%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUN024^1 : TPTP v9.3.1. Released v6.4.0.
% 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 : n005.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 10:35:55 AM UTC 2026
% Result : Theorem 9.40s 2.01s
% Output : CNFRefutation 9.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 319 ( 111 unt; 0 typ; 0 def)
% Number of atoms : 2169 (1316 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 2658 ( 80 ~; 366 |; 19 &;2182 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 100 ( 100 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-3 aty)
% Number of variables : 856 ( 0 ^; 851 !; 5 ?; 856 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_ite,type,
ite: $o > $i > $i > $i ).
thf(tp_s,type,
s: $i > $i ).
thf(tp_zero,type,
zero: $i ).
thf(1,conjecture,
( ( ! [X100: $o,U: $i,V: $i] :
( X100
=> ( ( ite @ X100 @ U @ V )
= U ) )
& ! [X100: $o,U: $i,V: $i] :
( ~ X100
=> ( ( ite @ X100 @ U @ V )
= V ) )
& ! [X: $i] :
( ( s @ X )
!= zero )
& ! [X: $i] :
( ( s @ X )
!= X ) )
=> ? [H: $i > $i] :
( ( ( H @ zero )
= ( s @ zero ) )
& ( ( H @ ( s @ zero ) )
= zero )
& ( ( H @ ( s @ ( s @ zero ) ) )
= zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n9) ).
thf(2,negated_conjecture,
( ( ( ! [X100: $o,U: $i,V: $i] :
( X100
=> ( ( ite @ X100 @ U @ V )
= U ) )
& ! [X100: $o,U: $i,V: $i] :
( ~ X100
=> ( ( ite @ X100 @ U @ V )
= V ) )
& ! [X: $i] :
( ( s @ X )
!= zero )
& ! [X: $i] :
( ( s @ X )
!= X ) )
=> ? [H: $i > $i] :
( ( ( H @ zero )
= ( s @ zero ) )
& ( ( H @ ( s @ zero ) )
= zero )
& ( ( H @ ( s @ ( s @ zero ) ) )
= zero ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [X100: $o,U: $i,V: $i] :
( X100
=> ( ( ite @ X100 @ U @ V )
= U ) )
& ! [X100: $o,U: $i,V: $i] :
( ~ X100
=> ( ( ite @ X100 @ U @ V )
= V ) )
& ! [X: $i] :
( ( s @ X )
!= zero )
& ! [X: $i] :
( ( s @ X )
!= X ) )
=> ? [H: $i > $i] :
( ( ( H @ zero )
= ( s @ zero ) )
& ( ( H @ ( s @ zero ) )
= zero )
& ( ( H @ ( s @ ( s @ zero ) ) )
= zero ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [X100: $o,U: $i,V: $i] :
( X100
=> ( ( ite @ X100 @ U @ V )
= U ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [X100: $o,U: $i,V: $i] :
( ~ X100
=> ( ( ite @ X100 @ U @ V )
= V ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [X: $i] :
( ( s @ X )
!= zero ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [X: $i] :
( ( s @ X )
!= X ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ? [H: $i > $i] :
( ( ( H @ zero )
= ( s @ zero ) )
& ( ( H @ ( s @ zero ) )
= zero )
& ( ( H @ ( s @ ( s @ zero ) ) )
= zero ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ~ ? [H: $i > $i] :
( ( ( H @ zero )
= ( s @ zero ) )
& ( ( H @ ( s @ zero ) )
= zero )
& ( ( H @ ( s @ ( s @ zero ) ) )
= zero ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [H: $i > $i] :
( ( ( H @ zero )
!= ( s @ zero ) )
| ( ( H @ ( s @ zero ) )
!= zero )
| ( ( H @ ( s @ ( s @ zero ) ) )
!= zero ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(11,plain,
( ( ! [X100: $o] :
( ~ X100
| ! [U: $i,V: $i] :
( ( ite @ X100 @ U @ V )
= U ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(12,plain,
( ( ! [X100: $o] :
( X100
| ! [U: $i,V: $i] :
( ( ite @ X100 @ U @ V )
= V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(13,plain,
( ( ! [X: $i] :
( ( s @ X )
!= zero ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(14,plain,
( ( ! [X: $i] :
( ( s @ X )
!= X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(15,plain,
( ( ! [X: $i] :
( ( s @ X )
!= X ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [X: $i] :
( ( s @ X )
!= zero ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [X100: $o] :
( X100
| ! [U: $i,V: $i] :
( ( ite @ X100 @ U @ V )
= V ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [X100: $o] :
( ~ X100
| ! [U: $i,V: $i] :
( ( ite @ X100 @ U @ V )
= U ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(19,plain,
( ( ! [H: $i > $i] :
( ( ( H @ zero )
!= ( s @ zero ) )
| ( ( H @ ( s @ zero ) )
!= zero )
| ( ( H @ ( s @ ( s @ zero ) ) )
!= zero ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(20,plain,
! [SV1: $i] :
( ( ( s @ SV1 )
!= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(21,plain,
! [SV2: $i] :
( ( ( s @ SV2 )
!= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(22,plain,
! [SV3: $o] :
( ( SV3
| ! [SY9: $i,SY10: $i] :
( ( ite @ SV3 @ SY9 @ SY10 )
= SY10 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[17]) ).
thf(24,plain,
( ( $false
| ! [SX0: $i,SX1: $i] :
( ( ite @ $false @ SX0 @ SX1 )
= SX1 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[17]) ).
thf(25,plain,
! [SV4: $o] :
( ( ~ SV4
| ! [SY11: $i,SY12: $i] :
( ( ite @ SV4 @ SY11 @ SY12 )
= SY11 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[18]) ).
thf(26,plain,
( ( ~ $true
| ! [SX0: $i,SX1: $i] :
( ( ite @ $true @ SX0 @ SX1 )
= SX0 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[18]) ).
thf(28,plain,
! [SV5: $i > $i] :
( ( ( ( SV5 @ zero )
!= ( s @ zero ) )
| ( ( SV5 @ ( s @ zero ) )
!= zero )
| ( ( SV5 @ ( s @ ( s @ zero ) ) )
!= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(29,plain,
! [SV1: $i] :
( ( ( s @ SV1 )
= SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(30,plain,
! [SV2: $i] :
( ( ( s @ SV2 )
= zero )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(31,plain,
! [SV3: $o] :
( ( SV3 = $true )
| ( ( ! [SY9: $i,SY10: $i] :
( ( ite @ SV3 @ SY9 @ SY10 )
= SY10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(33,plain,
( ( $false = $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ( ite @ $false @ SX0 @ SX1 )
= SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(34,plain,
! [SV4: $o] :
( ( ( ~ SV4 ) = $true )
| ( ( ! [SY11: $i,SY12: $i] :
( ( ite @ SV4 @ SY11 @ SY12 )
= SY11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(35,plain,
( ( ( ~ $true ) = $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ( ite @ $true @ SX0 @ SX1 )
= SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(37,plain,
! [SV5: $i > $i] :
( ( ( ( ( SV5 @ zero )
!= ( s @ zero ) )
| ( ( SV5 @ ( s @ zero ) )
!= zero ) )
= $true )
| ( ( ( SV5 @ ( s @ ( s @ zero ) ) )
!= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(38,plain,
! [SV6: $i,SV3: $o] :
( ( ( ! [SY13: $i] :
( ( ite @ SV3 @ SV6 @ SY13 )
= SY13 ) )
= $true )
| ( SV3 = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(40,plain,
! [SV8: $i] :
( ( ( ! [SY15: $i] :
( ( ite @ $false @ SV8 @ SY15 )
= SY15 ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(41,plain,
! [SV4: $o] :
( ( SV4 = $false )
| ( ( ! [SY11: $i,SY12: $i] :
( ( ite @ SV4 @ SY11 @ SY12 )
= SY11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(42,plain,
( ( $true = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ( ite @ $true @ SX0 @ SX1 )
= SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(44,plain,
! [SV5: $i > $i] :
( ( ( ( SV5 @ zero )
!= ( s @ zero ) )
= $true )
| ( ( ( SV5 @ ( s @ zero ) )
!= zero )
= $true )
| ( ( ( SV5 @ ( s @ ( s @ zero ) ) )
!= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV9: $i,SV6: $i,SV3: $o] :
( ( ( ( ite @ SV3 @ SV6 @ SV9 )
= SV9 )
= $true )
| ( SV3 = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(47,plain,
! [SV11: $i,SV8: $i] :
( ( ( ( ite @ $false @ SV8 @ SV11 )
= SV11 )
= $true )
| ( $false = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV12: $i,SV4: $o] :
( ( ( ! [SY16: $i] :
( ( ite @ SV4 @ SV12 @ SY16 )
= SV12 ) )
= $true )
| ( SV4 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(49,plain,
! [SV13: $i] :
( ( ( ! [SY17: $i] :
( ( ite @ $true @ SV13 @ SY17 )
= SV13 ) )
= $true )
| ( $true = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV5: $i > $i] :
( ( ( ( SV5 @ zero )
= ( s @ zero ) )
= $false )
| ( ( ( SV5 @ ( s @ zero ) )
!= zero )
= $true )
| ( ( ( SV5 @ ( s @ ( s @ zero ) ) )
!= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(52,plain,
! [SV15: $i,SV12: $i,SV4: $o] :
( ( ( ( ite @ SV4 @ SV12 @ SV15 )
= SV12 )
= $true )
| ( SV4 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV16: $i,SV13: $i] :
( ( ( ( ite @ $true @ SV13 @ SV16 )
= SV13 )
= $true )
| ( $true = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV5: $i > $i] :
( ( ( ( SV5 @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( SV5 @ zero )
= ( s @ zero ) )
= $false )
| ( ( ( SV5 @ ( s @ ( s @ zero ) ) )
!= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV5: $i > $i] :
( ( ( ( SV5 @ ( s @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( SV5 @ zero )
= ( s @ zero ) )
= $false )
| ( ( ( SV5 @ ( s @ zero ) )
= zero )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV9: $i,SV6: $i,SV19: $o] :
( ( ( ( ite @ ~ SV19 @ SV6 @ SV9 )
= SV9 )
= $true )
| ( ( ~ SV19 ) = $true ) ),
inference(prim_subst,[status(thm)],[45:[bind(SV3,$thf( ~ ( SV19 ) ))]]) ).
thf(62,plain,
! [SV15: $i,SV12: $i,SV18: $o] :
( ( ( ( ite @ ~ SV18 @ SV12 @ SV15 )
= SV12 )
= $true )
| ( ( ~ SV18 ) = $false ) ),
inference(prim_subst,[status(thm)],[52:[bind(SV4,$thf( ~ ( SV18 ) ))]]) ).
thf(63,plain,
! [SV9: $i,SV6: $i,SV3: $o] :
( ( SV3 = $true )
| ( ( ( ( ite @ SV3 @ SV6 @ SV9 )
= SV9 )
= SV3 )
= $false ) ),
inference(fac_restr,[status(thm)],[45]) ).
thf(66,plain,
! [SV15: $i,SV12: $i,SV4: $o] :
( ( SV4 = $false )
| ( ( SV4
= ( ( ite @ SV4 @ SV12 @ SV15 )
!= SV12 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[52]) ).
thf(67,plain,
! [SV9: $i,SV6: $i,SV3: $o] :
( ( ( ~ ( ( ( ite @ SV3 @ SV6 @ SV9 )
= SV9 )
| SV3 )
| ~ ( ( ( ite @ SV3 @ SV6 @ SV9 )
!= SV9 )
| ~ SV3 ) )
= $false )
| ( SV3 = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[63]) ).
thf(73,plain,
! [SV15: $i,SV12: $i,SV4: $o] :
( ( ( ~ ( SV4
| ( ( ite @ SV4 @ SV12 @ SV15 )
!= SV12 ) )
| ~ ( ~ SV4
| ~ ( ( ( ite @ SV4 @ SV12 @ SV15 )
!= SV12 ) ) ) )
= $false )
| ( SV4 = $false ) ),
inference(extcnf_equal_neg,[status(thm)],[66]) ).
