,
! [SV27: $i,SV42: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV42 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV27 ) )
= $false )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV27 )
= ( s @ tyop_2Emin_2Ebool @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(355,plain,
! [SV83: $i,SV67: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV67 ) @ ( s @ tyop_2Emin_2Ebool @ SV83 ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV67 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(356,plain,
! [SV68: $i,SV77: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV77 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV68 ) @ ( s @ tyop_2Emin_2Ebool @ SV77 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(357,plain,
! [SV46: $i,SV31: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV31 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV46 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV31 ) @ ( s @ tyop_2Emin_2Ebool @ SV46 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(358,plain,
! [SV32: $i,SV47: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV47 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV32 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV32 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV47 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(359,plain,
! [SV84: $i,SV69: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV69 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV84 ) ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV69 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(360,plain,
! [SV78: $i,SV70: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV70 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV78 ) ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(361,plain,
! [SV71: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV71 ) )
= $false )
| ( ( ! [SY119: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV71 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SY119 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(362,plain,
! [SV72: $i,SV80: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV80 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV72 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV80 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(363,plain,
! [SV85: $i,SV61: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV61 ) @ ( s @ tyop_2Emin_2Ebool @ SV85 ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV61 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(364,plain,
! [SV62: $i,SV74: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV74 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV62 ) @ ( s @ tyop_2Emin_2Ebool @ SV74 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(365,plain,
! [SV81: $i,SV63: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV63 ) @ ( s @ tyop_2Emin_2Ebool @ SV81 ) ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(366,plain,
! [SV75: $i,SV64: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV64 ) @ ( s @ tyop_2Emin_2Ebool @ SV75 ) ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(367,plain,
! [SV66: $i,SV76: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV76 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV66 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV76 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(368,plain,
! [SV68: $i,SV77: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV77 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV68 ) @ ( s @ tyop_2Emin_2Ebool @ SV77 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(369,plain,
! [SV84: $i,SV69: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV69 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV84 ) ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(370,plain,
! [SV78: $i,SV70: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV70 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV78 ) ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(371,plain,
! [SV86: $i,SV71: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV71 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV86 ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV71 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(372,plain,
! [SV72: $i,SV80: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV80 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ SV72 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ SV80 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(373,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[68,372,371,370,369,368,367,366,365,364,363,358,357,355,354,353,351,348,345,342,341,340,339,332,331,321,320,314,305,302,291,260,259,258,242,227,224,192,133,132,129,128,112,105]) ).
thf(374,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP001+1 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 2 21:19:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.38
% 0.19/0.38 No.of.Axioms: 23
% 0.19/0.38
% 0.19/0.38 Length.of.Defs: 0
% 0.19/0.38
% 0.19/0.38 Contains.Choice.Funs: false
% 0.19/0.42 .
% 0.19/0.42 (rf:0,axioms:23,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:25,loop_count:0,foatp_calls:0,translation:fof_full)..................................
% 0.55/0.75
% 0.55/0.75 ********************************
% 0.55/0.75 * All subproblems solved! *
% 0.55/0.75 ********************************
% 0.55/0.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:23,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:373,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.59/0.82
% 0.59/0.82 %**** Beginning of derivation protocol ****
% 0.59/0.82 % SZS output start CNFRefutation
% See solution above
% 0.59/0.82
% 0.59/0.82 %**** End of derivation protocol ****
% 0.59/0.82 %**** no. of clauses in derivation: 374 ****
% 0.59/0.82 %**** clause counter: 373 ****
% 0.59/0.82
% 0.59/0.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:23,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:373,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------