TSTP Solution File: SYO536^1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO536^1 : TPTP v8.1.0. Released v5.2.0.
% 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 17:35:26 EDT 2022
% Result : Theorem 1.14s 1.34s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 40
% Syntax : Number of formulae : 296 ( 36 unt; 37 typ; 2 def)
% Number of atoms : 2016 ( 549 equ; 0 cnn)
% Maximal formula atoms : 3 ( 7 avg)
% Number of connectives : 4217 (1353 ~; 260 |; 0 &;2601 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 673 ( 673 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 37 usr; 16 con; 0-2 aty)
% Number of variables : 1421 ( 432 ^ 980 !; 9 ?;1421 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_eps,type,
eps: ( $i > $o ) > $i ).
thf(tp_epsa,type,
epsa: ( ( $i > $i ) > $i > $o ) > $i > $i ).
thf(tp_epsb,type,
epsb: ( ( $i > $i ) > $i > $o ) > $i ).
thf(tp_epsii,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(tp_sK10_SY68,type,
sK10_SY68: $i > ( $i > $i ) > $i ).
thf(tp_sK11_SY81,type,
sK11_SY81: $i > ( $i > $i ) > $i ).
thf(tp_sK12_E,type,
sK12_E: $i > $i ).
thf(tp_sK13_E,type,
sK13_E: $i ).
thf(tp_sK14_E,type,
sK14_E: $i ).
thf(tp_sK15_SY103,type,
sK15_SY103: $i > ( $i > $i ) > $i ).
thf(tp_sK16_E,type,
sK16_E: $i ).
thf(tp_sK17_E,type,
sK17_E: $i ).
thf(tp_sK18_SY115,type,
sK18_SY115: $i > ( $i > $i ) > $i ).
thf(tp_sK19_E,type,
sK19_E: $i > $i ).
thf(tp_sK1_R,type,
sK1_R: ( $i > $i ) > $i > $o ).
thf(tp_sK20_E,type,
sK20_E: $i ).
thf(tp_sK21_E,type,
sK21_E: $i > $i ).
thf(tp_sK22_E,type,
sK22_E: $i ).
thf(tp_sK23_E,type,
sK23_E: $i ).
thf(tp_sK24_E,type,
sK24_E: $i > $i ).
thf(tp_sK25_E,type,
sK25_E: $i ).
thf(tp_sK26_E,type,
sK26_E: $i ).
thf(tp_sK27_E,type,
sK27_E: $i ).
thf(tp_sK28_SY137,type,
sK28_SY137: $i > ( $i > $i ) > $i ).
thf(tp_sK29_E,type,
sK29_E: $i ).
thf(tp_sK2_SY0,type,
sK2_SY0: $i > $i ).
thf(tp_sK30_E,type,
sK30_E: $i ).
thf(tp_sK31_SY149,type,
sK31_SY149: $i > ( $i > $i ) > $i ).
thf(tp_sK32_SY165,type,
sK32_SY165: $i > ( $i > $i ) > $i ).
thf(tp_sK33_SY170,type,
sK33_SY170: $i > ( $i > $i ) > $i ).
thf(tp_sK3_SY2,type,
sK3_SY2: $i ).
thf(tp_sK4_SY9,type,
sK4_SY9: $i > ( $i > $i ) > $i ).
thf(tp_sK5_SY22,type,
sK5_SY22: $i > ( $i > $i ) > $i ).
thf(tp_sK6_SY35,type,
sK6_SY35: $i > ( $i > $i ) > $i ).
thf(tp_sK7_SY48,type,
sK7_SY48: $i > ( $i > $i ) > $i ).
thf(tp_sK8_E,type,
sK8_E: $i ).
thf(tp_sK9_SY63,type,
sK9_SY63: $i > ( $i > $i ) > $i ).
thf(epsa,definition,
( epsa
= ( ^ [R: ( $i > $i ) > $i > $o] :
( epsii
@ ^ [X: $i > $i] :
? [Y: $i] : ( R @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epsa) ).
thf(epsb,definition,
( epsb
= ( ^ [R: ( $i > $i ) > $i > $o] :
( eps
@ ^ [Y: $i] : ( R @ ( epsa @ R ) @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epsb) ).
thf(3,conjecture,
! [R: ( $i > $i ) > $i > $o] :
( ? [X: $i > $i,Y: $i] : ( R @ X @ Y )
=> ( R @ ( epsa @ R ) @ ( epsb @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(4,negated_conjecture,
( ( ! [R: ( $i > $i ) > $i > $o] :
( ? [X: $i > $i,Y: $i] : ( R @ X @ Y )
=> ( R @ ( epsa @ R ) @ ( epsb @ R ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ? [SY0: $i > $i,SY1: $i] : ( sK1_R @ SY0 @ SY1 )
=> ( sK1_R @ ( epsa @ sK1_R ) @ ( epsb @ sK1_R ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ? [SY0: $i > $i,SY1: $i] : ( sK1_R @ SY0 @ SY1 ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( sK1_R @ ( epsa @ sK1_R ) @ ( epsb @ sK1_R ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ( sK1_R @ ( epsa @ sK1_R ) @ ( epsb @ sK1_R ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( sK1_R @ sK2_SY0 @ sK3_SY2 )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(14,plain,
( ( sK1_R @ sK2_SY0 @ sK3_SY2 )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(15,plain,
( ( ~ ( sK1_R @ ( epsa @ sK1_R ) @ ( epsb @ sK1_R ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,epsa,epsb]) ).
thf(19,plain,
( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(26,plain,
( ( ~ ~ ! [SY5: $i > $i] :
~ ~ ! [SY6: $i] :
~ ( sK1_R @ SY5 @ SY6 )
| ~ ! [SY9: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ),
inference(choice,[status(thm)],[19]) ).
thf(27,plain,
( ( ~ ~ ! [SY10: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY10 )
| ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ),
inference(choice,[status(thm)],[19]) ).
thf(28,plain,
( ( ~ ~ ! [SY18: $i > $i] :
~ ~ ! [SY19: $i] :
~ ( sK1_R @ SY18 @ SY19 )
| ~ ! [SY22: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ),
inference(choice,[status(thm)],[19]) ).
thf(29,plain,
( ( ( ~ ~ ! [SY5: $i > $i] :
~ ~ ! [SY6: $i] :
~ ( sK1_R @ SY5 @ SY6 ) )
= $true )
| ( ( ~ ! [SY9: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ( ~ ~ ! [SY10: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY10 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ( ~ ~ ! [SY18: $i > $i] :
~ ~ ! [SY19: $i] :
~ ( sK1_R @ SY18 @ SY19 ) )
= $true )
| ( ( ~ ! [SY22: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
( ( ( ~ ! [SY5: $i > $i] :
~ ~ ! [SY6: $i] :
~ ( sK1_R @ SY5 @ SY6 ) )
= $false )
| ( ( ~ ! [SY9: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( ( ~ ! [SY10: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY10 ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
( ( ( ~ ! [SY18: $i > $i] :
~ ~ ! [SY19: $i] :
~ ( sK1_R @ SY18 @ SY19 ) )
= $false )
| ( ( ~ ! [SY22: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
( ( ( ! [SY5: $i > $i] :
~ ~ ! [SY6: $i] :
~ ( sK1_R @ SY5 @ SY6 ) )
= $true )
| ( ( ~ ! [SY9: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(36,plain,
( ( ( ! [SY10: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY10 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(37,plain,
( ( ( ! [SY18: $i > $i] :
~ ~ ! [SY19: $i] :
~ ( sK1_R @ SY18 @ SY19 ) )
= $true )
| ( ( ~ ! [SY22: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV8: $i > $i] :
( ( ( ~ ~ ! [SY23: $i] :
~ ( sK1_R @ SV8 @ SY23 ) )
= $true )
| ( ( ~ ! [SY9: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV9: $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV9 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV10: $i > $i] :
( ( ( ~ ~ ! [SY26: $i] :
~ ( sK1_R @ SV10 @ SY26 ) )
= $true )
| ( ( ~ ! [SY22: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV8: $i > $i] :
( ( ( ~ ! [SY23: $i] :
~ ( sK1_R @ SV8 @ SY23 ) )
= $false )
| ( ( ~ ! [SY9: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV9: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV9 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV10: $i > $i] :
( ( ( ~ ! [SY26: $i] :
~ ( sK1_R @ SV10 @ SY26 ) )
= $false )
| ( ( ~ ! [SY22: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV8: $i > $i] :
( ( ( ! [SY23: $i] :
~ ( sK1_R @ SV8 @ SY23 ) )
= $true )
| ( ( ~ ! [SY9: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV10: $i > $i] :
( ( ( ! [SY26: $i] :
~ ( sK1_R @ SV10 @ SY26 ) )
= $true )
| ( ( ~ ! [SY22: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(46,plain,
! [SV11: $i,SV8: $i > $i] :
( ( ( ~ ( sK1_R @ SV8 @ SV11 ) )
= $true )
| ( ( ~ ! [SY9: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV12: $i,SV10: $i > $i] :
( ( ( ~ ( sK1_R @ SV10 @ SV12 ) )
= $true )
| ( ( ~ ! [SY22: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV11: $i,SV8: $i > $i] :
( ( ( sK1_R @ SV8 @ SV11 )
= $false )
| ( ( ~ ! [SY9: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(49,plain,
! [SV12: $i,SV10: $i > $i] :
( ( ( sK1_R @ SV10 @ SV12 )
= $false )
| ( ( ~ ! [SY22: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV11: $i,SV8: $i > $i] :
( ( ( ! [SY9: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $false )
| ( ( sK1_R @ SV8 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV12: $i,SV10: $i > $i] :
( ( ( ! [SY22: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $false )
| ( ( sK1_R @ SV10 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV8: $i > $i,SV11: $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ SV11 @ SV8 ) ) )
= $false )
| ( ( sK1_R @ SV8 @ SV11 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[50]) ).
