%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO535^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:08:40 AM UTC 2026
% Result : Theorem 0.11s 0.29s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 3
% Syntax : Number of formulae : 139 ( 30 unt; 0 typ; 2 def)
% Number of atoms : 962 ( 253 equ; 0 cnn)
% Maximal formula atoms : 2 ( 6 avg)
% Number of connectives : 2035 ( 737 ~; 119 |; 0 &;1176 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 421 ( 421 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 10 con; 0-3 aty)
% Number of variables : 690 ( 207 ^; 474 !; 9 ?; 690 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_eps,type,
eps: ( $i > $o ) > $i ).
thf(tp_epsa,type,
epsa: ( $i > ( $i > $i ) > $o ) > $i ).
thf(tp_epsb,type,
epsb: ( $i > ( $i > $i ) > $o ) > $i > $i ).
thf(tp_epsii,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(tp_sK10_E,type,
sK10_E: $i ).
thf(tp_sK11_SY69,type,
sK11_SY69: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK12_SY74,type,
sK12_SY74: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK13_SY87,type,
sK13_SY87: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK14_E,type,
sK14_E: $i ).
thf(tp_sK15_E,type,
sK15_E: $i ).
thf(tp_sK16_E,type,
sK16_E: $i ).
thf(tp_sK17_E,type,
sK17_E: $i > $i ).
thf(tp_sK18_E,type,
sK18_E: $i ).
thf(tp_sK19_E,type,
sK19_E: $i > $i ).
thf(tp_sK1_R,type,
sK1_R: $i > ( $i > $i ) > $o ).
thf(tp_sK20_SY112,type,
sK20_SY112: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK2_SY0,type,
sK2_SY0: $i ).
thf(tp_sK3_SY2,type,
sK3_SY2: $i > $i ).
thf(tp_sK4_SY9,type,
sK4_SY9: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK5_SY22,type,
sK5_SY22: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK6_SY35,type,
sK6_SY35: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK7_SY48,type,
sK7_SY48: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK8_E,type,
sK8_E: $i ).
thf(tp_sK9_E,type,
sK9_E: $i ).
thf(epsa,definition,
( epsa
= ( ^ [R: $i > ( $i > $i ) > $o] :
( eps
@ ^ [X: $i] :
? [Y: $i > $i] : ( R @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',epsad) ).
thf(epsb,definition,
( epsb
= ( ^ [R: $i > ( $i > $i ) > $o] :
( epsii
@ ^ [Y: $i > $i] : ( R @ ( epsa @ R ) @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',epsbd) ).
thf(3,conjecture,
! [R: $i > ( $i > $i ) > $o] :
( ? [X: $i,Y: $i > $i] : ( R @ X @ Y )
=> ( R @ ( epsa @ R ) @ ( epsb @ R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(4,negated_conjecture,
( ( ! [R: $i > ( $i > $i ) > $o] :
( ? [X: $i,Y: $i > $i] : ( R @ X @ Y )
=> ( R @ ( epsa @ R ) @ ( epsb @ R ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ? [SY0: $i,SY1: $i > $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,SY1: $i > $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
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,epsa,epsb]) ).
thf(19,plain,
( ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(26,plain,
( ( ~ ~ ! [SY5: $i] :
~ ~ ! [SY6: $i > $i] :
~ ( sK1_R @ SY5 @ SY6 )
| ~ ! [SY9: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ),
inference(choice,[status(thm)],[19]) ).
thf(27,plain,
( ( ~ ~ ! [SY10: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY10 )
| ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ),
inference(choice,[status(thm)],[19]) ).
thf(28,plain,
( ( ~ ~ ! [SY18: $i] :
~ ~ ! [SY19: $i > $i] :
~ ( sK1_R @ SY18 @ SY19 )
| ~ ! [SY22: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ),
inference(choice,[status(thm)],[19]) ).