thf(75,plain,
! [SV9: $i,SV6: $i,SV3: $o] :
( ( ( ~ ( ( ( ite @ SV3 @ SV6 @ SV9 )
= SV9 )
| SV3 ) )
= $false )
| ( SV3 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(82,plain,
! [SV15: $i,SV12: $i,SV4: $o] :
( ( ( ~ ( ~ SV4
| ~ ( ( ( ite @ SV4 @ SV12 @ SV15 )
!= SV12 ) ) ) )
= $false )
| ( SV4 = $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(83,plain,
! [SV9: $i,SV6: $i,SV3: $o] :
( ( ( ( ( ite @ SV3 @ SV6 @ SV9 )
= SV9 )
| SV3 )
= $true )
| ( SV3 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(90,plain,
! [SV15: $i,SV12: $i,SV4: $o] :
( ( ( ~ SV4
| ~ ( ( ( ite @ SV4 @ SV12 @ SV15 )
!= SV12 ) ) )
= $true )
| ( SV4 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(91,plain,
! [SV9: $i,SV6: $i,SV3: $o] :
( ( ( ( ite @ SV3 @ SV6 @ SV9 )
= SV9 )
= $true )
| ( SV3 = $true )
| ( SV3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(98,plain,
! [SV15: $i,SV12: $i,SV4: $o] :
( ( ( ~ SV4 ) = $true )
| ( ( ~ ( ( ( ite @ SV4 @ SV12 @ SV15 )
!= SV12 ) ) )
= $true )
| ( SV4 = $false ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(103,plain,
! [SV15: $i,SV12: $i,SV4: $o] :
( ( SV4 = $false )
| ( ( ~ ( ( ( ite @ SV4 @ SV12 @ SV15 )
!= SV12 ) ) )
= $true )
| ( SV4 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(107,plain,
! [SV15: $i,SV12: $i,SV4: $o] :
( ( ( ( ite @ SV4 @ SV12 @ SV15 )
!= SV12 )
= $false )
| ( SV4 = $false )
| ( SV4 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV15: $i,SV12: $i,SV4: $o] :
( ( ( ( ite @ SV4 @ SV12 @ SV15 )
= SV12 )
= $true )
| ( SV4 = $false )
| ( SV4 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(109,plain,
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[56:[bind(SV5,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(110,plain,
( ( zero
= ( s @ zero ) )
= $false ),
inference(extuni,[status(esa)],[56:[bind(SV5,$thf( ^ [SX0: $i] : zero ))]]) ).
thf(111,plain,
! [SV9: $i,SV6: $i,SV19: $o] :
( ( SV19 = $false )
| ( ( ( ite @ ~ SV19 @ SV6 @ SV9 )
= SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(112,plain,
! [SV15: $i,SV12: $i,SV18: $o] :
( ( SV18 = $true )
| ( ( ( ite @ ~ SV18 @ SV12 @ SV15 )
= SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(113,plain,
! [SV11: $i,SV8: $i] :
( ( ( ite @ $false @ SV8 @ SV11 )
= SV11 )
= $true ),
inference(sim,[status(thm)],[47]) ).
thf(114,plain,
! [SV16: $i,SV13: $i] :
( ( ( ite @ $true @ SV13 @ SV16 )
= SV13 )
= $true ),
inference(sim,[status(thm)],[53]) ).
thf(115,plain,
! [SV9: $i,SV6: $i,SV3: $o] :
( ( ( ( ite @ SV3 @ SV6 @ SV9 )
= SV9 )
= $true )
| ( SV3 = $true ) ),
inference(sim,[status(thm)],[91]) ).
thf(117,plain,
! [SV15: $i,SV12: $i,SV4: $o] :
( ( ( ( ite @ SV4 @ SV12 @ SV15 )
= SV12 )
= $true )
| ( SV4 = $false ) ),
inference(sim,[status(thm)],[108]) ).
thf(122,plain,
! [SV22: $i] :
( ( ( s @ SV22 )
= SV22 )
= $false ),
inference(rename,[status(thm)],[29]) ).
thf(123,plain,
! [SV23: $i] :
( ( ( s @ SV23 )
= zero )
= $false ),
inference(rename,[status(thm)],[30]) ).
thf(124,plain,
! [SV24: $i,SV25: $i] :
( ( ( ite @ $false @ SV25 @ SV24 )
= SV24 )
= $true ),
inference(rename,[status(thm)],[113]) ).
thf(125,plain,
! [SV24: $i,SV25: $i,SV23: $i] :
( ( ( ( ite @ $false @ SV25 @ SV24 )
= SV24 )
= ( ( s @ SV23 )
= zero ) )
= $false ),
inference(res,[status(thm)],[124,123]) ).
thf(126,plain,
! [SV24: $i,SV25: $i,SV22: $i] :
( ( ( ( ite @ $false @ SV25 @ SV24 )
= SV24 )
= ( ( s @ SV22 )
= SV22 ) )
= $false ),
inference(res,[status(thm)],[124,122]) ).
thf(127,plain,
! [SV24: $i,SV25: $i] :
( ( ( ( ite @ $false @ SV25 @ SV24 )
= SV24 )
= ( zero
= ( s @ zero ) ) )
= $false ),
inference(res,[status(thm)],[124,110]) ).
thf(128,plain,
! [SV25: $i] :
( ( ( ite @ $false @ SV25 @ zero )
= ( s @ zero ) )
= $false ),
inference(extuni,[status(esa)],[127:[bind(SV24,$thf( zero ))]]) ).
thf(129,plain,
! [SV25: $i] :
( ( ( ite @ $false @ SV25 @ ( s @ zero ) )
= zero )
= $false ),
inference(extuni,[status(esa)],[127:[bind(SV24,$thf( s @ zero ))]]) ).
thf(130,plain,
! [SV22: $i,SV25: $i] :
( ( ( ite @ $false @ SV25 @ SV22 )
= ( s @ SV22 ) )
= $false ),
inference(extuni,[status(esa)],[126:[bind(SV24,$thf( SV22 ))]]) ).
thf(131,plain,
! [SV23: $i,SV25: $i] :
( ( ( ite @ $false @ SV25 @ ( s @ SV23 ) )
= zero )
= $false ),
inference(extuni,[status(esa)],[125:[bind(SV24,$thf( s @ SV23 ))]]) ).
thf(132,plain,
! [SV23: $i,SV25: $i] :
( ( ( ite @ $false @ SV25 @ zero )
= ( s @ SV23 ) )
= $false ),
inference(extuni,[status(esa)],[125:[bind(SV24,$thf( zero ))]]) ).
thf(133,plain,
! [SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= $true )
| ( SV28 = $true ) ),
inference(rename,[status(thm)],[45]) ).
thf(134,plain,
! [SV26: $i,SV27: $i,SV28: $o,SV23: $i] :
( ( ( SV28
= ( ( s @ SV23 )
= zero ) )
= $false )
| ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= $true ) ),
inference(res,[status(thm)],[133,123]) ).
thf(135,plain,
! [SV26: $i,SV27: $i,SV28: $o,SV23: $i] :
( ( ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= ( ( s @ SV23 )
= zero ) )
= $false )
| ( SV28 = $true ) ),
inference(res,[status(thm)],[133,123]) ).
thf(136,plain,
! [SV26: $i,SV27: $i,SV28: $o,SV22: $i] :
( ( ( SV28
= ( ( s @ SV22 )
= SV22 ) )
= $false )
| ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= $true ) ),
inference(res,[status(thm)],[133,122]) ).
thf(137,plain,
! [SV26: $i,SV27: $i,SV28: $o,SV22: $i] :
( ( ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= ( ( s @ SV22 )
= SV22 ) )
= $false )
| ( SV28 = $true ) ),
inference(res,[status(thm)],[133,122]) ).
thf(138,plain,
! [SV26: $i,SV27: $i,SV28: $o] :
( ( ( SV28
= ( zero
= ( s @ zero ) ) )
= $false )
| ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= $true ) ),
inference(res,[status(thm)],[133,110]) ).
thf(139,plain,
! [SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= ( zero
= ( s @ zero ) ) )
= $false )
| ( SV28 = $true ) ),
inference(res,[status(thm)],[133,110]) ).
thf(143,plain,
! [SV26: $i,SV27: $i,SV33: $o] :
( ( ( ( ite @ ~ SV33 @ SV27 @ SV26 )
= SV26 )
= $true )
| ( ( ~ SV33 ) = $true ) ),
inference(prim_subst,[status(thm)],[133:[bind(SV28,$thf( ~ ( SV33 ) ))]]) ).
thf(144,plain,
! [SV26: $i,SV27: $i,SV32: $o,SV31: $o] :
( ( ( ( ite
@ ( SV31
| SV32 )
@ SV27
@ SV26 )
= SV26 )
= $true )
| ( ( SV31
| SV32 )
= $true ) ),
inference(prim_subst,[status(thm)],[133:[bind(SV28,$thf( SV31 | SV32 ))]]) ).
thf(145,plain,
! [SV26: $i,SV27: $i,SV30: $i,SV29: $i] :
( ( ( ( ite @ ( SV29 = SV30 ) @ SV27 @ SV26 )
= SV26 )
= $true )
| ( ( SV29 = SV30 )
= $true ) ),
inference(prim_subst,[status(thm)],[133:[bind(SV28,$thf( SV29 = SV30 ))]]) ).
thf(147,plain,
! [SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( ite @ SV28 @ SV27 @ zero )
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[139:[bind(SV26,$thf( zero ))]]) ).
thf(148,plain,
! [SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( ite @ SV28 @ SV27 @ ( s @ zero ) )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[139:[bind(SV26,$thf( s @ zero ))]]) ).
thf(149,plain,
! [SV26: $i,SV27: $i] :
( ( ( ite
@ ( zero
= ( s @ zero ) )
@ SV27
@ SV26 )
= SV26 )
= $true ),
inference(extuni,[status(esa)],[138:[bind(SV28,$thf( zero = ( s @ zero ) ))]]) ).
thf(150,plain,
! [SV22: $i,SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( ite @ SV28 @ SV27 @ SV22 )
= ( s @ SV22 ) )
= $false ) ),
inference(extuni,[status(esa)],[137:[bind(SV26,$thf( SV22 ))]]) ).
thf(151,plain,
! [SV26: $i,SV27: $i,SV22: $i] :
( ( ( ite
@ ( ( s @ SV22 )
= SV22 )
@ SV27
@ SV26 )
= SV26 )
= $true ),
inference(extuni,[status(esa)],[136:[bind(SV28,$thf( ( s @ SV22 ) = SV22 ))]]) ).
thf(152,plain,
! [SV23: $i,SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( ite @ SV28 @ SV27 @ ( s @ SV23 ) )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[135:[bind(SV26,$thf( s @ SV23 ))]]) ).
thf(153,plain,
! [SV23: $i,SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( ite @ SV28 @ SV27 @ zero )
= ( s @ SV23 ) )
= $false ) ),
inference(extuni,[status(esa)],[135:[bind(SV26,$thf( zero ))]]) ).
thf(154,plain,
! [SV26: $i,SV27: $i,SV23: $i] :
( ( ( ite
@ ( ( s @ SV23 )
= zero )
@ SV27
@ SV26 )
= SV26 )
= $true ),
inference(extuni,[status(esa)],[134:[bind(SV28,$thf( ( s @ SV23 ) = zero ))]]) ).
thf(155,plain,
! [SV26: $i,SV27: $i,SV33: $o] :
( ( SV33 = $false )
| ( ( ( ite @ ~ SV33 @ SV27 @ SV26 )
= SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(156,plain,
! [SV26: $i,SV27: $i,SV32: $o,SV31: $o] :
( ( SV31 = $true )
| ( SV32 = $true )
| ( ( ( ite
@ ( SV31
| SV32 )
@ SV27
@ SV26 )
= SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(157,plain,
! [SV34: $i,SV35: $i] :
( ( ( ite @ $true @ SV35 @ SV34 )
= SV35 )
= $true ),
inference(rename,[status(thm)],[114]) ).
thf(158,plain,
! [SV34: $i,SV35: $i,SV23: $i] :
( ( ( ( ite @ $true @ SV35 @ SV34 )
= SV35 )
= ( ( s @ SV23 )
= zero ) )
= $false ),
inference(res,[status(thm)],[157,123]) ).
thf(159,plain,
! [SV34: $i,SV35: $i,SV22: $i] :
( ( ( ( ite @ $true @ SV35 @ SV34 )
= SV35 )
= ( ( s @ SV22 )
= SV22 ) )
= $false ),
inference(res,[status(thm)],[157,122]) ).
thf(160,plain,
! [SV34: $i,SV35: $i] :
( ( ( ( ite @ $true @ SV35 @ SV34 )
= SV35 )
= ( zero
= ( s @ zero ) ) )
= $false ),
inference(res,[status(thm)],[157,110]) ).
thf(161,plain,
! [SV34: $i] :
( ( ( ite @ $true @ zero @ SV34 )
= ( s @ zero ) )
= $false ),
inference(extuni,[status(esa)],[160:[bind(SV35,$thf( zero ))]]) ).
thf(162,plain,
! [SV34: $i] :
( ( ( ite @ $true @ ( s @ zero ) @ SV34 )
= zero )
= $false ),
inference(extuni,[status(esa)],[160:[bind(SV35,$thf( s @ zero ))]]) ).
thf(163,plain,
! [SV34: $i,SV22: $i] :
( ( ( ite @ $true @ SV22 @ SV34 )
= ( s @ SV22 ) )
= $false ),
inference(extuni,[status(esa)],[159:[bind(SV35,$thf( SV22 ))]]) ).
thf(164,plain,
! [SV34: $i,SV23: $i] :
( ( ( ite @ $true @ ( s @ SV23 ) @ SV34 )
= zero )
= $false ),
inference(extuni,[status(esa)],[158:[bind(SV35,$thf( s @ SV23 ))]]) ).
