%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET557^1 : TPTP v9.3.1. Released v3.6.0.
% 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 : n007.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 10:40:20 AM UTC 2026
% Result : Theorem 0.05s 0.27s
% Output : CNFRefutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 1
% Syntax : Number of formulae : 126 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 783 ( 279 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 1733 ( 357 ~; 141 |; 0 &;1235 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 142 ( 142 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 509 ( 300 ^; 199 !; 10 ?; 509 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_SX0,type,
sK1_SX0: $i > $i > $o ).
thf(tp_sK2_SY5,type,
sK2_SY5: ( $i > $o ) > $i ).
thf(tp_sK3_E,type,
sK3_E: ( $i > $i > $o ) > $i ).
thf(tp_sK4_E,type,
sK4_E: ( $i > $i ) > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK5_E,type,
sK5_E: ( $i > $i > $o ) > $i ).
thf(tp_sK6_E,type,
sK6_E: ( $i > $i ) > $i > ( $i > $i > $o ) > $i ).
thf(1,conjecture,
~ ? [G: $i > $i > $o] :
! [F: $i > $o] :
? [X: $i] :
( ( G @ X )
= F ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjectiveCantorThm) ).
thf(2,negated_conjecture,
( ( ~ ? [G: $i > $i > $o] :
! [F: $i > $o] :
? [X: $i] :
( ( G @ X )
= F ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ~ ? [G: $i > $i > $o] :
! [F: $i > $o] :
? [X: $i] :
( ( G @ X )
= F ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ? [G: $i > $i > $o] :
! [F: $i > $o] :
? [X: $i] :
( ( G @ X )
= F ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ? [G: $i > $i > $o] :
! [F: $i > $o] :
? [X: $i] :
( ( G @ X )
= F ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ! [SX0: $i > $i > $o] :
~ ! [SX1: $i > $o] :
~ ! [SX2: $i] :
( ( SX0 @ SX2 )
!= SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SX0: $i > $i > $o] :
~ ! [SX1: $i > $o] :
~ ! [SX2: $i] :
( ( SX0 @ SX2 )
!= SX1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ! [SY3: $i > $o] :
~ ! [SY4: $i] :
( ( sK1_SX0 @ SY4 )
!= SY3 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [SY3: $i > $o] :
~ ! [SY4: $i] :
( ( sK1_SX0 @ SY4 )
!= SY3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: $i > $o] :
( ( ~ ! [SY5: $i] :
( ( sK1_SX0 @ SY5 )
!= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: $i > $o] :
( ( ! [SY5: $i] :
( ( sK1_SX0 @ SY5 )
!= SV1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(12,plain,
! [SV1: $i > $o] :
( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) )
!= SV1 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(13,plain,
! [SV1: $i > $o] :
( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[12]) ).
thf(14,plain,
! [SV1: $i > $o] :
( ( ! [SV2: $i] :
( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV2 )
= ( SV1 @ SV2 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[13]) ).
thf(15,plain,
! [SV1: $i > $o] :
( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
= ( SV1 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ~ ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
| ( SV1 @ SV3 ) )
| ~ ( ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
| ~ ( SV1 @ SV3 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[16]) ).
thf(18,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
= ( SV1 @ SV3 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[16]) ).
thf(19,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
| ( SV1 @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
| ~ ( SV1 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(20,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
| ( SV1 @ SV3 ) )
= $false )
| ( ( ~ ( ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
| ~ ( SV1 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(21,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
= $false )
| ( ( ~ ( ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
| ~ ( SV1 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(22,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ SV3 )
= $false )
| ( ( ~ ( ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
| ~ ( SV1 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(23,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
| ~ ( SV1 @ SV3 ) )
= $false )
| ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
| ~ ( SV1 @ SV3 ) )
= $false )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV3 ) )
= $false )
| ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(27,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) )
= $false )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(30,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ SV3 )
= $true )
| ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(31,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
= $true )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(34,plain,
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $true ) )
= ( ^ [SX0: $i] : $true ) )
= $true ),
inference(prim_subst,[status(thm)],[15:[bind(SV1,$thf( ^ [SV8: $i] : $true ))]]) ).
thf(35,plain,
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $false ) )
= ( ^ [SX0: $i] : $false ) )
= $true ),
inference(prim_subst,[status(thm)],[15:[bind(SV1,$thf( ^ [SV7: $i] : $false ))]]) ).
thf(36,plain,
! [SV6: $i > $o] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) ) )
= ( ^ [SX0: $i] :
~ ( SV6 @ SX0 ) ) )
= $true ),
inference(prim_subst,[status(thm)],[15:[bind(SV1,$thf( ^ [SV5: $i] : ~ ( SV6 @ SV5 ) ))]]) ).
