TSTP Solution File: SYO331^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO331^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n012.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 : Thu Jul 21 17:33:25 EDT 2022
% Result : Theorem 138.82s 139.21s
% Output : CNFRefutation 138.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 71
% Syntax : Number of formulae : 261 ( 26 unt; 70 typ; 0 def)
% Number of atoms : 2340 ( 740 equ; 0 cnn)
% Maximal formula atoms : 7 ( 12 avg)
% Number of connectives : 5654 (1555 ~;1068 |; 26 &;2972 @)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 628 ( 628 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 69 usr; 38 con; 0-5 aty)
% Number of variables : 1228 ( 259 ^ 951 !; 18 ?;1228 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cK,type,
cK: ( a > $o ) > a > $o ).
thf(tp_sK10_SX0,type,
sK10_SX0: a > a > a > $o ).
thf(tp_sK11_SX0,type,
sK11_SX0: a > a > a > $o ).
thf(tp_sK12_E,type,
sK12_E: a > a ).
thf(tp_sK13_SX0,type,
sK13_SX0: a > $o ).
thf(tp_sK14_SY464,type,
sK14_SY464: ( a > $o ) > a ).
thf(tp_sK15_E,type,
sK15_E: a ).
thf(tp_sK16_E,type,
sK16_E: a ).
thf(tp_sK17_E,type,
sK17_E: a > $o ).
thf(tp_sK18_E,type,
sK18_E: a ).
thf(tp_sK19_SX0,type,
sK19_SX0: ( a > $o ) > ( a > $o ) > a > a > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: a ).
thf(tp_sK20_E,type,
sK20_E: a ).
thf(tp_sK21_E,type,
sK21_E: a ).
thf(tp_sK22_E,type,
sK22_E: a ).
thf(tp_sK23_E,type,
sK23_E: a > $o ).
thf(tp_sK24_E,type,
sK24_E: a ).
thf(tp_sK25_E,type,
sK25_E: a ).
thf(tp_sK26_E,type,
sK26_E: a ).
thf(tp_sK27_E,type,
sK27_E: a > $o ).
thf(tp_sK28_E,type,
sK28_E: a ).
thf(tp_sK29_E,type,
sK29_E: a ).
thf(tp_sK2_SY391,type,
sK2_SY391: a > $o ).
thf(tp_sK30_E,type,
sK30_E: a ).
thf(tp_sK31_E,type,
sK31_E: a > $o ).
thf(tp_sK32_E,type,
sK32_E: a ).
thf(tp_sK33_SX0,type,
sK33_SX0: ( a > $o ) > ( a > $o ) > a > a > $o ).
thf(tp_sK34_SY570,type,
sK34_SY570: a > ( a > $o ) > ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK35_SY571,type,
sK35_SY571: a > ( a > $o ) > ( a > $o ) > ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK36_SY572,type,
sK36_SY572: ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK37_SY573,type,
sK37_SY573: ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK38_SY574,type,
sK38_SY574: ( a > $o ) > ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK39_SY575,type,
sK39_SY575: ( a > $o ) > ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK3_Xx,type,
sK3_Xx: ( a > $o ) > a ).
thf(tp_sK40_SY576,type,
sK40_SY576: ( a > $o ) > ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK41_SY577,type,
sK41_SY577: ( a > $o ) > ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK42_E,type,
sK42_E: a ).
thf(tp_sK43_E,type,
sK43_E: a ).
thf(tp_sK44_E,type,
sK44_E: a > $o ).
thf(tp_sK45_E,type,
sK45_E: a ).
thf(tp_sK46_E,type,
sK46_E: a ).
thf(tp_sK47_E,type,
sK47_E: a > $o ).
thf(tp_sK48_E,type,
sK48_E: a ).
thf(tp_sK49_E,type,
sK49_E: a ).
thf(tp_sK4_Xx0,type,
sK4_Xx0: ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK50_E,type,
sK50_E: a ).
thf(tp_sK51_E,type,
sK51_E: a ).
thf(tp_sK52_E,type,
sK52_E: a ).
thf(tp_sK53_E,type,
sK53_E: a > $o ).
thf(tp_sK54_E,type,
sK54_E: a ).
thf(tp_sK55_E,type,
sK55_E: a ).
thf(tp_sK56_E,type,
sK56_E: a > $o ).
thf(tp_sK57_E,type,
sK57_E: a ).
thf(tp_sK58_E,type,
sK58_E: a ).
thf(tp_sK59_E,type,
sK59_E: a ).
thf(tp_sK5_E,type,
sK5_E: a ).
thf(tp_sK60_E,type,
sK60_E: a ).
thf(tp_sK61_E,type,
sK61_E: a ).
thf(tp_sK62_E,type,
sK62_E: a > $o ).
thf(tp_sK63_E,type,
sK63_E: a ).
thf(tp_sK64_E,type,
sK64_E: a ).
thf(tp_sK65_E,type,
sK65_E: a > $o ).
thf(tp_sK66_E,type,
sK66_E: a ).
thf(tp_sK67_E,type,
sK67_E: a ).
thf(tp_sK68_E,type,
sK68_E: a ).
thf(tp_sK6_SX0,type,
sK6_SX0: a > a > $o ).
thf(tp_sK7_SX0,type,
sK7_SX0: a > a > $o ).
thf(tp_sK8_SX0,type,
sK8_SX0: a > a > $o ).
thf(tp_sK9_SX0,type,
sK9_SX0: a > a > $o ).
thf(1,conjecture,
( ! [X: a > $o] :
( ! [Xx: a] :
( ( X @ Xx )
=> ? [S: a > $o] :
( ! [Xx0: a] :
( ( S @ Xx0 )
=> ( cK @ S @ Xx0 ) )
& ( S @ Xx ) ) )
=> ! [Xx: a] :
( ( cK @ X @ Xx )
=> ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) ) )
=> ! [Xx: a] :
( ? [S: a > $o] :
( ! [Xx0: a] :
( ( S @ Xx0 )
=> ( cK @ S @ Xx0 ) )
& ( S @ Xx ) )
=> ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM116_2SS_pme) ).
thf(2,negated_conjecture,
( ( ! [X: a > $o] :
( ! [Xx: a] :
( ( X @ Xx )
=> ? [S: a > $o] :
( ! [Xx0: a] :
( ( S @ Xx0 )
=> ( cK @ S @ Xx0 ) )
& ( S @ Xx ) ) )
=> ! [Xx: a] :
( ( cK @ X @ Xx )
=> ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) ) )
=> ! [Xx: a] :
( ? [S: a > $o] :
( ! [Xx0: a] :
( ( S @ Xx0 )
=> ( cK @ S @ Xx0 ) )
& ( S @ Xx ) )
=> ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: a > $o] :
( ! [Xx: a] :
( ( X @ Xx )
=> ? [S: a > $o] :
( ! [Xx0: a] :
( ( S @ Xx0 )
=> ( cK @ S @ Xx0 ) )
& ( S @ Xx ) ) )
=> ! [Xx: a] :
( ( cK @ X @ Xx )
=> ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: a] :
( ? [S: a > $o] :
( ! [Xx0: a] :
( ( S @ Xx0 )
=> ( cK @ S @ Xx0 ) )
& ( S @ Xx ) )
=> ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(5,plain,
( ( ~ ! [Xx: a] :
( ? [S: a > $o] :
( ! [Xx0: a] :
( ( S @ Xx0 )
=> ( cK @ S @ Xx0 ) )
& ( S @ Xx ) )
=> ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY396: a] :
( ~ ( sK2_SY391 @ SY396 )
| ( cK @ sK2_SY391 @ SY396 ) )
& ( sK2_SY391 @ sK1_Xx )
& ~ ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ sK1_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [X: a > $o] :
( ( ( X @ ( sK3_Xx @ X ) )
& ! [SY397: a > $o] :
( ( ( SY397 @ ( sK4_Xx0 @ SY397 @ X ) )
& ~ ( cK @ SY397 @ ( sK4_Xx0 @ SY397 @ X ) ) )
| ~ ( SY397 @ ( sK3_Xx @ X ) ) ) )
| ! [Xx: a] :
( ~ ( cK @ X @ Xx )
| ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[3]) ).
