%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUN023^1 : 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 : n004.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 10:35:54 AM UTC 2026
% Result : Theorem 1.22s 0.43s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 1
% Syntax : Number of formulae : 210 ( 68 unt; 0 typ; 0 def)
% Number of atoms : 1237 ( 772 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1287 ( 66 ~; 205 |; 8 &; 997 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 75 ( 75 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-3 aty)
% Number of variables : 390 ( 0 ^; 385 !; 5 ?; 390 :)
% 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,
( ( ! [X: $o,U: $i,V: $i] :
( X
=> ( ( ite @ X @ U @ V )
= U ) )
& ! [X: $o,U: $i,V: $i] :
( ~ X
=> ( ( ite @ X @ U @ V )
= V ) ) )
=> ? [H: $i > $i] :
( ( ( H @ zero )
= ( s @ zero ) )
& ( ( H @ ( s @ zero ) )
= zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n8) ).
thf(2,negated_conjecture,
( ( ( ! [X: $o,U: $i,V: $i] :
( X
=> ( ( ite @ X @ U @ V )
= U ) )
& ! [X: $o,U: $i,V: $i] :
( ~ X
=> ( ( ite @ X @ U @ V )
= V ) ) )
=> ? [H: $i > $i] :
( ( ( H @ zero )
= ( s @ zero ) )
& ( ( H @ ( s @ zero ) )
= zero ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [X: $o,U: $i,V: $i] :
( X
=> ( ( ite @ X @ U @ V )
= U ) )
& ! [X: $o,U: $i,V: $i] :
( ~ X
=> ( ( ite @ X @ U @ V )
= V ) ) )
=> ? [H: $i > $i] :
( ( ( H @ zero )
= ( s @ zero ) )
& ( ( H @ ( s @ zero ) )
= zero ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [X: $o,U: $i,V: $i] :
( X
=> ( ( ite @ X @ U @ V )
= U ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [X: $o,U: $i,V: $i] :
( ~ X
=> ( ( ite @ X @ U @ V )
= V ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ? [H: $i > $i] :
( ( ( H @ zero )
= ( s @ zero ) )
& ( ( H @ ( s @ zero ) )
= zero ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ? [H: $i > $i] :
( ( ( H @ zero )
= ( s @ zero ) )
& ( ( H @ ( s @ zero ) )
= zero ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [H: $i > $i] :
( ( ( H @ zero )
!= ( s @ zero ) )
| ( ( H @ ( s @ zero ) )
!= zero ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [X: $o] :
( ~ X
| ! [U: $i,V: $i] :
( ( ite @ X @ U @ V )
= U ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [X: $o] :
( X
| ! [U: $i,V: $i] :
( ( ite @ X @ U @ V )
= V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(11,plain,
( ( ! [X: $o] :
( X
| ! [U: $i,V: $i] :
( ( ite @ X @ U @ V )
= V ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [X: $o] :
( ~ X
| ! [U: $i,V: $i] :
( ( ite @ X @ U @ V )
= U ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ! [H: $i > $i] :
( ( ( H @ zero )
!= ( s @ zero ) )
| ( ( H @ ( s @ zero ) )
!= zero ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
! [SV1: $o] :
( ( SV1
| ! [SY7: $i,SY8: $i] :
( ( ite @ SV1 @ SY7 @ SY8 )
= SY8 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[11]) ).
thf(16,plain,
( ( $false
| ! [SX0: $i,SX1: $i] :
( ( ite @ $false @ SX0 @ SX1 )
= SX1 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[11]) ).
thf(17,plain,
! [SV2: $o] :
( ( ~ SV2
| ! [SY9: $i,SY10: $i] :
( ( ite @ SV2 @ SY9 @ SY10 )
= SY9 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[12]) ).
thf(18,plain,
( ( ~ $true
| ! [SX0: $i,SX1: $i] :
( ( ite @ $true @ SX0 @ SX1 )
= SX0 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[12]) ).
thf(20,plain,
! [SV3: $i > $i] :
( ( ( ( SV3 @ zero )
!= ( s @ zero ) )
| ( ( SV3 @ ( s @ zero ) )
!= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(21,plain,
! [SV1: $o] :
( ( SV1 = $true )
| ( ( ! [SY7: $i,SY8: $i] :
( ( ite @ SV1 @ SY7 @ SY8 )
= SY8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(23,plain,
( ( $false = $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ( ite @ $false @ SX0 @ SX1 )
= SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(24,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $true )
| ( ( ! [SY9: $i,SY10: $i] :
( ( ite @ SV2 @ SY9 @ SY10 )
= SY9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(25,plain,
( ( ( ~ $true ) = $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ( ite @ $true @ SX0 @ SX1 )
= SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(27,plain,
! [SV3: $i > $i] :
( ( ( ( SV3 @ zero )
!= ( s @ zero ) )
= $true )
| ( ( ( SV3 @ ( s @ zero ) )
!= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV4: $i,SV1: $o] :
( ( ( ! [SY11: $i] :
( ( ite @ SV1 @ SV4 @ SY11 )
= SY11 ) )
= $true )
| ( SV1 = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(30,plain,
! [SV6: $i] :
( ( ( ! [SY13: $i] :
( ( ite @ $false @ SV6 @ SY13 )
= SY13 ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(31,plain,
! [SV2: $o] :
( ( SV2 = $false )
| ( ( ! [SY9: $i,SY10: $i] :
( ( ite @ SV2 @ SY9 @ SY10 )
= SY9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(32,plain,
( ( $true = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ( ite @ $true @ SX0 @ SX1 )
= SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(34,plain,
! [SV3: $i > $i] :
( ( ( ( SV3 @ zero )
= ( s @ zero ) )
= $false )
| ( ( ( SV3 @ ( s @ zero ) )
!= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV7: $i,SV4: $i,SV1: $o] :
( ( ( ( ite @ SV1 @ SV4 @ SV7 )
= SV7 )
= $true )
| ( SV1 = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(37,plain,
! [SV9: $i,SV6: $i] :
( ( ( ( ite @ $false @ SV6 @ SV9 )
= SV9 )
= $true )
| ( $false = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(38,plain,
! [SV10: $i,SV2: $o] :
( ( ( ! [SY14: $i] :
( ( ite @ SV2 @ SV10 @ SY14 )
= SV10 ) )
= $true )
| ( SV2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(39,plain,
! [SV11: $i] :
( ( ( ! [SY15: $i] :
( ( ite @ $true @ SV11 @ SY15 )
= SV11 ) )
= $true )
| ( $true = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(41,plain,
! [SV3: $i > $i] :
( ( ( ( SV3 @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( SV3 @ zero )
= ( s @ zero ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(42,plain,
! [SV13: $i,SV10: $i,SV2: $o] :
( ( ( ( ite @ SV2 @ SV10 @ SV13 )
= SV10 )
= $true )
| ( SV2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV14: $i,SV11: $i] :
( ( ( ( ite @ $true @ SV11 @ SV14 )
= SV11 )
= $true )
| ( $true = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV7: $i,SV4: $i] :
( ( ( ( ite @ $false @ SV4 @ SV7 )
= SV7 )
= $true )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[35:[bind(SV1,$thf( $false ))]]) ).