thf(165,plain,
! [SV23: $i,SV34: $i] :
( ( ( ite @ $true @ zero @ SV34 )
= ( s @ SV23 ) )
= $false ),
inference(extuni,[status(esa)],[158:[bind(SV35,$thf( zero ))]]) ).
thf(169,plain,
! [SV42: $i,SV43: $i,SV44: $o] :
( ( ( ( ite @ SV44 @ SV43 @ SV42 )
= SV43 )
= $true )
| ( SV44 = $false ) ),
inference(rename,[status(thm)],[52]) ).
thf(172,plain,
! [SV42: $i,SV43: $i,SV44: $o,SV34: $i,SV35: $i] :
( ( ( SV44
= ( ( ite @ $true @ SV35 @ SV34 )
= SV35 ) )
= $false )
| ( ( ( ite @ SV44 @ SV43 @ SV42 )
= SV43 )
= $true ) ),
inference(res,[status(thm)],[169,157]) ).
thf(173,plain,
! [SV42: $i,SV43: $i,SV44: $o,SV26: $i,SV27: $i,SV28: $o] :
( ( ( SV44 = SV28 )
= $false )
| ( ( ( ite @ SV44 @ SV43 @ SV42 )
= SV43 )
= $true )
| ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= $true ) ),
inference(res,[status(thm)],[169,133]) ).
thf(174,plain,
! [SV42: $i,SV43: $i,SV44: $o,SV26: $i,SV27: $i,SV28: $o] :
( ( ( SV44
= ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 ) )
= $false )
| ( ( ( ite @ SV44 @ SV43 @ SV42 )
= SV43 )
= $true )
| ( SV28 = $true ) ),
inference(res,[status(thm)],[169,133]) ).
thf(175,plain,
! [SV42: $i,SV43: $i,SV44: $o,SV24: $i,SV25: $i] :
( ( ( SV44
= ( ( ite @ $false @ SV25 @ SV24 )
= SV24 ) )
= $false )
| ( ( ( ite @ SV44 @ SV43 @ SV42 )
= SV43 )
= $true ) ),
inference(res,[status(thm)],[169,124]) ).
thf(176,plain,
! [SV42: $i,SV43: $i,SV44: $o,SV23: $i] :
( ( ( ( ( ite @ SV44 @ SV43 @ SV42 )
= SV43 )
= ( ( s @ SV23 )
= zero ) )
= $false )
| ( SV44 = $false ) ),
inference(res,[status(thm)],[169,123]) ).
thf(177,plain,
! [SV42: $i,SV43: $i,SV44: $o,SV22: $i] :
( ( ( ( ( ite @ SV44 @ SV43 @ SV42 )
= SV43 )
= ( ( s @ SV22 )
= SV22 ) )
= $false )
| ( SV44 = $false ) ),
inference(res,[status(thm)],[169,122]) ).
thf(178,plain,
! [SV42: $i,SV43: $i,SV44: $o] :
( ( ( ( ( ite @ SV44 @ SV43 @ SV42 )
= SV43 )
= ( zero
= ( s @ zero ) ) )
= $false )
| ( SV44 = $false ) ),
inference(res,[status(thm)],[169,110]) ).
thf(179,plain,
! [SV42: $i,SV43: $i] :
( ( ( ( ite @ $true @ SV43 @ SV42 )
= SV43 )
= $true )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[169:[bind(SV44,$thf( $true ))]]) ).
thf(180,plain,
! [SV42: $i,SV43: $i] :
( ( ( ite @ $true @ SV43 @ SV42 )
= SV43 )
= $true ),
inference(sim,[status(thm)],[179]) ).
thf(182,plain,
! [SV42: $i,SV43: $i,SV49: $o] :
( ( ( ( ite @ ~ SV49 @ SV43 @ SV42 )
= SV43 )
= $true )
| ( ( ~ SV49 ) = $false ) ),
inference(prim_subst,[status(thm)],[169:[bind(SV44,$thf( ~ ( SV49 ) ))]]) ).
thf(183,plain,
! [SV42: $i,SV43: $i,SV48: $o,SV47: $o] :
( ( ( ( ite
@ ( SV47
| SV48 )
@ SV43
@ SV42 )
= SV43 )
= $true )
| ( ( SV47
| SV48 )
= $false ) ),
inference(prim_subst,[status(thm)],[169:[bind(SV44,$thf( SV47 | SV48 ))]]) ).
thf(184,plain,
! [SV42: $i,SV43: $i,SV46: $i,SV45: $i] :
( ( ( ( ite @ ( SV45 = SV46 ) @ SV43 @ SV42 )
= SV43 )
= $true )
| ( ( SV45 = SV46 )
= $false ) ),
inference(prim_subst,[status(thm)],[169:[bind(SV44,$thf( SV45 = SV46 ))]]) ).
thf(186,plain,
! [SV42: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( ite @ SV44 @ zero @ SV42 )
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[178:[bind(SV43,$thf( zero ))]]) ).
thf(187,plain,
! [SV42: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( ite @ SV44 @ ( s @ zero ) @ SV42 )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[178:[bind(SV43,$thf( s @ zero ))]]) ).
thf(188,plain,
! [SV42: $i,SV22: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( ite @ SV44 @ SV22 @ SV42 )
= ( s @ SV22 ) )
= $false ) ),
inference(extuni,[status(esa)],[177:[bind(SV43,$thf( SV22 ))]]) ).
thf(189,plain,
! [SV42: $i,SV23: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( ite @ SV44 @ ( s @ SV23 ) @ SV42 )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[176:[bind(SV43,$thf( s @ SV23 ))]]) ).
thf(190,plain,
! [SV23: $i,SV42: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( ite @ SV44 @ zero @ SV42 )
= ( s @ SV23 ) )
= $false ) ),
inference(extuni,[status(esa)],[176:[bind(SV43,$thf( zero ))]]) ).
thf(191,plain,
! [SV42: $i,SV43: $i,SV24: $i,SV25: $i] :
( ( ( ite
@ ( ( ite @ $false @ SV25 @ SV24 )
= SV24 )
@ SV43
@ SV42 )
= SV43 )
= $true ),
inference(extuni,[status(esa)],[175:[bind(SV44,$thf( ( ite @ $false @ SV25 @ SV24 ) = SV24 ))]]) ).
thf(192,plain,
! [SV42: $i,SV43: $i,SV26: $i,SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( ite
@ ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
@ SV43
@ SV42 )
= SV43 )
= $true ) ),
inference(extuni,[status(esa)],[174:[bind(SV44,$thf( ( ite @ SV28 @ SV27 @ SV26 ) = SV26 ))]]) ).
thf(193,plain,
! [SV42: $i,SV43: $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= $true )
| ( ( ( ite @ SV28 @ SV43 @ SV42 )
= SV43 )
= $true ) ),
inference(extuni,[status(esa)],[173:[bind(SV44,$thf( SV28 ))]]) ).
thf(194,plain,
! [SV42: $i,SV43: $i,SV34: $i,SV35: $i] :
( ( ( ite
@ ( ( ite @ $true @ SV35 @ SV34 )
= SV35 )
@ SV43
@ SV42 )
= SV43 )
= $true ),
inference(extuni,[status(esa)],[172:[bind(SV44,$thf( ( ite @ $true @ SV35 @ SV34 ) = SV35 ))]]) ).
thf(195,plain,
! [SV42: $i,SV43: $i,SV46: $i] :
( ( ( ite @ ( SV46 = SV46 ) @ SV43 @ SV42 )
= SV43 )
= $true ),
inference(extuni,[status(esa)],[184:[bind(SV45,$thf( SV46 ))]]) ).
thf(196,plain,
! [SV42: $i,SV43: $i,SV49: $o] :
( ( SV49 = $true )
| ( ( ( ite @ ~ SV49 @ SV43 @ SV42 )
= SV43 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(197,plain,
! [SV42: $i,SV43: $i,SV48: $o,SV47: $o] :
( ( SV47 = $false )
| ( ( ( ite
@ ( SV47
| SV48 )
@ SV43
@ SV42 )
= SV43 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(198,plain,
! [SV42: $i,SV43: $i,SV47: $o,SV48: $o] :
( ( SV48 = $false )
| ( ( ( ite
@ ( SV47
| SV48 )
@ SV43
@ SV42 )
= SV43 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(201,plain,
! [SV54: $i] :
( ( ( ite @ $false @ SV54 @ zero )
= ( s @ zero ) )
= $false ),
inference(rename,[status(thm)],[128]) ).
thf(202,plain,
! [SV54: $i,SV42: $i,SV43: $i,SV44: $o] :
( ( ( ( ( ite @ $false @ SV54 @ zero )
= ( s @ zero ) )
= ( ( ite @ SV44 @ SV43 @ SV42 )
= SV43 ) )
= $false )
| ( SV44 = $false ) ),
inference(res,[status(thm)],[201,169]) ).
thf(203,plain,
! [SV54: $i,SV34: $i,SV35: $i] :
( ( ( ( ite @ $false @ SV54 @ zero )
= ( s @ zero ) )
= ( ( ite @ $true @ SV35 @ SV34 )
= SV35 ) )
= $false ),
inference(res,[status(thm)],[201,157]) ).
thf(204,plain,
! [SV54: $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( ite @ $false @ SV54 @ zero )
= ( s @ zero ) )
= SV28 )
= $false )
| ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= $true ) ),
inference(res,[status(thm)],[201,133]) ).
thf(205,plain,
! [SV54: $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( ite @ $false @ SV54 @ zero )
= ( s @ zero ) )
= ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 ) )
= $false )
| ( SV28 = $true ) ),
inference(res,[status(thm)],[201,133]) ).
thf(206,plain,
! [SV54: $i,SV24: $i,SV25: $i] :
( ( ( ( ite @ $false @ SV54 @ zero )
= ( s @ zero ) )
= ( ( ite @ $false @ SV25 @ SV24 )
= SV24 ) )
= $false ),
inference(res,[status(thm)],[201,124]) ).
thf(207,plain,
! [SV54: $i,SV25: $i] :
( ( ( s @ zero )
= ( ite @ $false @ SV25 @ ( ite @ $false @ SV54 @ zero ) ) )
= $false ),
inference(extuni,[status(esa)],[206:[bind(SV24,$thf( ite @ $false @ SV54 @ zero ))]]) ).
thf(208,plain,
( ( ( s @ zero )
= zero )
= $false ),
inference(extuni,[status(esa)],[206:[bind(SV24,$thf( zero )),bind(SV54,$thf( SV25 ))]]) ).
thf(209,plain,
! [SV25: $i,SV54: $i] :
( ( ( ite @ $false @ SV54 @ zero )
= ( ite @ $false @ SV25 @ ( s @ zero ) ) )
= $false ),
inference(extuni,[status(esa)],[206:[bind(SV24,$thf( s @ zero ))]]) ).
thf(210,plain,
! [SV54: $i,SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( s @ zero )
= ( ite @ SV28 @ SV27 @ ( ite @ $false @ SV54 @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV26,$thf( ite @ $false @ SV54 @ zero ))]]) ).
thf(211,plain,
( ( $false = $true )
| ( ( ( s @ zero )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV26,$thf( zero )),bind(SV54,$thf( SV27 )),bind(SV28,$thf( $false ))]]) ).
thf(212,plain,
! [SV27: $i,SV54: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( ite @ $false @ SV54 @ zero )
= ( ite @ SV28 @ SV27 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV26,$thf( s @ zero ))]]) ).
thf(213,plain,
! [SV26: $i,SV27: $i,SV54: $i] :
( ( ( ite
@ ( ( ite @ $false @ SV54 @ zero )
= ( s @ zero ) )
@ SV27
@ SV26 )
= SV26 )
= $true ),
inference(extuni,[status(esa)],[204:[bind(SV28,$thf( ( ite @ $false @ SV54 @ zero ) = ( s @ zero ) ))]]) ).
thf(214,plain,
! [SV34: $i,SV54: $i] :
( ( ( s @ zero )
= ( ite @ $true @ ( ite @ $false @ SV54 @ zero ) @ SV34 ) )
= $false ),
inference(extuni,[status(esa)],[203:[bind(SV35,$thf( ite @ $false @ SV54 @ zero ))]]) ).
thf(217,plain,
! [SV34: $i,SV54: $i] :
( ( ( ite @ $false @ SV54 @ zero )
= ( ite @ $true @ ( s @ zero ) @ SV34 ) )
= $false ),
inference(extuni,[status(esa)],[203:[bind(SV35,$thf( s @ zero ))]]) ).
thf(218,plain,
! [SV42: $i,SV54: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( s @ zero )
= ( ite @ SV44 @ ( ite @ $false @ SV54 @ zero ) @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[202:[bind(SV43,$thf( ite @ $false @ SV54 @ zero ))]]) ).
thf(220,plain,
! [SV42: $i,SV54: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( ite @ $false @ SV54 @ zero )
= ( ite @ SV44 @ ( s @ zero ) @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[202:[bind(SV43,$thf( s @ zero ))]]) ).