thf(8,plain,
( ( ! [X: a > $o] :
( ( ( X @ ( sK3_Xx @ X ) )
& ! [SY397: a > $o] :
( ( ( SY397 @ ( sK4_Xx0 @ SY397 @ X ) )
& ~ ( cK @ SY397 @ ( sK4_Xx0 @ SY397 @ X ) ) )
| ~ ( SY397 @ ( sK3_Xx @ X ) ) ) )
| ! [Xx: a] :
( ~ ( cK @ X @ Xx )
| ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY396: a] :
( ~ ( sK2_SY391 @ SY396 )
| ( cK @ sK2_SY391 @ SY396 ) )
& ( sK2_SY391 @ sK1_Xx )
& ~ ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ sK1_Xx ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ! [SX0: a > $o] :
( ~ ( ~ ( SX0 @ ( sK3_Xx @ SX0 ) )
| ~ ! [SX1: a > $o] :
( ~ ( ~ ( SX1 @ ( sK4_Xx0 @ SX1 @ SX0 ) )
| ~ ~ ( cK @ SX1 @ ( sK4_Xx0 @ SX1 @ SX0 ) ) )
| ~ ( SX1 @ ( sK3_Xx @ SX0 ) ) ) )
| ! [SX1: a] :
( ~ ( cK @ SX0 @ SX1 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: a] :
( ~ ( sK2_SY391 @ SX0 )
| ( cK @ sK2_SY391 @ SX0 ) )
| ~ ( sK2_SY391 @ sK1_Xx ) )
| ~ ~ ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ sK1_Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: a > $o] :
( ( ~ ( ~ ( SV1 @ ( sK3_Xx @ SV1 ) )
| ~ ! [SY399: a > $o] :
( ~ ( ~ ( SY399 @ ( sK4_Xx0 @ SY399 @ SV1 ) )
| ~ ~ ( cK @ SY399 @ ( sK4_Xx0 @ SY399 @ SV1 ) ) )
| ~ ( SY399 @ ( sK3_Xx @ SV1 ) ) ) )
| ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ~ ( ~ ! [SX0: a] :
( ~ ( sK2_SY391 @ SX0 )
| ( cK @ sK2_SY391 @ SX0 ) )
| ~ ( sK2_SY391 @ sK1_Xx ) )
| ~ ~ ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ sK1_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: a > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK3_Xx @ SV1 ) )
| ~ ! [SY399: a > $o] :
( ~ ( ~ ( SY399 @ ( sK4_Xx0 @ SY399 @ SV1 ) )
| ~ ~ ( cK @ SY399 @ ( sK4_Xx0 @ SY399 @ SV1 ) ) )
| ~ ( SY399 @ ( sK3_Xx @ SV1 ) ) ) ) )
= $true )
| ( ( ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ~ ( ~ ! [SX0: a] :
( ~ ( sK2_SY391 @ SX0 )
| ( cK @ sK2_SY391 @ SX0 ) )
| ~ ( sK2_SY391 @ sK1_Xx ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ~ ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK3_Xx @ SV1 ) )
| ~ ! [SY399: a > $o] :
( ~ ( ~ ( SY399 @ ( sK4_Xx0 @ SY399 @ SV1 ) )
| ~ ~ ( cK @ SY399 @ ( sK4_Xx0 @ SY399 @ SV1 ) ) )
| ~ ( SY399 @ ( sK3_Xx @ SV1 ) ) ) )
= $false )
| ( ( ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ( ~ ! [SX0: a] :
( ~ ( sK2_SY391 @ SX0 )
| ( cK @ sK2_SY391 @ SX0 ) )
| ~ ( sK2_SY391 @ sK1_Xx ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ sK1_Xx ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) )
= $false )
| ( ( ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: a > $o] :
( ( ( ~ ! [SY399: a > $o] :
( ~ ( ~ ( SY399 @ ( sK4_Xx0 @ SY399 @ SV1 ) )
| ~ ~ ( cK @ SY399 @ ( sK4_Xx0 @ SY399 @ SV1 ) ) )
| ~ ( SY399 @ ( sK3_Xx @ SV1 ) ) ) )
= $false )
| ( ( ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
( ( ~ ! [SX0: a] :
( ~ ( sK2_SY391 @ SX0 )
| ( cK @ sK2_SY391 @ SX0 ) )
| ~ ( sK2_SY391 @ sK1_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(23,plain,
( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ sK1_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV1: a > $o] :
( ( ( SV1 @ ( sK3_Xx @ SV1 ) )
= $true )
| ( ( ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
! [SV1: a > $o] :
( ( ( ! [SY399: a > $o] :
( ~ ( ~ ( SY399 @ ( sK4_Xx0 @ SY399 @ SV1 ) )
| ~ ~ ( cK @ SY399 @ ( sK4_Xx0 @ SY399 @ SV1 ) ) )
| ~ ( SY399 @ ( sK3_Xx @ SV1 ) ) ) )
= $true )
| ( ( ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ! [SX0: a] :
( ~ ( sK2_SY391 @ SX0 )
| ( cK @ sK2_SY391 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( ~ ( sK2_SY391 @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(28,plain,
! [SV2: a,SV1: a > $o] :
( ( ( ~ ( cK @ SV1 @ SV2 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SV2 ) )
= $true )
| ( ( SV1 @ ( sK3_Xx @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV1: a > $o,SV3: a > $o] :
( ( ( ~ ( ~ ( SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) )
| ~ ~ ( cK @ SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) ) )
| ~ ( SV3 @ ( sK3_Xx @ SV1 ) ) )
= $true )
| ( ( ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
( ( ! [SX0: a] :
( ~ ( sK2_SY391 @ SX0 )
| ( cK @ sK2_SY391 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(31,plain,
( ( sK2_SY391 @ sK1_Xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(32,plain,
! [SV2: a,SV1: a > $o] :
( ( ( ~ ( cK @ SV1 @ SV2 ) )
= $true )
| ( ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SV2 )
= $true )
| ( ( SV1 @ ( sK3_Xx @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV1: a > $o,SV3: a > $o] :
( ( ( ~ ( ~ ( SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) )
| ~ ~ ( cK @ SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( SV3 @ ( sK3_Xx @ SV1 ) ) )
= $true )
| ( ( ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV4: a] :
( ( ~ ( sK2_SY391 @ SV4 )
| ( cK @ sK2_SY391 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV2: a,SV1: a > $o] :
( ( ( cK @ SV1 @ SV2 )
= $false )
| ( ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SV2 )
= $true )
| ( ( SV1 @ ( sK3_Xx @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV1: a > $o,SV3: a > $o] :
( ( ( ~ ( SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) )
| ~ ~ ( cK @ SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) ) )
= $false )
| ( ( ~ ( SV3 @ ( sK3_Xx @ SV1 ) ) )
= $true )
| ( ( ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV4: a] :
( ( ( ~ ( sK2_SY391 @ SV4 ) )
= $true )
| ( ( cK @ sK2_SY391 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV1: a > $o,SV3: a > $o] :
( ( ( ~ ( SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) ) )
= $false )
| ( ( ~ ( SV3 @ ( sK3_Xx @ SV1 ) ) )
= $true )
| ( ( ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(39,plain,
! [SV1: a > $o,SV3: a > $o] :
( ( ( ~ ~ ( cK @ SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) ) )
= $false )
| ( ( ~ ( SV3 @ ( sK3_Xx @ SV1 ) ) )
= $true )
| ( ( ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(40,plain,
! [SV4: a] :
( ( ( sK2_SY391 @ SV4 )
= $false )
| ( ( cK @ sK2_SY391 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV1: a > $o,SV3: a > $o] :
( ( ( SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) )
= $true )
| ( ( ~ ( SV3 @ ( sK3_Xx @ SV1 ) ) )
= $true )
| ( ( ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV1: a > $o,SV3: a > $o] :
( ( ( ~ ( cK @ SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) ) )
= $true )
| ( ( ~ ( SV3 @ ( sK3_Xx @ SV1 ) ) )
= $true )
| ( ( ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(43,plain,
! [SV1: a > $o,SV3: a > $o] :
( ( ( SV3 @ ( sK3_Xx @ SV1 ) )
= $false )
| ( ( SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) )
= $true )
| ( ( ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV1: a > $o,SV3: a > $o] :
( ( ( cK @ SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) )
= $false )
| ( ( ~ ( SV3 @ ( sK3_Xx @ SV1 ) ) )
= $true )
| ( ( ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV3: a > $o,SV5: a,SV1: a > $o] :
( ( ( ~ ( cK @ SV1 @ SV5 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SV5 ) )
= $true )
| ( ( SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) )
= $true )
| ( ( SV3 @ ( sK3_Xx @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV1: a > $o,SV3: a > $o] :
( ( ( SV3 @ ( sK3_Xx @ SV1 ) )
= $false )
| ( ( cK @ SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) )
= $false )
| ( ( ! [SY400: a] :
( ~ ( cK @ SV1 @ SY400 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SY400 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV3: a > $o,SV5: a,SV1: a > $o] :
( ( ( ~ ( cK @ SV1 @ SV5 ) )
= $true )
| ( ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SV5 )
= $true )
| ( ( SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) )
= $true )
| ( ( SV3 @ ( sK3_Xx @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV3: a > $o,SV6: a,SV1: a > $o] :
( ( ( ~ ( cK @ SV1 @ SV6 )
| ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SV6 ) )
= $true )
| ( ( cK @ SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) )
= $false )
| ( ( SV3 @ ( sK3_Xx @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(49,plain,
! [SV3: a > $o,SV5: a,SV1: a > $o] :
( ( ( cK @ SV1 @ SV5 )
= $false )
| ( ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SV5 )
= $true )
| ( ( SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) )
= $true )
| ( ( SV3 @ ( sK3_Xx @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV3: a > $o,SV6: a,SV1: a > $o] :
( ( ( ~ ( cK @ SV1 @ SV6 ) )
= $true )
| ( ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SV6 )
= $true )
| ( ( cK @ SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) )
= $false )
| ( ( SV3 @ ( sK3_Xx @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV3: a > $o,SV6: a,SV1: a > $o] :
( ( ( cK @ SV1 @ SV6 )
= $false )
| ( ( cK
@ ^ [SX2: a] :
~ ! [SX3: a > $o] :
~ ~ ( ~ ! [SX4: a] :
( ~ ( SX3 @ SX4 )
| ( cK @ SX3 @ SX4 ) )
| ~ ( SX3 @ SX2 ) )
@ SV6 )
= $true )
| ( ( cK @ SV3 @ ( sK4_Xx0 @ SV3 @ SV1 ) )
= $false )
| ( ( SV3 @ ( sK3_Xx @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV2: a] :
( ( ( cK
@ ^ [SX0: a] : $false
@ SV2 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV2 )
= $true )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[35:[bind(SV1,$thf( ^ [SV14: a] : $false ))]]) ).
thf(54,plain,
! [SV2: a,SV13: a > $o] :
( ( ( cK
@ ^ [SX0: a] :
~ ( SV13 @ SX0 )
@ SV2 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV2 )
= $true )
| ( ( ~ ( SV13
@ ( sK3_Xx
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[35:[bind(SV1,$thf( ^ [SV12: a] : ~ ( SV13 @ SV12 ) ))]]) ).
thf(57,plain,
! [SV8: a > $o,SV5: a,SV1: a > $o] :
( ( ( cK @ SV1 @ SV5 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV5 )
= $true )
| ( ( ~ ( SV8
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV1 ) ) )
= $true )
| ( ( ~ ( SV8 @ ( sK3_Xx @ SV1 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[49:[bind(SV3,$thf( ^ [SV7: a] : ~ ( SV8 @ SV7 ) ))]]) ).