thf(53,plain,
! [SV10: $i > $i,SV12: $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( sK5_SY22 @ SV12 @ SV10 ) ) )
= $false )
| ( ( sK1_R @ SV10 @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(54,plain,
! [SV8: $i > $i,SV11: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ SV11 @ SV8 ) )
= $true )
| ( ( sK1_R @ SV8 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(55,plain,
! [SV10: $i > $i,SV12: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( sK5_SY22 @ SV12 @ SV10 ) )
= $true )
| ( ( sK1_R @ SV10 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(56,plain,
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= ( sK1_R @ sK2_SY0 @ sK3_SY2 ) )
= $false ),
inference(res,[status(thm)],[19,14]) ).
thf(57,plain,
( ( ~ ~ ! [SY31: $i > $i] :
~ ~ ! [SY32: $i] :
~ ( sK1_R @ SY31 @ SY32 )
| ~ ! [SY35: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ),
inference(choice,[status(thm)],[19]) ).
thf(59,plain,
( ( ~ ~ ! [SY44: $i > $i] :
~ ~ ! [SY45: $i] :
~ ( sK1_R @ SY44 @ SY45 )
| ~ ! [SY48: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ),
inference(choice,[status(thm)],[19]) ).
thf(60,plain,
( ( ( ~ ~ ! [SY31: $i > $i] :
~ ~ ! [SY32: $i] :
~ ( sK1_R @ SY31 @ SY32 ) )
= $true )
| ( ( ~ ! [SY35: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(62,plain,
( ( ( ~ ~ ! [SY44: $i > $i] :
~ ~ ! [SY45: $i] :
~ ( sK1_R @ SY44 @ SY45 ) )
= $true )
| ( ( ~ ! [SY48: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(63,plain,
( ( ( ~ ! [SY31: $i > $i] :
~ ~ ! [SY32: $i] :
~ ( sK1_R @ SY31 @ SY32 ) )
= $false )
| ( ( ~ ! [SY35: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(65,plain,
( ( ( ~ ! [SY44: $i > $i] :
~ ~ ! [SY45: $i] :
~ ( sK1_R @ SY44 @ SY45 ) )
= $false )
| ( ( ~ ! [SY48: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(66,plain,
( ( ( ! [SY31: $i > $i] :
~ ~ ! [SY32: $i] :
~ ( sK1_R @ SY31 @ SY32 ) )
= $true )
| ( ( ~ ! [SY35: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(68,plain,
( ( ( ! [SY44: $i > $i] :
~ ~ ! [SY45: $i] :
~ ( sK1_R @ SY44 @ SY45 ) )
= $true )
| ( ( ~ ! [SY48: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(69,plain,
! [SV16: $i > $i] :
( ( ( ~ ~ ! [SY49: $i] :
~ ( sK1_R @ SV16 @ SY49 ) )
= $true )
| ( ( ~ ! [SY35: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV18: $i > $i] :
( ( ( ~ ~ ! [SY52: $i] :
~ ( sK1_R @ SV18 @ SY52 ) )
= $true )
| ( ( ~ ! [SY48: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV16: $i > $i] :
( ( ( ~ ! [SY49: $i] :
~ ( sK1_R @ SV16 @ SY49 ) )
= $false )
| ( ( ~ ! [SY35: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(74,plain,
! [SV18: $i > $i] :
( ( ( ~ ! [SY52: $i] :
~ ( sK1_R @ SV18 @ SY52 ) )
= $false )
| ( ( ~ ! [SY48: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV16: $i > $i] :
( ( ( ! [SY49: $i] :
~ ( sK1_R @ SV16 @ SY49 ) )
= $true )
| ( ( ~ ! [SY35: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(76,plain,
! [SV18: $i > $i] :
( ( ( ! [SY52: $i] :
~ ( sK1_R @ SV18 @ SY52 ) )
= $true )
| ( ( ~ ! [SY48: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(77,plain,
! [SV19: $i,SV16: $i > $i] :
( ( ( ~ ( sK1_R @ SV16 @ SV19 ) )
= $true )
| ( ( ~ ! [SY35: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(78,plain,
! [SV20: $i,SV18: $i > $i] :
( ( ( ~ ( sK1_R @ SV18 @ SV20 ) )
= $true )
| ( ( ~ ! [SY48: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(79,plain,
! [SV19: $i,SV16: $i > $i] :
( ( ( sK1_R @ SV16 @ SV19 )
= $false )
| ( ( ~ ! [SY35: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(80,plain,
! [SV20: $i,SV18: $i > $i] :
( ( ( sK1_R @ SV18 @ SV20 )
= $false )
| ( ( ~ ! [SY48: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(81,plain,
! [SV19: $i,SV16: $i > $i] :
( ( ( ! [SY35: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $false )
| ( ( sK1_R @ SV16 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(82,plain,
! [SV20: $i,SV18: $i > $i] :
( ( ( ! [SY48: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $false )
| ( ( sK1_R @ SV18 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(83,plain,
! [SV16: $i > $i,SV19: $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ SV19 @ SV16 ) ) )
= $false )
| ( ( sK1_R @ SV16 @ SV19 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[81]) ).
thf(84,plain,
! [SV18: $i > $i,SV20: $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( sK7_SY48 @ SV20 @ SV18 ) ) )
= $false )
| ( ( sK1_R @ SV18 @ SV20 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[82]) ).
thf(85,plain,
! [SV16: $i > $i,SV19: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ SV19 @ SV16 ) )
= $true )
| ( ( sK1_R @ SV16 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(86,plain,
! [SV18: $i > $i,SV20: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( sK7_SY48 @ SV20 @ SV18 ) )
= $true )
| ( ( sK1_R @ SV18 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(87,plain,
( ( ( ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) )
= sK3_SY2 )
= $false )
| ( ( ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 )
@ sK8_E )
= ( sK2_SY0 @ sK8_E ) )
= $false ) ),
inference(extuni,[status(esa)],[56]) ).
thf(88,plain,
! [SV21: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(rename,[status(thm)],[42]) ).
thf(91,plain,
! [SV21: $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 )
= $false ) ),
inference(res,[status(thm)],[88,19]) ).
thf(92,plain,
! [SV21: $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 )
= ( sK1_R @ sK2_SY0 @ sK3_SY2 ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[88,14]) ).
thf(93,plain,
( ( ~ ~ ! [SY59: $i > $i] :
~ ~ ! [SY60: $i] :
~ ( sK1_R @ SY59 @ SY60 )
| ~ ! [SY63: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY63 ) )
= $true ),
inference(choice,[status(thm)],[88]) ).
