%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP001+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:22:55 AM UTC 2026
% Result : Theorem 0.49s 0.32s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 151 ( 81 unt; 0 typ; 0 def)
% Number of atoms : 879 ( 290 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 2596 ( 300 ~; 258 |; 3 &;2008 @)
% ( 21 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 16 con; 0-2 aty)
% Number of variables : 253 ( 0 ^; 253 !; 0 ?; 253 :)
% 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_SX0,type,
sK1_SX0: $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/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ET__DEF) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_2F_5C) ).
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/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).
thf(20,axiom,
~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
thf(21,axiom,
p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
thf(24,conjecture,
p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
file('/export/starexec/sandbox2/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,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(29,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(30,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(31,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(32,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(33,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(34,plain,
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(35,plain,
( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(36,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(37,plain,
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(38,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(copy,[status(thm)],[36]) ).
thf(39,plain,
( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(40,plain,
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(41,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)],[33]) ).
thf(42,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(copy,[status(thm)],[32]) ).
thf(43,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(copy,[status(thm)],[31]) ).
thf(44,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(copy,[status(thm)],[30]) ).
thf(45,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(copy,[status(thm)],[29]) ).
thf(46,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(copy,[status(thm)],[28]) ).
thf(47,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(copy,[status(thm)],[27]) ).
thf(48,plain,
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(49,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 ) ) )
| ~ ( ~ ( ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( 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)],[43]) ).
thf(50,plain,
( ( ! [SX0: $i,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 ) ) )
| ~ ( ( ( s @ SX0 @ SX1 )
!= ( s @ SX0 @ SX2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SX0 @ SX1 ) @ ( s @ SX0 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(51,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 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ( 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(unfold_def,[status(thm)],[42]) ).
thf(52,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ( ~ ~ ( 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)],[44]) ).
thf(53,plain,
( ( ~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ! [SX0: $i] :
( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ( ~ ! [SX0: $i] :
( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(54,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 ) ) )
| ~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( 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(unfold_def,[status(thm)],[45]) ).
thf(55,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) ) )
| ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SX1 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
| ( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(56,plain,
( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(57,plain,
! [SV1: $i] :
( ( ( ( s @ tyop_2Emin_2Ebool @ SV1 )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ SV1 )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(58,plain,
( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(59,plain,
! [SV2: $i] :
( ( ! [SY14: $i] :
~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SY14 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SY14 ) ) )
| ~ ( ~ ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SY14 ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SY14 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(60,plain,
! [SV3: $i] :
( ( ! [SY15: $i,SY16: $i] :
~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV3 @ SY15 ) @ ( s @ SV3 @ SY16 ) ) ) )
| ( ( s @ SV3 @ SY15 )
= ( s @ SV3 @ SY16 ) ) )
| ~ ( ( ( s @ SV3 @ SY15 )
!= ( s @ SV3 @ SY16 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV3 @ SY15 ) @ ( s @ SV3 @ SY16 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(61,plain,
! [SV4: $i] :
( ( ! [SY17: $i] :
~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SY17 ) ) ) )
| ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SY17 ) ) ) )
| ~ ( ~ ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SY17 ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SY17 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(62,plain,
! [SV5: $i] :
( ( ~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) )
| ~ ( ~ ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV5 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(63,plain,
( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ! [SX0: $i] :
( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
| ~ ( ~ ! [SX0: $i] :
( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(64,plain,
! [SV6: $i] :
( ( ! [SY18: $i] :
~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SY18 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SY18 ) ) )
| ~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SY18 ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SY18 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(65,plain,
! [SV7: $i] :
( ( ! [SY19: $i] :
( ~ ~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SY19 ) ) )
| ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SY19 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) ) ) )
| ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(66,plain,
! [SV1: $i] :
( ( ( ( s @ tyop_2Emin_2Ebool @ SV1 )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV1 )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) )
| ~ ( ~ ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(68,plain,
! [SV9: $i,SV3: $i] :
( ( ! [SY20: $i] :
~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV3 @ SV9 ) @ ( s @ SV3 @ SY20 ) ) ) )