thf(61,plain,
! [SV6: a,SV1: a > $o] :
( ( ( cK @ SV1 @ SV6 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV6 )
= $true )
| ( ( cK
@ ^ [SX0: a] : $true
@ ( sK4_Xx0
@ ^ [SX0: a] : $true
@ SV1 ) )
= $false )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[51:[bind(SV3,$thf( ^ [SV10: a] : $true ))]]) ).
thf(63,plain,
! [SV8: a > $o,SV6: a,SV1: a > $o] :
( ( ( cK @ SV1 @ SV6 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV6 )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV1 ) )
= $false )
| ( ( ~ ( SV8 @ ( sK3_Xx @ SV1 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[51:[bind(SV3,$thf( ^ [SV7: a] : ~ ( SV8 @ SV7 ) ))]]) ).
thf(64,plain,
! [SV3: a > $o,SV6: a] :
( ( ( cK
@ ^ [SX0: a] : $true
@ SV6 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV6 )
= $true )
| ( ( cK @ SV3
@ ( sK4_Xx0 @ SV3
@ ^ [SX0: a] : $true ) )
= $false )
| ( ( SV3
@ ( sK3_Xx
@ ^ [SX0: a] : $true ) )
= $false ) ),
inference(prim_subst,[status(thm)],[51:[bind(SV1,$thf( ^ [SV15: a] : $true ))]]) ).
thf(65,plain,
! [SV3: a > $o,SV6: a] :
( ( ( cK
@ ^ [SX0: a] : $false
@ SV6 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV6 )
= $true )
| ( ( cK @ SV3
@ ( sK4_Xx0 @ SV3
@ ^ [SX0: a] : $false ) )
= $false )
| ( ( SV3
@ ( sK3_Xx
@ ^ [SX0: a] : $false ) )
= $false ) ),
inference(prim_subst,[status(thm)],[51:[bind(SV1,$thf( ^ [SV14: a] : $false ))]]) ).
thf(66,plain,
! [SV3: a > $o,SV6: a,SV13: a > $o] :
( ( ( cK
@ ^ [SX0: a] :
~ ( SV13 @ SX0 )
@ SV6 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV6 )
= $true )
| ( ( cK @ SV3
@ ( sK4_Xx0 @ SV3
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false )
| ( ( SV3
@ ( sK3_Xx
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[51:[bind(SV1,$thf( ^ [SV12: a] : ~ ( SV13 @ SV12 ) ))]]) ).
thf(67,plain,
! [SV2: a,SV13: a > $o] :
( ( ( SV13
@ ( sK3_Xx
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV2 )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ( SV13 @ SX0 )
@ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(68,plain,
! [SV5: a,SV1: a > $o,SV8: a > $o] :
( ( ( SV8
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV1 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV5 )
= $true )
| ( ( cK @ SV1 @ SV5 )
= $false )
| ( ( ~ ( SV8 @ ( sK3_Xx @ SV1 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(69,plain,
! [SV6: a,SV1: a > $o,SV8: a > $o] :
( ( ( SV8 @ ( sK3_Xx @ SV1 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV1 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV6 )
= $true )
| ( ( cK @ SV1 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(70,plain,
! [SV5: a,SV1: a > $o,SV8: a > $o] :
( ( ( SV8 @ ( sK3_Xx @ SV1 ) )
= $true )
| ( ( cK @ SV1 @ SV5 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV5 )
= $true )
| ( ( SV8
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(71,plain,
! [SV2: a] :
( ( ( cK
@ ^ [SX0: a] : $false
@ SV2 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV2 )
= $true ) ),
inference(sim,[status(thm)],[53]) ).
thf(72,plain,
! [SV6: a,SV1: a > $o] :
( ( ( cK @ SV1 @ SV6 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV6 )
= $true )
| ( ( cK
@ ^ [SX0: a] : $true
@ ( sK4_Xx0
@ ^ [SX0: a] : $true
@ SV1 ) )
= $false ) ),
inference(sim,[status(thm)],[61]) ).
thf(74,plain,
! [SV17: a,SV18: a > $o] :
( ( ( cK @ SV18 @ SV17 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true ) ),
inference(rename,[status(thm)],[35]) ).
thf(81,plain,
! [SV17: a,SV18: a > $o] :
( ( ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ sK1_Xx ) )
= $false )
| ( ( cK @ SV18 @ SV17 )
= $false )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true ) ),
inference(res,[status(thm)],[74,23]) ).
thf(83,plain,
! [SV17: a] :
( ( ( cK
@ ^ [SX0: a] : $false
@ SV17 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[74:[bind(SV18,$thf( ^ [SV21: a] : $false ))]]) ).
thf(84,plain,
! [SV17: a] :
( ( ( cK
@ ^ [SX0: a] : $false
@ SV17 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true ) ),
inference(sim,[status(thm)],[83]) ).
thf(85,plain,
! [SV17: a,SV20: a > $o] :
( ( ( cK
@ ^ [SX0: a] :
~ ( SV20 @ SX0 )
@ SV17 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( ~ ( SV20
@ ( sK3_Xx
@ ^ [SX0: a] :
~ ( SV20 @ SX0 ) ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[74:[bind(SV18,$thf( ^ [SV19: a] : ~ ( SV20 @ SV19 ) ))]]) ).
thf(86,plain,
! [SV17: a] :
( ( ( cK
@ ^ [SX0: a] : ( SX0 = sK1_Xx )
@ SV17 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( ( sK3_Xx
@ ^ [SX0: a] : ( SX0 = sK1_Xx ) )
= sK1_Xx )
= $true ) ),
inference(prim_subst,[status(thm)],[74:[bind(SV18,$thf( ^ [SV23: a] : ( SV23 = sK1_Xx ) ))]]) ).
thf(87,plain,
! [SV17: a] :
( ( ( cK
@ ^ [SX0: a] : ( SX0 = sK5_E )
@ SV17 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( ( sK3_Xx
@ ^ [SX0: a] : ( SX0 = sK5_E ) )
= sK5_E )
= $true ) ),
inference(prim_subst,[status(thm)],[74:[bind(SV18,$thf( ^ [SV24: a] : ( SV24 = sK5_E ) ))]]) ).
thf(88,plain,
! [SV18: a > $o] :
( ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true )
| ( ( cK @ SV18 @ sK1_Xx )
= $false ) ),
inference(extuni,[status(esa)],[81:[bind(SV17,$thf( sK1_Xx ))]]) ).
thf(93,plain,
! [SV17: a,SV20: a > $o] :
( ( ( SV20
@ ( sK3_Xx
@ ^ [SX0: a] :
~ ( SV20 @ SX0 ) ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ( SV20 @ SX0 )
@ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(158,plain,
! [SV65: a] :
( ( ( sK2_SY391 @ SV65 )
= $false )
| ( ( cK @ sK2_SY391 @ SV65 )
= $true ) ),
inference(rename,[status(thm)],[40]) ).
thf(163,plain,
! [SV65: a,SV17: a,SV18: a > $o] :
( ( ( ( cK @ sK2_SY391 @ SV65 )
= ( cK @ SV18 @ SV17 ) )
= $false )
| ( ( sK2_SY391 @ SV65 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true ) ),
inference(res,[status(thm)],[158,74]) ).
thf(164,plain,
! [SV65: a] :
( ( ( ( sK2_SY391 @ SV65 )
= ( sK2_SY391 @ sK1_Xx ) )
= $false )
| ( ( cK @ sK2_SY391 @ SV65 )
= $true ) ),
inference(res,[status(thm)],[158,31]) ).
thf(165,plain,
! [SV65: a] :
( ( ( ( cK @ sK2_SY391 @ SV65 )
= ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ sK1_Xx ) )
= $false )
| ( ( sK2_SY391 @ SV65 )
= $false ) ),
inference(res,[status(thm)],[158,23]) ).
thf(166,plain,
( ( ( sK2_SY391 @ sK1_Xx )
= $false )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $true )
| ( ( ~ ! [SX0: a > $o] :
~ ~ ( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cK @ SX0 @ SX1 ) )
| ~ ( SX0 @ ( sK12_E @ sK1_Xx ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[165:[bind(SV65,$thf( sK1_Xx ))]]) ).
thf(167,plain,
( ( ( sK2_SY391 @ sK1_Xx )
= $false )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $false )
| ( ( ~ ! [SX0: a > $o] :
~ ~ ( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cK @ SX0 @ SX1 ) )
| ~ ( SX0 @ ( sK12_E @ sK1_Xx ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[165:[bind(SV65,$thf( sK1_Xx ))]]) ).
thf(168,plain,
( ( cK @ sK2_SY391 @ sK1_Xx )
= $true ),
inference(extuni,[status(esa)],[164:[bind(SV65,$thf( sK1_Xx ))]]) ).
thf(169,plain,
! [SV17: a] :
( ( ( sK2_SY391 @ ( sK3_Xx @ sK2_SY391 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( sK2_SY391 @ SV17 )
= $false ) ),
inference(extuni,[status(esa)],[163:[bind(SV65,$thf( SV17 )),bind(SV18,$thf( sK2_SY391 ))]]) ).
thf(170,plain,
( ( ( ! [SX0: a > $o] :
~ ~ ( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cK @ SX0 @ SX1 ) )
| ~ ( SX0 @ ( sK12_E @ sK1_Xx ) ) ) )
= $true )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $false )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(171,plain,
( ( ( ! [SX0: a > $o] :
~ ~ ( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cK @ SX0 @ SX1 ) )
| ~ ( SX0 @ ( sK12_E @ sK1_Xx ) ) ) )
= $false )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $true )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(172,plain,
! [SV66: a > $o] :
( ( ( ~ ~ ( ~ ! [SY464: a] :
( ~ ( SV66 @ SY464 )
| ( cK @ SV66 @ SY464 ) )
| ~ ( SV66 @ ( sK12_E @ sK1_Xx ) ) ) )
= $true )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $false )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(173,plain,
( ( ( ~ ~ ( ~ ! [SY465: a] :
( ~ ( sK13_SX0 @ SY465 )
| ( cK @ sK13_SX0 @ SY465 ) )
| ~ ( sK13_SX0 @ ( sK12_E @ sK1_Xx ) ) ) )
= $false )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $true )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[171]) ).