thf(37,plain,
! [SV3: $i] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $true )
@ SV3 )
= $true )
= $true ),
inference(prim_subst,[status(thm)],[18:[bind(SV1,$thf( ^ [SV8: $i] : $true ))]]) ).
thf(38,plain,
! [SV3: $i] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $false )
@ SV3 )
= $false )
= $true ),
inference(prim_subst,[status(thm)],[18:[bind(SV1,$thf( ^ [SV7: $i] : $false ))]]) ).
thf(39,plain,
! [SV3: $i,SV6: $i > $o] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV3 )
= ( ~ ( SV6 @ SV3 ) ) )
= $true ),
inference(prim_subst,[status(thm)],[18:[bind(SV1,$thf( ^ [SV5: $i] : ~ ( SV6 @ SV5 ) ))]]) ).
thf(44,plain,
! [SV3: $i] :
( ( $false = $true )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $false )
@ SV3 )
= $false ) ),
inference(prim_subst,[status(thm)],[30:[bind(SV1,$thf( ^ [SV7: $i] : $false ))]]) ).
thf(45,plain,
! [SV3: $i,SV6: $i > $o] :
( ( ( ~ ( SV6 @ SV3 ) )
= $true )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV3 )
= $false ) ),
inference(prim_subst,[status(thm)],[30:[bind(SV1,$thf( ^ [SV5: $i] : ~ ( SV6 @ SV5 ) ))]]) ).
thf(46,plain,
! [SV3: $i] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $true )
@ SV3 )
= $true )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[31:[bind(SV1,$thf( ^ [SV8: $i] : $true ))]]) ).
thf(48,plain,
! [SV3: $i,SV6: $i > $o] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV3 )
= $true )
| ( ( ~ ( SV6 @ SV3 ) )
= $false ) ),
inference(prim_subst,[status(thm)],[31:[bind(SV1,$thf( ^ [SV5: $i] : ~ ( SV6 @ SV5 ) ))]]) ).
thf(49,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ SV3 )
= $true )
| ( ( ( SV1 @ SV3 )
= ( ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[30]) ).
thf(50,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ SV3 )
= $false )
| ( ( ( SV1 @ SV3 )
= ( ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[31]) ).
thf(51,plain,
! [SV1: $i > $o,SV9: $i] :
( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV9 )
= ( SV1 @ SV9 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[15]) ).
thf(52,plain,
! [SV1: $i > $o,SV9: $i] :
( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV9 )
= $true )
| ( ( SV1 @ SV9 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[51]) ).
thf(53,plain,
! [SV1: $i > $o,SV9: $i] :
( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV9 )
= $false )
| ( ( SV1 @ SV9 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[51]) ).
thf(54,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
= $true )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[18]) ).
thf(55,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
= $false )
| ( ( SV1 @ SV3 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[18]) ).
thf(56,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( ( SV1 @ SV3 )
| ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) )
| ~ ( ~ ( SV1 @ SV3 )
| ~ ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[49]) ).
thf(57,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ( SV1 @ SV3 )
= ( ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[49]) ).
thf(58,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( ( SV1 @ SV3 )
| ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) )
| ~ ( ~ ( SV1 @ SV3 )
| ~ ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[50]) ).
thf(59,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ( SV1 @ SV3 )
= ( ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[50]) ).
thf(60,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( ( SV1 @ SV3 )
| ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(63,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( ~ ( SV1 @ SV3 )
| ~ ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(64,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ( SV1 @ SV3 )
| ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) )
= $true )
| ( ( SV1 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(67,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV3 )
| ~ ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ SV3 )
= $true )
| ( ( ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) )
= $true )
| ( ( SV1 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV3 ) )
= $true )
| ( ( ~ ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(72,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
= $false )
| ( ( SV1 @ SV3 )
= $true )
| ( ( SV1 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ SV3 )
= $false )
| ( ( ~ ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) )
= $true )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 ) )
= $false )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(79,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
= $true )
| ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(80,plain,
! [SV27: $i > $i > $o] :
( ( ( ~ ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV27
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( sK1_SX0 @ SX1
@ ( sK2_SY5
@ ^ [SX2: $i] :
~ ( SV27 @ SX1 @ SX2 ) ) ) )
@ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV27
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ( sK1_SX0
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV27
@ ( sK3_E
@ ^ [SX1: $i,SX2: $i] :
~ ( SV27 @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[57:[bind(SV3,$thf( sK2_SY5 @ ^ [SX0: $i] : ~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ^ [SX1: $i] : ~ ( SV27 @ SX0 @ SX1 ) ) ) )),bind(SV1,$thf( ^ [SX0: $i] : ~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ^ [SX1: $i] : ~ ( SV27 @ SX0 @ SX1 ) ) ) ))]]) ).
