TSTP Solution File: NUM824^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM824^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n020.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 : Mon Jul 18 11:55:47 EDT 2022
% Result : Theorem 0.23s 0.46s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 11
% Syntax : Number of formulae : 124 ( 33 unt; 10 typ; 0 def)
% Number of atoms : 845 ( 342 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 2168 ( 411 ~; 443 |; 30 &;1252 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 212 ( 212 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 314 ( 0 ^ 314 !; 0 ?; 314 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c0,type,
c0: $i ).
thf(tp_cEVEN,type,
cEVEN: $i > $o ).
thf(tp_cN,type,
cN: $i > $o ).
thf(tp_cODD,type,
cODD: $i > $o ).
thf(tp_cS,type,
cS: $i > $i ).
thf(tp_sK1_Xm,type,
sK1_Xm: $i ).
thf(tp_sK2_Xu,type,
sK2_Xu: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK3_Xv,type,
sK3_Xv: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK4_Xu,type,
sK4_Xu: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK5_Xv,type,
sK5_Xv: ( $i > $o ) > ( $i > $o ) > $i ).
thf(1,conjecture,
( ( ! [Xp: $i > $o,Xq: $i > $o] :
( ( ( Xp @ c0 )
& ! [Xu: $i] :
( ( Xp @ Xu )
=> ( Xq @ ( cS @ Xu ) ) )
& ! [Xv: $i] :
( ( Xq @ Xv )
=> ( Xp @ ( cS @ Xv ) ) ) )
=> ( ! [Xx: $i] :
( ( cEVEN @ Xx )
=> ( Xp @ Xx ) )
& ! [Xx: $i] :
( ( cODD @ Xx )
=> ( Xq @ Xx ) ) ) )
& ( cN @ c0 )
& ! [Xn: $i] :
( ( cN @ Xn )
=> ( cN @ ( cS @ Xn ) ) ) )
=> ! [Xm: $i] :
( ( ( cEVEN @ Xm )
| ( cODD @ Xm ) )
=> ( cN @ Xm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM623_pme) ).
thf(2,negated_conjecture,
( ( ( ! [Xp: $i > $o,Xq: $i > $o] :
( ( ( Xp @ c0 )
& ! [Xu: $i] :
( ( Xp @ Xu )
=> ( Xq @ ( cS @ Xu ) ) )
& ! [Xv: $i] :
( ( Xq @ Xv )
=> ( Xp @ ( cS @ Xv ) ) ) )
=> ( ! [Xx: $i] :
( ( cEVEN @ Xx )
=> ( Xp @ Xx ) )
& ! [Xx: $i] :
( ( cODD @ Xx )
=> ( Xq @ Xx ) ) ) )
& ( cN @ c0 )
& ! [Xn: $i] :
( ( cN @ Xn )
=> ( cN @ ( cS @ Xn ) ) ) )
=> ! [Xm: $i] :
( ( ( cEVEN @ Xm )
| ( cODD @ Xm ) )
=> ( cN @ Xm ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [Xp: $i > $o,Xq: $i > $o] :
( ( ( Xp @ c0 )
& ! [Xu: $i] :
( ( Xp @ Xu )
=> ( Xq @ ( cS @ Xu ) ) )
& ! [Xv: $i] :
( ( Xq @ Xv )
=> ( Xp @ ( cS @ Xv ) ) ) )
=> ( ! [Xx: $i] :
( ( cEVEN @ Xx )
=> ( Xp @ Xx ) )
& ! [Xx: $i] :
( ( cODD @ Xx )
=> ( Xq @ Xx ) ) ) )
& ( cN @ c0 )
& ! [Xn: $i] :
( ( cN @ Xn )
=> ( cN @ ( cS @ Xn ) ) ) )
=> ! [Xm: $i] :
( ( ( cEVEN @ Xm )
| ( cODD @ Xm ) )
=> ( cN @ Xm ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xp: $i > $o,Xq: $i > $o] :
( ( ( Xp @ c0 )
& ! [Xu: $i] :
( ( Xp @ Xu )
=> ( Xq @ ( cS @ Xu ) ) )
& ! [Xv: $i] :
( ( Xq @ Xv )
=> ( Xp @ ( cS @ Xv ) ) ) )
=> ( ! [Xx: $i] :
( ( cEVEN @ Xx )
=> ( Xp @ Xx ) )
& ! [Xx: $i] :
( ( cODD @ Xx )
=> ( Xq @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( cN @ c0 )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xn: $i] :
( ( cN @ Xn )
=> ( cN @ ( cS @ Xn ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xm: $i] :
( ( ( cEVEN @ Xm )
| ( cODD @ Xm ) )
=> ( cN @ Xm ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [Xm: $i] :
( ( ( cEVEN @ Xm )
| ( cODD @ Xm ) )
=> ( cN @ Xm ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ( ( cEVEN @ sK1_Xm )
| ( cODD @ sK1_Xm ) )
& ~ ( cN @ sK1_Xm ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [Xp: $i > $o] :
( ! [Xq: $i > $o] :
( ( ( Xq @ ( sK5_Xv @ Xq @ Xp ) )
& ~ ( Xp @ ( cS @ ( sK5_Xv @ Xq @ Xp ) ) ) )
| ( ( Xp @ ( sK4_Xu @ Xq @ Xp ) )
& ~ ( Xq @ ( cS @ ( sK4_Xu @ Xq @ Xp ) ) ) )
| ~ ( Xp @ c0 ) )
| ! [Xx: $i] :
( ~ ( cEVEN @ Xx )
| ( Xp @ Xx ) ) )
& ! [Xp: $i > $o,Xq: $i > $o] :
( ( ( Xq @ ( sK3_Xv @ Xq @ Xp ) )
& ~ ( Xp @ ( cS @ ( sK3_Xv @ Xq @ Xp ) ) ) )
| ( ( Xp @ ( sK2_Xu @ Xq @ Xp ) )
& ~ ( Xq @ ( cS @ ( sK2_Xu @ Xq @ Xp ) ) ) )