| ( ( s @ SV3 @ SV9 )
= ( s @ SV3 @ SY20 ) ) )
| ~ ( ( ( s @ SV3 @ SV9 )
!= ( s @ SV3 @ SY20 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV3 @ SV9 ) @ ( s @ SV3 @ SY20 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(69,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
| ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
| ~ ( ~ ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(70,plain,
! [SV5: $i] :
( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) )
| ~ ( ~ ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV5 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(71,plain,
( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ! [SX0: $i] :
( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(72,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(73,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) )
| ~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(74,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) ) )
| ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) ) ) )
| ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(75,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) )
| ~ ( ~ ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(76,plain,
! [SV13: $i,SV9: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV3 @ SV9 ) @ ( s @ SV3 @ SV13 ) ) ) )
| ( ( s @ SV3 @ SV9 )
= ( s @ SV3 @ SV13 ) ) )
| ~ ( ( ( s @ SV3 @ SV9 )
!= ( s @ SV3 @ SV13 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV3 @ SV9 ) @ ( s @ SV3 @ SV13 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(77,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
| ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
| ~ ( ~ ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV5: $i] :
( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(79,plain,
! [SV5: $i] :
( ( ~ ( ~ ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV5 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(80,plain,
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ! [SX0: $i] :
( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(81,plain,
( ( ~ ! [SX0: $i] :
( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(82,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) )
| ~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV12: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) ) )
| ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) ) ) ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(84,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(85,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( ~ ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(86,plain,
! [SV13: $i,SV9: $i,SV3: $i] :
( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV3 @ SV9 ) @ ( s @ SV3 @ SV13 ) ) ) )
| ( ( s @ SV3 @ SV9 )
= ( s @ SV3 @ SV13 ) ) )
| ~ ( ( ( s @ SV3 @ SV9 )
!= ( s @ SV3 @ SV13 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV3 @ SV9 ) @ ( s @ SV3 @ SV13 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(87,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
| ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(88,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(89,plain,
! [SV5: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(90,plain,
! [SV5: $i] :
( ( ~ ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV5 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(91,plain,
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
= $true )
| ( ( ! [SX0: $i] :
( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(92,plain,
( ( ( ~ ! [SX0: $i] :
( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(93,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(94,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(95,plain,
! [SV12: $i,SV7: $i] :
( ( ( ~ ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) ) )
| ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) ) ) ) )
= $false )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(96,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(97,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(98,plain,
! [SV13: $i,SV9: $i,SV3: $i] :
( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV3 @ SV9 ) @ ( s @ SV3 @ SV13 ) ) ) )
| ( ( s @ SV3 @ SV9 )
= ( s @ SV3 @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(99,plain,
! [SV13: $i,SV9: $i,SV3: $i] :
( ( ~ ( ( ( s @ SV3 @ SV9 )
!= ( s @ SV3 @ SV13 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV3 @ SV9 ) @ ( s @ SV3 @ SV13 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(100,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
| ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(101,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(102,plain,
! [SV5: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) ) ) )
= $true )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(103,plain,
! [SV5: $i] :
( ( ( ~ ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(104,plain,
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $false )
| ( ( ! [SX0: $i] :
( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(105,plain,
( ( ( ! [SX0: $i] :
( ( s @ tyop_2Emin_2Ebool @ SX0 )
= ( s @ tyop_2Emin_2Ebool @ SX0 ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(106,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(107,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(108,plain,
! [SV12: $i,SV7: $i] :
( ( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) ) )
| ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) ) ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(109,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) ) )
= $true )
| ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(110,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(111,plain,
! [SV13: $i,SV9: $i,SV3: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV3 @ SV9 ) @ ( s @ SV3 @ SV13 ) ) ) )
| ( ( s @ SV3 @ SV9 )
= ( s @ SV3 @ SV13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(112,plain,
! [SV13: $i,SV9: $i,SV3: $i] :
( ( ( ( s @ SV3 @ SV9 )
!= ( s @ SV3 @ SV13 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV3 @ SV9 ) @ ( s @ SV3 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(113,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(114,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(115,plain,
! [SV5: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) ) )
= $false )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(116,plain,
! [SV5: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(117,plain,
! [SV14: $i] :
( ( ( ( s @ tyop_2Emin_2Ebool @ SV14 )
= ( s @ tyop_2Emin_2Ebool @ SV14 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(118,plain,
( ( ( ( s @ tyop_2Emin_2Ebool @ sK1_SX0 )
= ( s @ tyop_2Emin_2Ebool @ sK1_SX0 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[105]) ).