thf(94,plain,
( ( ~ ~ ! [SY64: $i > $i] :
~ ~ ! [SY65: $i] :
~ ( sK1_R @ SY64 @ SY65 )
| ~ ! [SY68: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY68 ) )
= $true ),
inference(choice,[status(thm)],[88]) ).
thf(95,plain,
( ( ~ ~ ! [SY69: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY69 )
| ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ),
inference(choice,[status(thm)],[88]) ).
thf(96,plain,
( ( ~ ~ ! [SY77: $i > $i] :
~ ~ ! [SY78: $i] :
~ ( sK1_R @ SY77 @ SY78 )
| ~ ! [SY81: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY81 ) )
= $true ),
inference(choice,[status(thm)],[88]) ).
thf(97,plain,
( ( ( ~ ~ ! [SY59: $i > $i] :
~ ~ ! [SY60: $i] :
~ ( sK1_R @ SY59 @ SY60 ) )
= $true )
| ( ( ~ ! [SY63: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(98,plain,
( ( ( ~ ~ ! [SY64: $i > $i] :
~ ~ ! [SY65: $i] :
~ ( sK1_R @ SY64 @ SY65 ) )
= $true )
| ( ( ~ ! [SY68: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(99,plain,
( ( ( ~ ~ ! [SY69: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY69 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(100,plain,
( ( ( ~ ~ ! [SY77: $i > $i] :
~ ~ ! [SY78: $i] :
~ ( sK1_R @ SY77 @ SY78 ) )
= $true )
| ( ( ~ ! [SY81: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(101,plain,
( ( ( ~ ! [SY59: $i > $i] :
~ ~ ! [SY60: $i] :
~ ( sK1_R @ SY59 @ SY60 ) )
= $false )
| ( ( ~ ! [SY63: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(102,plain,
( ( ( ~ ! [SY64: $i > $i] :
~ ~ ! [SY65: $i] :
~ ( sK1_R @ SY64 @ SY65 ) )
= $false )
| ( ( ~ ! [SY68: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(103,plain,
( ( ( ~ ! [SY69: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY69 ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(104,plain,
( ( ( ~ ! [SY77: $i > $i] :
~ ~ ! [SY78: $i] :
~ ( sK1_R @ SY77 @ SY78 ) )
= $false )
| ( ( ~ ! [SY81: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(105,plain,
( ( ( ! [SY59: $i > $i] :
~ ~ ! [SY60: $i] :
~ ( sK1_R @ SY59 @ SY60 ) )
= $true )
| ( ( ~ ! [SY63: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(106,plain,
( ( ( ! [SY64: $i > $i] :
~ ~ ! [SY65: $i] :
~ ( sK1_R @ SY64 @ SY65 ) )
= $true )
| ( ( ~ ! [SY68: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(107,plain,
( ( ( ! [SY69: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY69 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(108,plain,
( ( ( ! [SY77: $i > $i] :
~ ~ ! [SY78: $i] :
~ ( sK1_R @ SY77 @ SY78 ) )
= $true )
| ( ( ~ ! [SY81: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY81 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(109,plain,
! [SV26: $i > $i] :
( ( ( ~ ~ ! [SY82: $i] :
~ ( sK1_R @ SV26 @ SY82 ) )
= $true )
| ( ( ~ ! [SY63: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY63 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(110,plain,
! [SV27: $i > $i] :
( ( ( ~ ~ ! [SY83: $i] :
~ ( sK1_R @ SV27 @ SY83 ) )
= $true )
| ( ( ~ ! [SY68: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY68 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(111,plain,
! [SV28: $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV28 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV29: $i > $i] :
( ( ( ~ ~ ! [SY86: $i] :
~ ( sK1_R @ SV29 @ SY86 ) )
= $true )
| ( ( ~ ! [SY81: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY81 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(113,plain,
! [SV26: $i > $i] :
( ( ( ~ ! [SY82: $i] :
~ ( sK1_R @ SV26 @ SY82 ) )
= $false )
| ( ( ~ ! [SY63: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(114,plain,
! [SV27: $i > $i] :
( ( ( ~ ! [SY83: $i] :
~ ( sK1_R @ SV27 @ SY83 ) )
= $false )
| ( ( ~ ! [SY68: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(115,plain,
! [SV28: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV28 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(116,plain,
! [SV29: $i > $i] :
( ( ( ~ ! [SY86: $i] :
~ ( sK1_R @ SV29 @ SY86 ) )
= $false )
| ( ( ~ ! [SY81: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(117,plain,
! [SV26: $i > $i] :
( ( ( ! [SY82: $i] :
~ ( sK1_R @ SV26 @ SY82 ) )
= $true )
| ( ( ~ ! [SY63: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(118,plain,
! [SV27: $i > $i] :
( ( ( ! [SY83: $i] :
~ ( sK1_R @ SV27 @ SY83 ) )
= $true )
| ( ( ~ ! [SY68: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(119,plain,
! [SV29: $i > $i] :
( ( ( ! [SY86: $i] :
~ ( sK1_R @ SV29 @ SY86 ) )
= $true )
| ( ( ~ ! [SY81: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY81 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(120,plain,
! [SV30: $i,SV26: $i > $i] :
( ( ( ~ ( sK1_R @ SV26 @ SV30 ) )
= $true )
| ( ( ~ ! [SY63: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY63 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(121,plain,
! [SV31: $i,SV27: $i > $i] :
( ( ( ~ ( sK1_R @ SV27 @ SV31 ) )
= $true )
| ( ( ~ ! [SY68: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY68 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(122,plain,
! [SV32: $i,SV29: $i > $i] :
( ( ( ~ ( sK1_R @ SV29 @ SV32 ) )
= $true )
| ( ( ~ ! [SY81: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY81 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(123,plain,
! [SV30: $i,SV26: $i > $i] :
( ( ( sK1_R @ SV26 @ SV30 )
= $false )
| ( ( ~ ! [SY63: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(124,plain,
! [SV31: $i,SV27: $i > $i] :
( ( ( sK1_R @ SV27 @ SV31 )
= $false )
| ( ( ~ ! [SY68: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(125,plain,
! [SV32: $i,SV29: $i > $i] :
( ( ( sK1_R @ SV29 @ SV32 )
= $false )
| ( ( ~ ! [SY81: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(126,plain,
! [SV30: $i,SV26: $i > $i] :
( ( ( ! [SY63: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY63 ) )
= $false )
| ( ( sK1_R @ SV26 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(127,plain,
! [SV31: $i,SV27: $i > $i] :
( ( ( ! [SY68: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY68 ) )
= $false )
| ( ( sK1_R @ SV27 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(128,plain,
! [SV32: $i,SV29: $i > $i] :
( ( ( ! [SY81: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY81 ) )
= $false )
| ( ( sK1_R @ SV29 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(129,plain,
! [SV26: $i > $i,SV30: $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK9_SY63 @ SV30 @ SV26 ) ) )
= $false )
| ( ( sK1_R @ SV26 @ SV30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[126]) ).
thf(130,plain,
! [SV27: $i > $i,SV31: $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK10_SY68 @ SV31 @ SV27 ) ) )
= $false )
| ( ( sK1_R @ SV27 @ SV31 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[127]) ).
thf(131,plain,
! [SV29: $i > $i,SV32: $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( sK11_SY81 @ SV32 @ SV29 ) ) )
= $false )
| ( ( sK1_R @ SV29 @ SV32 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[128]) ).
thf(132,plain,
! [SV26: $i > $i,SV30: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK9_SY63 @ SV30 @ SV26 ) )
= $true )
| ( ( sK1_R @ SV26 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(133,plain,
! [SV27: $i > $i,SV31: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK10_SY68 @ SV31 @ SV27 ) )
= $true )
| ( ( sK1_R @ SV27 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(134,plain,
! [SV29: $i > $i,SV32: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( sK11_SY81 @ SV32 @ SV29 ) )
= $true )
| ( ( sK1_R @ SV29 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(135,plain,
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true )
| ( ( ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 )
@ ( sK12_E @ sK3_SY2 ) )
= ( sK2_SY0 @ ( sK12_E @ sK3_SY2 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[92:[bind(SV21,$thf( sK3_SY2 ))]]) ).