thf(29,plain,
( ( ( ~ ~ ! [SY5: $i] :
~ ~ ! [SY6: $i > $i] :
~ ( sK1_R @ SY5 @ SY6 ) )
= $true )
| ( ( ~ ! [SY9: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ( ~ ~ ! [SY10: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY10 ) )
= $true )
| ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ( ~ ~ ! [SY18: $i] :
~ ~ ! [SY19: $i > $i] :
~ ( sK1_R @ SY18 @ SY19 ) )
= $true )
| ( ( ~ ! [SY22: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
( ( ( ~ ! [SY5: $i] :
~ ~ ! [SY6: $i > $i] :
~ ( sK1_R @ SY5 @ SY6 ) )
= $false )
| ( ( ~ ! [SY9: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( ( ~ ! [SY10: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY10 ) )
= $false )
| ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
( ( ( ~ ! [SY18: $i] :
~ ~ ! [SY19: $i > $i] :
~ ( sK1_R @ SY18 @ SY19 ) )
= $false )
| ( ( ~ ! [SY22: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
( ( ( ! [SY5: $i] :
~ ~ ! [SY6: $i > $i] :
~ ( sK1_R @ SY5 @ SY6 ) )
= $true )
| ( ( ~ ! [SY9: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(36,plain,
( ( ( ! [SY10: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY10 ) )
= $true )
| ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(37,plain,
( ( ( ! [SY18: $i] :
~ ~ ! [SY19: $i > $i] :
~ ( sK1_R @ SY18 @ SY19 ) )
= $true )
| ( ( ~ ! [SY22: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV8: $i] :
( ( ( ~ ~ ! [SY23: $i > $i] :
~ ( sK1_R @ SV8 @ SY23 ) )
= $true )
| ( ( ~ ! [SY9: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV9: $i > $i] :
( ( ( ~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV9 ) )
= $true )
| ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV10: $i] :
( ( ( ~ ~ ! [SY26: $i > $i] :
~ ( sK1_R @ SV10 @ SY26 ) )
= $true )
| ( ( ~ ! [SY22: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV8: $i] :
( ( ( ~ ! [SY23: $i > $i] :
~ ( sK1_R @ SV8 @ SY23 ) )
= $false )
| ( ( ~ ! [SY9: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV9: $i > $i] :
( ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV9 )
= $false )
| ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV10: $i] :
( ( ( ~ ! [SY26: $i > $i] :
~ ( sK1_R @ SV10 @ SY26 ) )
= $false )
| ( ( ~ ! [SY22: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV8: $i] :
( ( ( ! [SY23: $i > $i] :
~ ( sK1_R @ SV8 @ SY23 ) )
= $true )
| ( ( ~ ! [SY9: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV10: $i] :
( ( ( ! [SY26: $i > $i] :
~ ( sK1_R @ SV10 @ SY26 ) )
= $true )
| ( ( ~ ! [SY22: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(46,plain,
! [SV11: $i > $i,SV8: $i] :
( ( ( ~ ( sK1_R @ SV8 @ SV11 ) )
= $true )
| ( ( ~ ! [SY9: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV12: $i > $i,SV10: $i] :
( ( ( ~ ( sK1_R @ SV10 @ SV12 ) )
= $true )
| ( ( ~ ! [SY22: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV11: $i > $i,SV8: $i] :
( ( ( sK1_R @ SV8 @ SV11 )
= $false )
| ( ( ~ ! [SY9: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(49,plain,
! [SV12: $i > $i,SV10: $i] :
( ( ( sK1_R @ SV10 @ SV12 )
= $false )
| ( ( ~ ! [SY22: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV11: $i > $i,SV8: $i] :
( ( ( ! [SY9: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY9 ) )
= $false )
| ( ( sK1_R @ SV8 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV12: $i > $i,SV10: $i] :
( ( ( ! [SY22: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY22 ) )
= $false )
| ( ( sK1_R @ SV10 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV8: $i,SV11: $i > $i] :
( ( ( ~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $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,SV12: $i > $i] :
( ( ( ~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $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,SV11: $i > $i] :
( ( ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $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,SV12: $i > $i] :
( ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $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
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= ( sK1_R @ sK2_SY0 @ sK3_SY2 ) )
= $false ),
inference(res,[status(thm)],[19,14]) ).