thf(174,plain,
! [SV66: a > $o] :
( ( ( ~ ( ~ ! [SY464: a] :
( ~ ( SV66 @ SY464 )
| ( cK @ SV66 @ SY464 ) )
| ~ ( SV66 @ ( sK12_E @ sK1_Xx ) ) ) )
= $false )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $false )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(175,plain,
( ( ( ~ ( ~ ! [SY465: a] :
( ~ ( sK13_SX0 @ SY465 )
| ( cK @ sK13_SX0 @ SY465 ) )
| ~ ( sK13_SX0 @ ( sK12_E @ sK1_Xx ) ) ) )
= $true )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $true )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(176,plain,
! [SV66: a > $o] :
( ( ( ~ ! [SY464: a] :
( ~ ( SV66 @ SY464 )
| ( cK @ SV66 @ SY464 ) )
| ~ ( SV66 @ ( sK12_E @ sK1_Xx ) ) )
= $true )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $false )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(177,plain,
( ( ( ~ ! [SY465: a] :
( ~ ( sK13_SX0 @ SY465 )
| ( cK @ sK13_SX0 @ SY465 ) )
| ~ ( sK13_SX0 @ ( sK12_E @ sK1_Xx ) ) )
= $false )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $true )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(178,plain,
! [SV66: a > $o] :
( ( ( ~ ! [SY464: a] :
( ~ ( SV66 @ SY464 )
| ( cK @ SV66 @ SY464 ) ) )
= $true )
| ( ( ~ ( SV66 @ ( sK12_E @ sK1_Xx ) ) )
= $true )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $false )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(179,plain,
( ( ( ~ ! [SY465: a] :
( ~ ( sK13_SX0 @ SY465 )
| ( cK @ sK13_SX0 @ SY465 ) ) )
= $false )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $true )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(180,plain,
( ( ( ~ ( sK13_SX0 @ ( sK12_E @ sK1_Xx ) ) )
= $false )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $true )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(181,plain,
! [SV66: a > $o] :
( ( ( ! [SY464: a] :
( ~ ( SV66 @ SY464 )
| ( cK @ SV66 @ SY464 ) ) )
= $false )
| ( ( ~ ( SV66 @ ( sK12_E @ sK1_Xx ) ) )
= $true )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $false )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(182,plain,
( ( ( ! [SY465: a] :
( ~ ( sK13_SX0 @ SY465 )
| ( cK @ sK13_SX0 @ SY465 ) ) )
= $true )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $true )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(183,plain,
( ( ( sK13_SX0 @ ( sK12_E @ sK1_Xx ) )
= $true )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $true )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(184,plain,
! [SV66: a > $o] :
( ( ( ~ ( SV66 @ ( sK14_SY464 @ SV66 ) )
| ( cK @ SV66 @ ( sK14_SY464 @ SV66 ) ) )
= $false )
| ( ( ~ ( SV66 @ ( sK12_E @ sK1_Xx ) ) )
= $true )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $false )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[181]) ).
thf(185,plain,
! [SV67: a] :
( ( ( ~ ( sK13_SX0 @ SV67 )
| ( cK @ sK13_SX0 @ SV67 ) )
= $true )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $true )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(186,plain,
! [SV66: a > $o] :
( ( ( ~ ( SV66 @ ( sK14_SY464 @ SV66 ) ) )
= $false )
| ( ( ~ ( SV66 @ ( sK12_E @ sK1_Xx ) ) )
= $true )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $false )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(187,plain,
! [SV66: a > $o] :
( ( ( cK @ SV66 @ ( sK14_SY464 @ SV66 ) )
= $false )
| ( ( ~ ( SV66 @ ( sK12_E @ sK1_Xx ) ) )
= $true )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $false )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(188,plain,
! [SV67: a] :
( ( ( ~ ( sK13_SX0 @ SV67 ) )
= $true )
| ( ( cK @ sK13_SX0 @ SV67 )
= $true )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $true )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(189,plain,
! [SV66: a > $o] :
( ( ( SV66 @ ( sK14_SY464 @ SV66 ) )
= $true )
| ( ( ~ ( SV66 @ ( sK12_E @ sK1_Xx ) ) )
= $true )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $false )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(190,plain,
! [SV66: a > $o] :
( ( ( SV66 @ ( sK12_E @ sK1_Xx ) )
= $false )
| ( ( cK @ SV66 @ ( sK14_SY464 @ SV66 ) )
= $false )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $false )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(191,plain,
! [SV67: a] :
( ( ( sK13_SX0 @ SV67 )
= $false )
| ( ( cK @ sK13_SX0 @ SV67 )
= $true )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $true )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(192,plain,
! [SV66: a > $o] :
( ( ( SV66 @ ( sK12_E @ sK1_Xx ) )
= $false )
| ( ( SV66 @ ( sK14_SY464 @ SV66 ) )
= $true )
| ( ( sK2_SY391 @ ( sK12_E @ sK1_Xx ) )
= $false )
| ( ( sK2_SY391 @ sK1_Xx )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(193,plain,
! [SV68: a > $o,SV69: a,SV70: a > $o] :
( ( ( cK @ SV70 @ SV69 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV69 )
= $true )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false ) ),
inference(rename,[status(thm)],[49]) ).
thf(203,plain,
! [SV68: a > $o,SV69: a,SV70: a > $o,SV65: a] :
( ( ( ( cK @ SV70 @ SV69 )
= ( cK @ sK2_SY391 @ SV65 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV69 )
= $true )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( sK2_SY391 @ SV65 )
= $false ) ),
inference(res,[status(thm)],[193,158]) ).
thf(209,plain,
! [SV68: a > $o,SV69: a,SV70: a > $o,SV17: a,SV18: a > $o] :
( ( ( ( cK @ SV70 @ SV69 )
= ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV69 )
= $true )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( cK @ SV18 @ SV17 )
= $false )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true ) ),
inference(res,[status(thm)],[193,74]) ).
thf(211,plain,
! [SV68: a > $o,SV69: a,SV70: a > $o,SV17: a,SV18: a > $o] :
( ( ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV69 )
= ( cK @ SV18 @ SV17 ) )
= $false )
| ( ( cK @ SV70 @ SV69 )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true ) ),
inference(res,[status(thm)],[193,74]) ).
thf(215,plain,
! [SV68: a > $o,SV69: a,SV70: a > $o] :
( ( ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV69 )
= ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ sK1_Xx ) )
= $false )
| ( ( cK @ SV70 @ SV69 )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false ) ),
inference(res,[status(thm)],[193,23]) ).
thf(218,plain,
! [SV72: a > $o,SV69: a,SV70: a > $o] :
( ( ( cK @ SV70 @ SV69 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV69 )
= $true )
| ( ( ~ ( SV72
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ( SV72 @ SX0 )
@ SV70 ) ) )
= $true )
| ( ( ~ ( SV72 @ ( sK3_Xx @ SV70 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[193:[bind(SV68,$thf( ^ [SV71: a] : ~ ( SV72 @ SV71 ) ))]]) ).
thf(226,plain,
! [SV107: a > $o,SV69: a,SV70: a > $o] :
( ( ( cK @ SV70 @ SV69 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV69 )
= $true )
| ( ( ~ ( SV107
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ( SV107 @ SX0 )
@ SV70 ) ) )
= $true )
| ( ( ~ ( SV107 @ ( sK3_Xx @ SV70 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[193:[bind(SV68,$thf( ^ [SV106: a] : ~ ( SV107 @ SV106 ) ))]]) ).
thf(232,plain,
! [SV70: a > $o,SV68: a > $o] :
( ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( cK @ SV70 @ sK1_Xx )
= $false ) ),
inference(extuni,[status(esa)],[215:[bind(SV69,$thf( sK1_Xx ))]]) ).
thf(233,plain,
! [SV70: a > $o,SV68: a > $o,SV17: a] :
( ( ( ~ ! [SX0: a > $o] :
~ ~ ( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cK @ SX0 @ SX1 ) )
| ~ ( SX0
@ ( sK3_Xx
@ ^ [SX1: a] :
~ ! [SX2: a > $o] :
~ ~ ( ~ ! [SX3: a] :
( ~ ( SX2 @ SX3 )
| ( cK @ SX2 @ SX3 ) )
| ~ ( SX2 @ SX1 ) ) ) ) ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( cK @ SV70 @ SV17 )
= $false ) ),
inference(extuni,[status(esa)],[211:[bind(SV69,$thf( SV17 )),bind(SV18,$thf( ^ [SX0: a] : ~ ( ! [SX1: a > $o] : ~ ( ~ ( ~ ( ! [SX2: a] : ( ~ ( SX1 @ SX2 ) | ( cK @ SX1 @ SX2 ) ) ) | ~ ( SX1 @ SX0 ) ) ) ) ))]]) ).
thf(234,plain,
! [SV68: a > $o,SV17: a,SV18: a > $o] :
( ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true )
| ( ( cK @ SV18 @ SV17 )
= $false )
| ( ( SV68
@ ( sK3_Xx
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) ) ) )
= $false )
| ( ( SV68
@ ( sK4_Xx0 @ SV68
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) ) ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true ) ),
inference(extuni,[status(esa)],[209:[bind(SV69,$thf( SV17 )),bind(SV70,$thf( ^ [SX0: a] : ~ ( ! [SX1: a > $o] : ~ ( ~ ( ~ ( ! [SX2: a] : ( ~ ( SX1 @ SX2 ) | ( cK @ SX1 @ SX2 ) ) ) | ~ ( SX1 @ SX0 ) ) ) ) ))]]) ).
thf(235,plain,
! [SV68: a > $o,SV65: a] :
( ( ( sK2_SY391 @ SV65 )
= $false )
| ( ( SV68 @ ( sK3_Xx @ sK2_SY391 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ sK2_SY391 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV65 )
= $true ) ),
inference(extuni,[status(esa)],[203:[bind(SV69,$thf( SV65 )),bind(SV70,$thf( sK2_SY391 ))]]) ).