| ~ ( Xp @ c0 )
| ! [Xx: $i] :
( ~ ( cODD @ Xx )
| ( Xq @ Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(11,plain,
( ( ! [Xn: $i] :
( ~ ( cN @ Xn )
| ( cN @ ( cS @ Xn ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(12,plain,
( ( ! [Xn: $i] :
( ~ ( cN @ Xn )
| ( cN @ ( cS @ Xn ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(13,plain,
( ( cN @ c0 )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [Xp: $i > $o] :
( ! [Xq: $i > $o] :
( ( ( Xq @ ( sK5_Xv @ Xq @ Xp ) )
& ~ ( Xp @ ( cS @ ( sK5_Xv @ Xq @ Xp ) ) ) )
| ( ( Xp @ ( sK4_Xu @ Xq @ Xp ) )
& ~ ( Xq @ ( cS @ ( sK4_Xu @ Xq @ Xp ) ) ) )
| ~ ( Xp @ c0 ) )
| ! [Xx: $i] :
( ~ ( cEVEN @ Xx )
| ( Xp @ Xx ) ) )
& ! [Xp: $i > $o,Xq: $i > $o] :
( ( ( Xq @ ( sK3_Xv @ Xq @ Xp ) )
& ~ ( Xp @ ( cS @ ( sK3_Xv @ Xq @ Xp ) ) ) )
| ( ( Xp @ ( sK2_Xu @ Xq @ Xp ) )
& ~ ( Xq @ ( cS @ ( sK2_Xu @ Xq @ Xp ) ) ) )
| ~ ( Xp @ c0 )
| ! [Xx: $i] :
( ~ ( cODD @ Xx )
| ( Xq @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( ( ( cEVEN @ sK1_Xm )
| ( cODD @ sK1_Xm ) )
& ~ ( cN @ sK1_Xm ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(16,plain,
( ( ~ ( ~ ! [SX0: $i > $o] :
( ! [SX1: $i > $o] :
( ~ ( ~ ( SX1 @ ( sK5_Xv @ SX1 @ SX0 ) )
| ~ ~ ( SX0 @ ( cS @ ( sK5_Xv @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( SX0 @ ( sK4_Xu @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( cS @ ( sK4_Xu @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ c0 ) )
| ! [SX1: $i] :
( ~ ( cEVEN @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ~ ( SX1 @ ( sK3_Xv @ SX1 @ SX0 ) )
| ~ ~ ( SX0 @ ( cS @ ( sK3_Xv @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( SX0 @ ( sK2_Xu @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( cS @ ( sK2_Xu @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ c0 )
| ! [SX2: $i] :
( ~ ( cODD @ SX2 )
| ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( ~ ( ( cEVEN @ sK1_Xm )
| ( cODD @ sK1_Xm ) )
| ~ ~ ( cN @ sK1_Xm ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: $i] :
( ( ~ ( cN @ SV1 )
| ( cN @ ( cS @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(19,plain,
( ( ~ ! [SX0: $i > $o] :
( ! [SX1: $i > $o] :
( ~ ( ~ ( SX1 @ ( sK5_Xv @ SX1 @ SX0 ) )
| ~ ~ ( SX0 @ ( cS @ ( sK5_Xv @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( SX0 @ ( sK4_Xu @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( cS @ ( sK4_Xu @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ c0 ) )
| ! [SX1: $i] :
( ~ ( cEVEN @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ~ ( SX1 @ ( sK3_Xv @ SX1 @ SX0 ) )
| ~ ~ ( SX0 @ ( cS @ ( sK3_Xv @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( SX0 @ ( sK2_Xu @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( cS @ ( sK2_Xu @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ c0 )
| ! [SX2: $i] :
( ~ ( cODD @ SX2 )
| ( SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( ( cEVEN @ sK1_Xm )
| ( cODD @ sK1_Xm ) )
| ~ ~ ( cN @ sK1_Xm ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: $i] :
( ( ( ~ ( cN @ SV1 ) )
= $true )
| ( ( cN @ ( cS @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ! [SX0: $i > $o] :
( ! [SX1: $i > $o] :
( ~ ( ~ ( SX1 @ ( sK5_Xv @ SX1 @ SX0 ) )
| ~ ~ ( SX0 @ ( cS @ ( sK5_Xv @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( SX0 @ ( sK4_Xu @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( cS @ ( sK4_Xu @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ c0 ) )
| ! [SX1: $i] :
( ~ ( cEVEN @ SX1 )
| ( SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ~ ( SX1 @ ( sK3_Xv @ SX1 @ SX0 ) )
| ~ ~ ( SX0 @ ( cS @ ( sK3_Xv @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( SX0 @ ( sK2_Xu @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( cS @ ( sK2_Xu @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ c0 )
| ! [SX2: $i] :
( ~ ( cODD @ SX2 )
| ( SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( ~ ( ( cEVEN @ sK1_Xm )