thf(57,plain,
( ( ~ ~ ! [SY31: $i] :
~ ~ ! [SY32: $i > $i] :
~ ( sK1_R @ SY31 @ SY32 )
| ~ ! [SY35: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ),
inference(choice,[status(thm)],[19]) ).
thf(58,plain,
( ( ~ ~ ! [SY36: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY36 )
| ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ),
inference(choice,[status(thm)],[19]) ).
thf(59,plain,
( ( ~ ~ ! [SY44: $i] :
~ ~ ! [SY45: $i > $i] :
~ ( sK1_R @ SY44 @ SY45 )
| ~ ! [SY48: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ),
inference(choice,[status(thm)],[19]) ).
thf(60,plain,
( ( ( ~ ~ ! [SY31: $i] :
~ ~ ! [SY32: $i > $i] :
~ ( sK1_R @ SY31 @ SY32 ) )
= $true )
| ( ( ~ ! [SY35: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(61,plain,
( ( ( ~ ~ ! [SY36: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY36 ) )
= $true )
| ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(62,plain,
( ( ( ~ ~ ! [SY44: $i] :
~ ~ ! [SY45: $i > $i] :
~ ( sK1_R @ SY44 @ SY45 ) )
= $true )
| ( ( ~ ! [SY48: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(63,plain,
( ( ( ~ ! [SY31: $i] :
~ ~ ! [SY32: $i > $i] :
~ ( sK1_R @ SY31 @ SY32 ) )
= $false )
| ( ( ~ ! [SY35: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(64,plain,
( ( ( ~ ! [SY36: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY36 ) )
= $false )
| ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(65,plain,
( ( ( ~ ! [SY44: $i] :
~ ~ ! [SY45: $i > $i] :
~ ( sK1_R @ SY44 @ SY45 ) )
= $false )
| ( ( ~ ! [SY48: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(66,plain,
( ( ( ! [SY31: $i] :
~ ~ ! [SY32: $i > $i] :
~ ( sK1_R @ SY31 @ SY32 ) )
= $true )
| ( ( ~ ! [SY35: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(67,plain,
( ( ( ! [SY36: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY36 ) )
= $true )
| ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(68,plain,
( ( ( ! [SY44: $i] :
~ ~ ! [SY45: $i > $i] :
~ ( sK1_R @ SY44 @ SY45 ) )
= $true )
| ( ( ~ ! [SY48: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(69,plain,
! [SV16: $i] :
( ( ( ~ ~ ! [SY49: $i > $i] :
~ ( sK1_R @ SV16 @ SY49 ) )
= $true )
| ( ( ~ ! [SY35: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(70,plain,
! [SV17: $i > $i] :
( ( ( ~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV17 ) )
= $true )
| ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(71,plain,
! [SV18: $i] :
( ( ( ~ ~ ! [SY52: $i > $i] :
~ ( sK1_R @ SV18 @ SY52 ) )
= $true )
| ( ( ~ ! [SY48: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV16: $i] :
( ( ( ~ ! [SY49: $i > $i] :
~ ( sK1_R @ SV16 @ SY49 ) )
= $false )
| ( ( ~ ! [SY35: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(73,plain,
! [SV17: $i > $i] :
( ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV17 )
= $false )
| ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(74,plain,
! [SV18: $i] :
( ( ( ~ ! [SY52: $i > $i] :
~ ( sK1_R @ SV18 @ SY52 ) )
= $false )
| ( ( ~ ! [SY48: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV16: $i] :
( ( ( ! [SY49: $i > $i] :
~ ( sK1_R @ SV16 @ SY49 ) )
= $true )
| ( ( ~ ! [SY35: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(76,plain,
! [SV18: $i] :
( ( ( ! [SY52: $i > $i] :
~ ( sK1_R @ SV18 @ SY52 ) )
= $true )