thf(238,plain,
! [SV70: a > $o,SV68: a > $o,SV17: a] :
( ( ( ! [SX0: a > $o] :
~ ~ ( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cK @ SX0 @ SX1 ) )
| ~ ( SX0
@ ( sK3_Xx
@ ^ [SX1: a] :
~ ! [SX2: a > $o] :
~ ~ ( ~ ! [SX3: a] :
( ~ ( SX2 @ SX3 )
| ( cK @ SX2 @ SX3 ) )
| ~ ( SX2 @ SX1 ) ) ) ) ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( cK @ SV70 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(239,plain,
! [SV69: a,SV70: a > $o,SV72: a > $o] :
( ( ( SV72
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ( SV72 @ SX0 )
@ SV70 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV69 )
= $true )
| ( ( cK @ SV70 @ SV69 )
= $false )
| ( ( ~ ( SV72 @ ( sK3_Xx @ SV70 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(240,plain,
! [SV69: a,SV70: a > $o,SV107: a > $o] :
( ( ( SV107
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ( SV107 @ SX0 )
@ SV70 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV69 )
= $true )
| ( ( cK @ SV70 @ SV69 )
= $false )
| ( ( ~ ( SV107 @ ( sK3_Xx @ SV70 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(241,plain,
! [SV17: a,SV68: a > $o,SV70: a > $o] :
( ( ( ~ ~ ( ~ ! [SY512: a] :
( ~ ( sK19_SX0 @ SV70 @ SV68 @ SV17 @ SY512 )
| ( cK @ ( sK19_SX0 @ SV70 @ SV68 @ SV17 ) @ SY512 ) )
| ~ ( sK19_SX0 @ SV70 @ SV68 @ SV17
@ ( sK3_Xx
@ ^ [SX1: a] :
~ ! [SX2: a > $o] :
~ ~ ( ~ ! [SX3: a] :
( ~ ( SX2 @ SX3 )
| ( cK @ SX2 @ SX3 ) )
| ~ ( SX2 @ SX1 ) ) ) ) ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( cK @ SV70 @ SV17 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[238]) ).
thf(242,plain,
! [SV69: a,SV70: a > $o,SV72: a > $o] :
( ( ( SV72 @ ( sK3_Xx @ SV70 ) )
= $true )
| ( ( cK @ SV70 @ SV69 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV69 )
= $true )
| ( ( SV72
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ( SV72 @ SX0 )
@ SV70 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(243,plain,
! [SV69: a,SV70: a > $o,SV107: a > $o] :
( ( ( SV107 @ ( sK3_Xx @ SV70 ) )
= $true )
| ( ( cK @ SV70 @ SV69 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV69 )
= $true )
| ( ( SV107
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ( SV107 @ SX0 )
@ SV70 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(244,plain,
! [SV17: a,SV68: a > $o,SV70: a > $o] :
( ( ( ~ ( ~ ! [SY512: a] :
( ~ ( sK19_SX0 @ SV70 @ SV68 @ SV17 @ SY512 )
| ( cK @ ( sK19_SX0 @ SV70 @ SV68 @ SV17 ) @ SY512 ) )
| ~ ( sK19_SX0 @ SV70 @ SV68 @ SV17
@ ( sK3_Xx
@ ^ [SX1: a] :
~ ! [SX2: a > $o] :
~ ~ ( ~ ! [SX3: a] :
( ~ ( SX2 @ SX3 )
| ( cK @ SX2 @ SX3 ) )
| ~ ( SX2 @ SX1 ) ) ) ) ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( cK @ SV70 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(245,plain,
! [SV17: a,SV68: a > $o,SV70: a > $o] :
( ( ( ~ ! [SY512: a] :
( ~ ( sK19_SX0 @ SV70 @ SV68 @ SV17 @ SY512 )
| ( cK @ ( sK19_SX0 @ SV70 @ SV68 @ SV17 ) @ SY512 ) )
| ~ ( sK19_SX0 @ SV70 @ SV68 @ SV17
@ ( sK3_Xx
@ ^ [SX1: a] :
~ ! [SX2: a > $o] :
~ ~ ( ~ ! [SX3: a] :
( ~ ( SX2 @ SX3 )
| ( cK @ SX2 @ SX3 ) )
| ~ ( SX2 @ SX1 ) ) ) ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( cK @ SV70 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(246,plain,
! [SV17: a,SV68: a > $o,SV70: a > $o] :
( ( ( ~ ! [SY512: a] :
( ~ ( sK19_SX0 @ SV70 @ SV68 @ SV17 @ SY512 )
| ( cK @ ( sK19_SX0 @ SV70 @ SV68 @ SV17 ) @ SY512 ) ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( cK @ SV70 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(247,plain,
! [SV17: a,SV68: a > $o,SV70: a > $o] :
( ( ( ~ ( sK19_SX0 @ SV70 @ SV68 @ SV17
@ ( sK3_Xx
@ ^ [SX1: a] :
~ ! [SX2: a > $o] :
~ ~ ( ~ ! [SX3: a] :
( ~ ( SX2 @ SX3 )
| ( cK @ SX2 @ SX3 ) )
| ~ ( SX2 @ SX1 ) ) ) ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( cK @ SV70 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(248,plain,
! [SV17: a,SV68: a > $o,SV70: a > $o] :
( ( ( ! [SY512: a] :
( ~ ( sK19_SX0 @ SV70 @ SV68 @ SV17 @ SY512 )
| ( cK @ ( sK19_SX0 @ SV70 @ SV68 @ SV17 ) @ SY512 ) ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( cK @ SV70 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(249,plain,
! [SV17: a,SV68: a > $o,SV70: a > $o] :
( ( ( sK19_SX0 @ SV70 @ SV68 @ SV17
@ ( sK3_Xx
@ ^ [SX1: a] :
~ ! [SX2: a > $o] :
~ ~ ( ~ ! [SX3: a] :
( ~ ( SX2 @ SX3 )
| ( cK @ SX2 @ SX3 ) )
| ~ ( SX2 @ SX1 ) ) ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( cK @ SV70 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(250,plain,
! [SV171: a,SV17: a,SV68: a > $o,SV70: a > $o] :
( ( ( ~ ( sK19_SX0 @ SV70 @ SV68 @ SV17 @ SV171 )
| ( cK @ ( sK19_SX0 @ SV70 @ SV68 @ SV17 ) @ SV171 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( cK @ SV70 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(251,plain,
! [SV171: a,SV17: a,SV68: a > $o,SV70: a > $o] :
( ( ( ~ ( sK19_SX0 @ SV70 @ SV68 @ SV17 @ SV171 ) )
= $true )
| ( ( cK @ ( sK19_SX0 @ SV70 @ SV68 @ SV17 ) @ SV171 )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( cK @ SV70 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(252,plain,
! [SV171: a,SV17: a,SV68: a > $o,SV70: a > $o] :
( ( ( sK19_SX0 @ SV70 @ SV68 @ SV17 @ SV171 )
= $false )
| ( ( cK @ ( sK19_SX0 @ SV70 @ SV68 @ SV17 ) @ SV171 )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( cK @ SV70 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(253,plain,
! [SV172: a > $o,SV173: a,SV174: a > $o] :
( ( ( cK @ SV174 @ SV173 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false ) ),
inference(rename,[status(thm)],[51]) ).
thf(265,plain,
! [SV172: a > $o,SV173: a,SV174: a > $o,SV68: a > $o,SV69: a,SV70: a > $o] :
( ( ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV69 ) )
= $false )
| ( ( cK @ SV174 @ SV173 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV70 @ SV69 )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false ) ),
inference(res,[status(thm)],[253,193]) ).
thf(266,plain,
! [SV172: a > $o,SV173: a,SV174: a > $o,SV68: a > $o,SV69: a,SV70: a > $o] :
( ( ( ( cK @ SV174 @ SV173 )
= ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV69 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV70 @ SV69 )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false ) ),
inference(res,[status(thm)],[253,193]) ).
thf(267,plain,
! [SV172: a > $o,SV173: a,SV174: a > $o,SV68: a > $o,SV69: a,SV70: a > $o] :
( ( ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= ( cK @ SV70 @ SV69 ) )
= $false )
| ( ( cK @ SV174 @ SV173 )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV69 )
= $true )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false ) ),
inference(res,[status(thm)],[253,193]) ).
thf(269,plain,
! [SV172: a > $o,SV173: a,SV174: a > $o,SV65: a] :
( ( ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= ( cK @ sK2_SY391 @ SV65 ) )
= $false )
| ( ( cK @ SV174 @ SV173 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( sK2_SY391 @ SV65 )
= $false ) ),
inference(res,[status(thm)],[253,158]) ).
thf(270,plain,
! [SV172: a > $o,SV173: a,SV174: a > $o,SV65: a] :
( ( ( ( cK @ SV174 @ SV173 )
= ( cK @ sK2_SY391 @ SV65 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( sK2_SY391 @ SV65 )
= $false ) ),
inference(res,[status(thm)],[253,158]) ).
thf(276,plain,
! [SV172: a > $o,SV173: a,SV174: a > $o,SV17: a,SV18: a > $o] :
( ( ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 ) )
= $false )
| ( ( cK @ SV174 @ SV173 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV18 @ SV17 )
= $false )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true ) ),
inference(res,[status(thm)],[253,74]) ).
thf(277,plain,
! [SV172: a > $o,SV173: a,SV174: a > $o,SV17: a,SV18: a > $o] :
( ( ( ( cK @ SV174 @ SV173 )
= ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV18 @ SV17 )
= $false )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true ) ),
inference(res,[status(thm)],[253,74]) ).
thf(278,plain,
! [SV172: a > $o,SV173: a,SV174: a > $o,SV17: a,SV18: a > $o] :
( ( ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= ( cK @ SV18 @ SV17 ) )
= $false )
| ( ( cK @ SV174 @ SV173 )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true ) ),
inference(res,[status(thm)],[253,74]) ).
