%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO537^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 0.09s 0.29s
% Output : CNFRefutation 0.09s
% 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 : 2045 ( 737 ~; 119 |; 0 &;1186 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 702 ( 702 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 6 con; 0-3 aty)
% Number of variables : 690 ( 207 ^; 474 !; 9 ?; 690 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_epsa,type,
epsa: ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).
thf(tp_epsb,type,
epsb: ( ( $i > $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_E,type,
sK11_E: $i > $i ).
thf(tp_sK12_SY70,type,
sK12_SY70: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(tp_sK13_SY75,type,
sK13_SY75: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(tp_sK14_SY88,type,
sK14_SY88: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(tp_sK15_E,type,
sK15_E: ( $i > $i ) > $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 > $i ).
thf(tp_sK19_E,type,
sK19_E: $i > $i ).
thf(tp_sK1_R,type,
sK1_R: ( $i > $i ) > ( $i > $i ) > $o ).
thf(tp_sK20_E,type,
sK20_E: $i > $i ).
thf(tp_sK21_E,type,
sK21_E: $i > $i ).
thf(tp_sK22_SY115,type,
sK22_SY115: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(tp_sK23_E,type,
sK23_E: ( $i > $i ) > $i ).
thf(tp_sK2_SY0,type,
sK2_SY0: $i > $i ).
thf(tp_sK3_SY2,type,
sK3_SY2: $i > $i ).
thf(tp_sK4_SY8,type,
sK4_SY8: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(tp_sK5_SY21,type,
sK5_SY21: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(tp_sK6_SY34,type,
sK6_SY34: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(tp_sK7_SY47,type,
sK7_SY47: ( $i > $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 > $i ) > $o] :
( epsii
@ ^ [X: $i > $i] :
? [Y: $i > $i] : ( R @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epsad) ).
thf(epsb,definition,
( epsb
= ( ^ [R: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [Y: $i > $i] : ( R @ ( epsa @ R ) @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epsbd) ).
thf(2,conjecture,
! [R: ( $i > $i ) > ( $i > $i ) > $o] :
( ? [X: $i > $i,Y: $i > $i] : ( R @ X @ Y )
=> ( R @ ( epsa @ R ) @ ( epsb @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(3,negated_conjecture,
( ( ! [R: ( $i > $i ) > ( $i > $i ) > $o] :
( ? [X: $i > $i,Y: $i > $i] : ( R @ X @ Y )
=> ( R @ ( epsa @ R ) @ ( epsb @ R ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ? [SY0: $i > $i,SY1: $i > $i] : ( sK1_R @ SY0 @ SY1 )
=> ( sK1_R @ ( epsa @ sK1_R ) @ ( epsb @ sK1_R ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ? [SY0: $i > $i,SY1: $i > $i] : ( sK1_R @ SY0 @ SY1 ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( sK1_R @ ( epsa @ sK1_R ) @ ( epsb @ sK1_R ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ( sK1_R @ ( epsa @ sK1_R ) @ ( epsb @ sK1_R ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( sK1_R @ sK2_SY0 @ sK3_SY2 )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(11,plain,
( ( sK1_R @ sK2_SY0 @ sK3_SY2 )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ( sK1_R @ ( epsa @ sK1_R ) @ ( epsb @ sK1_R ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(13,plain,
( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,epsa,epsb]) ).
thf(15,plain,
( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(19,plain,
( ( ~ ~ ! [SY4: $i > $i] :
~ ~ ! [SY5: $i > $i] :
~ ( sK1_R @ SY4 @ SY5 )
| ~ ! [SY8: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY8 ) )
= $true ),
inference(choice,[status(thm)],[15]) ).
thf(20,plain,
( ( ~ ~ ! [SY9: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY9 )
| ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ),
inference(choice,[status(thm)],[15]) ).
thf(21,plain,
( ( ~ ~ ! [SY17: $i > $i] :
~ ~ ! [SY18: $i > $i] :
~ ( sK1_R @ SY17 @ SY18 )
| ~ ! [SY21: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY21 ) )
= $true ),
inference(choice,[status(thm)],[15]) ).