thf(119,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) ) )
= $true )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(120,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(121,plain,
! [SV12: $i,SV7: $i] :
( ( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) ) ) )
= $true )
| ( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) ) ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(122,plain,
! [SV8: $i,SV2: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) )
= $false )
| ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(123,plain,
! [SV8: $i,SV2: $i] :
( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV2 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(124,plain,
! [SV13: $i,SV9: $i,SV3: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV3 @ SV9 ) @ ( s @ SV3 @ SV13 ) ) ) ) )
= $true )
| ( ( ( s @ SV3 @ SV9 )
= ( s @ SV3 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(125,plain,
! [SV13: $i,SV9: $i,SV3: $i] :
( ( ( ( s @ SV3 @ SV9 )
!= ( s @ SV3 @ SV13 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV3 @ SV9 ) @ ( s @ SV3 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(126,plain,
! [SV10: $i,SV4: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $false )
| ( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(127,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(128,plain,
! [SV5: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV5 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(129,plain,
! [SV5: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV5 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(130,plain,
! [SV11: $i,SV6: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) )
= $false )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(131,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(132,plain,
! [SV12: $i,SV7: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) ) )
= $false )
| ( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) ) ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(133,plain,
! [SV8: $i,SV2: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV2 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV8 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(134,plain,
! [SV8: $i,SV2: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV2 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(135,plain,
! [SV2: $i,SV8: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV8 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV2 ) @ ( s @ tyop_2Emin_2Ebool @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(136,plain,
! [SV13: $i,SV9: $i,SV3: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV3 @ SV9 ) @ ( s @ SV3 @ SV13 ) ) ) )
= $false )
| ( ( ( s @ SV3 @ SV9 )
= ( s @ SV3 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV13: $i,SV9: $i,SV3: $i] :
( ( ( ( s @ SV3 @ SV9 )
= ( s @ SV3 @ SV13 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ SV3 @ SV9 ) @ ( s @ SV3 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(139,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(140,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV11 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(141,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(142,plain,
! [SV6: $i,SV11: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV11 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(143,plain,
! [SV12: $i,SV7: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) ) )
= $false )
| ( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) ) ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(144,plain,
! [SV7: $i,SV12: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $false )
| ( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) ) ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(145,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(146,plain,
! [SV4: $i,SV10: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(147,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) ) )
= $true )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(148,plain,
! [SV11: $i,SV6: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV11 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(149,plain,
! [SV11: $i,SV6: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV6 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV6 ) @ ( s @ tyop_2Emin_2Ebool @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(150,plain,
! [SV12: $i,SV7: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) )
= $true )
| ( ( ~ ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) ) ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(151,plain,
! [SV7: $i,SV12: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $false )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(152,plain,
! [SV10: $i,SV4: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(153,plain,
! [SV4: $i,SV10: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(154,plain,
! [SV10: $i,SV4: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
= $false )
| ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(155,plain,
! [SV7: $i,SV12: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(156,plain,
! [SV7: $i,SV12: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $false )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(157,plain,
! [SV12: $i,SV7: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $false )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(158,plain,
! [SV4: $i,SV10: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV10 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV4 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ SV4 ) @ ( s @ tyop_2Emin_2Ebool @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(159,plain,
! [SV7: $i,SV12: $i] :
( ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(160,plain,
! [SV12: $i,SV7: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) )
= $false )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(161,plain,
! [SV7: $i,SV12: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $false )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(162,plain,
! [SV7: $i,SV12: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ SV7 ) )
= $true )
| ( ( ( s @ tyop_2Emin_2Ebool @ SV7 )
= ( s @ tyop_2Emin_2Ebool @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(163,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[39,162,161,160,158,157,153,152,149,148,142,137,136,135,134,133,129,128,118,117,66,58,56]) ).
thf(164,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP001+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n010.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 11:07:04 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.49/0.32
% 0.49/0.32 No.of.Axioms: 10
% 0.49/0.32
% 0.49/0.32 Length.of.Defs: 0
% 0.49/0.32
% 0.49/0.32 Contains.Choice.Funs: false
% 0.49/0.32 ....
% 0.49/0.32
% 0.49/0.32 ********************************
% 0.49/0.32 * All subproblems solved! *
% 0.49/0.32 ********************************
% 0.49/0.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:10,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:163,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.49/0.32
% 0.49/0.32 %**** Beginning of derivation protocol ****
% 0.49/0.32 % SZS output start CNFRefutation
% See solution above
% 0.49/0.32
% 0.49/0.32 %**** End of derivation protocol ****
% 0.49/0.32 %**** no. of clauses in derivation: 151 ****
% 0.49/0.32 %**** clause counter: 163 ****
% 0.49/0.32
% 0.49/0.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:10,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:163,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------