thf(136,plain,
! [SV21: $i] :
( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 )
= $false ),
inference(extuni,[status(esa)],[91]) ).
thf(139,plain,
! [SV33: $i > $i,SV34: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ SV34 @ SV33 ) )
= $true )
| ( ( sK1_R @ SV33 @ SV34 )
= $false ) ),
inference(rename,[status(thm)],[54]) ).
thf(142,plain,
! [SV33: $i > $i,SV34: $i,SV21: $i] :
( ( ( ( sK1_R @ SV33 @ SV34 )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ SV34 @ SV33 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 )
= $false ) ),
inference(res,[status(thm)],[139,88]) ).
thf(143,plain,
! [SV33: $i > $i,SV34: $i,SV21: $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ SV34 @ SV33 ) )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 ) )
= $false )
| ( ( sK1_R @ SV33 @ SV34 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[139,88]) ).
thf(144,plain,
! [SV33: $i > $i,SV34: $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ SV34 @ SV33 ) )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false )
| ( ( sK1_R @ SV33 @ SV34 )
= $false ) ),
inference(res,[status(thm)],[139,19]) ).
thf(145,plain,
! [SV33: $i > $i,SV34: $i] :
( ( ( ( sK1_R @ SV33 @ SV34 )
= ( sK1_R @ sK2_SY0 @ sK3_SY2 ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ SV34 @ SV33 ) )
= $true ) ),
inference(res,[status(thm)],[139,14]) ).
thf(146,plain,
( ( ~ ~ ! [SY99: $i > $i] :
~ ~ ! [SY100: $i] :
~ ( sK1_R @ SY99 @ SY100 )
| ~ ! [SY103: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY103 ) )
= $true ),
inference(choice,[status(thm)],[139]) ).
thf(147,plain,
( ( ( ~ ~ ! [SY99: $i > $i] :
~ ~ ! [SY100: $i] :
~ ( sK1_R @ SY99 @ SY100 ) )
= $true )
| ( ( ~ ! [SY103: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(148,plain,
( ( ( ~ ! [SY99: $i > $i] :
~ ~ ! [SY100: $i] :
~ ( sK1_R @ SY99 @ SY100 ) )
= $false )
| ( ( ~ ! [SY103: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(149,plain,
( ( ( ! [SY99: $i > $i] :
~ ~ ! [SY100: $i] :
~ ( sK1_R @ SY99 @ SY100 ) )
= $true )
| ( ( ~ ! [SY103: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY103 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(150,plain,
! [SV36: $i > $i] :
( ( ( ~ ~ ! [SY104: $i] :
~ ( sK1_R @ SV36 @ SY104 ) )
= $true )
| ( ( ~ ! [SY103: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY103 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(151,plain,
! [SV36: $i > $i] :
( ( ( ~ ! [SY104: $i] :
~ ( sK1_R @ SV36 @ SY104 ) )
= $false )
| ( ( ~ ! [SY103: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(152,plain,
! [SV36: $i > $i] :
( ( ( ! [SY104: $i] :
~ ( sK1_R @ SV36 @ SY104 ) )
= $true )
| ( ( ~ ! [SY103: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY103 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(153,plain,
! [SV37: $i,SV36: $i > $i] :
( ( ( ~ ( sK1_R @ SV36 @ SV37 ) )
= $true )
| ( ( ~ ! [SY103: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY103 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(154,plain,
! [SV37: $i,SV36: $i > $i] :
( ( ( sK1_R @ SV36 @ SV37 )
= $false )
| ( ( ~ ! [SY103: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(155,plain,
! [SV37: $i,SV36: $i > $i] :
( ( ( ! [SY103: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY103 ) )
= $false )
| ( ( sK1_R @ SV36 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(156,plain,
! [SV36: $i > $i,SV37: $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK15_SY103 @ SV37 @ SV36 ) ) )
= $false )
| ( ( sK1_R @ SV36 @ SV37 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[155]) ).
thf(157,plain,
! [SV36: $i > $i,SV37: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK15_SY103 @ SV37 @ SV36 ) )
= $true )
| ( ( sK1_R @ SV36 @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(158,plain,
( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ sK3_SY2 @ sK2_SY0 ) )
= $true ),
inference(extuni,[status(esa)],[145:[bind(SV34,$thf( sK3_SY2 )),bind(SV33,$thf( sK2_SY0 ))]]) ).
thf(159,plain,
! [SV34: $i,SV33: $i > $i] :
( ( ( sK1_R @ SV33 @ SV34 )
= $false )
| ( ( ( sK4_SY9 @ SV34 @ SV33 )
= ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[144]) ).
thf(160,plain,
! [SV34: $i,SV33: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true )
| ( ( sK1_R @ SV33 @ SV34 )
= $false ) ),
inference(extuni,[status(esa)],[143:[bind(SV21,$thf( sK4_SY9 @ SV34 @ SV33 ))]]) ).
thf(161,plain,
! [SV21: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[142:[bind(SV34,$thf( eps @ ^ [SX0: $i] : ( sK1_R @ ( epsii @ ^ [SX1: $i > $i] : ~ ( ! [SX2: $i] : ~ ( sK1_R @ SX1 @ SX2 ) ) ) @ SX0 ) )),bind(SV33,$thf( epsii @ ^ [SX0: $i > $i] : ~ ( ! [SX1: $i] : ~ ( sK1_R @ SX0 @ SX1 ) ) ))]]) ).
thf(162,plain,
! [SV38: $i > $i,SV39: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK5_SY22 @ SV39 @ SV38 ) )
= $true )
| ( ( sK1_R @ SV38 @ SV39 )
= $false ) ),
inference(rename,[status(thm)],[55]) ).
thf(165,plain,
! [SV38: $i > $i,SV39: $i,SV33: $i > $i,SV34: $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK5_SY22 @ SV39 @ SV38 ) )
= ( sK1_R @ SV33 @ SV34 ) )
= $false )
| ( ( sK1_R @ SV38 @ SV39 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ SV34 @ SV33 ) )
= $true ) ),
inference(res,[status(thm)],[162,139]) ).
thf(166,plain,
! [SV38: $i > $i,SV39: $i,SV33: $i > $i,SV34: $i] :
( ( ( ( sK1_R @ SV38 @ SV39 )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ SV34 @ SV33 ) ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK5_SY22 @ SV39 @ SV38 ) )
= $true )
| ( ( sK1_R @ SV33 @ SV34 )
= $false ) ),
inference(res,[status(thm)],[162,139]) ).
thf(167,plain,
! [SV38: $i > $i,SV39: $i,SV21: $i] :
( ( ( ( sK1_R @ SV38 @ SV39 )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK5_SY22 @ SV39 @ SV38 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 )
= $false ) ),
inference(res,[status(thm)],[162,88]) ).
thf(168,plain,
! [SV38: $i > $i,SV39: $i,SV21: $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK5_SY22 @ SV39 @ SV38 ) )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 ) )
= $false )
| ( ( sK1_R @ SV38 @ SV39 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[162,88]) ).
thf(169,plain,
! [SV38: $i > $i,SV39: $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK5_SY22 @ SV39 @ SV38 ) )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false )
| ( ( sK1_R @ SV38 @ SV39 )
= $false ) ),
inference(res,[status(thm)],[162,19]) ).
thf(170,plain,
! [SV38: $i > $i,SV39: $i] :
( ( ( ( sK1_R @ SV38 @ SV39 )
= ( sK1_R @ sK2_SY0 @ sK3_SY2 ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK5_SY22 @ SV39 @ SV38 ) )
= $true ) ),
inference(res,[status(thm)],[162,14]) ).
thf(171,plain,
( ( ~ ~ ! [SY111: $i > $i] :
~ ~ ! [SY112: $i] :
~ ( sK1_R @ SY111 @ SY112 )
| ~ ! [SY115: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ),
inference(choice,[status(thm)],[162]) ).