| ( ( ~ ! [SY48: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(77,plain,
! [SV19: $i > $i,SV16: $i] :
( ( ( ~ ( sK1_R @ SV16 @ SV19 ) )
= $true )
| ( ( ~ ! [SY35: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(78,plain,
! [SV20: $i > $i,SV18: $i] :
( ( ( ~ ( sK1_R @ SV18 @ SV20 ) )
= $true )
| ( ( ~ ! [SY48: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(79,plain,
! [SV19: $i > $i,SV16: $i] :
( ( ( sK1_R @ SV16 @ SV19 )
= $false )
| ( ( ~ ! [SY35: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(80,plain,
! [SV20: $i > $i,SV18: $i] :
( ( ( sK1_R @ SV18 @ SV20 )
= $false )
| ( ( ~ ! [SY48: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(81,plain,
! [SV19: $i > $i,SV16: $i] :
( ( ( ! [SY35: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY35 ) )
= $false )
| ( ( sK1_R @ SV16 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(82,plain,
! [SV20: $i > $i,SV18: $i] :
( ( ( ! [SY48: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY48 ) )
= $false )
| ( ( sK1_R @ SV18 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(83,plain,
! [SV16: $i,SV19: $i > $i] :
( ( ( ~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $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,SV20: $i > $i] :
( ( ( ~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $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,SV19: $i > $i] :
( ( ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $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,SV20: $i > $i] :
( ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $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,
( ( ( ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 )
@ sK8_E )
= ( sK3_SY2 @ sK8_E ) )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
= sK2_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[56]) ).
thf(88,plain,
! [SV21: $i > $i] :
( ( ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 )
= $false )
| ( ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(rename,[status(thm)],[42]) ).
thf(91,plain,
! [SV21: $i > $i] :
( ( ( ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false )
| ( ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 )
= $false ) ),
inference(res,[status(thm)],[88,19]) ).
thf(92,plain,
! [SV21: $i > $i] :
( ( ( ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 )
= ( sK1_R @ sK2_SY0 @ sK3_SY2 ) )
= $false )
| ( ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[88,14]) ).
thf(93,plain,
( ( ~ ~ ! [SY65: $i] :
~ ~ ! [SY66: $i > $i] :
~ ( sK1_R @ SY65 @ SY66 )
| ~ ! [SY69: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY69 ) )
= $true ),
inference(choice,[status(thm)],[88]) ).
thf(94,plain,
( ( ~ ~ ! [SY70: $i] :
~ ~ ! [SY71: $i > $i] :
~ ( sK1_R @ SY70 @ SY71 )
| ~ ! [SY74: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY74 ) )
= $true ),
inference(choice,[status(thm)],[88]) ).
thf(95,plain,
( ( ~ ~ ! [SY75: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY75 )
| ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ),
inference(choice,[status(thm)],[88]) ).
thf(96,plain,
( ( ~ ~ ! [SY83: $i] :
~ ~ ! [SY84: $i > $i] :
~ ( sK1_R @ SY83 @ SY84 )
| ~ ! [SY87: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY87 ) )
= $true ),
inference(choice,[status(thm)],[88]) ).