thf(22,plain,
( ( ( ~ ~ ! [SY4: $i > $i] :
~ ~ ! [SY5: $i > $i] :
~ ( sK1_R @ SY4 @ SY5 ) )
= $true )
| ( ( ~ ! [SY8: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ( ~ ~ ! [SY9: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY9 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ( ~ ~ ! [SY17: $i > $i] :
~ ~ ! [SY18: $i > $i] :
~ ( sK1_R @ SY17 @ SY18 ) )
= $true )
| ( ( ~ ! [SY21: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ( ~ ! [SY4: $i > $i] :
~ ~ ! [SY5: $i > $i] :
~ ( sK1_R @ SY4 @ SY5 ) )
= $false )
| ( ( ~ ! [SY8: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ( ~ ! [SY9: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY9 ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ( ~ ! [SY17: $i > $i] :
~ ~ ! [SY18: $i > $i] :
~ ( sK1_R @ SY17 @ SY18 ) )
= $false )
| ( ( ~ ! [SY21: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(28,plain,
( ( ( ! [SY4: $i > $i] :
~ ~ ! [SY5: $i > $i] :
~ ( sK1_R @ SY4 @ SY5 ) )
= $true )
| ( ( ~ ! [SY8: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
( ( ( ! [SY9: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY9 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( ( ! [SY17: $i > $i] :
~ ~ ! [SY18: $i > $i] :
~ ( sK1_R @ SY17 @ SY18 ) )
= $true )
| ( ( ~ ! [SY21: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(31,plain,
! [SV6: $i > $i] :
( ( ( ~ ~ ! [SY22: $i > $i] :
~ ( sK1_R @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ! [SY8: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV7: $i > $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV7 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV8: $i > $i] :
( ( ( ~ ~ ! [SY25: $i > $i] :
~ ( sK1_R @ SV8 @ SY25 ) )
= $true )
| ( ( ~ ! [SY21: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY21 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV6: $i > $i] :
( ( ( ~ ! [SY22: $i > $i] :
~ ( sK1_R @ SV6 @ SY22 ) )
= $false )
| ( ( ~ ! [SY8: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV7: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV7 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV8: $i > $i] :
( ( ( ~ ! [SY25: $i > $i] :
~ ( sK1_R @ SV8 @ SY25 ) )
= $false )
| ( ( ~ ! [SY21: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV6: $i > $i] :
( ( ( ! [SY22: $i > $i] :
~ ( sK1_R @ SV6 @ SY22 ) )
= $true )
| ( ( ~ ! [SY8: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV8: $i > $i] :
( ( ( ! [SY25: $i > $i] :
~ ( sK1_R @ SV8 @ SY25 ) )
= $true )
| ( ( ~ ! [SY21: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(39,plain,
! [SV9: $i > $i,SV6: $i > $i] :
( ( ( ~ ( sK1_R @ SV6 @ SV9 ) )
= $true )
| ( ( ~ ! [SY8: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV10: $i > $i,SV8: $i > $i] :
( ( ( ~ ( sK1_R @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ! [SY21: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY21 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV9: $i > $i,SV6: $i > $i] :
( ( ( sK1_R @ SV6 @ SV9 )
= $false )
| ( ( ~ ! [SY8: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV10: $i > $i,SV8: $i > $i] :
( ( ( sK1_R @ SV8 @ SV10 )
= $false )
| ( ( ~ ! [SY21: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV9: $i > $i,SV6: $i > $i] :
( ( ( ! [SY8: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY8 ) )
= $false )
| ( ( sK1_R @ SV6 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV10: $i > $i,SV8: $i > $i] :
( ( ( ! [SY21: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY21 ) )
= $false )
| ( ( sK1_R @ SV8 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV6: $i > $i,SV9: $i > $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY8 @ SV9 @ SV6 ) ) )
= $false )
| ( ( sK1_R @ SV6 @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[43]) ).
thf(46,plain,
! [SV8: $i > $i,SV10: $i > $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( sK5_SY21 @ SV10 @ SV8 ) ) )
= $false )
| ( ( sK1_R @ SV8 @ SV10 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(47,plain,
! [SV6: $i > $i,SV9: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK4_SY8 @ SV9 @ SV6 ) )
= $true )
| ( ( sK1_R @ SV6 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(48,plain,
! [SV8: $i > $i,SV10: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( sK5_SY21 @ SV10 @ SV8 ) )
= $true )
| ( ( sK1_R @ SV8 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(49,plain,
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= ( sK1_R @ sK2_SY0 @ sK3_SY2 ) )
= $false ),
inference(res,[status(thm)],[15,11]) ).