thf(172,plain,
( ( ( ~ ~ ! [SY111: $i > $i] :
~ ~ ! [SY112: $i] :
~ ( sK1_R @ SY111 @ SY112 ) )
= $true )
| ( ( ~ ! [SY115: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(173,plain,
( ( ( ~ ! [SY111: $i > $i] :
~ ~ ! [SY112: $i] :
~ ( sK1_R @ SY111 @ SY112 ) )
= $false )
| ( ( ~ ! [SY115: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(174,plain,
( ( ( ! [SY111: $i > $i] :
~ ~ ! [SY112: $i] :
~ ( sK1_R @ SY111 @ SY112 ) )
= $true )
| ( ( ~ ! [SY115: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(175,plain,
! [SV41: $i > $i] :
( ( ( ~ ~ ! [SY116: $i] :
~ ( sK1_R @ SV41 @ SY116 ) )
= $true )
| ( ( ~ ! [SY115: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(176,plain,
! [SV41: $i > $i] :
( ( ( ~ ! [SY116: $i] :
~ ( sK1_R @ SV41 @ SY116 ) )
= $false )
| ( ( ~ ! [SY115: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(177,plain,
! [SV41: $i > $i] :
( ( ( ! [SY116: $i] :
~ ( sK1_R @ SV41 @ SY116 ) )
= $true )
| ( ( ~ ! [SY115: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(178,plain,
! [SV42: $i,SV41: $i > $i] :
( ( ( ~ ( sK1_R @ SV41 @ SV42 ) )
= $true )
| ( ( ~ ! [SY115: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(179,plain,
! [SV42: $i,SV41: $i > $i] :
( ( ( sK1_R @ SV41 @ SV42 )
= $false )
| ( ( ~ ! [SY115: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(180,plain,
! [SV42: $i,SV41: $i > $i] :
( ( ( ! [SY115: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $false )
| ( ( sK1_R @ SV41 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(181,plain,
! [SV41: $i > $i,SV42: $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK18_SY115 @ SV42 @ SV41 ) ) )
= $false )
| ( ( sK1_R @ SV41 @ SV42 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[180]) ).
thf(182,plain,
! [SV41: $i > $i,SV42: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK18_SY115 @ SV42 @ SV41 ) )
= $true )
| ( ( sK1_R @ SV41 @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(183,plain,
( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK5_SY22 @ sK3_SY2 @ sK2_SY0 ) )
= $true ),
inference(extuni,[status(esa)],[170:[bind(SV39,$thf( sK3_SY2 )),bind(SV38,$thf( sK2_SY0 ))]]) ).
thf(184,plain,
! [SV39: $i,SV38: $i > $i] :
( ( ( sK1_R @ SV38 @ SV39 )
= $false )
| ( ( ( sK5_SY22 @ SV39 @ SV38 )
= ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[169]) ).
thf(185,plain,
! [SV39: $i,SV38: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true )
| ( ( sK1_R @ SV38 @ SV39 )
= $false ) ),
inference(extuni,[status(esa)],[168:[bind(SV21,$thf( sK5_SY22 @ SV39 @ SV38 ))]]) ).
thf(186,plain,
! [SV21: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK5_SY22
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[167:[bind(SV39,$thf( eps @ ^ [SX0: $i] : ( sK1_R @ ( epsii @ ^ [SX1: $i > $i] : ~ ( ! [SX2: $i] : ~ ( sK1_R @ SX1 @ SX2 ) ) ) @ SX0 ) )),bind(SV38,$thf( epsii @ ^ [SX0: $i > $i] : ~ ( ! [SX1: $i] : ~ ( sK1_R @ SX0 @ SX1 ) ) ))]]) ).
thf(187,plain,
! [SV34: $i,SV33: $i > $i] :
( ( ( sK1_R @ SV33 @ SV34 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK5_SY22 @ ( sK4_SY9 @ SV34 @ SV33 )
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[166:[bind(SV39,$thf( sK4_SY9 @ SV34 @ SV33 )),bind(SV38,$thf( epsii @ ^ [SX0: $i > $i] : ~ ( ! [SX1: $i] : ~ ( sK1_R @ SX0 @ SX1 ) ) ))]]) ).
thf(188,plain,
! [SV38: $i > $i,SV39: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ ( sK5_SY22 @ SV39 @ SV38 )
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( sK1_R @ SV38 @ SV39 )
= $false ) ),
inference(extuni,[status(esa)],[165:[bind(SV34,$thf( sK5_SY22 @ SV39 @ SV38 )),bind(SV33,$thf( epsii @ ^ [SX0: $i > $i] : ~ ( ! [SX1: $i] : ~ ( sK1_R @ SX0 @ SX1 ) ) ))]]) ).
thf(190,plain,
! [SV44: $i > $i,SV45: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ SV45 @ SV44 ) )
= $true )
| ( ( sK1_R @ SV44 @ SV45 )
= $false ) ),
inference(rename,[status(thm)],[85]) ).
thf(193,plain,
! [SV44: $i > $i,SV45: $i,SV38: $i > $i,SV39: $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ SV45 @ SV44 ) )
= ( sK1_R @ SV38 @ SV39 ) )
= $false )
| ( ( sK1_R @ SV44 @ SV45 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK5_SY22 @ SV39 @ SV38 ) )
= $true ) ),
inference(res,[status(thm)],[190,162]) ).
thf(194,plain,
! [SV44: $i > $i,SV45: $i,SV38: $i > $i,SV39: $i] :
( ( ( ( sK1_R @ SV44 @ SV45 )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK5_SY22 @ SV39 @ SV38 ) ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ SV45 @ SV44 ) )
= $true )
| ( ( sK1_R @ SV38 @ SV39 )
= $false ) ),
inference(res,[status(thm)],[190,162]) ).
thf(195,plain,
! [SV44: $i > $i,SV45: $i,SV33: $i > $i,SV34: $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ SV45 @ SV44 ) )
= ( sK1_R @ SV33 @ SV34 ) )
= $false )
| ( ( sK1_R @ SV44 @ SV45 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ SV34 @ SV33 ) )
= $true ) ),
inference(res,[status(thm)],[190,139]) ).
thf(196,plain,
! [SV44: $i > $i,SV45: $i,SV33: $i > $i,SV34: $i] :
( ( ( ( sK1_R @ SV44 @ SV45 )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ SV34 @ SV33 ) ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ SV45 @ SV44 ) )
= $true )
| ( ( sK1_R @ SV33 @ SV34 )
= $false ) ),
inference(res,[status(thm)],[190,139]) ).
thf(197,plain,
! [SV44: $i > $i,SV45: $i,SV21: $i] :
( ( ( ( sK1_R @ SV44 @ SV45 )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ SV45 @ SV44 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 )
= $false ) ),
inference(res,[status(thm)],[190,88]) ).
thf(198,plain,
! [SV44: $i > $i,SV45: $i,SV21: $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ SV45 @ SV44 ) )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 ) )
= $false )
| ( ( sK1_R @ SV44 @ SV45 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[190,88]) ).
thf(199,plain,
! [SV44: $i > $i,SV45: $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ SV45 @ SV44 ) )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false )
| ( ( sK1_R @ SV44 @ SV45 )
= $false ) ),
inference(res,[status(thm)],[190,19]) ).
thf(200,plain,
! [SV44: $i > $i,SV45: $i] :
( ( ( ( sK1_R @ SV44 @ SV45 )
= ( sK1_R @ sK2_SY0 @ sK3_SY2 ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ SV45 @ SV44 ) )
= $true ) ),
inference(res,[status(thm)],[190,14]) ).
thf(201,plain,
( ( ~ ~ ! [SY133: $i > $i] :
~ ~ ! [SY134: $i] :
~ ( sK1_R @ SY133 @ SY134 )
| ~ ! [SY137: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY137 ) )
= $true ),
inference(choice,[status(thm)],[190]) ).