thf(81,plain,
! [SV27: $i > $i > $o] :
( ( ( ~ ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV27
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( sK1_SX0 @ SX1
@ ( sK2_SY5
@ ^ [SX2: $i] :
~ ( SV27 @ SX1 @ SX2 ) ) ) )
@ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV27
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ( sK1_SX0
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV27
@ ( sK3_E
@ ^ [SX1: $i,SX2: $i] :
~ ( SV27 @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[57:[bind(SV3,$thf( sK2_SY5 @ ^ [SX0: $i] : ~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ^ [SX1: $i] : ~ ( SV27 @ SX0 @ SX1 ) ) ) )),bind(SV1,$thf( ^ [SX0: $i] : ~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ^ [SX1: $i] : ~ ( SV27 @ SX0 @ SX1 ) ) ) ))]]) ).
thf(82,plain,
! [SV22: $i > $i > $o] :
( ( ( ~ ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV22 @ SX0 ) ) ) )
@ ( sK2_SY5
@ ( SV22
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV22 @ SX0 ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK2_SY5
@ ( SV22
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV22 @ SX0 ) ) ) ) ) )
= ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV22 @ SX0 ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[57:[bind(SV3,$thf( sK2_SY5 @ ^ [SX0: $i] : ~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV22 @ SX0 ) ) ) )),bind(SV1,$thf( ^ [SX0: $i] : ~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV22 @ SX0 ) ) ) ))]]) ).
thf(83,plain,
( ( ~ ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ SX0 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ SX0 ) ) ) )
= $true ),
inference(extuni,[status(esa)],[57:[bind(SV3,$thf( sK2_SY5 @ ^ [SX0: $i] : ~ ( sK1_SX0 @ SX0 @ SX0 ) )),bind(SV1,$thf( ^ [SX0: $i] : ~ ( sK1_SX0 @ SX0 @ SX0 ) ))]]) ).
thf(85,plain,
! [SV16: $i > $i,SV3: $i,SV15: $i > $i] :
( ( ( ~ ( sK1_SX0 @ ( SV15 @ SV3 ) @ ( SV16 @ SV3 ) ) )
= $true )
| ( ( sK1_SX0 @ ( SV15 @ SV3 ) @ ( SV16 @ SV3 ) )
= $false )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ ( SV15 @ SX0 ) @ ( SV16 @ SX0 ) ) )
@ SV3 )
= $false ) ),
inference(extuni,[status(esa)],[57:[bind(SV1,$thf( ^ [SX0: $i] : ~ ( sK1_SX0 @ ( SV15 @ SX0 ) @ ( SV16 @ SX0 ) ) ))]]) ).
thf(86,plain,
! [SV3: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ SV3 ) )
= $true )
| ( ( ~ ( SV12 @ SV3 ) )
= $true )
| ( ( ~ ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) )
@ SV3 ) )
= $true ) ),
inference(extuni,[status(esa)],[57:[bind(SV1,$thf( ^ [SX0: $i] : ~ ( SV12 @ SX0 ) ))]]) ).
thf(88,plain,
! [SV67: $i > $i > $o] :
( ( ( ~ ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV67
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( sK1_SX0 @ SX1
@ ( sK2_SY5
@ ^ [SX2: $i] :
~ ( SV67 @ SX1 @ SX2 ) ) ) )
@ SX0 ) ) ) )
= $false )
| ( ( ~ ( SV67
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ( sK1_SX0
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV67
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] :
~ ( SV67 @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[59:[bind(SV3,$thf( sK2_SY5 @ ^ [SX0: $i] : ~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ^ [SX1: $i] : ~ ( SV67 @ SX0 @ SX1 ) ) ) )),bind(SV1,$thf( ^ [SX0: $i] : ~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ^ [SX1: $i] : ~ ( SV67 @ SX0 @ SX1 ) ) ) ))]]) ).