thf(282,plain,
! [SV172: a > $o,SV173: a,SV174: a > $o] :
( ( ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ sK1_Xx ) )
= $false )
| ( ( cK @ SV174 @ SV173 )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false ) ),
inference(res,[status(thm)],[253,23]) ).
thf(283,plain,
! [SV173: a,SV174: a > $o] :
( ( ( cK @ SV174 @ SV173 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK
@ ^ [SX0: a] : $true
@ ( sK4_Xx0
@ ^ [SX0: a] : $true
@ SV174 ) )
= $false )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[253:[bind(SV172,$thf( ^ [SV178: a] : $true ))]]) ).
thf(284,plain,
! [SV173: a,SV174: a > $o] :
( ( ( cK @ SV174 @ SV173 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK
@ ^ [SX0: a] : $true
@ ( sK4_Xx0
@ ^ [SX0: a] : $true
@ SV174 ) )
= $false ) ),
inference(sim,[status(thm)],[283]) ).
thf(286,plain,
! [SV176: a > $o,SV173: a,SV174: a > $o] :
( ( ( cK @ SV174 @ SV173 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ( SV176 @ SX0 )
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ( SV176 @ SX0 )
@ SV174 ) )
= $false )
| ( ( ~ ( SV176 @ ( sK3_Xx @ SV174 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[253:[bind(SV172,$thf( ^ [SV175: a] : ~ ( SV176 @ SV175 ) ))]]) ).
thf(302,plain,
! [SV174: a > $o,SV172: a > $o] :
( ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( cK @ SV174 @ sK1_Xx )
= $false ) ),
inference(extuni,[status(esa)],[282:[bind(SV173,$thf( sK1_Xx ))]]) ).
thf(303,plain,
! [SV174: a > $o,SV172: a > $o,SV17: a] :
( ( ( ~ ! [SX0: a > $o] :
~ ~ ( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cK @ SX0 @ SX1 ) )
| ~ ( SX0
@ ( sK3_Xx
@ ^ [SX1: a] :
~ ! [SX2: a > $o] :
~ ~ ( ~ ! [SX3: a] :
( ~ ( SX2 @ SX3 )
| ( cK @ SX2 @ SX3 ) )
| ~ ( SX2 @ SX1 ) ) ) ) ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( cK @ SV174 @ SV17 )
= $false ) ),
inference(extuni,[status(esa)],[278:[bind(SV173,$thf( SV17 )),bind(SV18,$thf( ^ [SX0: a] : ~ ( ! [SX1: a > $o] : ~ ( ~ ( ~ ( ! [SX2: a] : ( ~ ( SX1 @ SX2 ) | ( cK @ SX1 @ SX2 ) ) ) | ~ ( SX1 @ SX0 ) ) ) ) ))]]) ).
thf(304,plain,
! [SV172: a > $o,SV17: a,SV18: a > $o] :
( ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true )
| ( ( cK @ SV18 @ SV17 )
= $false )
| ( ( SV172
@ ( sK3_Xx
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) ) ) )
= $false )
| ( ( cK @ SV172
@ ( sK4_Xx0 @ SV172
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) ) ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true ) ),
inference(extuni,[status(esa)],[277:[bind(SV173,$thf( SV17 )),bind(SV174,$thf( ^ [SX0: a] : ~ ( ! [SX1: a > $o] : ~ ( ~ ( ~ ( ! [SX2: a] : ( ~ ( SX1 @ SX2 ) | ( cK @ SX1 @ SX2 ) ) ) | ~ ( SX1 @ SX0 ) ) ) ) ))]]) ).
thf(305,plain,
! [SV173: a,SV174: a > $o,SV18: a > $o] :
( ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true )
| ( ( cK @ SV18
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( ~ ! [SX0: a > $o] :
~ ~ ( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cK @ SX0 @ SX1 ) )
| ~ ( SX0 @ ( sK3_Xx @ SV174 ) ) ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extuni,[status(esa)],[276:[bind(SV17,$thf( sK4_Xx0 @ ^ [SX0: a] : ~ ( ! [SX1: a > $o] : ~ ( ~ ( ~ ( ! [SX2: a] : ( ~ ( SX1 @ SX2 ) | ( cK @ SX1 @ SX2 ) ) ) | ~ ( SX1 @ SX0 ) ) ) ) @ SV174 )),bind(SV172,$thf( ^ [SX0: a] : ~ ( ! [SX1: a > $o] : ~ ( ~ ( ~ ( ! [SX2: a] : ( ~ ( SX1 @ SX2 ) | ( cK @ SX1 @ SX2 ) ) ) | ~ ( SX1 @ SX0 ) ) ) ) ))]]) ).
thf(306,plain,
! [SV172: a > $o,SV65: a] :
( ( ( sK2_SY391 @ SV65 )
= $false )
| ( ( SV172 @ ( sK3_Xx @ sK2_SY391 ) )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ sK2_SY391 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV65 )
= $true ) ),
inference(extuni,[status(esa)],[270:[bind(SV173,$thf( SV65 )),bind(SV174,$thf( sK2_SY391 ))]]) ).
thf(307,plain,
! [SV173: a,SV174: a > $o] :
( ( ( sK2_SY391 @ ( sK4_Xx0 @ sK2_SY391 @ SV174 ) )
= $false )
| ( ( sK2_SY391 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extuni,[status(esa)],[269:[bind(SV65,$thf( sK4_Xx0 @ sK2_SY391 @ SV174 )),bind(SV172,$thf( sK2_SY391 ))]]) ).
thf(308,plain,
! [SV174: a > $o,SV172: a > $o,SV69: a,SV68: a > $o] :
( ( ( SV68
@ ( sK3_Xx
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) ) ) )
= $false )
| ( ( SV68
@ ( sK4_Xx0 @ SV68
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) ) ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV69 )
= $true )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( cK @ SV174 @ SV69 )
= $false ) ),
inference(extuni,[status(esa)],[267:[bind(SV173,$thf( SV69 )),bind(SV70,$thf( ^ [SX0: a] : ~ ( ! [SX1: a > $o] : ~ ( ~ ( ~ ( ! [SX2: a] : ( ~ ( SX1 @ SX2 ) | ( cK @ SX1 @ SX2 ) ) ) | ~ ( SX1 @ SX0 ) ) ) ) ))]]) ).
thf(309,plain,
! [SV172: a > $o,SV69: a,SV70: a > $o,SV68: a > $o] :
( ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( cK @ SV70 @ SV69 )
= $false )
| ( ( SV172
@ ( sK3_Xx
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) ) ) )
= $false )
| ( ( cK @ SV172
@ ( sK4_Xx0 @ SV172
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) ) ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV69 )
= $true ) ),
inference(extuni,[status(esa)],[266:[bind(SV173,$thf( SV69 )),bind(SV174,$thf( ^ [SX0: a] : ~ ( ! [SX1: a > $o] : ~ ( ~ ( ~ ( ! [SX2: a] : ( ~ ( SX1 @ SX2 ) | ( cK @ SX1 @ SX2 ) ) ) | ~ ( SX1 @ SX0 ) ) ) ) ))]]) ).
thf(310,plain,
! [SV173: a,SV174: a > $o,SV70: a > $o,SV68: a > $o] :
( ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( cK @ SV70
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( ~ ! [SX0: a > $o] :
~ ~ ( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cK @ SX0 @ SX1 ) )
| ~ ( SX0 @ ( sK3_Xx @ SV174 ) ) ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extuni,[status(esa)],[265:[bind(SV69,$thf( sK4_Xx0 @ ^ [SX0: a] : ~ ( ! [SX1: a > $o] : ~ ( ~ ( ~ ( ! [SX2: a] : ( ~ ( SX1 @ SX2 ) | ( cK @ SX1 @ SX2 ) ) ) | ~ ( SX1 @ SX0 ) ) ) ) @ SV174 )),bind(SV172,$thf( ^ [SX0: a] : ~ ( ! [SX1: a > $o] : ~ ( ~ ( ~ ( ! [SX2: a] : ( ~ ( SX1 @ SX2 ) | ( cK @ SX1 @ SX2 ) ) ) | ~ ( SX1 @ SX0 ) ) ) ) ))]]) ).
thf(315,plain,
! [SV174: a > $o,SV172: a > $o,SV17: a] :
( ( ( ! [SX0: a > $o] :
~ ~ ( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cK @ SX0 @ SX1 ) )
| ~ ( SX0
@ ( sK3_Xx
@ ^ [SX1: a] :
~ ! [SX2: a > $o] :
~ ~ ( ~ ! [SX3: a] :
( ~ ( SX2 @ SX3 )
| ( cK @ SX2 @ SX3 ) )
| ~ ( SX2 @ SX1 ) ) ) ) ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( cK @ SV174 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(316,plain,
! [SV173: a,SV18: a > $o,SV174: a > $o] :
( ( ( ! [SX0: a > $o] :
~ ~ ( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cK @ SX0 @ SX1 ) )
| ~ ( SX0 @ ( sK3_Xx @ SV174 ) ) ) )
= $true )
| ( ( cK @ SV18
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(317,plain,
! [SV173: a,SV68: a > $o,SV70: a > $o,SV174: a > $o] :
( ( ( ! [SX0: a > $o] :
~ ~ ( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cK @ SX0 @ SX1 ) )
| ~ ( SX0 @ ( sK3_Xx @ SV174 ) ) ) )
= $true )
| ( ( cK @ SV70
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(320,plain,
! [SV173: a,SV174: a > $o,SV176: a > $o] :
( ( ( SV176 @ ( sK3_Xx @ SV174 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ( SV176 @ SX0 )
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ( SV176 @ SX0 )
@ SV174 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(321,plain,
! [SV17: a,SV172: a > $o,SV174: a > $o] :
( ( ( ~ ~ ( ~ ! [SY566: a] :
( ~ ( sK33_SX0 @ SV174 @ SV172 @ SV17 @ SY566 )
| ( cK @ ( sK33_SX0 @ SV174 @ SV172 @ SV17 ) @ SY566 ) )
| ~ ( sK33_SX0 @ SV174 @ SV172 @ SV17
@ ( sK3_Xx
@ ^ [SX1: a] :
~ ! [SX2: a > $o] :
~ ~ ( ~ ! [SX3: a] :
( ~ ( SX2 @ SX3 )
| ( cK @ SX2 @ SX3 ) )
| ~ ( SX2 @ SX1 ) ) ) ) ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( cK @ SV174 @ SV17 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[315]) ).