thf(97,plain,
( ( ( ~ ~ ! [SY65: $i] :
~ ~ ! [SY66: $i > $i] :
~ ( sK1_R @ SY65 @ SY66 ) )
= $true )
| ( ( ~ ! [SY69: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(98,plain,
( ( ( ~ ~ ! [SY70: $i] :
~ ~ ! [SY71: $i > $i] :
~ ( sK1_R @ SY70 @ SY71 ) )
= $true )
| ( ( ~ ! [SY74: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(99,plain,
( ( ( ~ ~ ! [SY75: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY75 ) )
= $true )
| ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(100,plain,
( ( ( ~ ~ ! [SY83: $i] :
~ ~ ! [SY84: $i > $i] :
~ ( sK1_R @ SY83 @ SY84 ) )
= $true )
| ( ( ~ ! [SY87: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(101,plain,
( ( ( ~ ! [SY65: $i] :
~ ~ ! [SY66: $i > $i] :
~ ( sK1_R @ SY65 @ SY66 ) )
= $false )
| ( ( ~ ! [SY69: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(102,plain,
( ( ( ~ ! [SY70: $i] :
~ ~ ! [SY71: $i > $i] :
~ ( sK1_R @ SY70 @ SY71 ) )
= $false )
| ( ( ~ ! [SY74: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(103,plain,
( ( ( ~ ! [SY75: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY75 ) )
= $false )
| ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(104,plain,
( ( ( ~ ! [SY83: $i] :
~ ~ ! [SY84: $i > $i] :
~ ( sK1_R @ SY83 @ SY84 ) )
= $false )
| ( ( ~ ! [SY87: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(105,plain,
( ( ( ! [SY65: $i] :
~ ~ ! [SY66: $i > $i] :
~ ( sK1_R @ SY65 @ SY66 ) )
= $true )
| ( ( ~ ! [SY69: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(106,plain,
( ( ( ! [SY70: $i] :
~ ~ ! [SY71: $i > $i] :
~ ( sK1_R @ SY70 @ SY71 ) )
= $true )
| ( ( ~ ! [SY74: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(107,plain,
( ( ( ! [SY75: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY75 ) )
= $true )
| ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(108,plain,
( ( ( ! [SY83: $i] :
~ ~ ! [SY84: $i > $i] :
~ ( sK1_R @ SY83 @ SY84 ) )
= $true )
| ( ( ~ ! [SY87: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(109,plain,
! [SV26: $i] :
( ( ( ~ ~ ! [SY88: $i > $i] :
~ ( sK1_R @ SV26 @ SY88 ) )
= $true )
| ( ( ~ ! [SY69: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY69 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(110,plain,
! [SV27: $i] :
( ( ( ~ ~ ! [SY89: $i > $i] :
~ ( sK1_R @ SV27 @ SY89 ) )
= $true )
| ( ( ~ ! [SY74: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY74 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(111,plain,
! [SV28: $i > $i] :
( ( ( ~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV28 ) )
= $true )
| ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV29: $i] :
( ( ( ~ ~ ! [SY92: $i > $i] :
~ ( sK1_R @ SV29 @ SY92 ) )
= $true )
| ( ( ~ ! [SY87: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY87 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(113,plain,
! [SV26: $i] :
( ( ( ~ ! [SY88: $i > $i] :
~ ( sK1_R @ SV26 @ SY88 ) )
= $false )
| ( ( ~ ! [SY69: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(114,plain,
! [SV27: $i] :
( ( ( ~ ! [SY89: $i > $i] :
~ ( sK1_R @ SV27 @ SY89 ) )
= $false )
| ( ( ~ ! [SY74: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(115,plain,
! [SV28: $i > $i] :
( ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV28 )
= $false )
| ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(116,plain,
! [SV29: $i] :
( ( ( ~ ! [SY92: $i > $i] :
~ ( sK1_R @ SV29 @ SY92 ) )
= $false )
| ( ( ~ ! [SY87: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(117,plain,
! [SV26: $i] :
( ( ( ! [SY88: $i > $i] :
~ ( sK1_R @ SV26 @ SY88 ) )
= $true )
| ( ( ~ ! [SY69: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(118,plain,
! [SV27: $i] :
( ( ( ! [SY89: $i > $i] :
~ ( sK1_R @ SV27 @ SY89 ) )
= $true )
| ( ( ~ ! [SY74: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(119,plain,
! [SV29: $i] :
( ( ( ! [SY92: $i > $i] :
~ ( sK1_R @ SV29 @ SY92 ) )
= $true )
| ( ( ~ ! [SY87: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(120,plain,