thf(202,plain,
( ( ( ~ ~ ! [SY133: $i > $i] :
~ ~ ! [SY134: $i] :
~ ( sK1_R @ SY133 @ SY134 ) )
= $true )
| ( ( ~ ! [SY137: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(203,plain,
( ( ( ~ ! [SY133: $i > $i] :
~ ~ ! [SY134: $i] :
~ ( sK1_R @ SY133 @ SY134 ) )
= $false )
| ( ( ~ ! [SY137: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(204,plain,
( ( ( ! [SY133: $i > $i] :
~ ~ ! [SY134: $i] :
~ ( sK1_R @ SY133 @ SY134 ) )
= $true )
| ( ( ~ ! [SY137: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY137 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(205,plain,
! [SV47: $i > $i] :
( ( ( ~ ~ ! [SY138: $i] :
~ ( sK1_R @ SV47 @ SY138 ) )
= $true )
| ( ( ~ ! [SY137: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY137 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(206,plain,
! [SV47: $i > $i] :
( ( ( ~ ! [SY138: $i] :
~ ( sK1_R @ SV47 @ SY138 ) )
= $false )
| ( ( ~ ! [SY137: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(207,plain,
! [SV47: $i > $i] :
( ( ( ! [SY138: $i] :
~ ( sK1_R @ SV47 @ SY138 ) )
= $true )
| ( ( ~ ! [SY137: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY137 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(208,plain,
! [SV48: $i,SV47: $i > $i] :
( ( ( ~ ( sK1_R @ SV47 @ SV48 ) )
= $true )
| ( ( ~ ! [SY137: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY137 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(209,plain,
! [SV48: $i,SV47: $i > $i] :
( ( ( sK1_R @ SV47 @ SV48 )
= $false )
| ( ( ~ ! [SY137: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(210,plain,
! [SV48: $i,SV47: $i > $i] :
( ( ( ! [SY137: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY137 ) )
= $false )
| ( ( sK1_R @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(211,plain,
! [SV47: $i > $i,SV48: $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK28_SY137 @ SV48 @ SV47 ) ) )
= $false )
| ( ( sK1_R @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[210]) ).
thf(212,plain,
! [SV47: $i > $i,SV48: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK28_SY137 @ SV48 @ SV47 ) )
= $true )
| ( ( sK1_R @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(213,plain,
( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ sK3_SY2 @ sK2_SY0 ) )
= $true ),
inference(extuni,[status(esa)],[200:[bind(SV45,$thf( sK3_SY2 )),bind(SV44,$thf( sK2_SY0 ))]]) ).
thf(214,plain,
! [SV45: $i,SV44: $i > $i] :
( ( ( sK1_R @ SV44 @ SV45 )
= $false )
| ( ( ( sK6_SY35 @ SV45 @ SV44 )
= ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[199]) ).
thf(215,plain,
! [SV45: $i,SV44: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true )
| ( ( sK1_R @ SV44 @ SV45 )
= $false ) ),
inference(extuni,[status(esa)],[198:[bind(SV21,$thf( sK6_SY35 @ SV45 @ SV44 ))]]) ).
thf(216,plain,
! [SV21: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[197:[bind(SV45,$thf( eps @ ^ [SX0: $i] : ( sK1_R @ ( epsii @ ^ [SX1: $i > $i] : ~ ( ! [SX2: $i] : ~ ( sK1_R @ SX1 @ SX2 ) ) ) @ SX0 ) )),bind(SV44,$thf( epsii @ ^ [SX0: $i > $i] : ~ ( ! [SX1: $i] : ~ ( sK1_R @ SX0 @ SX1 ) ) ))]]) ).
thf(217,plain,
! [SV34: $i,SV33: $i > $i] :
( ( ( sK1_R @ SV33 @ SV34 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ ( sK4_SY9 @ SV34 @ SV33 )
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[196:[bind(SV45,$thf( sK4_SY9 @ SV34 @ SV33 )),bind(SV44,$thf( epsii @ ^ [SX0: $i > $i] : ~ ( ! [SX1: $i] : ~ ( sK1_R @ SX0 @ SX1 ) ) ))]]) ).
thf(218,plain,
! [SV44: $i > $i,SV45: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ ( sK6_SY35 @ SV45 @ SV44 )
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( sK1_R @ SV44 @ SV45 )
= $false ) ),
inference(extuni,[status(esa)],[195:[bind(SV34,$thf( sK6_SY35 @ SV45 @ SV44 )),bind(SV33,$thf( epsii @ ^ [SX0: $i > $i] : ~ ( ! [SX1: $i] : ~ ( sK1_R @ SX0 @ SX1 ) ) ))]]) ).
thf(219,plain,
! [SV39: $i,SV38: $i > $i] :
( ( ( sK1_R @ SV38 @ SV39 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ ( sK5_SY22 @ SV39 @ SV38 )
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[194:[bind(SV45,$thf( sK5_SY22 @ SV39 @ SV38 )),bind(SV44,$thf( epsii @ ^ [SX0: $i > $i] : ~ ( ! [SX1: $i] : ~ ( sK1_R @ SX0 @ SX1 ) ) ))]]) ).
thf(220,plain,
! [SV44: $i > $i,SV45: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK5_SY22 @ ( sK6_SY35 @ SV45 @ SV44 )
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( sK1_R @ SV44 @ SV45 )
= $false ) ),
inference(extuni,[status(esa)],[193:[bind(SV39,$thf( sK6_SY35 @ SV45 @ SV44 )),bind(SV38,$thf( epsii @ ^ [SX0: $i > $i] : ~ ( ! [SX1: $i] : ~ ( sK1_R @ SX0 @ SX1 ) ) ))]]) ).
thf(221,plain,
! [SV49: $i > $i,SV50: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK7_SY48 @ SV50 @ SV49 ) )
= $true )
| ( ( sK1_R @ SV49 @ SV50 )
= $false ) ),
inference(rename,[status(thm)],[86]) ).
thf(224,plain,
! [SV49: $i > $i,SV50: $i,SV44: $i > $i,SV45: $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK7_SY48 @ SV50 @ SV49 ) )
= ( sK1_R @ SV44 @ SV45 ) )
= $false )
| ( ( sK1_R @ SV49 @ SV50 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ SV45 @ SV44 ) )
= $true ) ),
inference(res,[status(thm)],[221,190]) ).
thf(225,plain,
! [SV49: $i > $i,SV50: $i,SV44: $i > $i,SV45: $i] :
( ( ( ( sK1_R @ SV49 @ SV50 )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ SV45 @ SV44 ) ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK7_SY48 @ SV50 @ SV49 ) )
= $true )
| ( ( sK1_R @ SV44 @ SV45 )
= $false ) ),
inference(res,[status(thm)],[221,190]) ).
thf(226,plain,
! [SV49: $i > $i,SV50: $i,SV38: $i > $i,SV39: $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK7_SY48 @ SV50 @ SV49 ) )
= ( sK1_R @ SV38 @ SV39 ) )
= $false )
| ( ( sK1_R @ SV49 @ SV50 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK5_SY22 @ SV39 @ SV38 ) )
= $true ) ),
inference(res,[status(thm)],[221,162]) ).
thf(227,plain,
! [SV49: $i > $i,SV50: $i,SV38: $i > $i,SV39: $i] :
( ( ( ( sK1_R @ SV49 @ SV50 )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK5_SY22 @ SV39 @ SV38 ) ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK7_SY48 @ SV50 @ SV49 ) )
= $true )
| ( ( sK1_R @ SV38 @ SV39 )
= $false ) ),
inference(res,[status(thm)],[221,162]) ).
thf(228,plain,
! [SV49: $i > $i,SV50: $i,SV33: $i > $i,SV34: $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK7_SY48 @ SV50 @ SV49 ) )
= ( sK1_R @ SV33 @ SV34 ) )
= $false )
| ( ( sK1_R @ SV49 @ SV50 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ SV34 @ SV33 ) )
= $true ) ),
inference(res,[status(thm)],[221,139]) ).
thf(229,plain,
! [SV49: $i > $i,SV50: $i,SV33: $i > $i,SV34: $i] :
( ( ( ( sK1_R @ SV49 @ SV50 )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ SV34 @ SV33 ) ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK7_SY48 @ SV50 @ SV49 ) )
= $true )
| ( ( sK1_R @ SV33 @ SV34 )
= $false ) ),
inference(res,[status(thm)],[221,139]) ).
thf(230,plain,
! [SV49: $i > $i,SV50: $i,SV21: $i] :
( ( ( ( sK1_R @ SV49 @ SV50 )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK7_SY48 @ SV50 @ SV49 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 )
= $false ) ),
inference(res,[status(thm)],[221,88]) ).