thf(50,plain,
( ( ~ ~ ! [SY30: $i > $i] :
~ ~ ! [SY31: $i > $i] :
~ ( sK1_R @ SY30 @ SY31 )
| ~ ! [SY34: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY34 ) )
= $true ),
inference(choice,[status(thm)],[15]) ).
thf(51,plain,
( ( ~ ~ ! [SY35: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY35 )
| ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ),
inference(choice,[status(thm)],[15]) ).
thf(52,plain,
( ( ~ ~ ! [SY43: $i > $i] :
~ ~ ! [SY44: $i > $i] :
~ ( sK1_R @ SY43 @ SY44 )
| ~ ! [SY47: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY47 ) )
= $true ),
inference(choice,[status(thm)],[15]) ).
thf(53,plain,
( ( ( ~ ~ ! [SY30: $i > $i] :
~ ~ ! [SY31: $i > $i] :
~ ( sK1_R @ SY30 @ SY31 ) )
= $true )
| ( ( ~ ! [SY34: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(54,plain,
( ( ( ~ ~ ! [SY35: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY35 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(55,plain,
( ( ( ~ ~ ! [SY43: $i > $i] :
~ ~ ! [SY44: $i > $i] :
~ ( sK1_R @ SY43 @ SY44 ) )
= $true )
| ( ( ~ ! [SY47: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(56,plain,
( ( ( ~ ! [SY30: $i > $i] :
~ ~ ! [SY31: $i > $i] :
~ ( sK1_R @ SY30 @ SY31 ) )
= $false )
| ( ( ~ ! [SY34: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(57,plain,
( ( ( ~ ! [SY35: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY35 ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
( ( ( ~ ! [SY43: $i > $i] :
~ ~ ! [SY44: $i > $i] :
~ ( sK1_R @ SY43 @ SY44 ) )
= $false )
| ( ( ~ ! [SY47: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(59,plain,
( ( ( ! [SY30: $i > $i] :
~ ~ ! [SY31: $i > $i] :
~ ( sK1_R @ SY30 @ SY31 ) )
= $true )
| ( ( ~ ! [SY34: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(60,plain,
( ( ( ! [SY35: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY35 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(61,plain,
( ( ( ! [SY43: $i > $i] :
~ ~ ! [SY44: $i > $i] :
~ ( sK1_R @ SY43 @ SY44 ) )
= $true )
| ( ( ~ ! [SY47: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(62,plain,
! [SV14: $i > $i] :
( ( ( ~ ~ ! [SY48: $i > $i] :
~ ( sK1_R @ SV14 @ SY48 ) )
= $true )
| ( ( ~ ! [SY34: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV15: $i > $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV15 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV16: $i > $i] :
( ( ( ~ ~ ! [SY51: $i > $i] :
~ ( sK1_R @ SV16 @ SY51 ) )
= $true )
| ( ( ~ ! [SY47: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY47 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV14: $i > $i] :
( ( ( ~ ! [SY48: $i > $i] :
~ ( sK1_R @ SV14 @ SY48 ) )
= $false )
| ( ( ~ ! [SY34: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV15: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV15 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(67,plain,
! [SV16: $i > $i] :
( ( ( ~ ! [SY51: $i > $i] :
~ ( sK1_R @ SV16 @ SY51 ) )
= $false )
| ( ( ~ ! [SY47: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(68,plain,
! [SV14: $i > $i] :
( ( ( ! [SY48: $i > $i] :
~ ( sK1_R @ SV14 @ SY48 ) )
= $true )
| ( ( ~ ! [SY34: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(69,plain,
! [SV16: $i > $i] :
( ( ( ! [SY51: $i > $i] :
~ ( sK1_R @ SV16 @ SY51 ) )
= $true )
| ( ( ~ ! [SY47: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(70,plain,
! [SV17: $i > $i,SV14: $i > $i] :
( ( ( ~ ( sK1_R @ SV14 @ SV17 ) )
= $true )
| ( ( ~ ! [SY34: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(71,plain,
! [SV18: $i > $i,SV16: $i > $i] :
( ( ( ~ ( sK1_R @ SV16 @ SV18 ) )
= $true )
| ( ( ~ ! [SY47: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY47 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(72,plain,
! [SV17: $i > $i,SV14: $i > $i] :
( ( ( sK1_R @ SV14 @ SV17 )
= $false )
| ( ( ~ ! [SY34: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(73,plain,
! [SV18: $i > $i,SV16: $i > $i] :
( ( ( sK1_R @ SV16 @ SV18 )
= $false )
| ( ( ~ ! [SY47: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(74,plain,
! [SV17: $i > $i,SV14: $i > $i] :
( ( ( ! [SY34: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY34 ) )
= $false )
| ( ( sK1_R @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(75,plain,
! [SV18: $i > $i,SV16: $i > $i] :
( ( ( ! [SY47: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY47 ) )
= $false )
| ( ( sK1_R @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(76,plain,
! [SV14: $i > $i,SV17: $i > $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY34 @ SV17 @ SV14 ) ) )
= $false )
| ( ( sK1_R @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[74]) ).