thf(221,plain,
( ( ( s @ zero )
= zero )
= $false ),
inference(sim,[status(thm)],[211]) ).
thf(222,plain,
! [SV55: $i] :
( ( ( ite @ $false @ SV55 @ ( s @ zero ) )
= zero )
= $false ),
inference(rename,[status(thm)],[129]) ).
thf(223,plain,
! [SV55: $i,SV42: $i,SV43: $i,SV44: $o] :
( ( ( ( ( ite @ $false @ SV55 @ ( s @ zero ) )
= zero )
= ( ( ite @ SV44 @ SV43 @ SV42 )
= SV43 ) )
= $false )
| ( SV44 = $false ) ),
inference(res,[status(thm)],[222,169]) ).
thf(224,plain,
! [SV55: $i,SV34: $i,SV35: $i] :
( ( ( ( ite @ $false @ SV55 @ ( s @ zero ) )
= zero )
= ( ( ite @ $true @ SV35 @ SV34 )
= SV35 ) )
= $false ),
inference(res,[status(thm)],[222,157]) ).
thf(225,plain,
! [SV55: $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( ite @ $false @ SV55 @ ( s @ zero ) )
= zero )
= SV28 )
= $false )
| ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= $true ) ),
inference(res,[status(thm)],[222,133]) ).
thf(226,plain,
! [SV55: $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( ite @ $false @ SV55 @ ( s @ zero ) )
= zero )
= ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 ) )
= $false )
| ( SV28 = $true ) ),
inference(res,[status(thm)],[222,133]) ).
thf(227,plain,
! [SV55: $i,SV24: $i,SV25: $i] :
( ( ( ( ite @ $false @ SV55 @ ( s @ zero ) )
= zero )
= ( ( ite @ $false @ SV25 @ SV24 )
= SV24 ) )
= $false ),
inference(res,[status(thm)],[222,124]) ).
thf(228,plain,
! [SV55: $i,SV25: $i] :
( ( zero
= ( ite @ $false @ SV25 @ ( ite @ $false @ SV55 @ ( s @ zero ) ) ) )
= $false ),
inference(extuni,[status(esa)],[227:[bind(SV24,$thf( ite @ $false @ SV55 @ ( s @ zero ) ))]]) ).
thf(229,plain,
( ( zero
= ( s @ zero ) )
= $false ),
inference(extuni,[status(esa)],[227:[bind(SV24,$thf( s @ zero )),bind(SV55,$thf( SV25 ))]]) ).
thf(230,plain,
! [SV25: $i,SV55: $i] :
( ( ( ite @ $false @ SV55 @ ( s @ zero ) )
= ( ite @ $false @ SV25 @ zero ) )
= $false ),
inference(extuni,[status(esa)],[227:[bind(SV24,$thf( zero ))]]) ).
thf(231,plain,
! [SV55: $i,SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( zero
= ( ite @ SV28 @ SV27 @ ( ite @ $false @ SV55 @ ( s @ zero ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[226:[bind(SV26,$thf( ite @ $false @ SV55 @ ( s @ zero ) ))]]) ).
thf(232,plain,
( ( $false = $true )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[226:[bind(SV26,$thf( s @ zero )),bind(SV55,$thf( SV27 )),bind(SV28,$thf( $false ))]]) ).
thf(233,plain,
! [SV27: $i,SV55: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( ite @ $false @ SV55 @ ( s @ zero ) )
= ( ite @ SV28 @ SV27 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[226:[bind(SV26,$thf( zero ))]]) ).
thf(234,plain,
! [SV26: $i,SV27: $i,SV55: $i] :
( ( ( ite
@ ( ( ite @ $false @ SV55 @ ( s @ zero ) )
= zero )
@ SV27
@ SV26 )
= SV26 )
= $true ),
inference(extuni,[status(esa)],[225:[bind(SV28,$thf( ( ite @ $false @ SV55 @ ( s @ zero ) ) = zero ))]]) ).
thf(235,plain,
! [SV34: $i,SV55: $i] :
( ( zero
= ( ite @ $true @ ( ite @ $false @ SV55 @ ( s @ zero ) ) @ SV34 ) )
= $false ),
inference(extuni,[status(esa)],[224:[bind(SV35,$thf( ite @ $false @ SV55 @ ( s @ zero ) ))]]) ).
thf(238,plain,
! [SV34: $i,SV55: $i] :
( ( ( ite @ $false @ SV55 @ ( s @ zero ) )
= ( ite @ $true @ zero @ SV34 ) )
= $false ),
inference(extuni,[status(esa)],[224:[bind(SV35,$thf( zero ))]]) ).
thf(239,plain,
! [SV42: $i,SV55: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( zero
= ( ite @ SV44 @ ( ite @ $false @ SV55 @ ( s @ zero ) ) @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[223:[bind(SV43,$thf( ite @ $false @ SV55 @ ( s @ zero ) ))]]) ).
thf(241,plain,
! [SV42: $i,SV55: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( ite @ $false @ SV55 @ ( s @ zero ) )
= ( ite @ SV44 @ zero @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[223:[bind(SV43,$thf( zero ))]]) ).
thf(242,plain,
( ( zero
= ( s @ zero ) )
= $false ),
inference(sim,[status(thm)],[232]) ).
thf(243,plain,
! [SV56: $i > $i] :
( ( ( ( SV56 @ ( s @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( SV56 @ zero )
= ( s @ zero ) )
= $false )
| ( ( ( SV56 @ ( s @ zero ) )
= zero )
= $false ) ),
inference(rename,[status(thm)],[56]) ).
thf(244,plain,
! [SV56: $i > $i,SV42: $i,SV43: $i,SV44: $o] :
( ( ( ( ( SV56 @ ( s @ zero ) )
= zero )
= ( ( ite @ SV44 @ SV43 @ SV42 )
= SV43 ) )
= $false )
| ( ( ( SV56 @ ( s @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( SV56 @ zero )
= ( s @ zero ) )
= $false )
| ( SV44 = $false ) ),
inference(res,[status(thm)],[243,169]) ).
thf(245,plain,
! [SV56: $i > $i,SV42: $i,SV43: $i,SV44: $o] :
( ( ( ( ( SV56 @ zero )
= ( s @ zero ) )
= ( ( ite @ SV44 @ SV43 @ SV42 )
= SV43 ) )
= $false )
| ( ( ( SV56 @ ( s @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( SV56 @ ( s @ zero ) )
= zero )
= $false )
| ( SV44 = $false ) ),
inference(res,[status(thm)],[243,169]) ).
thf(246,plain,
! [SV56: $i > $i,SV42: $i,SV43: $i,SV44: $o] :
( ( ( ( ( SV56 @ ( s @ ( s @ zero ) ) )
= zero )
= ( ( ite @ SV44 @ SV43 @ SV42 )
= SV43 ) )
= $false )
| ( ( ( SV56 @ zero )
= ( s @ zero ) )
= $false )
| ( ( ( SV56 @ ( s @ zero ) )
= zero )
= $false )
| ( SV44 = $false ) ),
inference(res,[status(thm)],[243,169]) ).
thf(247,plain,
! [SV56: $i > $i,SV34: $i,SV35: $i] :
( ( ( ( ( SV56 @ ( s @ zero ) )
= zero )
= ( ( ite @ $true @ SV35 @ SV34 )
= SV35 ) )
= $false )
| ( ( ( SV56 @ ( s @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( SV56 @ zero )
= ( s @ zero ) )
= $false ) ),
inference(res,[status(thm)],[243,157]) ).
thf(248,plain,
! [SV56: $i > $i,SV34: $i,SV35: $i] :
( ( ( ( ( SV56 @ zero )
= ( s @ zero ) )
= ( ( ite @ $true @ SV35 @ SV34 )
= SV35 ) )
= $false )
| ( ( ( SV56 @ ( s @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( SV56 @ ( s @ zero ) )
= zero )
= $false ) ),
inference(res,[status(thm)],[243,157]) ).
thf(249,plain,
! [SV56: $i > $i,SV34: $i,SV35: $i] :
( ( ( ( ( SV56 @ ( s @ ( s @ zero ) ) )
= zero )
= ( ( ite @ $true @ SV35 @ SV34 )
= SV35 ) )
= $false )
| ( ( ( SV56 @ zero )
= ( s @ zero ) )
= $false )
| ( ( ( SV56 @ ( s @ zero ) )
= zero )
= $false ) ),
inference(res,[status(thm)],[243,157]) ).
thf(250,plain,
! [SV56: $i > $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( SV56 @ ( s @ zero ) )
= zero )
= SV28 )
= $false )
| ( ( ( SV56 @ ( s @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( SV56 @ zero )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= $true ) ),
inference(res,[status(thm)],[243,133]) ).
thf(251,plain,
! [SV56: $i > $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( SV56 @ zero )
= ( s @ zero ) )
= SV28 )
= $false )
| ( ( ( SV56 @ ( s @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( SV56 @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= $true ) ),
inference(res,[status(thm)],[243,133]) ).
thf(252,plain,
! [SV56: $i > $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( SV56 @ ( s @ ( s @ zero ) ) )
= zero )
= SV28 )
= $false )
| ( ( ( SV56 @ zero )
= ( s @ zero ) )
= $false )
| ( ( ( SV56 @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= $true ) ),
inference(res,[status(thm)],[243,133]) ).
thf(253,plain,
! [SV56: $i > $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( SV56 @ ( s @ zero ) )
= zero )
= ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 ) )
= $false )
| ( ( ( SV56 @ ( s @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( SV56 @ zero )
= ( s @ zero ) )
= $false )
| ( SV28 = $true ) ),
inference(res,[status(thm)],[243,133]) ).
thf(254,plain,
! [SV56: $i > $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( SV56 @ zero )
= ( s @ zero ) )
= ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 ) )
= $false )
| ( ( ( SV56 @ ( s @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( SV56 @ ( s @ zero ) )
= zero )
= $false )
| ( SV28 = $true ) ),
inference(res,[status(thm)],[243,133]) ).
thf(255,plain,
! [SV56: $i > $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( SV56 @ ( s @ ( s @ zero ) ) )
= zero )
= ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 ) )
= $false )
| ( ( ( SV56 @ zero )
= ( s @ zero ) )
= $false )
| ( ( ( SV56 @ ( s @ zero ) )
= zero )
= $false )
| ( SV28 = $true ) ),
inference(res,[status(thm)],[243,133]) ).
thf(256,plain,
! [SV56: $i > $i,SV24: $i,SV25: $i] :
( ( ( ( ( SV56 @ ( s @ zero ) )
= zero )
= ( ( ite @ $false @ SV25 @ SV24 )
= SV24 ) )
= $false )
| ( ( ( SV56 @ ( s @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( SV56 @ zero )
= ( s @ zero ) )
= $false ) ),
inference(res,[status(thm)],[243,124]) ).
thf(257,plain,
! [SV56: $i > $i,SV24: $i,SV25: $i] :
( ( ( ( ( SV56 @ zero )
= ( s @ zero ) )
= ( ( ite @ $false @ SV25 @ SV24 )
= SV24 ) )
= $false )
| ( ( ( SV56 @ ( s @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( SV56 @ ( s @ zero ) )
= zero )
= $false ) ),
inference(res,[status(thm)],[243,124]) ).
thf(258,plain,
! [SV56: $i > $i,SV24: $i,SV25: $i] :
( ( ( ( ( SV56 @ ( s @ ( s @ zero ) ) )
= zero )
= ( ( ite @ $false @ SV25 @ SV24 )
= SV24 ) )
= $false )
| ( ( ( SV56 @ zero )
= ( s @ zero ) )
= $false )
| ( ( ( SV56 @ ( s @ zero ) )
= zero )
= $false ) ),
inference(res,[status(thm)],[243,124]) ).
thf(259,plain,
! [SV25: $i] :
( ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( zero
= ( ite @ $false @ SV25 @ ( s @ ( s @ ( s @ zero ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[258:[bind(SV56,$thf( ^ [SX0: $i] : ( s @ SX0 ) )),bind(SV24,$thf( s @ ( s @ ( s @ zero ) ) ))]]) ).
thf(260,plain,
! [SV25: $i] :
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( ite @ $false @ SV25 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[258:[bind(SV56,$thf( ^ [SX0: $i] : ( s @ zero ) )),bind(SV24,$thf( s @ zero ))]]) ).
thf(261,plain,
! [SV25: $i,SV59: $i > $i] :
( ( ( ( s @ ( SV59 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( s @ ( SV59 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ $false @ SV25 @ ( s @ ( SV59 @ ( s @ ( s @ zero ) ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[258:[bind(SV56,$thf( ^ [SX0: $i] : ( s @ ( SV59 @ SX0 ) ) )),bind(SV24,$thf( s @ ( SV59 @ ( s @ ( s @ zero ) ) ) ))]]) ).