thf(47,plain,
! [SV7: $i,SV4: $i,SV17: $o] :
( ( ( ( ite @ ~ SV17 @ SV4 @ SV7 )
= SV7 )
= $true )
| ( ( ~ SV17 ) = $true ) ),
inference(prim_subst,[status(thm)],[35:[bind(SV1,$thf( ~ ( SV17 ) ))]]) ).
thf(48,plain,
! [SV13: $i,SV10: $i] :
( ( ( ( ite @ $true @ SV10 @ SV13 )
= SV10 )
= $true )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[42:[bind(SV2,$thf( $true ))]]) ).
thf(50,plain,
! [SV13: $i,SV10: $i,SV16: $o] :
( ( ( ( ite @ ~ SV16 @ SV10 @ SV13 )
= SV10 )
= $true )
| ( ( ~ SV16 ) = $false ) ),
inference(prim_subst,[status(thm)],[42:[bind(SV2,$thf( ~ ( SV16 ) ))]]) ).
thf(51,plain,
! [SV7: $i,SV4: $i,SV1: $o] :
( ( SV1 = $true )
| ( ( ( ( ite @ SV1 @ SV4 @ SV7 )
= SV7 )
= SV1 )
= $false ) ),
inference(fac_restr,[status(thm)],[35]) ).
thf(54,plain,
! [SV3: $i > $i] :
( ( ( ( SV3 @ zero )
= ( s @ zero ) )
= $false )
| ( ( ( ( SV3 @ ( s @ zero ) )
= zero )
= ( ( SV3 @ zero )
= ( s @ zero ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[41]) ).
thf(55,plain,
! [SV13: $i,SV10: $i,SV2: $o] :
( ( SV2 = $false )
| ( ( SV2
= ( ( ite @ SV2 @ SV10 @ SV13 )
!= SV10 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[42]) ).
thf(56,plain,
! [SV7: $i,SV4: $i,SV1: $o] :
( ( ( ~ ( ( ( ite @ SV1 @ SV4 @ SV7 )
= SV7 )
| SV1 )
| ~ ( ( ( ite @ SV1 @ SV4 @ SV7 )
!= SV7 )
| ~ SV1 ) )
= $false )
| ( SV1 = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[51]) ).
thf(62,plain,
! [SV3: $i > $i] :
( ( ( ~ ( ( ( SV3 @ ( s @ zero ) )
= zero )
| ( ( SV3 @ zero )
= ( s @ zero ) ) )
| ~ ( ( ( SV3 @ ( s @ zero ) )
!= zero )
| ( ( SV3 @ zero )
!= ( s @ zero ) ) ) )
= $false )
| ( ( ( SV3 @ zero )
= ( s @ zero ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[54]) ).
thf(63,plain,
! [SV3: $i > $i] :
( ( ( ( ( SV3 @ ( s @ zero ) )
= zero )
= ( ( SV3 @ zero )
= ( s @ zero ) ) )
= $false )
| ( ( ( SV3 @ zero )
= ( s @ zero ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[54]) ).
thf(64,plain,
! [SV13: $i,SV10: $i,SV2: $o] :
( ( ( ~ ( SV2
| ( ( ite @ SV2 @ SV10 @ SV13 )
!= SV10 ) )
| ~ ( ~ SV2
| ~ ( ( ( ite @ SV2 @ SV10 @ SV13 )
!= SV10 ) ) ) )
= $false )
| ( SV2 = $false ) ),
inference(extcnf_equal_neg,[status(thm)],[55]) ).
thf(66,plain,
! [SV7: $i,SV4: $i,SV1: $o] :
( ( ( ~ ( ( ( ite @ SV1 @ SV4 @ SV7 )
= SV7 )
| SV1 ) )
= $false )
| ( SV1 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(73,plain,
! [SV3: $i > $i] :
( ( ( ~ ( ( ( SV3 @ ( s @ zero ) )
!= zero )
| ( ( SV3 @ zero )
!= ( s @ zero ) ) ) )
= $false )
| ( ( ( SV3 @ zero )
= ( s @ zero ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(75,plain,
! [SV13: $i,SV10: $i,SV2: $o] :
( ( ( ~ ( ~ SV2
| ~ ( ( ( ite @ SV2 @ SV10 @ SV13 )
!= SV10 ) ) ) )
= $false )
| ( SV2 = $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(76,plain,
! [SV7: $i,SV4: $i,SV1: $o] :
( ( ( ( ( ite @ SV1 @ SV4 @ SV7 )
= SV7 )
| SV1 )
= $true )
| ( SV1 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(83,plain,
! [SV3: $i > $i] :
( ( ( ( ( SV3 @ ( s @ zero ) )
!= zero )
| ( ( SV3 @ zero )
!= ( s @ zero ) ) )
= $true )
| ( ( ( SV3 @ zero )
= ( s @ zero ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(85,plain,
! [SV13: $i,SV10: $i,SV2: $o] :
( ( ( ~ SV2
| ~ ( ( ( ite @ SV2 @ SV10 @ SV13 )
!= SV10 ) ) )
= $true )
| ( SV2 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(86,plain,
! [SV7: $i,SV4: $i,SV1: $o] :
( ( ( ( ite @ SV1 @ SV4 @ SV7 )
= SV7 )
= $true )
| ( SV1 = $true )
| ( SV1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(93,plain,
! [SV3: $i > $i] :
( ( ( ( SV3 @ ( s @ zero ) )
!= zero )
= $true )
| ( ( ( SV3 @ zero )
!= ( s @ zero ) )
= $true )
| ( ( ( SV3 @ zero )
= ( s @ zero ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(95,plain,
! [SV13: $i,SV10: $i,SV2: $o] :
( ( ( ~ SV2 ) = $true )
| ( ( ~ ( ( ( ite @ SV2 @ SV10 @ SV13 )
!= SV10 ) ) )
= $true )
| ( SV2 = $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(99,plain,
! [SV3: $i > $i] :
( ( ( ( SV3 @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( SV3 @ zero )
!= ( s @ zero ) )
= $true )
| ( ( ( SV3 @ zero )
= ( s @ zero ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(101,plain,
! [SV13: $i,SV10: $i,SV2: $o] :
( ( SV2 = $false )
| ( ( ~ ( ( ( ite @ SV2 @ SV10 @ SV13 )
!= SV10 ) ) )
= $true )
| ( SV2 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV3: $i > $i] :
( ( ( ( SV3 @ zero )
= ( s @ zero ) )
= $false )
| ( ( ( SV3 @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( SV3 @ zero )
= ( s @ zero ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(106,plain,
! [SV13: $i,SV10: $i,SV2: $o] :
( ( ( ( ite @ SV2 @ SV10 @ SV13 )
!= SV10 )
= $false )
| ( SV2 = $false )
| ( SV2 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(107,plain,
! [SV13: $i,SV10: $i,SV2: $o] :
( ( ( ( ite @ SV2 @ SV10 @ SV13 )
= SV10 )
= $true )
| ( SV2 = $false )
| ( SV2 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(112,plain,
( ( ( s @ ( s @ zero ) )
= zero )
= $false ),
inference(extuni,[status(esa)],[105:[bind(SV3,$thf( ^ [SX0: $i] : ( s @ SX0 ) ))]]) ).
thf(113,plain,
( ( ( s @ zero )
= zero )
= $false ),
inference(extuni,[status(esa)],[105:[bind(SV3,$thf( ^ [SX0: $i] : ( s @ zero ) ))]]) ).