thf(231,plain,
! [SV49: $i > $i,SV50: $i,SV21: $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK7_SY48 @ SV50 @ SV49 ) )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 ) )
= $false )
| ( ( sK1_R @ SV49 @ SV50 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[221,88]) ).
thf(232,plain,
! [SV49: $i > $i,SV50: $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK7_SY48 @ SV50 @ SV49 ) )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false )
| ( ( sK1_R @ SV49 @ SV50 )
= $false ) ),
inference(res,[status(thm)],[221,19]) ).
thf(233,plain,
! [SV49: $i > $i,SV50: $i] :
( ( ( ( sK1_R @ SV49 @ SV50 )
= ( sK1_R @ sK2_SY0 @ sK3_SY2 ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK7_SY48 @ SV50 @ SV49 ) )
= $true ) ),
inference(res,[status(thm)],[221,14]) ).
thf(234,plain,
( ( ~ ~ ! [SY145: $i > $i] :
~ ~ ! [SY146: $i] :
~ ( sK1_R @ SY145 @ SY146 )
| ~ ! [SY149: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY149 ) )
= $true ),
inference(choice,[status(thm)],[221]) ).
thf(235,plain,
( ( ( ~ ~ ! [SY145: $i > $i] :
~ ~ ! [SY146: $i] :
~ ( sK1_R @ SY145 @ SY146 ) )
= $true )
| ( ( ~ ! [SY149: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(236,plain,
( ( ( ~ ! [SY145: $i > $i] :
~ ~ ! [SY146: $i] :
~ ( sK1_R @ SY145 @ SY146 ) )
= $false )
| ( ( ~ ! [SY149: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(237,plain,
( ( ( ! [SY145: $i > $i] :
~ ~ ! [SY146: $i] :
~ ( sK1_R @ SY145 @ SY146 ) )
= $true )
| ( ( ~ ! [SY149: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY149 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(238,plain,
! [SV52: $i > $i] :
( ( ( ~ ~ ! [SY150: $i] :
~ ( sK1_R @ SV52 @ SY150 ) )
= $true )
| ( ( ~ ! [SY149: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY149 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(239,plain,
! [SV52: $i > $i] :
( ( ( ~ ! [SY150: $i] :
~ ( sK1_R @ SV52 @ SY150 ) )
= $false )
| ( ( ~ ! [SY149: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(240,plain,
! [SV52: $i > $i] :
( ( ( ! [SY150: $i] :
~ ( sK1_R @ SV52 @ SY150 ) )
= $true )
| ( ( ~ ! [SY149: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY149 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(241,plain,
! [SV53: $i,SV52: $i > $i] :
( ( ( ~ ( sK1_R @ SV52 @ SV53 ) )
= $true )
| ( ( ~ ! [SY149: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY149 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(242,plain,
! [SV53: $i,SV52: $i > $i] :
( ( ( sK1_R @ SV52 @ SV53 )
= $false )
| ( ( ~ ! [SY149: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(243,plain,
! [SV53: $i,SV52: $i > $i] :
( ( ( ! [SY149: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY149 ) )
= $false )
| ( ( sK1_R @ SV52 @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(244,plain,
! [SV52: $i > $i,SV53: $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK31_SY149 @ SV53 @ SV52 ) ) )
= $false )
| ( ( sK1_R @ SV52 @ SV53 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[243]) ).
thf(245,plain,
! [SV52: $i > $i,SV53: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK31_SY149 @ SV53 @ SV52 ) )
= $true )
| ( ( sK1_R @ SV52 @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(246,plain,
( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK7_SY48 @ sK3_SY2 @ sK2_SY0 ) )
= $true ),
inference(extuni,[status(esa)],[233:[bind(SV50,$thf( sK3_SY2 )),bind(SV49,$thf( sK2_SY0 ))]]) ).
thf(247,plain,
! [SV50: $i,SV49: $i > $i] :
( ( ( sK1_R @ SV49 @ SV50 )
= $false )
| ( ( ( sK7_SY48 @ SV50 @ SV49 )
= ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[232]) ).
thf(248,plain,
! [SV50: $i,SV49: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true )
| ( ( sK1_R @ SV49 @ SV50 )
= $false ) ),
inference(extuni,[status(esa)],[231:[bind(SV21,$thf( sK7_SY48 @ SV50 @ SV49 ))]]) ).
thf(249,plain,
! [SV21: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK7_SY48
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[230:[bind(SV50,$thf( eps @ ^ [SX0: $i] : ( sK1_R @ ( epsii @ ^ [SX1: $i > $i] : ~ ( ! [SX2: $i] : ~ ( sK1_R @ SX1 @ SX2 ) ) ) @ SX0 ) )),bind(SV49,$thf( epsii @ ^ [SX0: $i > $i] : ~ ( ! [SX1: $i] : ~ ( sK1_R @ SX0 @ SX1 ) ) ))]]) ).
thf(250,plain,
! [SV34: $i,SV33: $i > $i] :
( ( ( sK1_R @ SV33 @ SV34 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK7_SY48 @ ( sK4_SY9 @ SV34 @ SV33 )
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[229:[bind(SV50,$thf( sK4_SY9 @ SV34 @ SV33 )),bind(SV49,$thf( epsii @ ^ [SX0: $i > $i] : ~ ( ! [SX1: $i] : ~ ( sK1_R @ SX0 @ SX1 ) ) ))]]) ).
thf(251,plain,
! [SV49: $i > $i,SV50: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY9 @ ( sK7_SY48 @ SV50 @ SV49 )
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( sK1_R @ SV49 @ SV50 )
= $false ) ),
inference(extuni,[status(esa)],[228:[bind(SV34,$thf( sK7_SY48 @ SV50 @ SV49 )),bind(SV33,$thf( epsii @ ^ [SX0: $i > $i] : ~ ( ! [SX1: $i] : ~ ( sK1_R @ SX0 @ SX1 ) ) ))]]) ).
thf(252,plain,
! [SV39: $i,SV38: $i > $i] :
( ( ( sK1_R @ SV38 @ SV39 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK7_SY48 @ ( sK5_SY22 @ SV39 @ SV38 )
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[227:[bind(SV50,$thf( sK5_SY22 @ SV39 @ SV38 )),bind(SV49,$thf( epsii @ ^ [SX0: $i > $i] : ~ ( ! [SX1: $i] : ~ ( sK1_R @ SX0 @ SX1 ) ) ))]]) ).
thf(253,plain,
! [SV49: $i > $i,SV50: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK5_SY22 @ ( sK7_SY48 @ SV50 @ SV49 )
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( sK1_R @ SV49 @ SV50 )
= $false ) ),
inference(extuni,[status(esa)],[226:[bind(SV39,$thf( sK7_SY48 @ SV50 @ SV49 )),bind(SV38,$thf( epsii @ ^ [SX0: $i > $i] : ~ ( ! [SX1: $i] : ~ ( sK1_R @ SX0 @ SX1 ) ) ))]]) ).
thf(254,plain,
! [SV45: $i,SV44: $i > $i] :
( ( ( sK1_R @ SV44 @ SV45 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK7_SY48 @ ( sK6_SY35 @ SV45 @ SV44 )
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[225:[bind(SV50,$thf( sK6_SY35 @ SV45 @ SV44 )),bind(SV49,$thf( epsii @ ^ [SX0: $i > $i] : ~ ( ! [SX1: $i] : ~ ( sK1_R @ SX0 @ SX1 ) ) ))]]) ).
thf(255,plain,
! [SV49: $i > $i,SV50: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY35 @ ( sK7_SY48 @ SV50 @ SV49 )
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( sK1_R @ SV49 @ SV50 )
= $false ) ),
inference(extuni,[status(esa)],[224:[bind(SV45,$thf( sK7_SY48 @ SV50 @ SV49 )),bind(SV44,$thf( epsii @ ^ [SX0: $i > $i] : ~ ( ! [SX1: $i] : ~ ( sK1_R @ SX0 @ SX1 ) ) ))]]) ).
thf(268,plain,
( ( ( ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 )
@ sK8_E )
= ( sK2_SY0 @ sK8_E ) )
= $false )
| ( ( ( ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) )
= sK3_SY2 )
= ( ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 )
@ sK8_E )
= ( sK2_SY0 @ sK8_E ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[87]) ).