thf(262,plain,
! [SV25: $i] :
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ $false @ SV25 @ ( s @ ( s @ zero ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[258:[bind(SV56,$thf( ^ [SX0: $i] : SX0 )),bind(SV24,$thf( s @ ( s @ zero ) ))]]) ).
thf(263,plain,
! [SV66: $i > $i,SV65: $i > $i] :
( ( ( ( ite @ $false @ ( SV65 @ ( s @ zero ) ) @ ( SV66 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ $false @ ( SV65 @ zero ) @ ( SV66 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( SV66 @ ( s @ ( s @ zero ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[258:[bind(SV24,$thf( SV66 @ ( s @ ( s @ zero ) ) )),bind(SV25,$thf( SV65 @ ( s @ ( s @ zero ) ) )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ $false @ ( SV65 @ SX0 ) @ ( SV66 @ SX0 ) ) ))]]) ).
thf(264,plain,
! [SV25: $i,SV66: $i > $i,SV65: $i > $i,SV64: $i > $o] :
( ( ( ( ite @ ( SV64 @ ( s @ zero ) ) @ ( SV65 @ ( s @ zero ) ) @ ( SV66 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV64 @ zero ) @ ( SV65 @ zero ) @ ( SV66 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ ( SV64 @ ( s @ ( s @ zero ) ) ) @ ( SV65 @ ( s @ ( s @ zero ) ) ) @ ( SV66 @ ( s @ ( s @ zero ) ) ) )
= ( ite @ $false @ SV25 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[258:[bind(SV24,$thf( zero )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV64 @ SX0 ) @ ( SV65 @ SX0 ) @ ( SV66 @ SX0 ) ) ))]]) ).
thf(265,plain,
! [SV25: $i] :
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( s @ zero ) )
= ( ite @ $false @ SV25 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[258:[bind(SV24,$thf( zero )),bind(SV56,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(266,plain,
! [SV25: $i] :
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( s @ zero )
= ( ite @ $false @ SV25 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[257:[bind(SV56,$thf( ^ [SX0: $i] : SX0 )),bind(SV24,$thf( zero ))]]) ).
thf(267,plain,
! [SV25: $i] :
( ( ( s @ zero )
= ( ite @ $false @ SV25 @ zero ) )
= $false ),
inference(extuni,[status(esa)],[257:[bind(SV56,$thf( ^ [SX0: $i] : zero )),bind(SV24,$thf( zero ))]]) ).
thf(268,plain,
! [SV75: $i > $i,SV74: $i > $i] :
( ( ( ( ite @ $false @ ( SV74 @ ( s @ zero ) ) @ ( SV75 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ $false @ ( SV74 @ ( s @ ( s @ zero ) ) ) @ ( SV75 @ ( s @ ( s @ zero ) ) ) )
= zero )
= $false )
| ( ( ( s @ zero )
= ( SV75 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[257:[bind(SV24,$thf( SV75 @ zero )),bind(SV25,$thf( SV74 @ zero )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ $false @ ( SV74 @ SX0 ) @ ( SV75 @ SX0 ) ) ))]]) ).
thf(269,plain,
! [SV25: $i,SV75: $i > $i,SV74: $i > $i,SV73: $i > $o] :
( ( ( ( ite @ ( SV73 @ ( s @ zero ) ) @ ( SV74 @ ( s @ zero ) ) @ ( SV75 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV73 @ ( s @ ( s @ zero ) ) ) @ ( SV74 @ ( s @ ( s @ zero ) ) ) @ ( SV75 @ ( s @ ( s @ zero ) ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV73 @ zero ) @ ( SV74 @ zero ) @ ( SV75 @ zero ) )
= ( ite @ $false @ SV25 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[257:[bind(SV24,$thf( s @ zero )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV73 @ SX0 ) @ ( SV74 @ SX0 ) @ ( SV75 @ SX0 ) ) ))]]) ).
thf(270,plain,
! [SV25: $i] :
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( zero
= ( ite @ $false @ SV25 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[257:[bind(SV24,$thf( s @ zero )),bind(SV56,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(271,plain,
! [SV25: $i] :
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( zero
= ( ite @ $false @ SV25 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[256:[bind(SV56,$thf( ^ [SX0: $i] : SX0 )),bind(SV24,$thf( s @ zero ))]]) ).
thf(272,plain,
! [SV25: $i] :
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ $false @ SV25 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[256:[bind(SV56,$thf( ^ [SX0: $i] : zero )),bind(SV24,$thf( zero ))]]) ).
thf(273,plain,
! [SV84: $i > $i,SV83: $i > $i] :
( ( ( ( ite @ $false @ ( SV83 @ zero ) @ ( SV84 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ $false @ ( SV83 @ ( s @ ( s @ zero ) ) ) @ ( SV84 @ ( s @ ( s @ zero ) ) ) )
= zero )
= $false )
| ( ( zero
= ( SV84 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[256:[bind(SV24,$thf( SV84 @ ( s @ zero ) )),bind(SV25,$thf( SV83 @ ( s @ zero ) )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ $false @ ( SV83 @ SX0 ) @ ( SV84 @ SX0 ) ) ))]]) ).
thf(274,plain,
! [SV25: $i,SV84: $i > $i,SV83: $i > $i,SV82: $i > $o] :
( ( ( ( ite @ ( SV82 @ zero ) @ ( SV83 @ zero ) @ ( SV84 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ ( SV82 @ ( s @ ( s @ zero ) ) ) @ ( SV83 @ ( s @ ( s @ zero ) ) ) @ ( SV84 @ ( s @ ( s @ zero ) ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV82 @ ( s @ zero ) ) @ ( SV83 @ ( s @ zero ) ) @ ( SV84 @ ( s @ zero ) ) )
= ( ite @ $false @ SV25 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[256:[bind(SV24,$thf( zero )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV82 @ SX0 ) @ ( SV83 @ SX0 ) @ ( SV84 @ SX0 ) ) ))]]) ).
thf(275,plain,
! [SV25: $i] :
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( s @ zero )
= ( ite @ $false @ SV25 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[256:[bind(SV24,$thf( zero )),bind(SV56,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(276,plain,
! [SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( zero
= ( ite @ SV28 @ SV27 @ ( s @ ( s @ ( s @ zero ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[255:[bind(SV56,$thf( ^ [SX0: $i] : ( s @ SX0 ) )),bind(SV26,$thf( s @ ( s @ ( s @ zero ) ) ))]]) ).
thf(277,plain,
! [SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( ite @ SV28 @ SV27 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[255:[bind(SV56,$thf( ^ [SX0: $i] : ( s @ zero ) )),bind(SV26,$thf( s @ zero ))]]) ).
thf(278,plain,
! [SV27: $i,SV89: $i > $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( s @ ( SV89 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( s @ ( SV89 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ SV28 @ SV27 @ ( s @ ( SV89 @ ( s @ ( s @ zero ) ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[255:[bind(SV56,$thf( ^ [SX0: $i] : ( s @ ( SV89 @ SX0 ) ) )),bind(SV26,$thf( s @ ( SV89 @ ( s @ ( s @ zero ) ) ) ))]]) ).
thf(279,plain,
! [SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ SV28 @ SV27 @ ( s @ ( s @ zero ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[255:[bind(SV56,$thf( ^ [SX0: $i] : SX0 )),bind(SV26,$thf( s @ ( s @ zero ) ))]]) ).
thf(280,plain,
! [SV96: $i > $i,SV95: $i > $i,SV94: $i > $o] :
( ( ( SV94 @ ( s @ ( s @ zero ) ) )
= $true )
| ( ( ( ite @ ( SV94 @ ( s @ zero ) ) @ ( SV95 @ ( s @ zero ) ) @ ( SV96 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV94 @ zero ) @ ( SV95 @ zero ) @ ( SV96 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( SV96 @ ( s @ ( s @ zero ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[255:[bind(SV26,$thf( SV96 @ ( s @ ( s @ zero ) ) )),bind(SV27,$thf( SV95 @ ( s @ ( s @ zero ) ) )),bind(SV28,$thf( SV94 @ ( s @ ( s @ zero ) ) )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV94 @ SX0 ) @ ( SV95 @ SX0 ) @ ( SV96 @ SX0 ) ) ))]]) ).
thf(281,plain,
! [SV27: $i,SV96: $i > $i,SV95: $i > $i,SV94: $i > $o,SV28: $o] :
( ( SV28 = $true )
| ( ( ( ite @ ( SV94 @ ( s @ zero ) ) @ ( SV95 @ ( s @ zero ) ) @ ( SV96 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV94 @ zero ) @ ( SV95 @ zero ) @ ( SV96 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ ( SV94 @ ( s @ ( s @ zero ) ) ) @ ( SV95 @ ( s @ ( s @ zero ) ) ) @ ( SV96 @ ( s @ ( s @ zero ) ) ) )
= ( ite @ SV28 @ SV27 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[255:[bind(SV26,$thf( zero )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV94 @ SX0 ) @ ( SV95 @ SX0 ) @ ( SV96 @ SX0 ) ) ))]]) ).
thf(282,plain,
! [SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( s @ zero ) )
= ( ite @ SV28 @ SV27 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[255:[bind(SV26,$thf( zero )),bind(SV56,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(283,plain,
! [SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( s @ zero )
= zero )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( s @ zero )
= ( ite @ SV28 @ SV27 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[254:[bind(SV56,$thf( ^ [SX0: $i] : SX0 )),bind(SV26,$thf( zero ))]]) ).
thf(284,plain,
! [SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( s @ zero )
= ( ite @ SV28 @ SV27 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[254:[bind(SV56,$thf( ^ [SX0: $i] : zero )),bind(SV26,$thf( zero ))]]) ).
thf(285,plain,
! [SV103: $i > $i,SV102: $i > $i,SV101: $i > $o] :
( ( ( SV101 @ zero )
= $true )
| ( ( ( ite @ ( SV101 @ ( s @ zero ) ) @ ( SV102 @ ( s @ zero ) ) @ ( SV103 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV101 @ ( s @ ( s @ zero ) ) ) @ ( SV102 @ ( s @ ( s @ zero ) ) ) @ ( SV103 @ ( s @ ( s @ zero ) ) ) )
= zero )
= $false )
| ( ( ( s @ zero )
= ( SV103 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[254:[bind(SV26,$thf( SV103 @ zero )),bind(SV27,$thf( SV102 @ zero )),bind(SV28,$thf( SV101 @ zero )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV101 @ SX0 ) @ ( SV102 @ SX0 ) @ ( SV103 @ SX0 ) ) ))]]) ).
thf(286,plain,
! [SV27: $i,SV103: $i > $i,SV102: $i > $i,SV101: $i > $o,SV28: $o] :
( ( SV28 = $true )
| ( ( ( ite @ ( SV101 @ ( s @ zero ) ) @ ( SV102 @ ( s @ zero ) ) @ ( SV103 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV101 @ ( s @ ( s @ zero ) ) ) @ ( SV102 @ ( s @ ( s @ zero ) ) ) @ ( SV103 @ ( s @ ( s @ zero ) ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV101 @ zero ) @ ( SV102 @ zero ) @ ( SV103 @ zero ) )
= ( ite @ SV28 @ SV27 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[254:[bind(SV26,$thf( s @ zero )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV101 @ SX0 ) @ ( SV102 @ SX0 ) @ ( SV103 @ SX0 ) ) ))]]) ).
thf(287,plain,
! [SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( s @ zero )
= zero )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( zero
= ( ite @ SV28 @ SV27 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[254:[bind(SV26,$thf( s @ zero )),bind(SV56,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(288,plain,
! [SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( zero
= ( ite @ SV28 @ SV27 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[253:[bind(SV56,$thf( ^ [SX0: $i] : SX0 )),bind(SV26,$thf( s @ zero ))]]) ).
thf(289,plain,
! [SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ SV28 @ SV27 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[253:[bind(SV56,$thf( ^ [SX0: $i] : zero )),bind(SV26,$thf( zero ))]]) ).
thf(290,plain,
! [SV110: $i > $i,SV109: $i > $i,SV108: $i > $o] :
( ( ( SV108 @ ( s @ zero ) )
= $true )
| ( ( ( ite @ ( SV108 @ zero ) @ ( SV109 @ zero ) @ ( SV110 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ ( SV108 @ ( s @ ( s @ zero ) ) ) @ ( SV109 @ ( s @ ( s @ zero ) ) ) @ ( SV110 @ ( s @ ( s @ zero ) ) ) )
= zero )
= $false )
| ( ( zero
= ( SV110 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[253:[bind(SV26,$thf( SV110 @ ( s @ zero ) )),bind(SV27,$thf( SV109 @ ( s @ zero ) )),bind(SV28,$thf( SV108 @ ( s @ zero ) )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV108 @ SX0 ) @ ( SV109 @ SX0 ) @ ( SV110 @ SX0 ) ) ))]]) ).