| ( cODD @ sK1_Xm ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ~ ( cN @ sK1_Xm ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(26,plain,
! [SV1: $i] :
( ( ( cN @ SV1 )
= $false )
| ( ( cN @ ( cS @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(27,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i > $o] :
( ~ ( ~ ( SX1 @ ( sK5_Xv @ SX1 @ SX0 ) )
| ~ ~ ( SX0 @ ( cS @ ( sK5_Xv @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( SX0 @ ( sK4_Xu @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( cS @ ( sK4_Xu @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ c0 ) )
| ! [SX1: $i] :
( ~ ( cEVEN @ SX1 )
| ( SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(28,plain,
( ( ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ~ ( SX1 @ ( sK3_Xv @ SX1 @ SX0 ) )
| ~ ~ ( SX0 @ ( cS @ ( sK3_Xv @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( SX0 @ ( sK2_Xu @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( cS @ ( sK2_Xu @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ c0 )
| ! [SX2: $i] :
( ~ ( cODD @ SX2 )
| ( SX1 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(29,plain,
( ( ( cEVEN @ sK1_Xm )
| ( cODD @ sK1_Xm ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(30,plain,
( ( ~ ( cN @ sK1_Xm ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(31,plain,
! [SV2: $i > $o] :
( ( ! [SY8: $i > $o] :
( ~ ( ~ ( SY8 @ ( sK5_Xv @ SY8 @ SV2 ) )
| ~ ~ ( SV2 @ ( cS @ ( sK5_Xv @ SY8 @ SV2 ) ) ) )
| ~ ( ~ ( SV2 @ ( sK4_Xu @ SY8 @ SV2 ) )
| ~ ~ ( SY8 @ ( cS @ ( sK4_Xu @ SY8 @ SV2 ) ) ) )
| ~ ( SV2 @ c0 ) )
| ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV3: $i > $o] :
( ( ! [SY10: $i > $o] :
( ~ ( ~ ( SY10 @ ( sK3_Xv @ SY10 @ SV3 ) )
| ~ ~ ( SV3 @ ( cS @ ( sK3_Xv @ SY10 @ SV3 ) ) ) )
| ~ ( ~ ( SV3 @ ( sK2_Xu @ SY10 @ SV3 ) )
| ~ ~ ( SY10 @ ( cS @ ( sK2_Xu @ SY10 @ SV3 ) ) ) )
| ~ ( SV3 @ c0 )
| ! [SX2: $i] :
( ~ ( cODD @ SX2 )
| ( SY10 @ SX2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( ( cEVEN @ sK1_Xm )
= $true )
| ( ( cODD @ sK1_Xm )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(34,plain,
( ( cN @ sK1_Xm )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV2: $i > $o] :
( ( ( ! [SY8: $i > $o] :
( ~ ( ~ ( SY8 @ ( sK5_Xv @ SY8 @ SV2 ) )
| ~ ~ ( SV2 @ ( cS @ ( sK5_Xv @ SY8 @ SV2 ) ) ) )
| ~ ( ~ ( SV2 @ ( sK4_Xu @ SY8 @ SV2 ) )
| ~ ~ ( SY8 @ ( cS @ ( sK4_Xu @ SY8 @ SV2 ) ) ) )
| ~ ( SV2 @ c0 ) ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV3: $i > $o,SV4: $i > $o] :
( ( ~ ( ~ ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
| ~ ~ ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) ) )
| ~ ( ~ ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
| ~ ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) )
| ~ ( SV3 @ c0 )
| ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV2: $i > $o,SV5: $i > $o] :
( ( ( ~ ( ~ ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
| ~ ~ ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) ) )
| ~ ( ~ ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
| ~ ~ ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) ) )
| ~ ( SV2 @ c0 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV3: $i > $o,SV4: $i > $o] :
( ( ( ~ ( ~ ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
| ~ ~ ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) ) )
| ~ ( ~ ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
| ~ ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) )
| ~ ( SV3 @ c0 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV2: $i > $o,SV5: $i > $o] :
( ( ( ~ ( ~ ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
| ~ ~ ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
| ~ ~ ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) ) )
| ~ ( SV2 @ c0 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV3: $i > $o,SV4: $i > $o] :