thf(322,plain,
! [SV173: a,SV18: a > $o,SV174: a > $o,SV239: a > $o] :
( ( ( ~ ~ ( ~ ! [SY570: a] :
( ~ ( SV239 @ SY570 )
| ( cK @ SV239 @ SY570 ) )
| ~ ( SV239 @ ( sK3_Xx @ SV174 ) ) ) )
= $true )
| ( ( cK @ SV18
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(323,plain,
! [SV173: a,SV68: a > $o,SV70: a > $o,SV174: a > $o,SV240: a > $o] :
( ( ( ~ ~ ( ~ ! [SY571: a] :
( ~ ( SV240 @ SY571 )
| ( cK @ SV240 @ SY571 ) )
| ~ ( SV240 @ ( sK3_Xx @ SV174 ) ) ) )
= $true )
| ( ( cK @ SV70
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(326,plain,
! [SV17: a,SV172: a > $o,SV174: a > $o] :
( ( ( ~ ( ~ ! [SY566: a] :
( ~ ( sK33_SX0 @ SV174 @ SV172 @ SV17 @ SY566 )
| ( cK @ ( sK33_SX0 @ SV174 @ SV172 @ SV17 ) @ SY566 ) )
| ~ ( sK33_SX0 @ SV174 @ SV172 @ SV17
@ ( sK3_Xx
@ ^ [SX1: a] :
~ ! [SX2: a > $o] :
~ ~ ( ~ ! [SX3: a] :
( ~ ( SX2 @ SX3 )
| ( cK @ SX2 @ SX3 ) )
| ~ ( SX2 @ SX1 ) ) ) ) ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( cK @ SV174 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(327,plain,
! [SV173: a,SV18: a > $o,SV174: a > $o,SV239: a > $o] :
( ( ( ~ ( ~ ! [SY570: a] :
( ~ ( SV239 @ SY570 )
| ( cK @ SV239 @ SY570 ) )
| ~ ( SV239 @ ( sK3_Xx @ SV174 ) ) ) )
= $false )
| ( ( cK @ SV18
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(328,plain,
! [SV173: a,SV68: a > $o,SV70: a > $o,SV174: a > $o,SV240: a > $o] :
( ( ( ~ ( ~ ! [SY571: a] :
( ~ ( SV240 @ SY571 )
| ( cK @ SV240 @ SY571 ) )
| ~ ( SV240 @ ( sK3_Xx @ SV174 ) ) ) )
= $false )
| ( ( cK @ SV70
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(331,plain,
! [SV17: a,SV172: a > $o,SV174: a > $o] :
( ( ( ~ ! [SY566: a] :
( ~ ( sK33_SX0 @ SV174 @ SV172 @ SV17 @ SY566 )
| ( cK @ ( sK33_SX0 @ SV174 @ SV172 @ SV17 ) @ SY566 ) )
| ~ ( sK33_SX0 @ SV174 @ SV172 @ SV17
@ ( sK3_Xx
@ ^ [SX1: a] :
~ ! [SX2: a > $o] :
~ ~ ( ~ ! [SX3: a] :
( ~ ( SX2 @ SX3 )
| ( cK @ SX2 @ SX3 ) )
| ~ ( SX2 @ SX1 ) ) ) ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( cK @ SV174 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(332,plain,
! [SV173: a,SV18: a > $o,SV174: a > $o,SV239: a > $o] :
( ( ( ~ ! [SY570: a] :
( ~ ( SV239 @ SY570 )
| ( cK @ SV239 @ SY570 ) )
| ~ ( SV239 @ ( sK3_Xx @ SV174 ) ) )
= $true )
| ( ( cK @ SV18
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(333,plain,
! [SV173: a,SV68: a > $o,SV70: a > $o,SV174: a > $o,SV240: a > $o] :
( ( ( ~ ! [SY571: a] :
( ~ ( SV240 @ SY571 )
| ( cK @ SV240 @ SY571 ) )
| ~ ( SV240 @ ( sK3_Xx @ SV174 ) ) )
= $true )
| ( ( cK @ SV70
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(336,plain,
! [SV17: a,SV172: a > $o,SV174: a > $o] :
( ( ( ~ ! [SY566: a] :
( ~ ( sK33_SX0 @ SV174 @ SV172 @ SV17 @ SY566 )
| ( cK @ ( sK33_SX0 @ SV174 @ SV172 @ SV17 ) @ SY566 ) ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( cK @ SV174 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(337,plain,
! [SV17: a,SV172: a > $o,SV174: a > $o] :
( ( ( ~ ( sK33_SX0 @ SV174 @ SV172 @ SV17
@ ( sK3_Xx
@ ^ [SX1: a] :
~ ! [SX2: a > $o] :
~ ~ ( ~ ! [SX3: a] :
( ~ ( SX2 @ SX3 )
| ( cK @ SX2 @ SX3 ) )
| ~ ( SX2 @ SX1 ) ) ) ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( cK @ SV174 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(338,plain,
! [SV173: a,SV18: a > $o,SV174: a > $o,SV239: a > $o] :
( ( ( ~ ! [SY570: a] :
( ~ ( SV239 @ SY570 )
| ( cK @ SV239 @ SY570 ) ) )
= $true )
| ( ( ~ ( SV239 @ ( sK3_Xx @ SV174 ) ) )
= $true )
| ( ( cK @ SV18
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(339,plain,
! [SV173: a,SV68: a > $o,SV70: a > $o,SV174: a > $o,SV240: a > $o] :
( ( ( ~ ! [SY571: a] :
( ~ ( SV240 @ SY571 )
| ( cK @ SV240 @ SY571 ) ) )
= $true )
| ( ( ~ ( SV240 @ ( sK3_Xx @ SV174 ) ) )
= $true )
| ( ( cK @ SV70
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(342,plain,
! [SV17: a,SV172: a > $o,SV174: a > $o] :
( ( ( ! [SY566: a] :
( ~ ( sK33_SX0 @ SV174 @ SV172 @ SV17 @ SY566 )
| ( cK @ ( sK33_SX0 @ SV174 @ SV172 @ SV17 ) @ SY566 ) ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( cK @ SV174 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(343,plain,
! [SV17: a,SV172: a > $o,SV174: a > $o] :
( ( ( sK33_SX0 @ SV174 @ SV172 @ SV17
@ ( sK3_Xx
@ ^ [SX1: a] :
~ ! [SX2: a > $o] :
~ ~ ( ~ ! [SX3: a] :
( ~ ( SX2 @ SX3 )
| ( cK @ SX2 @ SX3 ) )
| ~ ( SX2 @ SX1 ) ) ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( cK @ SV174 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(344,plain,
! [SV173: a,SV18: a > $o,SV174: a > $o,SV239: a > $o] :
( ( ( ! [SY570: a] :
( ~ ( SV239 @ SY570 )
| ( cK @ SV239 @ SY570 ) ) )
= $false )
| ( ( ~ ( SV239 @ ( sK3_Xx @ SV174 ) ) )
= $true )
| ( ( cK @ SV18
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(345,plain,
! [SV173: a,SV68: a > $o,SV70: a > $o,SV174: a > $o,SV240: a > $o] :
( ( ( ! [SY571: a] :
( ~ ( SV240 @ SY571 )
| ( cK @ SV240 @ SY571 ) ) )
= $false )
| ( ( ~ ( SV240 @ ( sK3_Xx @ SV174 ) ) )
= $true )
| ( ( cK @ SV70
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(348,plain,
! [SV243: a,SV17: a,SV172: a > $o,SV174: a > $o] :
( ( ( ~ ( sK33_SX0 @ SV174 @ SV172 @ SV17 @ SV243 )
| ( cK @ ( sK33_SX0 @ SV174 @ SV172 @ SV17 ) @ SV243 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( cK @ SV174 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(349,plain,
! [SV174: a > $o,SV18: a > $o,SV173: a,SV239: a > $o] :
( ( ( ~ ( SV239 @ ( sK34_SY570 @ SV173 @ SV18 @ SV174 @ SV239 ) )
| ( cK @ SV239 @ ( sK34_SY570 @ SV173 @ SV18 @ SV174 @ SV239 ) ) )
= $false )
| ( ( ~ ( SV239 @ ( sK3_Xx @ SV174 ) ) )
= $true )
| ( ( cK @ SV18
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[344]) ).
thf(350,plain,
! [SV174: a > $o,SV70: a > $o,SV68: a > $o,SV173: a,SV240: a > $o] :
( ( ( ~ ( SV240 @ ( sK35_SY571 @ SV173 @ SV68 @ SV70 @ SV174 @ SV240 ) )
| ( cK @ SV240 @ ( sK35_SY571 @ SV173 @ SV68 @ SV70 @ SV174 @ SV240 ) ) )
= $false )
| ( ( ~ ( SV240 @ ( sK3_Xx @ SV174 ) ) )
= $true )
| ( ( cK @ SV70
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[345]) ).