thf(116,plain,
! [SV25: $i > $i] :
( ( ( ( s @ ( SV25 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( SV25 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( s @ ( SV25 @ zero ) )
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[105:[bind(SV3,$thf( ^ [SX0: $i] : ( s @ ( SV25 @ SX0 ) ) ))]]) ).
thf(117,plain,
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[105:[bind(SV3,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(118,plain,
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[63:[bind(SV3,$thf( ^ [SX0: $i] : ( s @ SX0 ) ))]]) ).
thf(119,plain,
( ( zero
= ( s @ zero ) )
= $false ),
inference(extuni,[status(esa)],[63:[bind(SV3,$thf( ^ [SX0: $i] : ( s @ zero ) ))]]) ).
thf(120,plain,
( ( ( ( s @ ( s @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[63:[bind(SV3,$thf( ^ [SX0: $i] : ( s @ SX0 ) ))]]) ).
thf(122,plain,
! [SV32: $i > $i] :
( ( ( ( s @ ( SV32 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( SV32 @ ( s @ zero ) ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( s @ ( SV32 @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[63:[bind(SV3,$thf( ^ [SX0: $i] : ( s @ ( SV32 @ SX0 ) ) ))]]) ).
thf(124,plain,
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[63:[bind(SV3,$thf( ^ [SX0: $i] : ( s @ SX0 ) ))]]) ).
thf(125,plain,
( ( ( ( s @ ( s @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[63:[bind(SV3,$thf( ^ [SX0: $i] : ( s @ SX0 ) ))]]) ).
thf(127,plain,
! [SV39: $i > $i] :
( ( ( ( s @ ( SV39 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( SV39 @ ( s @ zero ) )
= ( SV39 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[63:[bind(SV3,$thf( ^ [SX0: $i] : ( s @ ( SV39 @ SX0 ) ) ))]]) ).
thf(128,plain,
! [SV39: $i > $i] :
( ( ( ( s @ ( SV39 @ ( s @ zero ) ) )
= ( s @ ( SV39 @ zero ) ) )
= $false )
| ( ( ( s @ ( SV39 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[63:[bind(SV3,$thf( ^ [SX0: $i] : ( s @ ( SV39 @ SX0 ) ) ))]]) ).
thf(129,plain,
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[63:[bind(SV3,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(130,plain,
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ zero )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[41:[bind(SV3,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(132,plain,
! [SV7: $i,SV4: $i,SV17: $o] :
( ( SV17 = $false )
| ( ( ( ite @ ~ SV17 @ SV4 @ SV7 )
= SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(133,plain,
! [SV13: $i,SV10: $i,SV16: $o] :
( ( SV16 = $true )
| ( ( ( ite @ ~ SV16 @ SV10 @ SV13 )
= SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(134,plain,
! [SV9: $i,SV6: $i] :
( ( ( ite @ $false @ SV6 @ SV9 )
= SV9 )
= $true ),
inference(sim,[status(thm)],[37]) ).
thf(135,plain,
! [SV14: $i,SV11: $i] :
( ( ( ite @ $true @ SV11 @ SV14 )
= SV11 )
= $true ),
inference(sim,[status(thm)],[43]) ).
thf(136,plain,
! [SV7: $i,SV4: $i,SV1: $o] :
( ( ( ( ite @ SV1 @ SV4 @ SV7 )
= SV7 )
= $true )
| ( SV1 = $true ) ),
inference(sim,[status(thm)],[86]) ).
thf(138,plain,
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ zero )
= zero )
= $false ) ),
inference(sim,[status(thm)],[117]) ).
thf(139,plain,
! [SV25: $i > $i] :
( ( ( ( s @ ( SV25 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( SV25 @ ( s @ zero ) ) )
= zero )
= $false ) ),
inference(sim,[status(thm)],[116]) ).
thf(142,plain,
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(sim,[status(thm)],[129]) ).
thf(145,plain,
! [SV13: $i,SV10: $i,SV2: $o] :
( ( ( ( ite @ SV2 @ SV10 @ SV13 )
= SV10 )
= $true )
| ( SV2 = $false ) ),
inference(sim,[status(thm)],[107]) ).
thf(146,plain,
! [SV9: $i,SV6: $i] :
( ( ( ite @ $false @ SV6 @ SV9 )
= SV9 )
= $true ),
inference(sim,[status(thm)],[37]) ).
thf(147,plain,
! [SV14: $i,SV11: $i] :
( ( ( ite @ $true @ SV11 @ SV14 )
= SV11 )
= $true ),
inference(sim,[status(thm)],[43]) ).
thf(148,plain,
! [SV7: $i,SV4: $i] :
( ( ( ite @ $false @ SV4 @ SV7 )
= SV7 )
= $true ),
inference(sim,[status(thm)],[46]) ).
thf(149,plain,
! [SV13: $i,SV10: $i] :
( ( ( ite @ $true @ SV10 @ SV13 )
= SV10 )
= $true ),
inference(sim,[status(thm)],[48]) ).
thf(150,plain,
! [SV44: $i,SV45: $i,SV46: $o] :
( ( ( ( ite @ SV46 @ SV45 @ SV44 )
= SV44 )
= $true )
| ( SV46 = $true ) ),
inference(rename,[status(thm)],[35]) ).
thf(151,plain,
! [SV44: $i,SV45: $i,SV46: $o] :
( ( ( SV46
= ( zero
= ( s @ zero ) ) )
= $false )
| ( ( ( ite @ SV46 @ SV45 @ SV44 )
= SV44 )
= $true ) ),
inference(res,[status(thm)],[150,119]) ).
thf(152,plain,
! [SV44: $i,SV45: $i,SV46: $o] :
( ( ( ( ( ite @ SV46 @ SV45 @ SV44 )
= SV44 )
= ( zero
= ( s @ zero ) ) )
= $false )
| ( SV46 = $true ) ),
inference(res,[status(thm)],[150,119]) ).
thf(153,plain,
! [SV44: $i,SV45: $i,SV46: $o] :
( ( ( SV46
= ( ( s @ zero )
= zero ) )
= $false )
| ( ( ( ite @ SV46 @ SV45 @ SV44 )
= SV44 )
= $true ) ),
inference(res,[status(thm)],[150,113]) ).
thf(154,plain,
! [SV44: $i,SV45: $i,SV46: $o] :
( ( ( ( ( ite @ SV46 @ SV45 @ SV44 )
= SV44 )
= ( ( s @ zero )
= zero ) )
= $false )
| ( SV46 = $true ) ),
inference(res,[status(thm)],[150,113]) ).
thf(155,plain,
! [SV44: $i,SV45: $i,SV46: $o] :
( ( ( SV46
= ( ( s @ ( s @ zero ) )
= zero ) )
= $false )
| ( ( ( ite @ SV46 @ SV45 @ SV44 )
= SV44 )
= $true ) ),
inference(res,[status(thm)],[150,112]) ).
thf(156,plain,
! [SV44: $i,SV45: $i,SV46: $o] :
( ( ( ( ( ite @ SV46 @ SV45 @ SV44 )
= SV44 )
= ( ( s @ ( s @ zero ) )
= zero ) )
= $false )
| ( SV46 = $true ) ),
inference(res,[status(thm)],[150,112]) ).