thf(269,plain,
( ( ~ ~ ! [SY153: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY153 )
| ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ),
inference(choice,[status(thm)],[87]) ).
thf(270,plain,
( ( ~ ~ ! [SY161: $i > $i] :
~ ~ ! [SY162: $i] :
~ ( sK1_R @ SY161 @ SY162 )
| ~ ! [SY165: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY165 ) )
= $true ),
inference(choice,[status(thm)],[87]) ).
thf(271,plain,
( ( ~ ~ ! [SY166: $i > $i] :
~ ~ ! [SY167: $i] :
~ ( sK1_R @ SY166 @ SY167 )
| ~ ! [SY170: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY170 ) )
= $true ),
inference(choice,[status(thm)],[87]) ).
thf(272,plain,
( ( ( ~ ~ ! [SY153: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY153 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(273,plain,
( ( ( ~ ~ ! [SY161: $i > $i] :
~ ~ ! [SY162: $i] :
~ ( sK1_R @ SY161 @ SY162 ) )
= $true )
| ( ( ~ ! [SY165: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(274,plain,
( ( ( ~ ~ ! [SY166: $i > $i] :
~ ~ ! [SY167: $i] :
~ ( sK1_R @ SY166 @ SY167 ) )
= $true )
| ( ( ~ ! [SY170: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(275,plain,
( ( ( ~ ! [SY153: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY153 ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(276,plain,
( ( ( ~ ! [SY161: $i > $i] :
~ ~ ! [SY162: $i] :
~ ( sK1_R @ SY161 @ SY162 ) )
= $false )
| ( ( ~ ! [SY165: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(277,plain,
( ( ( ~ ! [SY166: $i > $i] :
~ ~ ! [SY167: $i] :
~ ( sK1_R @ SY166 @ SY167 ) )
= $false )
| ( ( ~ ! [SY170: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(278,plain,
( ( ( ! [SY153: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY153 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(279,plain,
( ( ( ! [SY161: $i > $i] :
~ ~ ! [SY162: $i] :
~ ( sK1_R @ SY161 @ SY162 ) )
= $true )
| ( ( ~ ! [SY165: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(280,plain,
( ( ( ! [SY166: $i > $i] :
~ ~ ! [SY167: $i] :
~ ( sK1_R @ SY166 @ SY167 ) )
= $true )
| ( ( ~ ! [SY170: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(281,plain,
! [SV57: $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV57 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(282,plain,
! [SV58: $i > $i] :
( ( ( ~ ~ ! [SY173: $i] :
~ ( sK1_R @ SV58 @ SY173 ) )
= $true )
| ( ( ~ ! [SY165: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY165 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(283,plain,
! [SV59: $i > $i] :
( ( ( ~ ~ ! [SY174: $i] :
~ ( sK1_R @ SV59 @ SY174 ) )
= $true )
| ( ( ~ ! [SY170: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY170 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(284,plain,
! [SV57: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV57 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(285,plain,
! [SV58: $i > $i] :
( ( ( ~ ! [SY173: $i] :
~ ( sK1_R @ SV58 @ SY173 ) )
= $false )
| ( ( ~ ! [SY165: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(286,plain,
! [SV59: $i > $i] :
( ( ( ~ ! [SY174: $i] :
~ ( sK1_R @ SV59 @ SY174 ) )
= $false )
| ( ( ~ ! [SY170: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(287,plain,
! [SV58: $i > $i] :
( ( ( ! [SY173: $i] :
~ ( sK1_R @ SV58 @ SY173 ) )
= $true )
| ( ( ~ ! [SY165: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(288,plain,
! [SV59: $i > $i] :
( ( ( ! [SY174: $i] :
~ ( sK1_R @ SV59 @ SY174 ) )
= $true )
| ( ( ~ ! [SY170: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(289,plain,
! [SV60: $i,SV58: $i > $i] :
( ( ( ~ ( sK1_R @ SV58 @ SV60 ) )
= $true )
| ( ( ~ ! [SY165: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY165 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(290,plain,
! [SV61: $i,SV59: $i > $i] :
( ( ( ~ ( sK1_R @ SV59 @ SV61 ) )
= $true )
| ( ( ~ ! [SY170: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY170 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(291,plain,
! [SV60: $i,SV58: $i > $i] :
( ( ( sK1_R @ SV58 @ SV60 )
= $false )
| ( ( ~ ! [SY165: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(292,plain,
! [SV61: $i,SV59: $i > $i] :
( ( ( sK1_R @ SV59 @ SV61 )
= $false )
| ( ( ~ ! [SY170: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(293,plain,
! [SV60: $i,SV58: $i > $i] :
( ( ( ! [SY165: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY165 ) )
= $false )
| ( ( sK1_R @ SV58 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(294,plain,
! [SV61: $i,SV59: $i > $i] :
( ( ( ! [SY170: $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY170 ) )
= $false )
| ( ( sK1_R @ SV59 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(295,plain,
! [SV58: $i > $i,SV60: $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( sK32_SY165 @ SV60 @ SV58 ) ) )
= $false )
| ( ( sK1_R @ SV58 @ SV60 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[293]) ).
thf(296,plain,
! [SV59: $i > $i,SV61: $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK33_SY170 @ SV61 @ SV59 ) ) )
= $false )
| ( ( sK1_R @ SV59 @ SV61 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[294]) ).
thf(297,plain,
! [SV58: $i > $i,SV60: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( sK32_SY165 @ SV60 @ SV58 ) )
= $true )
| ( ( sK1_R @ SV58 @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(298,plain,
! [SV59: $i > $i,SV61: $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK33_SY170 @ SV61 @ SV59 ) )
= $true )
| ( ( sK1_R @ SV59 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(299,plain,
( ( ( ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) )
= ( sK2_SY0 @ sK8_E ) )
= $false )
| ( ( sK3_SY2
= ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 )
@ sK8_E ) )
= $false )
| ( ( ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 )
@ sK8_E )
= ( sK2_SY0 @ sK8_E ) )
= $false ) ),
inference(extuni,[status(esa)],[268]) ).
thf(300,plain,
( ( ( sK3_SY2
= ( sK2_SY0 @ sK8_E ) )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) )
= ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 )
@ sK8_E ) )
= $false )
| ( ( ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i] :
~ ( sK1_R @ SX0 @ SX1 )
@ sK8_E )
= ( sK2_SY0 @ sK8_E ) )
= $false ) ),
inference(extuni,[status(esa)],[268]) ).
thf(301,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,300,299,298,297,284,255,254,253,252,251,250,249,248,247,246,245,221,220,219,218,217,216,215,214,213,212,190,188,187,186,185,184,183,182,162,161,160,159,158,157,139,136,135,134,133,132,115,88,87,19]) ).
thf(302,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYO536^1 : TPTP v8.1.0. Released v5.2.0.
% 0.13/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Fri Jul 8 20:31:44 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.36
% 0.21/0.36 No.of.Axioms: 2
% 0.21/0.36
% 0.21/0.36 Length.of.Defs: 321
% 0.21/0.36
% 0.21/0.36 Contains.Choice.Funs: true
% 0.21/0.36 (rf:0,axioms:2,ps:3,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:4,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.21/0.40
% 0.21/0.40 *** Modified list of choice operators: eps ***
% 0.21/0.40
% 0.21/0.40 *** Modified list of choice operators: epsii, eps ***
% 0.21/0.40 ............................................................................
% 1.14/1.34
% 1.14/1.34 ********************************
% 1.14/1.34 * All subproblems solved! *
% 1.14/1.34 ********************************
% 1.14/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,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:301,loop_count:10,foatp_calls:3,translation:fof_full)
% 1.20/1.37
% 1.20/1.37 %**** Beginning of derivation protocol ****
% 1.20/1.37 % SZS output start CNFRefutation
% See solution above
% 1.20/1.37
% 1.20/1.37 %**** End of derivation protocol ****
% 1.20/1.37 %**** no. of clauses in derivation: 257 ****
% 1.20/1.37 %**** clause counter: 301 ****
% 1.20/1.37
% 1.20/1.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,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:301,loop_count:10,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------