thf(353,plain,
! [SV243: a,SV17: a,SV172: a > $o,SV174: a > $o] :
( ( ( ~ ( sK33_SX0 @ SV174 @ SV172 @ SV17 @ SV243 ) )
= $true )
| ( ( cK @ ( sK33_SX0 @ SV174 @ SV172 @ SV17 ) @ SV243 )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( cK @ SV174 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(354,plain,
! [SV174: a > $o,SV18: a > $o,SV173: a,SV239: a > $o] :
( ( ( ~ ( SV239 @ ( sK34_SY570 @ SV173 @ SV18 @ SV174 @ SV239 ) ) )
= $false )
| ( ( ~ ( SV239 @ ( sK3_Xx @ SV174 ) ) )
= $true )
| ( ( cK @ SV18
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(355,plain,
! [SV174: a > $o,SV18: a > $o,SV173: a,SV239: a > $o] :
( ( ( cK @ SV239 @ ( sK34_SY570 @ SV173 @ SV18 @ SV174 @ SV239 ) )
= $false )
| ( ( ~ ( SV239 @ ( sK3_Xx @ SV174 ) ) )
= $true )
| ( ( cK @ SV18
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(356,plain,
! [SV174: a > $o,SV70: a > $o,SV68: a > $o,SV173: a,SV240: a > $o] :
( ( ( ~ ( SV240 @ ( sK35_SY571 @ SV173 @ SV68 @ SV70 @ SV174 @ SV240 ) ) )
= $false )
| ( ( ~ ( SV240 @ ( sK3_Xx @ SV174 ) ) )
= $true )
| ( ( cK @ SV70
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[350]) ).
thf(357,plain,
! [SV174: a > $o,SV70: a > $o,SV68: a > $o,SV173: a,SV240: a > $o] :
( ( ( cK @ SV240 @ ( sK35_SY571 @ SV173 @ SV68 @ SV70 @ SV174 @ SV240 ) )
= $false )
| ( ( ~ ( SV240 @ ( sK3_Xx @ SV174 ) ) )
= $true )
| ( ( cK @ SV70
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[350]) ).
thf(362,plain,
! [SV243: a,SV17: a,SV172: a > $o,SV174: a > $o] :
( ( ( sK33_SX0 @ SV174 @ SV172 @ SV17 @ SV243 )
= $false )
| ( ( cK @ ( sK33_SX0 @ SV174 @ SV172 @ SV17 ) @ SV243 )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV17 )
= $true )
| ( ( SV172 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV172 @ ( sK4_Xx0 @ SV172 @ SV174 ) )
= $false )
| ( ( cK @ SV174 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(363,plain,
! [SV174: a > $o,SV18: a > $o,SV173: a,SV239: a > $o] :
( ( ( SV239 @ ( sK34_SY570 @ SV173 @ SV18 @ SV174 @ SV239 ) )
= $true )
| ( ( ~ ( SV239 @ ( sK3_Xx @ SV174 ) ) )
= $true )
| ( ( cK @ SV18
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(364,plain,
! [SV18: a > $o,SV173: a,SV174: a > $o,SV239: a > $o] :
( ( ( SV239 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV239 @ ( sK34_SY570 @ SV173 @ SV18 @ SV174 @ SV239 ) )
= $false )
| ( ( cK @ SV18
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(365,plain,
! [SV174: a > $o,SV70: a > $o,SV68: a > $o,SV173: a,SV240: a > $o] :
( ( ( SV240 @ ( sK35_SY571 @ SV173 @ SV68 @ SV70 @ SV174 @ SV240 ) )
= $true )
| ( ( ~ ( SV240 @ ( sK3_Xx @ SV174 ) ) )
= $true )
| ( ( cK @ SV70
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[356]) ).
thf(366,plain,
! [SV70: a > $o,SV68: a > $o,SV173: a,SV174: a > $o,SV240: a > $o] :
( ( ( SV240 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( cK @ SV240 @ ( sK35_SY571 @ SV173 @ SV68 @ SV70 @ SV174 @ SV240 ) )
= $false )
| ( ( cK @ SV70
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(371,plain,
! [SV18: a > $o,SV173: a,SV174: a > $o,SV239: a > $o] :
( ( ( SV239 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( SV239 @ ( sK34_SY570 @ SV173 @ SV18 @ SV174 @ SV239 ) )
= $true )
| ( ( cK @ SV18
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV18 @ ( sK3_Xx @ SV18 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(372,plain,
! [SV70: a > $o,SV68: a > $o,SV173: a,SV174: a > $o,SV240: a > $o] :
( ( ( SV240 @ ( sK3_Xx @ SV174 ) )
= $false )
| ( ( SV240 @ ( sK35_SY571 @ SV173 @ SV68 @ SV70 @ SV174 @ SV240 ) )
= $true )
| ( ( cK @ SV70
@ ( sK4_Xx0
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV174 ) )
= $false )
| ( ( SV68 @ ( sK4_Xx0 @ SV68 @ SV70 ) )
= $true )
| ( ( SV68 @ ( sK3_Xx @ SV70 ) )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ SV173 )
= $true )
| ( ( cK @ SV174 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(426,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,372,371,366,364,362,343,320,309,308,307,306,304,302,284,253,252,249,243,242,235,234,232,193,192,191,190,183,169,168,158,93,88,87,86,84,74,72,71,70,69,67,66,65,64,31]) ).
thf(427,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[426]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO331^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 : Sat Jul 9 05:00:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 0
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)......eprover: CPU time limit exceeded, terminating
% 25.22/25.44 ...eprover: CPU time limit exceeded, terminating
% 50.49/50.72 .
% 50.74/50.97
% 50.74/50.97 Prim_subst applied to clause
% 50.74/50.97
% 50.74/50.97 80:[ 0:<(cK@SV18)@SV17 = $false>-w(1)-i() 1:<(cK@(^[SX0:a]: (~ (![SX1:(a>$o)]: (~ (~ ((~ (![SX2:a]: ((~ (SX1@SX2)) | ((cK@SX1)@SX2)))) | (~ (SX1@SX0)))))))))@SV17 = $true>-w(1)-i() 2:<SV18@(sK3_Xx@SV18) = $true>-w(1)-i() ]-mln(3)-w(3)-i(rename 36)-o(AXIOM)-fv([ SV17 SV18 ])
% 50.80/51.04 ...............................................................................
% 77.79/78.06 (rf:0,axioms:0,ps:2,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)......eprover: CPU time limit exceeded, terminating
% 102.85/103.11 ...eprover: CPU time limit exceeded, terminating
% 128.20/128.53
% 128.20/128.53
% 128.20/128.53 Prim_subst applied to clause
% 128.20/128.53
% 128.20/128.53 74:[ 0:<(cK@SV18)@SV17 = $false>-w(1)-i() 1:<(cK@(^[SX0:a]: (~ (![SX1:(a>$o)]: (~ (~ ((~ (![SX2:a]: ((~ (SX1@SX2)) | ((cK@SX1)@SX2)))) | (~ (SX1@SX0)))))))))@SV17 = $true>-w(1)-i() 2:<SV18@(sK3_Xx@SV18) = $true>-w(1)-i() ]-mln(3)-w(3)-i(rename 35)-o(AXIOM)-fv([ SV17 SV18 ])
% 128.28/128.57 ............................
% 128.72/128.99
% 128.72/128.99 Prim_subst applied to clause
% 128.72/128.99
% 128.72/128.99 193:[ 0:<(cK@SV70)@SV69 = $false>-w(1)-i() 1:<(cK@(^[SX0:a]: (~ (![SX1:(a>$o)]: (~ (~ ((~ (![SX2:a]: ((~ (SX1@SX2)) | ((cK@SX1)@SX2)))) | (~ (SX1@SX0)))))))))@SV69 = $true>-w(1)-i() 2:<SV68@((sK4_Xx0@SV68)@SV70) = $true>-w(1)-i() 3:<SV68@(sK3_Xx@SV70) = $false>-w(1)-i() ]-mln(4)-w(4)-i(rename 49)-o(AXIOM)-fv([ SV68 SV69 SV70 ])
% 128.72/129.00 .
% 128.76/129.08
% 128.76/129.08 Prim_subst applied to clause
% 128.76/129.08
% 128.76/129.08 193:[ 0:<(cK@SV70)@SV69 = $false>-w(1)-i() 1:<(cK@(^[SX0:a]: (~ (![SX1:(a>$o)]: (~ (~ ((~ (![SX2:a]: ((~ (SX1@SX2)) | ((cK@SX1)@SX2)))) | (~ (SX1@SX0)))))))))@SV69 = $true>-w(1)-i() 2:<SV68@((sK4_Xx0@SV68)@SV70) = $true>-w(1)-i() 3:<SV68@(sK3_Xx@SV70) = $false>-w(1)-i() ]-mln(4)-w(4)-i(rename 49)-o(AXIOM)-fv([ SV68 SV69 SV70 ])
% 128.89/129.24 ....................
% 129.78/130.07
% 129.78/130.07 Prim_subst applied to clause
% 129.78/130.07
% 129.78/130.07 253:[ 0:<(cK@SV174)@SV173 = $false>-w(1)-i() 1:<(cK@(^[SX0:a]: (~ (![SX1:(a>$o)]: (~ (~ ((~ (![SX2:a]: ((~ (SX1@SX2)) | ((cK@SX1)@SX2)))) | (~ (SX1@SX0)))))))))@SV173 = $true>-w(1)-i() 2:<(cK@SV172)@((sK4_Xx0@SV172)@SV174) = $false>-w(1)-i() 3:<SV172@(sK3_Xx@SV174) = $false>-w(1)-i() ]-mln(4)-w(4)-i(rename 51)-o(AXIOM)-fv([ SV172 SV173 SV174 ])
% 130.07/130.40 ...........................................................................
% 138.82/139.21
% 138.82/139.21 ********************************
% 138.82/139.21 * All subproblems solved! *
% 138.82/139.21 ********************************
% 138.82/139.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:2,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:19,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:426,loop_count:10,foatp_calls:3,translation:fof_full)
% 138.91/139.26
% 138.91/139.26 %**** Beginning of derivation protocol ****
% 138.91/139.26 % SZS output start CNFRefutation
% See solution above
% 138.91/139.26
% 138.91/139.26 %**** End of derivation protocol ****
% 138.91/139.26 %**** no. of clauses in derivation: 191 ****
% 138.91/139.26 %**** clause counter: 426 ****
% 138.91/139.26
% 138.91/139.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:2,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:19,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:426,loop_count:10,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------