thf(77,plain,
! [SV16: $i > $i,SV18: $i > $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( sK7_SY47 @ SV18 @ SV16 ) ) )
= $false )
| ( ( sK1_R @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[75]) ).
thf(78,plain,
! [SV14: $i > $i,SV17: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK6_SY34 @ SV17 @ SV14 ) )
= $true )
| ( ( sK1_R @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(79,plain,
! [SV16: $i > $i,SV18: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( sK7_SY47 @ SV18 @ SV16 ) )
= $true )
| ( ( sK1_R @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(80,plain,
( ( ( ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 )
@ sK9_E )
= ( sK3_SY2 @ sK9_E ) )
= $false )
| ( ( ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 )
@ sK8_E )
= ( sK2_SY0 @ sK8_E ) )
= $false ) ),
inference(extuni,[status(esa)],[49]) ).
thf(81,plain,
! [SV19: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV19 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(rename,[status(thm)],[35]) ).
thf(84,plain,
! [SV19: $i > $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV19 )
= $false ) ),
inference(res,[status(thm)],[81,15]) ).
thf(85,plain,
! [SV19: $i > $i] :
( ( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV19 )
= ( sK1_R @ sK2_SY0 @ sK3_SY2 ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[81,11]) ).
thf(86,plain,
( ( ~ ~ ! [SY66: $i > $i] :
~ ~ ! [SY67: $i > $i] :
~ ( sK1_R @ SY66 @ SY67 )
| ~ ! [SY70: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY70 ) )
= $true ),
inference(choice,[status(thm)],[81]) ).
thf(87,plain,
( ( ~ ~ ! [SY71: $i > $i] :
~ ~ ! [SY72: $i > $i] :
~ ( sK1_R @ SY71 @ SY72 )
| ~ ! [SY75: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY75 ) )
= $true ),
inference(choice,[status(thm)],[81]) ).
thf(88,plain,
( ( ~ ~ ! [SY76: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY76 )
| ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ),
inference(choice,[status(thm)],[81]) ).
thf(89,plain,
( ( ~ ~ ! [SY84: $i > $i] :
~ ~ ! [SY85: $i > $i] :
~ ( sK1_R @ SY84 @ SY85 )
| ~ ! [SY88: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY88 ) )
= $true ),
inference(choice,[status(thm)],[81]) ).