thf(291,plain,
! [SV27: $i,SV110: $i > $i,SV109: $i > $i,SV108: $i > $o,SV28: $o] :
( ( SV28 = $true )
| ( ( ( ite @ ( SV108 @ zero ) @ ( SV109 @ zero ) @ ( SV110 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ ( SV108 @ ( s @ ( s @ zero ) ) ) @ ( SV109 @ ( s @ ( s @ zero ) ) ) @ ( SV110 @ ( s @ ( s @ zero ) ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV108 @ ( s @ zero ) ) @ ( SV109 @ ( s @ zero ) ) @ ( SV110 @ ( s @ zero ) ) )
= ( ite @ SV28 @ SV27 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[253:[bind(SV26,$thf( zero )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV108 @ SX0 ) @ ( SV109 @ SX0 ) @ ( SV110 @ SX0 ) ) ))]]) ).
thf(292,plain,
! [SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( s @ zero )
= ( ite @ SV28 @ SV27 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[253:[bind(SV26,$thf( zero )),bind(SV56,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(293,plain,
! [SV26: $i,SV27: $i] :
( ( ( ( ite
@ ( ( s @ ( s @ ( s @ zero ) ) )
= zero )
@ SV27
@ SV26 )
= SV26 )
= $true )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[252:[bind(SV56,$thf( ^ [SX0: $i] : ( s @ SX0 ) )),bind(SV28,$thf( ( s @ ( s @ ( s @ zero ) ) ) = zero ))]]) ).
thf(294,plain,
! [SV26: $i,SV27: $i] :
( ( ( ( ite
@ ( ( s @ zero )
= zero )
@ SV27
@ SV26 )
= SV26 )
= $true )
| ( ( ( s @ zero )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[252:[bind(SV56,$thf( ^ [SX0: $i] : ( s @ zero ) )),bind(SV28,$thf( ( s @ zero ) = zero ))]]) ).
thf(295,plain,
! [SV26: $i,SV27: $i,SV113: $i > $i] :
( ( ( ( ite
@ ( ( s @ ( SV113 @ ( s @ ( s @ zero ) ) ) )
= zero )
@ SV27
@ SV26 )
= SV26 )
= $true )
| ( ( ( s @ ( SV113 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( s @ ( SV113 @ zero ) )
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[252:[bind(SV56,$thf( ^ [SX0: $i] : ( s @ ( SV113 @ SX0 ) ) )),bind(SV28,$thf( ( s @ ( SV113 @ ( s @ ( s @ zero ) ) ) ) = zero ))]]) ).
thf(296,plain,
! [SV26: $i,SV27: $i] :
( ( ( ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ SV27
@ SV26 )
= SV26 )
= $true )
| ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[252:[bind(SV56,$thf( ^ [SX0: $i] : SX0 )),bind(SV28,$thf( ( s @ ( s @ zero ) ) = zero ))]]) ).
thf(297,plain,
! [SV26: $i,SV27: $i] :
( ( ( ( ite
@ ( zero
= ( s @ zero ) )
@ SV27
@ SV26 )
= SV26 )
= $true )
| ( ( ( s @ zero )
= zero )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[251:[bind(SV56,$thf( ^ [SX0: $i] : SX0 )),bind(SV28,$thf( zero = ( s @ zero ) ))]]) ).
thf(298,plain,
! [SV26: $i,SV27: $i] :
( ( ( ite
@ ( zero
= ( s @ zero ) )
@ SV27
@ SV26 )
= SV26 )
= $true ),
inference(extuni,[status(esa)],[251:[bind(SV56,$thf( ^ [SX0: $i] : zero )),bind(SV28,$thf( zero = ( s @ zero ) ))]]) ).
thf(299,plain,
! [SV26: $i,SV27: $i] :
( ( ( ( ite
@ ( ( s @ zero )
= zero )
@ SV27
@ SV26 )
= SV26 )
= $true )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[250:[bind(SV56,$thf( ^ [SX0: $i] : SX0 )),bind(SV28,$thf( ( s @ zero ) = zero ))]]) ).
thf(300,plain,
! [SV26: $i,SV27: $i] :
( ( ( ( ite @ ( zero = zero ) @ SV27 @ SV26 )
= SV26 )
= $true )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[250:[bind(SV56,$thf( ^ [SX0: $i] : zero )),bind(SV28,$thf( zero = zero ))]]) ).
thf(301,plain,
! [SV34: $i] :
( ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( zero
= ( ite @ $true @ ( s @ ( s @ ( s @ zero ) ) ) @ SV34 ) )
= $false ) ),
inference(extuni,[status(esa)],[249:[bind(SV56,$thf( ^ [SX0: $i] : ( s @ SX0 ) )),bind(SV35,$thf( s @ ( s @ ( s @ zero ) ) ))]]) ).
thf(302,plain,
! [SV34: $i] :
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( ite @ $true @ ( s @ zero ) @ SV34 ) )
= $false ) ),
inference(extuni,[status(esa)],[249:[bind(SV56,$thf( ^ [SX0: $i] : ( s @ zero ) )),bind(SV35,$thf( s @ zero ))]]) ).
thf(303,plain,
! [SV34: $i,SV122: $i > $i] :
( ( ( ( s @ ( SV122 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( s @ ( SV122 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ $true @ ( s @ ( SV122 @ ( s @ ( s @ zero ) ) ) ) @ SV34 ) )
= $false ) ),
inference(extuni,[status(esa)],[249:[bind(SV56,$thf( ^ [SX0: $i] : ( s @ ( SV122 @ SX0 ) ) )),bind(SV35,$thf( s @ ( SV122 @ ( s @ ( s @ zero ) ) ) ))]]) ).
thf(304,plain,
! [SV34: $i] :
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ $true @ ( s @ ( s @ zero ) ) @ SV34 ) )
= $false ) ),
inference(extuni,[status(esa)],[249:[bind(SV56,$thf( ^ [SX0: $i] : SX0 )),bind(SV35,$thf( s @ ( s @ zero ) ))]]) ).
thf(305,plain,
! [SV129: $i > $i,SV128: $i > $i] :
( ( ( ( ite @ $true @ ( SV128 @ ( s @ zero ) ) @ ( SV129 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ $true @ ( SV128 @ zero ) @ ( SV129 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( SV128 @ ( s @ ( s @ zero ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[249:[bind(SV34,$thf( SV129 @ ( s @ ( s @ zero ) ) )),bind(SV35,$thf( SV128 @ ( s @ ( s @ zero ) ) )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ $true @ ( SV128 @ SX0 ) @ ( SV129 @ SX0 ) ) ))]]) ).
thf(306,plain,
! [SV34: $i,SV129: $i > $i,SV128: $i > $i,SV127: $i > $o] :
( ( ( ( ite @ ( SV127 @ ( s @ zero ) ) @ ( SV128 @ ( s @ zero ) ) @ ( SV129 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV127 @ zero ) @ ( SV128 @ zero ) @ ( SV129 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ ( SV127 @ ( s @ ( s @ zero ) ) ) @ ( SV128 @ ( s @ ( s @ zero ) ) ) @ ( SV129 @ ( s @ ( s @ zero ) ) ) )
= ( ite @ $true @ zero @ SV34 ) )
= $false ) ),
inference(extuni,[status(esa)],[249:[bind(SV35,$thf( zero )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV127 @ SX0 ) @ ( SV128 @ SX0 ) @ ( SV129 @ SX0 ) ) ))]]) ).
thf(307,plain,
! [SV34: $i] :
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( s @ zero ) )
= ( ite @ $true @ zero @ SV34 ) )
= $false ) ),
inference(extuni,[status(esa)],[249:[bind(SV35,$thf( zero )),bind(SV56,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(308,plain,
! [SV34: $i] :
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( s @ zero )
= ( ite @ $true @ zero @ SV34 ) )
= $false ) ),
inference(extuni,[status(esa)],[248:[bind(SV56,$thf( ^ [SX0: $i] : SX0 )),bind(SV35,$thf( zero ))]]) ).
thf(309,plain,
! [SV34: $i] :
( ( ( s @ zero )
= ( ite @ $true @ zero @ SV34 ) )
= $false ),
inference(extuni,[status(esa)],[248:[bind(SV56,$thf( ^ [SX0: $i] : zero )),bind(SV35,$thf( zero ))]]) ).
thf(310,plain,
! [SV138: $i > $i,SV137: $i > $i] :
( ( ( ( ite @ $true @ ( SV137 @ ( s @ zero ) ) @ ( SV138 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ $true @ ( SV137 @ ( s @ ( s @ zero ) ) ) @ ( SV138 @ ( s @ ( s @ zero ) ) ) )
= zero )
= $false )
| ( ( ( s @ zero )
= ( SV137 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[248:[bind(SV34,$thf( SV138 @ zero )),bind(SV35,$thf( SV137 @ zero )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ $true @ ( SV137 @ SX0 ) @ ( SV138 @ SX0 ) ) ))]]) ).
thf(311,plain,
! [SV34: $i,SV138: $i > $i,SV137: $i > $i,SV136: $i > $o] :
( ( ( ( ite @ ( SV136 @ ( s @ zero ) ) @ ( SV137 @ ( s @ zero ) ) @ ( SV138 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV136 @ ( s @ ( s @ zero ) ) ) @ ( SV137 @ ( s @ ( s @ zero ) ) ) @ ( SV138 @ ( s @ ( s @ zero ) ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV136 @ zero ) @ ( SV137 @ zero ) @ ( SV138 @ zero ) )
= ( ite @ $true @ ( s @ zero ) @ SV34 ) )
= $false ) ),
inference(extuni,[status(esa)],[248:[bind(SV35,$thf( s @ zero )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV136 @ SX0 ) @ ( SV137 @ SX0 ) @ ( SV138 @ SX0 ) ) ))]]) ).
thf(312,plain,
! [SV34: $i] :
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( zero
= ( ite @ $true @ ( s @ zero ) @ SV34 ) )
= $false ) ),
inference(extuni,[status(esa)],[248:[bind(SV35,$thf( s @ zero )),bind(SV56,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(313,plain,
! [SV34: $i] :
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( zero
= ( ite @ $true @ ( s @ zero ) @ SV34 ) )
= $false ) ),
inference(extuni,[status(esa)],[247:[bind(SV56,$thf( ^ [SX0: $i] : SX0 )),bind(SV35,$thf( s @ zero ))]]) ).
thf(314,plain,
! [SV34: $i] :
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ $true @ zero @ SV34 ) )
= $false ) ),
inference(extuni,[status(esa)],[247:[bind(SV56,$thf( ^ [SX0: $i] : zero )),bind(SV35,$thf( zero ))]]) ).
thf(315,plain,
! [SV147: $i > $i,SV146: $i > $i] :
( ( ( ( ite @ $true @ ( SV146 @ zero ) @ ( SV147 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ $true @ ( SV146 @ ( s @ ( s @ zero ) ) ) @ ( SV147 @ ( s @ ( s @ zero ) ) ) )
= zero )
= $false )
| ( ( zero
= ( SV146 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[247:[bind(SV34,$thf( SV147 @ ( s @ zero ) )),bind(SV35,$thf( SV146 @ ( s @ zero ) )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ $true @ ( SV146 @ SX0 ) @ ( SV147 @ SX0 ) ) ))]]) ).
thf(316,plain,
! [SV34: $i,SV147: $i > $i,SV146: $i > $i,SV145: $i > $o] :
( ( ( ( ite @ ( SV145 @ zero ) @ ( SV146 @ zero ) @ ( SV147 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ ( SV145 @ ( s @ ( s @ zero ) ) ) @ ( SV146 @ ( s @ ( s @ zero ) ) ) @ ( SV147 @ ( s @ ( s @ zero ) ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV145 @ ( s @ zero ) ) @ ( SV146 @ ( s @ zero ) ) @ ( SV147 @ ( s @ zero ) ) )
= ( ite @ $true @ zero @ SV34 ) )
= $false ) ),
inference(extuni,[status(esa)],[247:[bind(SV35,$thf( zero )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV145 @ SX0 ) @ ( SV146 @ SX0 ) @ ( SV147 @ SX0 ) ) ))]]) ).
thf(317,plain,
! [SV34: $i] :
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( s @ zero )
= ( ite @ $true @ zero @ SV34 ) )
= $false ) ),
inference(extuni,[status(esa)],[247:[bind(SV35,$thf( zero )),bind(SV56,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(318,plain,
! [SV42: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( zero
= ( ite @ SV44 @ ( s @ ( s @ ( s @ zero ) ) ) @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[246:[bind(SV56,$thf( ^ [SX0: $i] : ( s @ SX0 ) )),bind(SV43,$thf( s @ ( s @ ( s @ zero ) ) ))]]) ).
thf(319,plain,
! [SV42: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( ite @ SV44 @ ( s @ zero ) @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[246:[bind(SV56,$thf( ^ [SX0: $i] : ( s @ zero ) )),bind(SV43,$thf( s @ zero ))]]) ).