( ( ( ~ ( ~ ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
| ~ ~ ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
| ~ ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) )
| ~ ( SV3 @ c0 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV2: $i > $o,SV5: $i > $o] :
( ( ( ~ ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
| ~ ~ ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
| ~ ~ ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) ) )
| ~ ( SV2 @ c0 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV3: $i > $o,SV4: $i > $o] :
( ( ( ~ ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
| ~ ~ ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
| ~ ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) )
| ~ ( SV3 @ c0 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV2: $i > $o,SV5: $i > $o] :
( ( ( ~ ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( ~ ( ~ ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
| ~ ~ ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) ) )
| ~ ( SV2 @ c0 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(44,plain,
! [SV5: $i > $o,SV2: $i > $o] :
( ( ( ~ ~ ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
| ~ ~ ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) ) )
| ~ ( SV2 @ c0 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV3: $i > $o,SV4: $i > $o] :
( ( ( ~ ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( ~ ( ~ ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
| ~ ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) )
| ~ ( SV3 @ c0 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV4: $i > $o,SV3: $i > $o] :
( ( ( ~ ~ ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
| ~ ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) )
| ~ ( SV3 @ c0 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(47,plain,
! [SV2: $i > $o,SV5: $i > $o] :
( ( ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
= $true )
| ( ( ~ ( ~ ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
| ~ ~ ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) ) )
| ~ ( SV2 @ c0 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(48,plain,
! [SV5: $i > $o,SV2: $i > $o] :
( ( ( ~ ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
| ~ ~ ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) ) )
| ~ ( SV2 @ c0 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(49,plain,
! [SV3: $i > $o,SV4: $i > $o] :
( ( ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
= $true )
| ( ( ~ ( ~ ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
| ~ ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) )
| ~ ( SV3 @ c0 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(50,plain,
! [SV4: $i > $o,SV3: $i > $o] :
( ( ( ~ ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
| ~ ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) )
| ~ ( SV3 @ c0 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(51,plain,
! [SV5: $i > $o,SV2: $i > $o] :
( ( ( ~ ( ~ ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
| ~ ~ ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) ) ) )
= $true )
| ( ( ~ ( SV2 @ c0 ) )
= $true )
| ( ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV5: $i > $o,SV2: $i > $o] :
( ( ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( ~ ( ~ ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
| ~ ~ ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) ) )
| ~ ( SV2 @ c0 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV4: $i > $o,SV3: $i > $o] :
( ( ( ~ ( ~ ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
| ~ ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) ) )
= $true )
| ( ( ~ ( SV3 @ c0 ) )
= $true )
| ( ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV4: $i > $o,SV3: $i > $o] :
( ( ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( ~ ( ~ ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
| ~ ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) )
| ~ ( SV3 @ c0 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV5: $i > $o,SV2: $i > $o] :
( ( ( ~ ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
| ~ ~ ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) ) )
= $false )
| ( ( ~ ( SV2 @ c0 ) )
= $true )
| ( ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV5: $i > $o,SV2: $i > $o] :
( ( ( ~ ( ~ ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
| ~ ~ ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) ) ) )
= $true )
| ( ( ~ ( SV2 @ c0 ) )
= $true )
| ( ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV4: $i > $o,SV3: $i > $o] :
( ( ( ~ ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
| ~ ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) )
= $false )
| ( ( ~ ( SV3 @ c0 ) )
= $true )
| ( ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV4: $i > $o,SV3: $i > $o] :
( ( ( ~ ( ~ ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
| ~ ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) ) )
= $true )
| ( ( ~ ( SV3 @ c0 ) )
= $true )
| ( ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV5: $i > $o,SV2: $i > $o] :
( ( ( ~ ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) ) )
= $false )
| ( ( ~ ( SV2 @ c0 ) )
= $true )
| ( ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV2: $i > $o,SV5: $i > $o] :
( ( ( ~ ~ ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) ) )
= $false )
| ( ( ~ ( SV2 @ c0 ) )
= $true )
| ( ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(61,plain,
! [SV5: $i > $o,SV2: $i > $o] :
( ( ( ~ ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
| ~ ~ ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) ) )
= $false )
| ( ( ~ ( SV2 @ c0 ) )
= $true )
| ( ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV4: $i > $o,SV3: $i > $o] :
( ( ( ~ ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) ) )
= $false )
| ( ( ~ ( SV3 @ c0 ) )
= $true )
| ( ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(63,plain,
! [SV3: $i > $o,SV4: $i > $o] :
( ( ( ~ ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) )
= $false )
| ( ( ~ ( SV3 @ c0 ) )
= $true )
| ( ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(64,plain,
! [SV4: $i > $o,SV3: $i > $o] :
( ( ( ~ ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
| ~ ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) )
= $false )
| ( ( ~ ( SV3 @ c0 ) )
= $true )
| ( ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV5: $i > $o,SV2: $i > $o] :
( ( ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
= $true )
| ( ( ~ ( SV2 @ c0 ) )
= $true )
| ( ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(66,plain,
! [SV2: $i > $o,SV5: $i > $o] :
( ( ( ~ ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) ) )
= $true )
| ( ( ~ ( SV2 @ c0 ) )
= $true )
| ( ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(67,plain,
! [SV5: $i > $o,SV2: $i > $o] :
( ( ( ~ ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) ) )
= $false )
| ( ( ~ ( SV2 @ c0 ) )
= $true )
| ( ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(68,plain,
! [SV2: $i > $o,SV5: $i > $o] :
( ( ( ~ ~ ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) ) )
= $false )
| ( ( ~ ( SV2 @ c0 ) )
= $true )
| ( ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(69,plain,
! [SV4: $i > $o,SV3: $i > $o] :
( ( ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
= $true )
| ( ( ~ ( SV3 @ c0 ) )
= $true )
| ( ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(70,plain,
! [SV3: $i > $o,SV4: $i > $o] :
( ( ( ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) )
= $true )
| ( ( ~ ( SV3 @ c0 ) )
= $true )
| ( ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(71,plain,
! [SV4: $i > $o,SV3: $i > $o] :