thf(158,plain,
! [SV44: $i,SV45: $i] :
( ( ( ( ite @ $false @ SV45 @ SV44 )
= SV44 )
= $true )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[150:[bind(SV46,$thf( $false ))]]) ).
thf(159,plain,
! [SV44: $i,SV45: $i] :
( ( ( ite @ $false @ SV45 @ SV44 )
= SV44 )
= $true ),
inference(sim,[status(thm)],[158]) ).
thf(160,plain,
! [SV44: $i,SV45: $i,SV51: $o] :
( ( ( ( ite @ ~ SV51 @ SV45 @ SV44 )
= SV44 )
= $true )
| ( ( ~ SV51 ) = $true ) ),
inference(prim_subst,[status(thm)],[150:[bind(SV46,$thf( ~ ( SV51 ) ))]]) ).
thf(161,plain,
! [SV44: $i,SV45: $i,SV50: $o,SV49: $o] :
( ( ( ( ite
@ ( SV49
| SV50 )
@ SV45
@ SV44 )
= SV44 )
= $true )
| ( ( SV49
| SV50 )
= $true ) ),
inference(prim_subst,[status(thm)],[150:[bind(SV46,$thf( SV49 | SV50 ))]]) ).
thf(162,plain,
! [SV44: $i,SV45: $i,SV48: $i,SV47: $i] :
( ( ( ( ite @ ( SV47 = SV48 ) @ SV45 @ SV44 )
= SV44 )
= $true )
| ( ( SV47 = SV48 )
= $true ) ),
inference(prim_subst,[status(thm)],[150:[bind(SV46,$thf( SV47 = SV48 ))]]) ).
thf(164,plain,
! [SV45: $i,SV46: $o] :
( ( SV46 = $true )
| ( ( ( ite @ SV46 @ SV45 @ ( s @ ( s @ zero ) ) )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[156:[bind(SV44,$thf( s @ ( s @ zero ) ))]]) ).
thf(165,plain,
! [SV45: $i,SV46: $o] :
( ( SV46 = $true )
| ( ( ( ite @ SV46 @ SV45 @ zero )
= ( s @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[156:[bind(SV44,$thf( zero ))]]) ).
thf(166,plain,
! [SV44: $i,SV45: $i] :
( ( ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ SV45
@ SV44 )
= SV44 )
= $true ),
inference(extuni,[status(esa)],[155:[bind(SV46,$thf( ( s @ ( s @ zero ) ) = zero ))]]) ).
thf(167,plain,
! [SV45: $i,SV46: $o] :
( ( SV46 = $true )
| ( ( ( ite @ SV46 @ SV45 @ ( s @ zero ) )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[154:[bind(SV44,$thf( s @ zero ))]]) ).
thf(168,plain,
! [SV45: $i,SV46: $o] :
( ( SV46 = $true )
| ( ( ( ite @ SV46 @ SV45 @ zero )
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[154:[bind(SV44,$thf( zero ))]]) ).
thf(169,plain,
! [SV44: $i,SV45: $i] :
( ( ( ite
@ ( ( s @ zero )
= zero )
@ SV45
@ SV44 )
= SV44 )
= $true ),
inference(extuni,[status(esa)],[153:[bind(SV46,$thf( ( s @ zero ) = zero ))]]) ).
thf(170,plain,
! [SV45: $i,SV46: $o] :
( ( SV46 = $true )
| ( ( ( ite @ SV46 @ SV45 @ zero )
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[152:[bind(SV44,$thf( zero ))]]) ).
thf(171,plain,
! [SV45: $i,SV46: $o] :
( ( SV46 = $true )
| ( ( ( ite @ SV46 @ SV45 @ ( s @ zero ) )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[152:[bind(SV44,$thf( s @ zero ))]]) ).
thf(172,plain,
! [SV44: $i,SV45: $i] :
( ( ( ite
@ ( zero
= ( s @ zero ) )
@ SV45
@ SV44 )
= SV44 )
= $true ),
inference(extuni,[status(esa)],[151:[bind(SV46,$thf( zero = ( s @ zero ) ))]]) ).
thf(173,plain,
! [SV44: $i,SV45: $i,SV51: $o] :
( ( SV51 = $false )
| ( ( ( ite @ ~ SV51 @ SV45 @ SV44 )
= SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(174,plain,
! [SV44: $i,SV45: $i,SV50: $o,SV49: $o] :
( ( SV49 = $true )
| ( SV50 = $true )
| ( ( ( ite
@ ( SV49
| SV50 )
@ SV45
@ SV44 )
= SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(175,plain,
! [SV52: $i,SV53: $i] :
( ( ( ite @ $false @ SV53 @ SV52 )
= SV52 )
= $true ),
inference(rename,[status(thm)],[134]) ).
thf(176,plain,
! [SV52: $i,SV53: $i] :
( ( ( ( ite @ $false @ SV53 @ SV52 )
= SV52 )
= ( zero
= ( s @ zero ) ) )
= $false ),
inference(res,[status(thm)],[175,119]) ).
thf(177,plain,
! [SV52: $i,SV53: $i] :
( ( ( ( ite @ $false @ SV53 @ SV52 )
= SV52 )
= ( ( s @ zero )
= zero ) )
= $false ),
inference(res,[status(thm)],[175,113]) ).
thf(178,plain,
! [SV52: $i,SV53: $i] :
( ( ( ( ite @ $false @ SV53 @ SV52 )
= SV52 )
= ( ( s @ ( s @ zero ) )
= zero ) )
= $false ),
inference(res,[status(thm)],[175,112]) ).
thf(179,plain,
! [SV53: $i] :
( ( ( ite @ $false @ SV53 @ ( s @ ( s @ zero ) ) )
= zero )
= $false ),
inference(extuni,[status(esa)],[178:[bind(SV52,$thf( s @ ( s @ zero ) ))]]) ).
thf(180,plain,
! [SV53: $i] :
( ( ( ite @ $false @ SV53 @ zero )
= ( s @ ( s @ zero ) ) )
= $false ),
inference(extuni,[status(esa)],[178:[bind(SV52,$thf( zero ))]]) ).
thf(181,plain,
! [SV53: $i] :
( ( ( ite @ $false @ SV53 @ ( s @ zero ) )
= zero )
= $false ),
inference(extuni,[status(esa)],[177:[bind(SV52,$thf( s @ zero ))]]) ).
thf(182,plain,
! [SV53: $i] :
( ( ( ite @ $false @ SV53 @ zero )
= ( s @ zero ) )
= $false ),
inference(extuni,[status(esa)],[177:[bind(SV52,$thf( zero ))]]) ).
thf(183,plain,
! [SV53: $i] :
( ( ( ite @ $false @ SV53 @ zero )
= ( s @ zero ) )
= $false ),
inference(extuni,[status(esa)],[176:[bind(SV52,$thf( zero ))]]) ).
thf(184,plain,
! [SV53: $i] :
( ( ( ite @ $false @ SV53 @ ( s @ zero ) )
= zero )
= $false ),
inference(extuni,[status(esa)],[176:[bind(SV52,$thf( s @ zero ))]]) ).