thf(320,plain,
! [SV42: $i,SV152: $i > $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( s @ ( SV152 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( s @ ( SV152 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ SV44 @ ( s @ ( SV152 @ ( s @ ( s @ zero ) ) ) ) @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[246:[bind(SV56,$thf( ^ [SX0: $i] : ( s @ ( SV152 @ SX0 ) ) )),bind(SV43,$thf( s @ ( SV152 @ ( s @ ( s @ zero ) ) ) ))]]) ).
thf(321,plain,
! [SV42: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ SV44 @ ( s @ ( s @ zero ) ) @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[246:[bind(SV56,$thf( ^ [SX0: $i] : SX0 )),bind(SV43,$thf( s @ ( s @ zero ) ))]]) ).
thf(322,plain,
! [SV159: $i > $i,SV158: $i > $i,SV157: $i > $o] :
( ( ( SV157 @ ( s @ ( s @ zero ) ) )
= $false )
| ( ( ( ite @ ( SV157 @ ( s @ zero ) ) @ ( SV158 @ ( s @ zero ) ) @ ( SV159 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV157 @ zero ) @ ( SV158 @ zero ) @ ( SV159 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( SV158 @ ( s @ ( s @ zero ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[246:[bind(SV42,$thf( SV159 @ ( s @ ( s @ zero ) ) )),bind(SV43,$thf( SV158 @ ( s @ ( s @ zero ) ) )),bind(SV44,$thf( SV157 @ ( s @ ( s @ zero ) ) )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV157 @ SX0 ) @ ( SV158 @ SX0 ) @ ( SV159 @ SX0 ) ) ))]]) ).
thf(323,plain,
! [SV42: $i,SV159: $i > $i,SV158: $i > $i,SV157: $i > $o,SV44: $o] :
( ( SV44 = $false )
| ( ( ( ite @ ( SV157 @ ( s @ zero ) ) @ ( SV158 @ ( s @ zero ) ) @ ( SV159 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV157 @ zero ) @ ( SV158 @ zero ) @ ( SV159 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ ( SV157 @ ( s @ ( s @ zero ) ) ) @ ( SV158 @ ( s @ ( s @ zero ) ) ) @ ( SV159 @ ( s @ ( s @ zero ) ) ) )
= ( ite @ SV44 @ zero @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[246:[bind(SV43,$thf( zero )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV157 @ SX0 ) @ ( SV158 @ SX0 ) @ ( SV159 @ SX0 ) ) ))]]) ).
thf(324,plain,
! [SV42: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( s @ zero ) )
= ( ite @ SV44 @ zero @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[246:[bind(SV43,$thf( zero )),bind(SV56,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(325,plain,
! [SV42: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( s @ zero )
= zero )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( s @ zero )
= ( ite @ SV44 @ zero @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[245:[bind(SV56,$thf( ^ [SX0: $i] : SX0 )),bind(SV43,$thf( zero ))]]) ).
thf(326,plain,
! [SV42: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( s @ zero )
= ( ite @ SV44 @ zero @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[245:[bind(SV56,$thf( ^ [SX0: $i] : zero )),bind(SV43,$thf( zero ))]]) ).
thf(327,plain,
! [SV166: $i > $i,SV165: $i > $i,SV164: $i > $o] :
( ( ( SV164 @ zero )
= $false )
| ( ( ( ite @ ( SV164 @ ( s @ zero ) ) @ ( SV165 @ ( s @ zero ) ) @ ( SV166 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV164 @ ( s @ ( s @ zero ) ) ) @ ( SV165 @ ( s @ ( s @ zero ) ) ) @ ( SV166 @ ( s @ ( s @ zero ) ) ) )
= zero )
= $false )
| ( ( ( s @ zero )
= ( SV165 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[245:[bind(SV42,$thf( SV166 @ zero )),bind(SV43,$thf( SV165 @ zero )),bind(SV44,$thf( SV164 @ zero )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV164 @ SX0 ) @ ( SV165 @ SX0 ) @ ( SV166 @ SX0 ) ) ))]]) ).
thf(328,plain,
! [SV42: $i,SV166: $i > $i,SV165: $i > $i,SV164: $i > $o,SV44: $o] :
( ( SV44 = $false )
| ( ( ( ite @ ( SV164 @ ( s @ zero ) ) @ ( SV165 @ ( s @ zero ) ) @ ( SV166 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV164 @ ( s @ ( s @ zero ) ) ) @ ( SV165 @ ( s @ ( s @ zero ) ) ) @ ( SV166 @ ( s @ ( s @ zero ) ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV164 @ zero ) @ ( SV165 @ zero ) @ ( SV166 @ zero ) )
= ( ite @ SV44 @ ( s @ zero ) @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[245:[bind(SV43,$thf( s @ zero )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV164 @ SX0 ) @ ( SV165 @ SX0 ) @ ( SV166 @ SX0 ) ) ))]]) ).
thf(329,plain,
! [SV42: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( s @ zero )
= zero )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( zero
= ( ite @ SV44 @ ( s @ zero ) @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[245:[bind(SV43,$thf( s @ zero )),bind(SV56,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(330,plain,
! [SV42: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( zero
= ( ite @ SV44 @ ( s @ zero ) @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[244:[bind(SV56,$thf( ^ [SX0: $i] : SX0 )),bind(SV43,$thf( s @ zero ))]]) ).
thf(331,plain,
! [SV42: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ SV44 @ zero @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[244:[bind(SV56,$thf( ^ [SX0: $i] : zero )),bind(SV43,$thf( zero ))]]) ).
thf(332,plain,
! [SV173: $i > $i,SV172: $i > $i,SV171: $i > $o] :
( ( ( SV171 @ ( s @ zero ) )
= $false )
| ( ( ( ite @ ( SV171 @ zero ) @ ( SV172 @ zero ) @ ( SV173 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ ( SV171 @ ( s @ ( s @ zero ) ) ) @ ( SV172 @ ( s @ ( s @ zero ) ) ) @ ( SV173 @ ( s @ ( s @ zero ) ) ) )
= zero )
= $false )
| ( ( zero
= ( SV172 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[244:[bind(SV42,$thf( SV173 @ ( s @ zero ) )),bind(SV43,$thf( SV172 @ ( s @ zero ) )),bind(SV44,$thf( SV171 @ ( s @ zero ) )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV171 @ SX0 ) @ ( SV172 @ SX0 ) @ ( SV173 @ SX0 ) ) ))]]) ).
thf(333,plain,
! [SV42: $i,SV173: $i > $i,SV172: $i > $i,SV171: $i > $o,SV44: $o] :
( ( SV44 = $false )
| ( ( ( ite @ ( SV171 @ zero ) @ ( SV172 @ zero ) @ ( SV173 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ ( SV171 @ ( s @ ( s @ zero ) ) ) @ ( SV172 @ ( s @ ( s @ zero ) ) ) @ ( SV173 @ ( s @ ( s @ zero ) ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV171 @ ( s @ zero ) ) @ ( SV172 @ ( s @ zero ) ) @ ( SV173 @ ( s @ zero ) ) )
= ( ite @ SV44 @ zero @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[244:[bind(SV43,$thf( zero )),bind(SV56,$thf( ^ [SX0: $i] : ( ite @ ( SV171 @ SX0 ) @ ( SV172 @ SX0 ) @ ( SV173 @ SX0 ) ) ))]]) ).
thf(334,plain,
! [SV42: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( s @ zero )
= ( ite @ SV44 @ zero @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[244:[bind(SV43,$thf( zero )),bind(SV56,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(335,plain,
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( s @ zero ) )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[243:[bind(SV56,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(336,plain,
( ( zero
= ( s @ zero ) )
= $false ),
inference(extuni,[status(esa)],[243:[bind(SV56,$thf( ^ [SX0: $i] : zero ))]]) ).
thf(337,plain,
! [SV176: $i,SV177: $i] :
( ( ( ite @ $false @ SV177 @ SV176 )
= ( s @ SV176 ) )
= $false ),
inference(rename,[status(thm)],[130]) ).
thf(338,plain,
! [SV176: $i,SV177: $i,SV42: $i,SV43: $i,SV44: $o] :
( ( ( ( ( ite @ $false @ SV177 @ SV176 )
= ( s @ SV176 ) )
= ( ( ite @ SV44 @ SV43 @ SV42 )
= SV43 ) )
= $false )
| ( SV44 = $false ) ),
inference(res,[status(thm)],[337,169]) ).
thf(339,plain,
! [SV176: $i,SV177: $i,SV34: $i,SV35: $i] :
( ( ( ( ite @ $false @ SV177 @ SV176 )
= ( s @ SV176 ) )
= ( ( ite @ $true @ SV35 @ SV34 )
= SV35 ) )
= $false ),
inference(res,[status(thm)],[337,157]) ).
thf(340,plain,
! [SV176: $i,SV177: $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( ite @ $false @ SV177 @ SV176 )
= ( s @ SV176 ) )
= SV28 )
= $false )
| ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= $true ) ),
inference(res,[status(thm)],[337,133]) ).
thf(341,plain,
! [SV176: $i,SV177: $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( ite @ $false @ SV177 @ SV176 )
= ( s @ SV176 ) )
= ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 ) )
= $false )
| ( SV28 = $true ) ),
inference(res,[status(thm)],[337,133]) ).
thf(342,plain,
! [SV176: $i,SV177: $i,SV24: $i,SV25: $i] :
( ( ( ( ite @ $false @ SV177 @ SV176 )
= ( s @ SV176 ) )
= ( ( ite @ $false @ SV25 @ SV24 )
= SV24 ) )
= $false ),
inference(res,[status(thm)],[337,124]) ).
thf(343,plain,
! [SV177: $i,SV25: $i,SV176: $i] :
( ( ( s @ SV176 )
= ( ite @ $false @ SV25 @ ( ite @ $false @ SV177 @ SV176 ) ) )
= $false ),
inference(extuni,[status(esa)],[342:[bind(SV24,$thf( ite @ $false @ SV177 @ SV176 ))]]) ).
thf(344,plain,
! [SV25: $i,SV176: $i,SV177: $i] :
( ( ( ite @ $false @ SV177 @ SV176 )
= ( ite @ $false @ SV25 @ ( s @ SV176 ) ) )
= $false ),
inference(extuni,[status(esa)],[342:[bind(SV24,$thf( s @ SV176 ))]]) ).
thf(345,plain,
! [SV177: $i,SV27: $i,SV176: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( s @ SV176 )
= ( ite @ SV28 @ SV27 @ ( ite @ $false @ SV177 @ SV176 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[341:[bind(SV26,$thf( ite @ $false @ SV177 @ SV176 ))]]) ).
thf(346,plain,
! [SV27: $i,SV176: $i,SV177: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( ite @ $false @ SV177 @ SV176 )
= ( ite @ SV28 @ SV27 @ ( s @ SV176 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[341:[bind(SV26,$thf( s @ SV176 ))]]) ).
thf(347,plain,
! [SV26: $i,SV27: $i,SV176: $i,SV177: $i] :
( ( ( ite
@ ( ( ite @ $false @ SV177 @ SV176 )
= ( s @ SV176 ) )
@ SV27
@ SV26 )
= SV26 )
= $true ),
inference(extuni,[status(esa)],[340:[bind(SV28,$thf( ( ite @ $false @ SV177 @ SV176 ) = ( s @ SV176 ) ))]]) ).
thf(348,plain,
! [SV34: $i,SV177: $i,SV176: $i] :
( ( ( s @ SV176 )
= ( ite @ $true @ ( ite @ $false @ SV177 @ SV176 ) @ SV34 ) )
= $false ),
inference(extuni,[status(esa)],[339:[bind(SV35,$thf( ite @ $false @ SV177 @ SV176 ))]]) ).
thf(351,plain,
! [SV34: $i,SV176: $i,SV177: $i] :
( ( ( ite @ $false @ SV177 @ SV176 )
= ( ite @ $true @ ( s @ SV176 ) @ SV34 ) )
= $false ),
inference(extuni,[status(esa)],[339:[bind(SV35,$thf( s @ SV176 ))]]) ).
thf(352,plain,
! [SV42: $i,SV177: $i,SV176: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( s @ SV176 )
= ( ite @ SV44 @ ( ite @ $false @ SV177 @ SV176 ) @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[338:[bind(SV43,$thf( ite @ $false @ SV177 @ SV176 ))]]) ).
thf(354,plain,
! [SV42: $i,SV176: $i,SV177: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( ite @ $false @ SV177 @ SV176 )
= ( ite @ SV44 @ ( s @ SV176 ) @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[338:[bind(SV43,$thf( s @ SV176 ))]]) ).
thf(355,plain,
! [SV178: $i,SV179: $i] :
( ( ( ite @ $false @ SV179 @ ( s @ SV178 ) )
= zero )
= $false ),
inference(rename,[status(thm)],[131]) ).
thf(356,plain,
! [SV178: $i,SV179: $i,SV42: $i,SV43: $i,SV44: $o] :
( ( ( ( ( ite @ $false @ SV179 @ ( s @ SV178 ) )
= zero )
= ( ( ite @ SV44 @ SV43 @ SV42 )
= SV43 ) )
= $false )
| ( SV44 = $false ) ),
inference(res,[status(thm)],[355,169]) ).