thf(90,plain,
( ( ( ~ ~ ! [SY66: $i > $i] :
~ ~ ! [SY67: $i > $i] :
~ ( sK1_R @ SY66 @ SY67 ) )
= $true )
| ( ( ~ ! [SY70: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(91,plain,
( ( ( ~ ~ ! [SY71: $i > $i] :
~ ~ ! [SY72: $i > $i] :
~ ( sK1_R @ SY71 @ SY72 ) )
= $true )
| ( ( ~ ! [SY75: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(92,plain,
( ( ( ~ ~ ! [SY76: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY76 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(93,plain,
( ( ( ~ ~ ! [SY84: $i > $i] :
~ ~ ! [SY85: $i > $i] :
~ ( sK1_R @ SY84 @ SY85 ) )
= $true )
| ( ( ~ ! [SY88: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(94,plain,
( ( ( ~ ! [SY66: $i > $i] :
~ ~ ! [SY67: $i > $i] :
~ ( sK1_R @ SY66 @ SY67 ) )
= $false )
| ( ( ~ ! [SY70: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(95,plain,
( ( ( ~ ! [SY71: $i > $i] :
~ ~ ! [SY72: $i > $i] :
~ ( sK1_R @ SY71 @ SY72 ) )
= $false )
| ( ( ~ ! [SY75: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(96,plain,
( ( ( ~ ! [SY76: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY76 ) )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(97,plain,
( ( ( ~ ! [SY84: $i > $i] :
~ ~ ! [SY85: $i > $i] :
~ ( sK1_R @ SY84 @ SY85 ) )
= $false )
| ( ( ~ ! [SY88: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(98,plain,
( ( ( ! [SY66: $i > $i] :
~ ~ ! [SY67: $i > $i] :
~ ( sK1_R @ SY66 @ SY67 ) )
= $true )
| ( ( ~ ! [SY70: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(99,plain,
( ( ( ! [SY71: $i > $i] :
~ ~ ! [SY72: $i > $i] :
~ ( sK1_R @ SY71 @ SY72 ) )
= $true )
| ( ( ~ ! [SY75: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY75 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(100,plain,
( ( ( ! [SY76: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY76 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(101,plain,
( ( ( ! [SY84: $i > $i] :
~ ~ ! [SY85: $i > $i] :
~ ( sK1_R @ SY84 @ SY85 ) )
= $true )
| ( ( ~ ! [SY88: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(102,plain,
! [SV24: $i > $i] :
( ( ( ~ ~ ! [SY89: $i > $i] :
~ ( sK1_R @ SV24 @ SY89 ) )
= $true )
| ( ( ~ ! [SY70: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY70 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(103,plain,
! [SV25: $i > $i] :
( ( ( ~ ~ ! [SY90: $i > $i] :
~ ( sK1_R @ SV25 @ SY90 ) )
= $true )
| ( ( ~ ! [SY75: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY75 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(104,plain,
! [SV26: $i > $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV26 ) )
= $true )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(105,plain,
! [SV27: $i > $i] :
( ( ( ~ ~ ! [SY93: $i > $i] :
~ ( sK1_R @ SV27 @ SY93 ) )
= $true )
| ( ( ~ ! [SY88: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY88 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(106,plain,
! [SV24: $i > $i] :
( ( ( ~ ! [SY89: $i > $i] :
~ ( sK1_R @ SV24 @ SY89 ) )
= $false )
| ( ( ~ ! [SY70: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(107,plain,
! [SV25: $i > $i] :
( ( ( ~ ! [SY90: $i > $i] :
~ ( sK1_R @ SV25 @ SY90 ) )
= $false )
| ( ( ~ ! [SY75: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV26: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SV26 )
= $false )
| ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(109,plain,
! [SV27: $i > $i] :
( ( ( ~ ! [SY93: $i > $i] :
~ ( sK1_R @ SV27 @ SY93 ) )
= $false )
| ( ( ~ ! [SY88: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(110,plain,
! [SV24: $i > $i] :
( ( ( ! [SY89: $i > $i] :
~ ( sK1_R @ SV24 @ SY89 ) )
= $true )
| ( ( ~ ! [SY70: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(111,plain,
! [SV25: $i > $i] :
( ( ( ! [SY90: $i > $i] :
~ ( sK1_R @ SV25 @ SY90 ) )
= $true )
| ( ( ~ ! [SY75: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY75 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(112,plain,
! [SV27: $i > $i] :
( ( ( ! [SY93: $i > $i] :
~ ( sK1_R @ SV27 @ SY93 ) )
= $true )
| ( ( ~ ! [SY88: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(113,plain,
! [SV28: $i > $i,SV24: $i > $i] :