thf(185,plain,
! [SV54: $i,SV55: $i] :
( ( ( ite @ $true @ SV55 @ SV54 )
= SV55 )
= $true ),
inference(rename,[status(thm)],[135]) ).
thf(186,plain,
! [SV54: $i,SV55: $i] :
( ( ( ( ite @ $true @ SV55 @ SV54 )
= SV55 )
= ( zero
= ( s @ zero ) ) )
= $false ),
inference(res,[status(thm)],[185,119]) ).
thf(187,plain,
! [SV54: $i,SV55: $i] :
( ( ( ( ite @ $true @ SV55 @ SV54 )
= SV55 )
= ( ( s @ zero )
= zero ) )
= $false ),
inference(res,[status(thm)],[185,113]) ).
thf(188,plain,
! [SV54: $i,SV55: $i] :
( ( ( ( ite @ $true @ SV55 @ SV54 )
= SV55 )
= ( ( s @ ( s @ zero ) )
= zero ) )
= $false ),
inference(res,[status(thm)],[185,112]) ).
thf(189,plain,
! [SV54: $i] :
( ( ( ite @ $true @ ( s @ ( s @ zero ) ) @ SV54 )
= zero )
= $false ),
inference(extuni,[status(esa)],[188:[bind(SV55,$thf( s @ ( s @ zero ) ))]]) ).
thf(190,plain,
! [SV54: $i] :
( ( ( ite @ $true @ zero @ SV54 )
= ( s @ ( s @ zero ) ) )
= $false ),
inference(extuni,[status(esa)],[188:[bind(SV55,$thf( zero ))]]) ).
thf(191,plain,
! [SV54: $i] :
( ( ( ite @ $true @ ( s @ zero ) @ SV54 )
= zero )
= $false ),
inference(extuni,[status(esa)],[187:[bind(SV55,$thf( s @ zero ))]]) ).
thf(192,plain,
! [SV54: $i] :
( ( ( ite @ $true @ zero @ SV54 )
= ( s @ zero ) )
= $false ),
inference(extuni,[status(esa)],[187:[bind(SV55,$thf( zero ))]]) ).
thf(193,plain,
! [SV54: $i] :
( ( ( ite @ $true @ zero @ SV54 )
= ( s @ zero ) )
= $false ),
inference(extuni,[status(esa)],[186:[bind(SV55,$thf( zero ))]]) ).
thf(194,plain,
! [SV54: $i] :
( ( ( ite @ $true @ ( s @ zero ) @ SV54 )
= zero )
= $false ),
inference(extuni,[status(esa)],[186:[bind(SV55,$thf( s @ zero ))]]) ).
thf(196,plain,
! [SV58: $i > $i] :
( ( ( ( SV58 @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( SV58 @ zero )
= ( s @ zero ) )
= $false ) ),
inference(rename,[status(thm)],[41]) ).
thf(197,plain,
! [SV58: $i > $i,SV54: $i,SV55: $i] :
( ( ( ( ( SV58 @ zero )
= ( s @ zero ) )
= ( ( ite @ $true @ SV55 @ SV54 )
= SV55 ) )
= $false )
| ( ( ( SV58 @ ( s @ zero ) )
= zero )
= $false ) ),
inference(res,[status(thm)],[196,185]) ).
thf(198,plain,
! [SV58: $i > $i,SV54: $i,SV55: $i] :
( ( ( ( ( SV58 @ ( s @ zero ) )
= zero )
= ( ( ite @ $true @ SV55 @ SV54 )
= SV55 ) )
= $false )
| ( ( ( SV58 @ zero )
= ( s @ zero ) )
= $false ) ),
inference(res,[status(thm)],[196,185]) ).
thf(199,plain,
! [SV58: $i > $i,SV52: $i,SV53: $i] :
( ( ( ( ( SV58 @ zero )
= ( s @ zero ) )
= ( ( ite @ $false @ SV53 @ SV52 )
= SV52 ) )
= $false )
| ( ( ( SV58 @ ( s @ zero ) )
= zero )
= $false ) ),
inference(res,[status(thm)],[196,175]) ).
thf(200,plain,
! [SV58: $i > $i,SV52: $i,SV53: $i] :
( ( ( ( ( SV58 @ ( s @ zero ) )
= zero )
= ( ( ite @ $false @ SV53 @ SV52 )
= SV52 ) )
= $false )
| ( ( ( SV58 @ zero )
= ( s @ zero ) )
= $false ) ),
inference(res,[status(thm)],[196,175]) ).
thf(201,plain,
! [SV58: $i > $i,SV44: $i,SV45: $i,SV46: $o] :
( ( ( ( ( SV58 @ zero )
= ( s @ zero ) )
= SV46 )
= $false )
| ( ( ( SV58 @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( ite @ SV46 @ SV45 @ SV44 )
= SV44 )
= $true ) ),
inference(res,[status(thm)],[196,150]) ).
thf(202,plain,
! [SV58: $i > $i,SV44: $i,SV45: $i,SV46: $o] :
( ( ( ( ( SV58 @ ( s @ zero ) )
= zero )
= SV46 )
= $false )
| ( ( ( SV58 @ zero )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ SV46 @ SV45 @ SV44 )
= SV44 )
= $true ) ),
inference(res,[status(thm)],[196,150]) ).
thf(203,plain,
! [SV58: $i > $i,SV44: $i,SV45: $i,SV46: $o] :
( ( ( ( ( SV58 @ zero )
= ( s @ zero ) )
= ( ( ite @ SV46 @ SV45 @ SV44 )
= SV44 ) )
= $false )
| ( ( ( SV58 @ ( s @ zero ) )
= zero )
= $false )
| ( SV46 = $true ) ),
inference(res,[status(thm)],[196,150]) ).
thf(204,plain,
! [SV58: $i > $i,SV44: $i,SV45: $i,SV46: $o] :
( ( ( ( ( SV58 @ ( s @ zero ) )
= zero )
= ( ( ite @ SV46 @ SV45 @ SV44 )
= SV44 ) )
= $false )
| ( ( ( SV58 @ zero )
= ( s @ zero ) )
= $false )
| ( SV46 = $true ) ),
inference(res,[status(thm)],[196,150]) ).
thf(205,plain,
! [SV58: $i > $i] :
( ( ( ( SV58 @ zero )
= ( s @ zero ) )
= $false )
| ( ( ( ( SV58 @ ( s @ zero ) )
= zero )
= ( ( SV58 @ zero )
= ( s @ zero ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[196]) ).
thf(206,plain,
! [SV45: $i,SV46: $o] :
( ( SV46 = $true )
| ( ( zero
= ( ite @ SV46 @ SV45 @ ( s @ ( s @ zero ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[204:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ SX0 ) )),bind(SV44,$thf( s @ ( s @ zero ) ))]]) ).
thf(207,plain,
! [SV45: $i,SV46: $o] :
( ( SV46 = $true )
| ( ( zero
= ( ite @ SV46 @ SV45 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[204:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ zero ) )),bind(SV44,$thf( s @ zero ))]]) ).
thf(208,plain,
! [SV45: $i,SV61: $i > $i,SV46: $o] :
( ( SV46 = $true )
| ( ( ( s @ ( SV61 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ SV46 @ SV45 @ ( s @ ( SV61 @ ( s @ zero ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[204:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ ( SV61 @ SX0 ) ) )),bind(SV44,$thf( s @ ( SV61 @ ( s @ zero ) ) ))]]) ).