( ( ( ~ ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) ) )
= $false )
| ( ( ~ ( SV3 @ c0 ) )
= $true )
| ( ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(72,plain,
! [SV3: $i > $o,SV4: $i > $o] :
( ( ( ~ ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) )
= $false )
| ( ( ~ ( SV3 @ c0 ) )
= $true )
| ( ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(73,plain,
! [SV5: $i > $o,SV2: $i > $o] :
( ( ( SV2 @ c0 )
= $false )
| ( ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
= $true )
| ( ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV2: $i > $o,SV5: $i > $o] :
( ( ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) )
= $false )
| ( ( ~ ( SV2 @ c0 ) )
= $true )
| ( ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(75,plain,
! [SV5: $i > $o,SV2: $i > $o] :
( ( ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
= $true )
| ( ( ~ ( SV2 @ c0 ) )
= $true )
| ( ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(76,plain,
! [SV2: $i > $o,SV5: $i > $o] :
( ( ( ~ ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) ) )
= $true )
| ( ( ~ ( SV2 @ c0 ) )
= $true )
| ( ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(77,plain,
! [SV4: $i > $o,SV3: $i > $o] :
( ( ( SV3 @ c0 )
= $false )
| ( ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
= $true )
| ( ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV3: $i > $o,SV4: $i > $o] :
( ( ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) )
= $false )
| ( ( ~ ( SV3 @ c0 ) )
= $true )
| ( ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV4: $i > $o,SV3: $i > $o] :
( ( ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
= $true )
| ( ( ~ ( SV3 @ c0 ) )
= $true )
| ( ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(80,plain,
! [SV3: $i > $o,SV4: $i > $o] :
( ( ( ~ ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) ) )
= $true )
| ( ( ~ ( SV3 @ c0 ) )
= $true )
| ( ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(81,plain,
! [SV5: $i > $o,SV2: $i > $o,SV6: $i] :
( ( ( ~ ( cEVEN @ SV6 )
| ( SV2 @ SV6 ) )
= $true )
| ( ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
= $true )
| ( ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
= $true )
| ( ( SV2 @ c0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(82,plain,
! [SV5: $i > $o,SV2: $i > $o] :
( ( ( SV2 @ c0 )
= $false )
| ( ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) )
= $false )
| ( ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(83,plain,
! [SV5: $i > $o,SV2: $i > $o] :
( ( ( SV2 @ c0 )
= $false )
| ( ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
= $true )
| ( ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(84,plain,
! [SV2: $i > $o,SV5: $i > $o] :
( ( ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) )
= $false )
| ( ( ~ ( SV2 @ c0 ) )
= $true )
| ( ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(85,plain,
! [SV3: $i > $o,SV4: $i > $o,SV7: $i] :
( ( ( ~ ( cODD @ SV7 )
| ( SV4 @ SV7 ) )
= $true )
| ( ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
= $true )
| ( ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
= $true )
| ( ( SV3 @ c0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(86,plain,
! [SV4: $i > $o,SV3: $i > $o] :
( ( ( SV3 @ c0 )
= $false )
| ( ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(87,plain,
! [SV4: $i > $o,SV3: $i > $o] :
( ( ( SV3 @ c0 )
= $false )
| ( ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
= $true )
| ( ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(88,plain,
! [SV3: $i > $o,SV4: $i > $o] :
( ( ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) )
= $false )
| ( ( ~ ( SV3 @ c0 ) )
= $true )
| ( ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV5: $i > $o,SV2: $i > $o,SV6: $i] :
( ( ( ~ ( cEVEN @ SV6 ) )
= $true )
| ( ( SV2 @ SV6 )
= $true )
| ( ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