( ( ( ~ ( sK1_R @ SV24 @ SV28 ) )
= $true )
| ( ( ~ ! [SY70: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY70 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(114,plain,
! [SV29: $i > $i,SV25: $i > $i] :
( ( ( ~ ( sK1_R @ SV25 @ SV29 ) )
= $true )
| ( ( ~ ! [SY75: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY75 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(115,plain,
! [SV30: $i > $i,SV27: $i > $i] :
( ( ( ~ ( sK1_R @ SV27 @ SV30 ) )
= $true )
| ( ( ~ ! [SY88: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY88 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(116,plain,
! [SV28: $i > $i,SV24: $i > $i] :
( ( ( sK1_R @ SV24 @ SV28 )
= $false )
| ( ( ~ ! [SY70: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(117,plain,
! [SV29: $i > $i,SV25: $i > $i] :
( ( ( sK1_R @ SV25 @ SV29 )
= $false )
| ( ( ~ ! [SY75: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(118,plain,
! [SV30: $i > $i,SV27: $i > $i] :
( ( ( sK1_R @ SV27 @ SV30 )
= $false )
| ( ( ~ ! [SY88: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(119,plain,
! [SV28: $i > $i,SV24: $i > $i] :
( ( ( ! [SY70: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY70 ) )
= $false )
| ( ( sK1_R @ SV24 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(120,plain,
! [SV29: $i > $i,SV25: $i > $i] :
( ( ( ! [SY75: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY75 ) )
= $false )
| ( ( sK1_R @ SV25 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(121,plain,
! [SV30: $i > $i,SV27: $i > $i] :
( ( ( ! [SY88: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SY88 ) )
= $false )
| ( ( sK1_R @ SV27 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(122,plain,
! [SV24: $i > $i,SV28: $i > $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK12_SY70 @ SV28 @ SV24 ) ) )
= $false )
| ( ( sK1_R @ SV24 @ SV28 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[119]) ).
thf(123,plain,
! [SV25: $i > $i,SV29: $i > $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK13_SY75 @ SV29 @ SV25 ) ) )
= $false )
| ( ( sK1_R @ SV25 @ SV29 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[120]) ).
thf(124,plain,
! [SV27: $i > $i,SV30: $i > $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( sK14_SY88 @ SV30 @ SV27 ) ) )
= $false )
| ( ( sK1_R @ SV27 @ SV30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[121]) ).
thf(125,plain,
! [SV24: $i > $i,SV28: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK12_SY70 @ SV28 @ SV24 ) )
= $true )
| ( ( sK1_R @ SV24 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(126,plain,
! [SV25: $i > $i,SV29: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK13_SY75 @ SV29 @ SV25 ) )
= $true )
| ( ( sK1_R @ SV25 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(127,plain,
! [SV27: $i > $i,SV30: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ ( sK14_SY88 @ SV30 @ SV27 ) )
= $true )
| ( ( sK1_R @ SV27 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(128,plain,
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( epsii
@ ^ [SX0: $i > $i] :
( sK1_R
@ ( epsii
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i > $i] :
~ ( sK1_R @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true )
| ( ( ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 )
@ ( sK15_E @ sK3_SY2 ) )
= ( sK2_SY0 @ ( sK15_E @ sK3_SY2 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[85:[bind(SV19,$thf( sK3_SY2 ))]]) ).
thf(129,plain,
! [SV19: $i > $i] :
( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV19 )
= $false ),
inference(extuni,[status(esa)],[84]) ).
thf(132,plain,
! [SV31: $i > $i] :
( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV31 )
= $false ),
inference(rename,[status(thm)],[129]) ).
thf(133,plain,
! [SV31: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SV31 )
= ( sK1_R @ sK2_SY0 @ sK3_SY2 ) )
= $false ),
inference(res,[status(thm)],[132,11]) ).
thf(134,plain,
( ( ~ ~ ! [SY111: $i > $i] :
~ ~ ! [SY112: $i > $i] :
~ ( sK1_R @ SY111 @ SY112 )
| ~ ! [SY115: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ),
inference(choice,[status(thm)],[132]) ).