thf(209,plain,
! [SV45: $i,SV46: $o] :
( ( SV46 = $true )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ SV46 @ SV45 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[204:[bind(SV58,$thf( ^ [SX0: $i] : SX0 )),bind(SV44,$thf( s @ zero ))]]) ).
thf(210,plain,
! [SV68: $i > $i,SV67: $i > $i,SV66: $i > $o] :
( ( ( SV66 @ ( s @ zero ) )
= $true )
| ( ( ( ite @ ( SV66 @ zero ) @ ( SV67 @ zero ) @ ( SV68 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( SV68 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[204:[bind(SV44,$thf( SV68 @ ( s @ zero ) )),bind(SV45,$thf( SV67 @ ( s @ zero ) )),bind(SV46,$thf( SV66 @ ( s @ zero ) )),bind(SV58,$thf( ^ [SX0: $i] : ( ite @ ( SV66 @ SX0 ) @ ( SV67 @ SX0 ) @ ( SV68 @ SX0 ) ) ))]]) ).
thf(211,plain,
! [SV45: $i,SV68: $i > $i,SV67: $i > $i,SV66: $i > $o,SV46: $o] :
( ( SV46 = $true )
| ( ( ( ite @ ( SV66 @ zero ) @ ( SV67 @ zero ) @ ( SV68 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ ( SV66 @ ( s @ zero ) ) @ ( SV67 @ ( s @ zero ) ) @ ( SV68 @ ( s @ zero ) ) )
= ( ite @ SV46 @ SV45 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[204:[bind(SV44,$thf( zero )),bind(SV58,$thf( ^ [SX0: $i] : ( ite @ ( SV66 @ SX0 ) @ ( SV67 @ SX0 ) @ ( SV68 @ SX0 ) ) ))]]) ).
thf(212,plain,
! [SV45: $i,SV46: $o] :
( ( SV46 = $true )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ zero )
= ( ite @ SV46 @ SV45 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[204:[bind(SV44,$thf( zero )),bind(SV58,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(213,plain,
! [SV45: $i,SV46: $o] :
( ( SV46 = $true )
| ( ( ( s @ zero )
= zero )
= $false )
| ( ( ( s @ zero )
= ( ite @ SV46 @ SV45 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[203:[bind(SV58,$thf( ^ [SX0: $i] : SX0 )),bind(SV44,$thf( zero ))]]) ).
thf(214,plain,
! [SV45: $i,SV46: $o] :
( ( SV46 = $true )
| ( ( ( s @ zero )
= ( ite @ SV46 @ SV45 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[203:[bind(SV58,$thf( ^ [SX0: $i] : zero )),bind(SV44,$thf( zero ))]]) ).
thf(215,plain,
! [SV75: $i > $i,SV74: $i > $i,SV73: $i > $o] :
( ( ( SV73 @ zero )
= $true )
| ( ( ( ite @ ( SV73 @ ( s @ zero ) ) @ ( SV74 @ ( s @ zero ) ) @ ( SV75 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( s @ zero )
= ( SV75 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[203:[bind(SV44,$thf( SV75 @ zero )),bind(SV45,$thf( SV74 @ zero )),bind(SV46,$thf( SV73 @ zero )),bind(SV58,$thf( ^ [SX0: $i] : ( ite @ ( SV73 @ SX0 ) @ ( SV74 @ SX0 ) @ ( SV75 @ SX0 ) ) ))]]) ).
thf(216,plain,
! [SV45: $i,SV75: $i > $i,SV74: $i > $i,SV73: $i > $o,SV46: $o] :
( ( SV46 = $true )
| ( ( ( ite @ ( SV73 @ ( s @ zero ) ) @ ( SV74 @ ( s @ zero ) ) @ ( SV75 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV73 @ zero ) @ ( SV74 @ zero ) @ ( SV75 @ zero ) )
= ( ite @ SV46 @ SV45 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[203:[bind(SV44,$thf( s @ zero )),bind(SV58,$thf( ^ [SX0: $i] : ( ite @ ( SV73 @ SX0 ) @ ( SV74 @ SX0 ) @ ( SV75 @ SX0 ) ) ))]]) ).
thf(217,plain,
! [SV45: $i,SV46: $o] :
( ( SV46 = $true )
| ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( ite @ SV46 @ SV45 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[203:[bind(SV44,$thf( s @ zero )),bind(SV58,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(218,plain,
! [SV44: $i,SV45: $i] :
( ( ( ite
@ ( ( s @ ( s @ zero ) )
= zero )
@ SV45
@ SV44 )
= SV44 )
= $true ),
inference(extuni,[status(esa)],[202:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ SX0 ) )),bind(SV46,$thf( ( s @ ( s @ zero ) ) = zero ))]]) ).
thf(219,plain,
! [SV44: $i,SV45: $i] :
( ( ( ite
@ ( ( s @ zero )
= zero )
@ SV45
@ SV44 )
= SV44 )
= $true ),
inference(extuni,[status(esa)],[202:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ zero ) )),bind(SV46,$thf( ( s @ zero ) = zero ))]]) ).
thf(220,plain,
! [SV44: $i,SV45: $i,SV78: $i > $i] :
( ( ( ( ite
@ ( ( s @ ( SV78 @ ( s @ zero ) ) )
= zero )
@ SV45
@ SV44 )
= SV44 )
= $true )
| ( ( ( s @ ( SV78 @ zero ) )
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[202:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ ( SV78 @ SX0 ) ) )),bind(SV46,$thf( ( s @ ( SV78 @ ( s @ zero ) ) ) = zero ))]]) ).
thf(221,plain,
! [SV44: $i,SV45: $i] :
( ( ( ( ite
@ ( ( s @ zero )
= zero )
@ SV45
@ SV44 )
= SV44 )
= $true )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[202:[bind(SV58,$thf( ^ [SX0: $i] : SX0 )),bind(SV46,$thf( ( s @ zero ) = zero ))]]) ).
thf(222,plain,
! [SV44: $i,SV45: $i] :
( ( ( ( ite
@ ( zero
= ( s @ zero ) )
@ SV45
@ SV44 )
= SV44 )
= $true )
| ( ( ( s @ zero )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[201:[bind(SV58,$thf( ^ [SX0: $i] : SX0 )),bind(SV46,$thf( zero = ( s @ zero ) ))]]) ).
thf(223,plain,
! [SV44: $i,SV45: $i] :
( ( ( ite
@ ( zero
= ( s @ zero ) )
@ SV45
@ SV44 )
= SV44 )
= $true ),
inference(extuni,[status(esa)],[201:[bind(SV58,$thf( ^ [SX0: $i] : zero )),bind(SV46,$thf( zero = ( s @ zero ) ))]]) ).
thf(224,plain,
! [SV53: $i] :
( ( zero
= ( ite @ $false @ SV53 @ ( s @ ( s @ zero ) ) ) )
= $false ),
inference(extuni,[status(esa)],[200:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ SX0 ) )),bind(SV52,$thf( s @ ( s @ zero ) ))]]) ).
thf(225,plain,
! [SV53: $i] :
( ( zero
= ( ite @ $false @ SV53 @ ( s @ zero ) ) )
= $false ),
inference(extuni,[status(esa)],[200:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ zero ) )),bind(SV52,$thf( s @ zero ))]]) ).