= $true )
| ( ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
= $true )
| ( ( SV2 @ c0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV5: $i > $o,SV2: $i > $o,SV8: $i] :
( ( ( ~ ( cEVEN @ SV8 )
| ( SV2 @ SV8 ) )
= $true )
| ( ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
= $true )
| ( ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) )
= $false )
| ( ( SV2 @ c0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV5: $i > $o,SV2: $i > $o,SV9: $i] :
( ( ( ~ ( cEVEN @ SV9 )
| ( SV2 @ SV9 ) )
= $true )
| ( ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
= $true )
| ( ( SV2 @ c0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV5: $i > $o,SV2: $i > $o] :
( ( ( SV2 @ c0 )
= $false )
| ( ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( ! [SY9: $i] :
( ~ ( cEVEN @ SY9 )
| ( SV2 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV3: $i > $o,SV4: $i > $o,SV7: $i] :
( ( ( ~ ( cODD @ SV7 ) )
= $true )
| ( ( SV4 @ SV7 )
= $true )
| ( ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
= $true )
| ( ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
= $true )
| ( ( SV3 @ c0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV3: $i > $o,SV4: $i > $o,SV10: $i] :
( ( ( ~ ( cODD @ SV10 )
| ( SV4 @ SV10 ) )
= $true )
| ( ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
= $true )
| ( ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV3 @ c0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV3: $i > $o,SV4: $i > $o,SV11: $i] :
( ( ( ~ ( cODD @ SV11 )
| ( SV4 @ SV11 ) )
= $true )
| ( ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
= $true )
| ( ( SV3 @ c0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(96,plain,
! [SV4: $i > $o,SV3: $i > $o] :
( ( ( SV3 @ c0 )
= $false )
| ( ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( ! [SY12: $i] :
( ~ ( cODD @ SY12 )
| ( SV4 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV5: $i > $o,SV2: $i > $o,SV6: $i] :
( ( ( cEVEN @ SV6 )
= $false )
| ( ( SV2 @ SV6 )
= $true )
| ( ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
= $true )
| ( ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
= $true )
| ( ( SV2 @ c0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(98,plain,
! [SV5: $i > $o,SV2: $i > $o,SV8: $i] :
( ( ( ~ ( cEVEN @ SV8 ) )
= $true )
| ( ( SV2 @ SV8 )
= $true )
| ( ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
= $true )
| ( ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) )
= $false )
| ( ( SV2 @ c0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(99,plain,
! [SV5: $i > $o,SV2: $i > $o,SV9: $i] :
( ( ( ~ ( cEVEN @ SV9 ) )
= $true )
| ( ( SV2 @ SV9 )
= $true )
| ( ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
= $true )
| ( ( SV2 @ c0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(100,plain,
! [SV5: $i > $o,SV2: $i > $o,SV12: $i] :
( ( ( ~ ( cEVEN @ SV12 )
| ( SV2 @ SV12 ) )
= $true )
| ( ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) )
= $false )
| ( ( SV2 @ c0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(101,plain,
! [SV3: $i > $o,SV4: $i > $o,SV7: $i] :
( ( ( cODD @ SV7 )
= $false )
| ( ( SV4 @ SV7 )
= $true )
| ( ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
= $true )
| ( ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
= $true )
| ( ( SV3 @ c0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(102,plain,
! [SV3: $i > $o,SV4: $i > $o,SV10: $i] :
( ( ( ~ ( cODD @ SV10 ) )
= $true )
| ( ( SV4 @ SV10 )
= $true )
| ( ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
= $true )
| ( ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV3 @ c0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(103,plain,
! [SV3: $i > $o,SV4: $i > $o,SV11: $i] :
( ( ( ~ ( cODD @ SV11 ) )
= $true )
| ( ( SV4 @ SV11 )
= $true )
| ( ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