thf(135,plain,
( ( ( ~ ~ ! [SY111: $i > $i] :
~ ~ ! [SY112: $i > $i] :
~ ( sK1_R @ SY111 @ SY112 ) )
= $true )
| ( ( ~ ! [SY115: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(136,plain,
( ( ( ~ ! [SY111: $i > $i] :
~ ~ ! [SY112: $i > $i] :
~ ( sK1_R @ SY111 @ SY112 ) )
= $false )
| ( ( ~ ! [SY115: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(137,plain,
( ( ( ! [SY111: $i > $i] :
~ ~ ! [SY112: $i > $i] :
~ ( sK1_R @ SY111 @ SY112 ) )
= $true )
| ( ( ~ ! [SY115: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(138,plain,
! [SV33: $i > $i] :
( ( ( ~ ~ ! [SY116: $i > $i] :
~ ( sK1_R @ SV33 @ SY116 ) )
= $true )
| ( ( ~ ! [SY115: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(139,plain,
! [SV33: $i > $i] :
( ( ( ~ ! [SY116: $i > $i] :
~ ( sK1_R @ SV33 @ SY116 ) )
= $false )
| ( ( ~ ! [SY115: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(140,plain,
! [SV33: $i > $i] :
( ( ( ! [SY116: $i > $i] :
~ ( sK1_R @ SV33 @ SY116 ) )
= $true )
| ( ( ~ ! [SY115: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(141,plain,
! [SV34: $i > $i,SV33: $i > $i] :
( ( ( ~ ( sK1_R @ SV33 @ SV34 ) )
= $true )
| ( ( ~ ! [SY115: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(142,plain,
! [SV34: $i > $i,SV33: $i > $i] :
( ( ( sK1_R @ SV33 @ SV34 )
= $false )
| ( ( ~ ! [SY115: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(143,plain,
! [SV34: $i > $i,SV33: $i > $i] :
( ( ( ! [SY115: $i > $i] :
~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ SY115 ) )
= $false )
| ( ( sK1_R @ SV33 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(144,plain,
! [SV33: $i > $i,SV34: $i > $i] :
( ( ( ~ ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK22_SY115 @ SV34 @ SV33 ) ) )
= $false )
| ( ( sK1_R @ SV33 @ SV34 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[143]) ).
thf(145,plain,
! [SV33: $i > $i,SV34: $i > $i] :
( ( ( sK1_R
@ ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 ) )
@ ( sK22_SY115 @ SV34 @ SV33 ) )
= $true )
| ( ( sK1_R @ SV33 @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(146,plain,
( ( ( epsii
@ ^ [SX0: $i > $i] :
~ ! [SX1: $i > $i] :
~ ( sK1_R @ SX0 @ SX1 )
@ ( sK23_E @ sK3_SY2 ) )
= ( sK2_SY0 @ ( sK23_E @ sK3_SY2 ) ) )
= $false ),
inference(extuni,[status(esa)],[133:[bind(SV31,$thf( sK3_SY2 ))]]) ).
thf(147,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[11,146,145,132,128,127,126,125,108,80,79,78,66,48,47]) ).
thf(148,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO537^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.15 % Computer : n014.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Tue Oct 6 17:42:11 UTC 2026
% 0.09/0.15 % CPUTime :
% 0.09/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.29
% 0.09/0.29 No.of.Axioms: 1
% 0.09/0.29
% 0.09/0.29 Length.of.Defs: 345
% 0.09/0.29
% 0.09/0.29 Contains.Choice.Funs: true
% 0.09/0.29
% 0.09/0.29 *** Modified list of choice operators: epsii ***
% 0.09/0.29 ......
% 0.09/0.29
% 0.09/0.29 ********************************
% 0.09/0.29 * All subproblems solved! *
% 0.09/0.29 ********************************
% 0.09/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:147,loop_count:5,foatp_calls:3,translation:fof_experiment)
% 0.09/0.29
% 0.09/0.29 %**** Beginning of derivation protocol ****
% 0.09/0.29 % SZS output start CNFRefutation
% See solution above
% 0.09/0.29
% 0.09/0.29 %**** End of derivation protocol ****
% 0.09/0.29 %**** no. of clauses in derivation: 137 ****
% 0.09/0.29 %**** clause counter: 147 ****
% 0.09/0.29
% 0.09/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:147,loop_count:5,foatp_calls:3,translation:fof_experiment)
%------------------------------------------------------------------------------