! [SV30: $i > $i,SV26: $i] :
( ( ( ~ ( sK1_R @ SV26 @ SV30 ) )
= $true )
| ( ( ~ ! [SY69: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY69 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(121,plain,
! [SV31: $i > $i,SV27: $i] :
( ( ( ~ ( sK1_R @ SV27 @ SV31 ) )
= $true )
| ( ( ~ ! [SY74: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY74 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(122,plain,
! [SV32: $i > $i,SV29: $i] :
( ( ( ~ ( sK1_R @ SV29 @ SV32 ) )
= $true )
| ( ( ~ ! [SY87: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY87 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(123,plain,
! [SV30: $i > $i,SV26: $i] :
( ( ( sK1_R @ SV26 @ SV30 )
= $false )
| ( ( ~ ! [SY69: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(124,plain,
! [SV31: $i > $i,SV27: $i] :
( ( ( sK1_R @ SV27 @ SV31 )
= $false )
| ( ( ~ ! [SY74: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(125,plain,
! [SV32: $i > $i,SV29: $i] :
( ( ( sK1_R @ SV29 @ SV32 )
= $false )
| ( ( ~ ! [SY87: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(126,plain,
! [SV30: $i > $i,SV26: $i] :
( ( ( ! [SY69: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY69 ) )
= $false )
| ( ( sK1_R @ SV26 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(127,plain,
! [SV31: $i > $i,SV27: $i] :
( ( ( ! [SY74: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY74 ) )
= $false )
| ( ( sK1_R @ SV27 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(128,plain,
! [SV32: $i > $i,SV29: $i] :
( ( ( ! [SY87: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY87 ) )
= $false )
| ( ( sK1_R @ SV29 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(129,plain,
! [SV26: $i,SV30: $i > $i] :
( ( ( ~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK11_SY69 @ SV30 @ SV26 ) ) )
= $false )
| ( ( sK1_R @ SV26 @ SV30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[126]) ).
thf(130,plain,
! [SV27: $i,SV31: $i > $i] :
( ( ( ~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK12_SY74 @ SV31 @ SV27 ) ) )
= $false )
| ( ( sK1_R @ SV27 @ SV31 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[127]) ).
thf(131,plain,
! [SV29: $i,SV32: $i > $i] :
( ( ( ~ ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( sK13_SY87 @ SV32 @ SV29 ) ) )
= $false )
| ( ( sK1_R @ SV29 @ SV32 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[128]) ).
thf(132,plain,
! [SV26: $i,SV30: $i > $i] :
( ( ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK11_SY69 @ SV30 @ SV26 ) )
= $true )
| ( ( sK1_R @ SV26 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(133,plain,
! [SV27: $i,SV31: $i > $i] :
( ( ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK12_SY74 @ SV31 @ SV27 ) )
= $true )
| ( ( sK1_R @ SV27 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(134,plain,
! [SV29: $i,SV32: $i > $i] :
( ( ( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( sK13_SY87 @ SV32 @ SV29 ) )
= $true )
| ( ( sK1_R @ SV29 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(135,plain,
( ( ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( eps
@ ^ [SX1: $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
= sK2_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[92:[bind(SV21,$thf( sK3_SY2 ))]]) ).
thf(136,plain,
! [SV21: $i > $i] :
( ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV21 )
= $false ),
inference(extuni,[status(esa)],[91]) ).
thf(139,plain,
! [SV33: $i > $i] :
( ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV33 )
= $false ),
inference(rename,[status(thm)],[136]) ).
thf(140,plain,
! [SV33: $i > $i] :
( ( ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV33 )
= ( sK1_R @ sK2_SY0 @ sK3_SY2 ) )
= $false ),
inference(res,[status(thm)],[139,14]) ).
thf(141,plain,
( ( ~ ~ ! [SY108: $i] :
~ ~ ! [SY109: $i > $i] :
~ ( sK1_R @ SY108 @ SY109 )
| ~ ! [SY112: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY112 ) )
= $true ),
inference(choice,[status(thm)],[139]) ).