thf(226,plain,
! [SV53: $i,SV85: $i > $i] :
( ( ( ( s @ ( SV85 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ $false @ SV53 @ ( s @ ( SV85 @ ( s @ zero ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[200:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ ( SV85 @ SX0 ) ) )),bind(SV52,$thf( s @ ( SV85 @ ( s @ zero ) ) ))]]) ).
thf(227,plain,
! [SV53: $i] :
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ $false @ SV53 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[200:[bind(SV58,$thf( ^ [SX0: $i] : SX0 )),bind(SV52,$thf( s @ zero ))]]) ).
thf(228,plain,
! [SV92: $i > $i,SV91: $i > $i] :
( ( ( ( ite @ $false @ ( SV91 @ zero ) @ ( SV92 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( SV92 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[200:[bind(SV52,$thf( SV92 @ ( s @ zero ) )),bind(SV53,$thf( SV91 @ ( s @ zero ) )),bind(SV58,$thf( ^ [SX0: $i] : ( ite @ $false @ ( SV91 @ SX0 ) @ ( SV92 @ SX0 ) ) ))]]) ).
thf(229,plain,
! [SV53: $i,SV92: $i > $i,SV91: $i > $i,SV90: $i > $o] :
( ( ( ( ite @ ( SV90 @ zero ) @ ( SV91 @ zero ) @ ( SV92 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ ( SV90 @ ( s @ zero ) ) @ ( SV91 @ ( s @ zero ) ) @ ( SV92 @ ( s @ zero ) ) )
= ( ite @ $false @ SV53 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[200:[bind(SV52,$thf( zero )),bind(SV58,$thf( ^ [SX0: $i] : ( ite @ ( SV90 @ SX0 ) @ ( SV91 @ SX0 ) @ ( SV92 @ SX0 ) ) ))]]) ).
thf(230,plain,
! [SV53: $i] :
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ zero )
= ( ite @ $false @ SV53 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[200:[bind(SV52,$thf( zero )),bind(SV58,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(231,plain,
! [SV53: $i] :
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( ( s @ zero )
= ( ite @ $false @ SV53 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[199:[bind(SV58,$thf( ^ [SX0: $i] : SX0 )),bind(SV52,$thf( zero ))]]) ).
thf(232,plain,
! [SV53: $i] :
( ( ( s @ zero )
= ( ite @ $false @ SV53 @ zero ) )
= $false ),
inference(extuni,[status(esa)],[199:[bind(SV58,$thf( ^ [SX0: $i] : zero )),bind(SV52,$thf( zero ))]]) ).
thf(233,plain,
! [SV101: $i > $i,SV100: $i > $i] :
( ( ( ( ite @ $false @ ( SV100 @ ( s @ zero ) ) @ ( SV101 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( s @ zero )
= ( SV101 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[199:[bind(SV52,$thf( SV101 @ zero )),bind(SV53,$thf( SV100 @ zero )),bind(SV58,$thf( ^ [SX0: $i] : ( ite @ $false @ ( SV100 @ SX0 ) @ ( SV101 @ SX0 ) ) ))]]) ).
thf(234,plain,
! [SV53: $i,SV101: $i > $i,SV100: $i > $i,SV99: $i > $o] :
( ( ( ( ite @ ( SV99 @ ( s @ zero ) ) @ ( SV100 @ ( s @ zero ) ) @ ( SV101 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV99 @ zero ) @ ( SV100 @ zero ) @ ( SV101 @ zero ) )
= ( ite @ $false @ SV53 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[199:[bind(SV52,$thf( s @ zero )),bind(SV58,$thf( ^ [SX0: $i] : ( ite @ ( SV99 @ SX0 ) @ ( SV100 @ SX0 ) @ ( SV101 @ SX0 ) ) ))]]) ).
thf(235,plain,
! [SV53: $i] :
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( ite @ $false @ SV53 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[199:[bind(SV52,$thf( s @ zero )),bind(SV58,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(236,plain,
! [SV54: $i] :
( ( zero
= ( ite @ $true @ ( s @ ( s @ zero ) ) @ SV54 ) )
= $false ),
inference(extuni,[status(esa)],[198:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ SX0 ) )),bind(SV55,$thf( s @ ( s @ zero ) ))]]) ).
thf(237,plain,
! [SV54: $i] :
( ( zero
= ( ite @ $true @ ( s @ zero ) @ SV54 ) )
= $false ),
inference(extuni,[status(esa)],[198:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ zero ) )),bind(SV55,$thf( s @ zero ))]]) ).
thf(238,plain,
! [SV54: $i,SV106: $i > $i] :
( ( ( ( s @ ( SV106 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ $true @ ( s @ ( SV106 @ ( s @ zero ) ) ) @ SV54 ) )
= $false ) ),
inference(extuni,[status(esa)],[198:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ ( SV106 @ SX0 ) ) )),bind(SV55,$thf( s @ ( SV106 @ ( s @ zero ) ) ))]]) ).
thf(239,plain,
! [SV54: $i] :
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( zero
= ( ite @ $true @ ( s @ zero ) @ SV54 ) )
= $false ) ),
inference(extuni,[status(esa)],[198:[bind(SV58,$thf( ^ [SX0: $i] : SX0 )),bind(SV55,$thf( s @ zero ))]]) ).
thf(240,plain,
! [SV113: $i > $i,SV112: $i > $i] :
( ( ( ( ite @ $true @ ( SV112 @ zero ) @ ( SV113 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( SV112 @ ( s @ zero ) ) )
= $false ) ),
inference(extuni,[status(esa)],[198:[bind(SV54,$thf( SV113 @ ( s @ zero ) )),bind(SV55,$thf( SV112 @ ( s @ zero ) )),bind(SV58,$thf( ^ [SX0: $i] : ( ite @ $true @ ( SV112 @ SX0 ) @ ( SV113 @ SX0 ) ) ))]]) ).
thf(241,plain,
! [SV54: $i,SV113: $i > $i,SV112: $i > $i,SV111: $i > $o] :
( ( ( ( ite @ ( SV111 @ zero ) @ ( SV112 @ zero ) @ ( SV113 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( ite @ ( SV111 @ ( s @ zero ) ) @ ( SV112 @ ( s @ zero ) ) @ ( SV113 @ ( s @ zero ) ) )
= ( ite @ $true @ zero @ SV54 ) )
= $false ) ),
inference(extuni,[status(esa)],[198:[bind(SV55,$thf( zero )),bind(SV58,$thf( ^ [SX0: $i] : ( ite @ ( SV111 @ SX0 ) @ ( SV112 @ SX0 ) @ ( SV113 @ SX0 ) ) ))]]) ).
thf(242,plain,
! [SV54: $i] :
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ zero )
= ( ite @ $true @ zero @ SV54 ) )
= $false ) ),
inference(extuni,[status(esa)],[198:[bind(SV55,$thf( zero )),bind(SV58,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(243,plain,
! [SV54: $i] :
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( ( s @ zero )
= ( ite @ $true @ zero @ SV54 ) )
= $false ) ),
inference(extuni,[status(esa)],[197:[bind(SV58,$thf( ^ [SX0: $i] : SX0 )),bind(SV55,$thf( zero ))]]) ).