= $true )
| ( ( SV3 @ c0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(104,plain,
! [SV3: $i > $o,SV4: $i > $o,SV13: $i] :
( ( ( ~ ( cODD @ SV13 )
| ( SV4 @ SV13 ) )
= $true )
| ( ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV3 @ c0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(105,plain,
! [SV5: $i > $o,SV2: $i > $o,SV8: $i] :
( ( ( cEVEN @ SV8 )
= $false )
| ( ( SV2 @ SV8 )
= $true )
| ( ( SV5 @ ( sK5_Xv @ SV5 @ SV2 ) )
= $true )
| ( ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) )
= $false )
| ( ( SV2 @ c0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(106,plain,
! [SV5: $i > $o,SV2: $i > $o,SV9: $i] :
( ( ( cEVEN @ SV9 )
= $false )
| ( ( SV2 @ SV9 )
= $true )
| ( ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK4_Xu @ SV5 @ SV2 ) )
= $true )
| ( ( SV2 @ c0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(107,plain,
! [SV5: $i > $o,SV2: $i > $o,SV12: $i] :
( ( ( ~ ( cEVEN @ SV12 ) )
= $true )
| ( ( SV2 @ SV12 )
= $true )
| ( ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) )
= $false )
| ( ( SV2 @ c0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(108,plain,
! [SV3: $i > $o,SV4: $i > $o,SV10: $i] :
( ( ( cODD @ SV10 )
= $false )
| ( ( SV4 @ SV10 )
= $true )
| ( ( SV4 @ ( sK3_Xv @ SV4 @ SV3 ) )
= $true )
| ( ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV3 @ c0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(109,plain,
! [SV3: $i > $o,SV4: $i > $o,SV11: $i] :
( ( ( cODD @ SV11 )
= $false )
| ( ( SV4 @ SV11 )
= $true )
| ( ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV3 @ ( sK2_Xu @ SV4 @ SV3 ) )
= $true )
| ( ( SV3 @ c0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(110,plain,
! [SV3: $i > $o,SV4: $i > $o,SV13: $i] :
( ( ( ~ ( cODD @ SV13 ) )
= $true )
| ( ( SV4 @ SV13 )
= $true )
| ( ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV3 @ c0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(111,plain,
! [SV5: $i > $o,SV2: $i > $o,SV12: $i] :
( ( ( cEVEN @ SV12 )
= $false )
| ( ( SV2 @ SV12 )
= $true )
| ( ( SV2 @ ( cS @ ( sK5_Xv @ SV5 @ SV2 ) ) )
= $false )
| ( ( SV5 @ ( cS @ ( sK4_Xu @ SV5 @ SV2 ) ) )
= $false )
| ( ( SV2 @ c0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV3: $i > $o,SV4: $i > $o,SV13: $i] :
( ( ( cODD @ SV13 )
= $false )
| ( ( SV4 @ SV13 )
= $true )
| ( ( SV3 @ ( cS @ ( sK3_Xv @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV4 @ ( cS @ ( sK2_Xu @ SV4 @ SV3 ) ) )
= $false )
| ( ( SV3 @ c0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(113,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[13,112,111,109,108,106,105,101,97,34,33,26]) ).
thf(114,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM824^5 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.15 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.16/0.36 % Computer : n020.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 600
% 0.16/0.37 % DateTime : Tue Jul 5 02:17:59 EDT 2022
% 0.16/0.37 % CPUTime :
% 0.16/0.37
% 0.16/0.37 No.of.Axioms: 0
% 0.16/0.37
% 0.16/0.37 Length.of.Defs: 0
% 0.16/0.37
% 0.16/0.37 Contains.Choice.Funs: false
% 0.16/0.38 (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.23/0.46
% 0.23/0.46 ********************************
% 0.23/0.46 * All subproblems solved! *
% 0.23/0.46 ********************************
% 0.23/0.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:113,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.23/0.46
% 0.23/0.46 %**** Beginning of derivation protocol ****
% 0.23/0.46 % SZS output start CNFRefutation
% See solution above
% 0.23/0.46
% 0.23/0.46 %**** End of derivation protocol ****
% 0.23/0.46 %**** no. of clauses in derivation: 114 ****
% 0.23/0.46 %**** clause counter: 113 ****
% 0.23/0.46
% 0.23/0.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:113,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------