thf(142,plain,
( ( ( ~ ~ ! [SY108: $i] :
~ ~ ! [SY109: $i > $i] :
~ ( sK1_R @ SY108 @ SY109 ) )
= $true )
| ( ( ~ ! [SY112: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(143,plain,
( ( ( ~ ! [SY108: $i] :
~ ~ ! [SY109: $i > $i] :
~ ( sK1_R @ SY108 @ SY109 ) )
= $false )
| ( ( ~ ! [SY112: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(144,plain,
( ( ( ! [SY108: $i] :
~ ~ ! [SY109: $i > $i] :
~ ( sK1_R @ SY108 @ SY109 ) )
= $true )
| ( ( ~ ! [SY112: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(145,plain,
! [SV35: $i] :
( ( ( ~ ~ ! [SY113: $i > $i] :
~ ( sK1_R @ SV35 @ SY113 ) )
= $true )
| ( ( ~ ! [SY112: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY112 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(146,plain,
! [SV35: $i] :
( ( ( ~ ! [SY113: $i > $i] :
~ ( sK1_R @ SV35 @ SY113 ) )
= $false )
| ( ( ~ ! [SY112: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(147,plain,
! [SV35: $i] :
( ( ( ! [SY113: $i > $i] :
~ ( sK1_R @ SV35 @ SY113 ) )
= $true )
| ( ( ~ ! [SY112: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(148,plain,
! [SV36: $i > $i,SV35: $i] :
( ( ( ~ ( sK1_R @ SV35 @ SV36 ) )
= $true )
| ( ( ~ ! [SY112: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY112 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(149,plain,
! [SV36: $i > $i,SV35: $i] :
( ( ( sK1_R @ SV35 @ SV36 )
= $false )
| ( ( ~ ! [SY112: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(150,plain,
! [SV36: $i > $i,SV35: $i] :
( ( ( ! [SY112: $i > $i] :
~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY112 ) )
= $false )
| ( ( sK1_R @ SV35 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(151,plain,
! [SV35: $i,SV36: $i > $i] :
( ( ( ~ ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK20_SY112 @ SV36 @ SV35 ) ) )
= $false )
| ( ( sK1_R @ SV35 @ SV36 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[150]) ).
thf(152,plain,
! [SV35: $i,SV36: $i > $i] :
( ( ( sK1_R
@ ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK20_SY112 @ SV36 @ SV35 ) )
= $true )
| ( ( sK1_R @ SV35 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(153,plain,
( ( ( eps
@ ^ [SX0: $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
= sK2_SY0 )
= $false ),
inference(extuni,[status(esa)],[140:[bind(SV33,$thf( sK3_SY2 ))]]) ).
thf(154,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,153,152,139,135,134,133,132,115,87,86,85,73,55,54]) ).
thf(155,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO535^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.16 % Computer : n009.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Oct 6 17:42:32 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.29
% 0.11/0.29 No.of.Axioms: 2
% 0.11/0.29
% 0.11/0.29 Length.of.Defs: 330
% 0.11/0.29
% 0.11/0.29 Contains.Choice.Funs: true
% 0.11/0.29
% 0.11/0.29 *** Modified list of choice operators: eps ***
% 0.11/0.29
% 0.11/0.29 *** Modified list of choice operators: epsii, eps ***
% 0.11/0.29 ......
% 0.11/0.29
% 0.11/0.29 ********************************
% 0.11/0.29 * All subproblems solved! *
% 0.11/0.29 ********************************
% 0.11/0.29 % SZS status Theorem for /export/starexec/sandbox2/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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:154,loop_count:5,foatp_calls:3,translation:fof_experiment)
% 0.11/0.29
% 0.11/0.29 %**** Beginning of derivation protocol ****
% 0.11/0.29 % SZS output start CNFRefutation
% See solution above
% 0.11/0.29
% 0.11/0.29 %**** End of derivation protocol ****
% 0.11/0.29 %**** no. of clauses in derivation: 137 ****
% 0.11/0.29 %**** clause counter: 154 ****
% 0.11/0.29
% 0.11/0.29 % SZS status Theorem for /export/starexec/sandbox2/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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:154,loop_count:5,foatp_calls:3,translation:fof_experiment)
%------------------------------------------------------------------------------