thf(244,plain,
! [SV54: $i] :
( ( ( s @ zero )
= ( ite @ $true @ zero @ SV54 ) )
= $false ),
inference(extuni,[status(esa)],[197:[bind(SV58,$thf( ^ [SX0: $i] : zero )),bind(SV55,$thf( zero ))]]) ).
thf(245,plain,
! [SV122: $i > $i,SV121: $i > $i] :
( ( ( ( ite @ $true @ ( SV121 @ ( s @ zero ) ) @ ( SV122 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( s @ zero )
= ( SV121 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[197:[bind(SV54,$thf( SV122 @ zero )),bind(SV55,$thf( SV121 @ zero )),bind(SV58,$thf( ^ [SX0: $i] : ( ite @ $true @ ( SV121 @ SX0 ) @ ( SV122 @ SX0 ) ) ))]]) ).
thf(246,plain,
! [SV54: $i,SV122: $i > $i,SV121: $i > $i,SV120: $i > $o] :
( ( ( ( ite @ ( SV120 @ ( s @ zero ) ) @ ( SV121 @ ( s @ zero ) ) @ ( SV122 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( ite @ ( SV120 @ zero ) @ ( SV121 @ zero ) @ ( SV122 @ zero ) )
= ( ite @ $true @ ( s @ zero ) @ SV54 ) )
= $false ) ),
inference(extuni,[status(esa)],[197:[bind(SV55,$thf( s @ zero )),bind(SV58,$thf( ^ [SX0: $i] : ( ite @ ( SV120 @ SX0 ) @ ( SV121 @ SX0 ) @ ( SV122 @ SX0 ) ) ))]]) ).
thf(247,plain,
! [SV54: $i] :
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( ite @ $true @ ( s @ zero ) @ SV54 ) )
= $false ) ),
inference(extuni,[status(esa)],[197:[bind(SV55,$thf( s @ zero )),bind(SV58,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(248,plain,
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ SX0 ) ))]]) ).
thf(249,plain,
( ( ( ( s @ ( s @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ SX0 ) ))]]) ).
thf(250,plain,
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ zero )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ SX0 ) ))]]) ).
thf(251,plain,
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( s @ zero ) )
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ SX0 ) ))]]) ).
thf(253,plain,
( ( ( ( s @ ( s @ zero ) )
= zero )
= $false )
| ( ( ( s @ zero )
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ SX0 ) ))]]) ).
thf(254,plain,
( ( zero
= ( s @ zero ) )
= $false ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ zero ) ))]]) ).
thf(255,plain,
( ( zero
= ( s @ zero ) )
= $false ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ zero ) ))]]) ).
thf(257,plain,
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( ( s @ zero )
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ zero ) ))]]) ).
thf(258,plain,
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ zero )
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ SX0 ) ))]]) ).
thf(259,plain,
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ zero )
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ zero ) ))]]) ).
thf(260,plain,
! [SV127: $i > $i] :
( ( ( ( s @ ( SV127 @ ( s @ zero ) ) )
= ( s @ zero ) )
= $false )
| ( ( zero
= ( s @ ( SV127 @ zero ) ) )
= $false )
| ( ( ( s @ ( SV127 @ zero ) )
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ ( SV127 @ SX0 ) ) ))]]) ).
thf(261,plain,
! [SV127: $i > $i] :
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( SV127 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( SV127 @ ( s @ zero ) )
= ( SV127 @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ ( SV127 @ SX0 ) ) ))]]) ).
thf(262,plain,
! [SV127: $i > $i] :
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( SV127 @ ( s @ zero ) ) )
= ( s @ ( SV127 @ zero ) ) )
= $false )
| ( ( ( s @ ( SV127 @ zero ) )
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ ( SV127 @ SX0 ) ) ))]]) ).
thf(264,plain,
! [SV127: $i > $i] :
( ( ( ( s @ ( SV127 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( s @ ( SV127 @ zero ) )
= ( s @ zero ) )
= $false )
| ( ( ( s @ ( SV127 @ zero ) )
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : ( s @ ( SV127 @ SX0 ) ) ))]]) ).
thf(265,plain,
( ( zero
= ( s @ zero ) )
= $false ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(266,plain,
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(268,plain,
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(extuni,[status(esa)],[205:[bind(SV58,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(269,plain,
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ zero )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[196:[bind(SV58,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(270,plain,
( ( zero
= ( s @ zero ) )
= $false ),
inference(extuni,[status(esa)],[196:[bind(SV58,$thf( ^ [SX0: $i] : zero ))]]) ).
thf(271,plain,
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(sim,[status(thm)],[268]) ).
thf(272,plain,
( ( ( zero
= ( s @ zero ) )
= $false )
| ( ( ( s @ zero )
= zero )
= $false ) ),
inference(sim,[status(thm)],[266]) ).
thf(273,plain,
! [SV127: $i > $i] :
( ( ( ( s @ ( SV127 @ ( s @ zero ) ) )
= zero )
= $false )
| ( ( ( s @ ( SV127 @ zero ) )
= ( s @ zero ) )
= $false ) ),
inference(sim,[status(thm)],[264]) ).
thf(274,plain,
( ( zero
= ( s @ zero ) )
= $false ),
inference(sim,[status(thm)],[259]) ).
thf(275,plain,
( ( ( ( s @ zero )
= zero )
= $false )
| ( ( zero
= ( s @ zero ) )
= $false ) ),
inference(sim,[status(thm)],[258]) ).
thf(276,plain,
( ( ( s @ zero )
= zero )
= $false ),
inference(sim,[status(thm)],[257]) ).
thf(277,plain,
( ( ( s @ ( s @ zero ) )
= zero )
= $false ),
inference(sim,[status(thm)],[253]) ).
thf(278,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[42,277,276,275,274,273,272,271,270,269,265,262,261,260,255,254,251,250,249,248,247,246,245,244,243,242,241,240,239,238,237,236,235,234,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,196,194,193,192,191,190,189,185,184,183,182,181,180,179,175,174,173,172,171,170,169,168,167,166,165,164,162,159,150,149,148,147,146,145,142,139,138,136,133,132,130,128,127,125,124,122,120,119,118,113,112]) ).
thf(279,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN023^1 : 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
% 0.07/0.17 % Computer : n004.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 13:46:09 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.22/0.43
% 1.22/0.43 No.of.Axioms: 0
% 1.22/0.43
% 1.22/0.43 Length.of.Defs: 0
% 1.22/0.43
% 1.22/0.43 Contains.Choice.Funs: false
% 1.22/0.43 ....
% 1.22/0.43
% 1.22/0.43 ********************************
% 1.22/0.43 * All subproblems solved! *
% 1.22/0.43 ********************************
% 1.22/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:278,loop_count:15,foatp_calls:5,translation:fof_full)
% 1.22/0.43
% 1.22/0.43 %**** Beginning of derivation protocol ****
% 1.22/0.43 % SZS output start CNFRefutation
% See solution above
% 1.22/0.43
% 1.22/0.43 %**** End of derivation protocol ****
% 1.22/0.43 %**** no. of clauses in derivation: 210 ****
% 1.22/0.43 %**** clause counter: 278 ****
% 1.22/0.43
% 1.22/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:278,loop_count:15,foatp_calls:5,translation:fof_full)
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