thf(357,plain,
! [SV178: $i,SV179: $i,SV34: $i,SV35: $i] :
( ( ( ( ite @ $false @ SV179 @ ( s @ SV178 ) )
= zero )
= ( ( ite @ $true @ SV35 @ SV34 )
= SV35 ) )
= $false ),
inference(res,[status(thm)],[355,157]) ).
thf(358,plain,
! [SV178: $i,SV179: $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( ite @ $false @ SV179 @ ( s @ SV178 ) )
= zero )
= SV28 )
= $false )
| ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= $true ) ),
inference(res,[status(thm)],[355,133]) ).
thf(359,plain,
! [SV178: $i,SV179: $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( ite @ $false @ SV179 @ ( s @ SV178 ) )
= zero )
= ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 ) )
= $false )
| ( SV28 = $true ) ),
inference(res,[status(thm)],[355,133]) ).
thf(360,plain,
! [SV178: $i,SV179: $i,SV24: $i,SV25: $i] :
( ( ( ( ite @ $false @ SV179 @ ( s @ SV178 ) )
= zero )
= ( ( ite @ $false @ SV25 @ SV24 )
= SV24 ) )
= $false ),
inference(res,[status(thm)],[355,124]) ).
thf(361,plain,
! [SV178: $i,SV179: $i,SV25: $i] :
( ( zero
= ( ite @ $false @ SV25 @ ( ite @ $false @ SV179 @ ( s @ SV178 ) ) ) )
= $false ),
inference(extuni,[status(esa)],[360:[bind(SV24,$thf( ite @ $false @ SV179 @ ( s @ SV178 ) ))]]) ).
thf(362,plain,
! [SV178: $i] :
( ( zero
= ( s @ SV178 ) )
= $false ),
inference(extuni,[status(esa)],[360:[bind(SV24,$thf( s @ SV178 )),bind(SV179,$thf( SV25 ))]]) ).
thf(363,plain,
! [SV25: $i,SV178: $i,SV179: $i] :
( ( ( ite @ $false @ SV179 @ ( s @ SV178 ) )
= ( ite @ $false @ SV25 @ zero ) )
= $false ),
inference(extuni,[status(esa)],[360:[bind(SV24,$thf( zero ))]]) ).
thf(364,plain,
! [SV178: $i,SV179: $i,SV27: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( zero
= ( ite @ SV28 @ SV27 @ ( ite @ $false @ SV179 @ ( s @ SV178 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[359:[bind(SV26,$thf( ite @ $false @ SV179 @ ( s @ SV178 ) ))]]) ).
thf(365,plain,
! [SV178: $i] :
( ( $false = $true )
| ( ( zero
= ( s @ SV178 ) )
= $false ) ),
inference(extuni,[status(esa)],[359:[bind(SV26,$thf( s @ SV178 )),bind(SV179,$thf( SV27 )),bind(SV28,$thf( $false ))]]) ).
thf(366,plain,
! [SV27: $i,SV178: $i,SV179: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( ite @ $false @ SV179 @ ( s @ SV178 ) )
= ( ite @ SV28 @ SV27 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[359:[bind(SV26,$thf( zero ))]]) ).
thf(367,plain,
! [SV26: $i,SV27: $i,SV178: $i,SV179: $i] :
( ( ( ite
@ ( ( ite @ $false @ SV179 @ ( s @ SV178 ) )
= zero )
@ SV27
@ SV26 )
= SV26 )
= $true ),
inference(extuni,[status(esa)],[358:[bind(SV28,$thf( ( ite @ $false @ SV179 @ ( s @ SV178 ) ) = zero ))]]) ).
thf(368,plain,
! [SV34: $i,SV178: $i,SV179: $i] :
( ( zero
= ( ite @ $true @ ( ite @ $false @ SV179 @ ( s @ SV178 ) ) @ SV34 ) )
= $false ),
inference(extuni,[status(esa)],[357:[bind(SV35,$thf( ite @ $false @ SV179 @ ( s @ SV178 ) ))]]) ).
thf(371,plain,
! [SV34: $i,SV178: $i,SV179: $i] :
( ( ( ite @ $false @ SV179 @ ( s @ SV178 ) )
= ( ite @ $true @ zero @ SV34 ) )
= $false ),
inference(extuni,[status(esa)],[357:[bind(SV35,$thf( zero ))]]) ).
thf(372,plain,
! [SV42: $i,SV178: $i,SV179: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( zero
= ( ite @ SV44 @ ( ite @ $false @ SV179 @ ( s @ SV178 ) ) @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[356:[bind(SV43,$thf( ite @ $false @ SV179 @ ( s @ SV178 ) ))]]) ).
thf(374,plain,
! [SV42: $i,SV178: $i,SV179: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( ite @ $false @ SV179 @ ( s @ SV178 ) )
= ( ite @ SV44 @ zero @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[356:[bind(SV43,$thf( zero ))]]) ).
thf(375,plain,
! [SV178: $i] :
( ( zero
= ( s @ SV178 ) )
= $false ),
inference(sim,[status(thm)],[365]) ).
thf(376,plain,
! [SV180: $i,SV181: $i] :
( ( ( ite @ $false @ SV181 @ zero )
= ( s @ SV180 ) )
= $false ),
inference(rename,[status(thm)],[132]) ).
thf(377,plain,
! [SV180: $i,SV181: $i,SV42: $i,SV43: $i,SV44: $o] :
( ( ( ( ( ite @ $false @ SV181 @ zero )
= ( s @ SV180 ) )
= ( ( ite @ SV44 @ SV43 @ SV42 )
= SV43 ) )
= $false )
| ( SV44 = $false ) ),
inference(res,[status(thm)],[376,169]) ).
thf(378,plain,
! [SV180: $i,SV181: $i,SV34: $i,SV35: $i] :
( ( ( ( ite @ $false @ SV181 @ zero )
= ( s @ SV180 ) )
= ( ( ite @ $true @ SV35 @ SV34 )
= SV35 ) )
= $false ),
inference(res,[status(thm)],[376,157]) ).
thf(379,plain,
! [SV180: $i,SV181: $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( ite @ $false @ SV181 @ zero )
= ( s @ SV180 ) )
= SV28 )
= $false )
| ( ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 )
= $true ) ),
inference(res,[status(thm)],[376,133]) ).
thf(380,plain,
! [SV180: $i,SV181: $i,SV26: $i,SV27: $i,SV28: $o] :
( ( ( ( ( ite @ $false @ SV181 @ zero )
= ( s @ SV180 ) )
= ( ( ite @ SV28 @ SV27 @ SV26 )
= SV26 ) )
= $false )
| ( SV28 = $true ) ),
inference(res,[status(thm)],[376,133]) ).
thf(381,plain,
! [SV180: $i,SV181: $i,SV24: $i,SV25: $i] :
( ( ( ( ite @ $false @ SV181 @ zero )
= ( s @ SV180 ) )
= ( ( ite @ $false @ SV25 @ SV24 )
= SV24 ) )
= $false ),
inference(res,[status(thm)],[376,124]) ).
thf(382,plain,
! [SV181: $i,SV25: $i,SV180: $i] :
( ( ( s @ SV180 )
= ( ite @ $false @ SV25 @ ( ite @ $false @ SV181 @ zero ) ) )
= $false ),
inference(extuni,[status(esa)],[381:[bind(SV24,$thf( ite @ $false @ SV181 @ zero ))]]) ).
thf(383,plain,
! [SV180: $i] :
( ( ( s @ SV180 )
= zero )
= $false ),
inference(extuni,[status(esa)],[381:[bind(SV24,$thf( zero )),bind(SV181,$thf( SV25 ))]]) ).
thf(384,plain,
! [SV180: $i,SV25: $i,SV181: $i] :
( ( ( ite @ $false @ SV181 @ zero )
= ( ite @ $false @ SV25 @ ( s @ SV180 ) ) )
= $false ),
inference(extuni,[status(esa)],[381:[bind(SV24,$thf( s @ SV180 ))]]) ).
thf(385,plain,
! [SV181: $i,SV27: $i,SV180: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( s @ SV180 )
= ( ite @ SV28 @ SV27 @ ( ite @ $false @ SV181 @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[380:[bind(SV26,$thf( ite @ $false @ SV181 @ zero ))]]) ).
thf(386,plain,
! [SV180: $i] :
( ( $false = $true )
| ( ( ( s @ SV180 )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[380:[bind(SV26,$thf( zero )),bind(SV181,$thf( SV27 )),bind(SV28,$thf( $false ))]]) ).
thf(387,plain,
! [SV180: $i,SV27: $i,SV181: $i,SV28: $o] :
( ( SV28 = $true )
| ( ( ( ite @ $false @ SV181 @ zero )
= ( ite @ SV28 @ SV27 @ ( s @ SV180 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[380:[bind(SV26,$thf( s @ SV180 ))]]) ).
thf(388,plain,
! [SV26: $i,SV27: $i,SV180: $i,SV181: $i] :
( ( ( ite
@ ( ( ite @ $false @ SV181 @ zero )
= ( s @ SV180 ) )
@ SV27
@ SV26 )
= SV26 )
= $true ),
inference(extuni,[status(esa)],[379:[bind(SV28,$thf( ( ite @ $false @ SV181 @ zero ) = ( s @ SV180 ) ))]]) ).
thf(389,plain,
! [SV34: $i,SV181: $i,SV180: $i] :
( ( ( s @ SV180 )
= ( ite @ $true @ ( ite @ $false @ SV181 @ zero ) @ SV34 ) )
= $false ),
inference(extuni,[status(esa)],[378:[bind(SV35,$thf( ite @ $false @ SV181 @ zero ))]]) ).
thf(392,plain,
! [SV34: $i,SV180: $i,SV181: $i] :
( ( ( ite @ $false @ SV181 @ zero )
= ( ite @ $true @ ( s @ SV180 ) @ SV34 ) )
= $false ),
inference(extuni,[status(esa)],[378:[bind(SV35,$thf( s @ SV180 ))]]) ).
thf(393,plain,
! [SV42: $i,SV181: $i,SV180: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( s @ SV180 )
= ( ite @ SV44 @ ( ite @ $false @ SV181 @ zero ) @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[377:[bind(SV43,$thf( ite @ $false @ SV181 @ zero ))]]) ).
thf(395,plain,
! [SV42: $i,SV180: $i,SV181: $i,SV44: $o] :
( ( SV44 = $false )
| ( ( ( ite @ $false @ SV181 @ zero )
= ( ite @ SV44 @ ( s @ SV180 ) @ SV42 ) )
= $false ) ),
inference(extuni,[status(esa)],[377:[bind(SV43,$thf( s @ SV180 ))]]) ).
thf(396,plain,
! [SV180: $i] :
( ( ( s @ SV180 )
= zero )
= $false ),
inference(sim,[status(thm)],[386]) ).
thf(398,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[109,396,395,393,392,389,388,387,385,384,383,382,376,375,374,372,371,368,367,366,364,363,362,361,355,354,352,351,348,347,346,345,344,343,337,336,335,334,333,332,331,330,329,328,327,326,325,324,323,322,321,320,319,318,317,316,315,314,313,312,311,310,309,308,307,306,305,304,303,302,301,300,299,298,297,296,295,294,293,292,291,290,289,288,287,286,285,284,283,282,281,280,279,278,277,276,275,274,273,272,271,270,269,268,267,266,265,264,263,262,261,260,259,243,242,241,239,238,235,234,233,231,230,229,228,221,220,218,217,214,213,212,210,209,208,207,198,197,196,195,194,193,192,191,190,189,188,187,186,180,169,165,164,163,162,161,157,156,155,154,153,152,151,150,149,148,147,145,133,124,123,122,117,115,112,111,110]) ).
thf(399,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[398]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN024^1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 13:45:59 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.40/2.01
% 9.40/2.01 No.of.Axioms: 0
% 9.40/2.01
% 9.40/2.01 Length.of.Defs: 0
% 9.40/2.01
% 9.40/2.01 Contains.Choice.Funs: false
% 9.40/2.01 .......
% 9.40/2.01
% 9.40/2.01 ********************************
% 9.40/2.01 * All subproblems solved! *
% 9.40/2.01 ********************************
% 9.40/2.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:398,loop_count:20,foatp_calls:6,translation:fof_experiment)
% 9.40/2.01
% 9.40/2.01 %**** Beginning of derivation protocol ****
% 9.40/2.01 % SZS output start CNFRefutation
% See solution above
% 9.40/2.01
% 9.40/2.01 %**** End of derivation protocol ****
% 9.40/2.01 %**** no. of clauses in derivation: 319 ****
% 9.40/2.01 %**** clause counter: 398 ****
% 9.40/2.01
% 9.40/2.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:398,loop_count:20,foatp_calls:6,translation:fof_experiment)
%------------------------------------------------------------------------------