thf(89,plain,
! [SV67: $i > $i > $o] :
( ( ( ~ ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV67
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( sK1_SX0 @ SX1
@ ( sK2_SY5
@ ^ [SX2: $i] :
~ ( SV67 @ SX1 @ SX2 ) ) ) )
@ SX0 ) ) ) )
= $false )
| ( ( ~ ( SV67
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ( sK1_SX0
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV67
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] :
~ ( SV67 @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[59:[bind(SV3,$thf( sK2_SY5 @ ^ [SX0: $i] : ~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ^ [SX1: $i] : ~ ( SV67 @ SX0 @ SX1 ) ) ) )),bind(SV1,$thf( ^ [SX0: $i] : ~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ^ [SX1: $i] : ~ ( SV67 @ SX0 @ SX1 ) ) ) ))]]) ).
thf(90,plain,
! [SV62: $i > $i > $o] :
( ( ( ~ ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV62 @ SX0 ) ) ) )
@ ( sK2_SY5
@ ( SV62
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV62 @ SX0 ) ) ) ) ) ) ) )
= $false )
| ( ( ( sK2_SY5
@ ( SV62
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV62 @ SX0 ) ) ) ) ) )
= ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV62 @ SX0 ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[59:[bind(SV3,$thf( sK2_SY5 @ ^ [SX0: $i] : ~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV62 @ SX0 ) ) ) )),bind(SV1,$thf( ^ [SX0: $i] : ~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV62 @ SX0 ) ) ) ))]]) ).
thf(91,plain,
( ( ~ ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ SX0 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ SX0 ) ) ) )
= $false ),
inference(extuni,[status(esa)],[59:[bind(SV3,$thf( sK2_SY5 @ ^ [SX0: $i] : ~ ( sK1_SX0 @ SX0 @ SX0 ) )),bind(SV1,$thf( ^ [SX0: $i] : ~ ( sK1_SX0 @ SX0 @ SX0 ) ))]]) ).
thf(92,plain,
! [SV56: $i > $i,SV3: $i,SV55: $i > $i] :
( ( ( ~ ( sK1_SX0 @ ( SV55 @ SV3 ) @ ( SV56 @ SV3 ) ) )
= $false )
| ( ( sK1_SX0 @ ( SV55 @ SV3 ) @ ( SV56 @ SV3 ) )
= $true )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ ( SV55 @ SX0 ) @ ( SV56 @ SX0 ) ) )
@ SV3 )
= $true ) ),
inference(extuni,[status(esa)],[59:[bind(SV1,$thf( ^ [SX0: $i] : ~ ( sK1_SX0 @ ( SV55 @ SX0 ) @ ( SV56 @ SX0 ) ) ))]]) ).
thf(95,plain,
! [SV3: $i,SV52: $i > $o] :
( ( ( ~ ( SV52 @ SV3 ) )
= $false )
| ( ( ~ ( SV52 @ SV3 ) )
= $false )
| ( ( ~ ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV52 @ SX0 ) )
@ SV3 ) )
= $false ) ),
inference(extuni,[status(esa)],[59:[bind(SV1,$thf( ^ [SX0: $i] : ~ ( SV52 @ SX0 ) ))]]) ).
thf(97,plain,
! [SV3: $i,SV12: $i > $o] :
( ( ( SV12 @ SV3 )
= $false )
| ( ( ~ ( SV12 @ SV3 ) )
= $true )
| ( ( ~ ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) )
@ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(98,plain,
! [SV16: $i > $i,SV3: $i,SV15: $i > $i] :
( ( ( sK1_SX0 @ ( SV15 @ SV3 ) @ ( SV16 @ SV3 ) )
= $false )
| ( ( sK1_SX0 @ ( SV15 @ SV3 ) @ ( SV16 @ SV3 ) )
= $false )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ ( SV15 @ SX0 ) @ ( SV16 @ SX0 ) ) )
@ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(100,plain,
( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ SX0 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(101,plain,
! [SV22: $i > $i > $o] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV22 @ SX0 ) ) ) )
@ ( sK2_SY5
@ ( SV22
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV22 @ SX0 ) ) ) ) ) ) )
= $false )
| ( ( ( sK2_SY5
@ ( SV22
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV22 @ SX0 ) ) ) ) ) )
= ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV22 @ SX0 ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(102,plain,
! [SV27: $i > $i > $o] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV27
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( sK1_SX0 @ SX1
@ ( sK2_SY5
@ ^ [SX2: $i] :
~ ( SV27 @ SX1 @ SX2 ) ) ) )
@ SX0 ) ) )
= $false )
| ( ( ~ ( SV27
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ( sK1_SX0
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV27
@ ( sK3_E
@ ^ [SX1: $i,SX2: $i] :
~ ( SV27 @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(103,plain,
! [SV27: $i > $i > $o] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV27
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( sK1_SX0 @ SX1
@ ( sK2_SY5
@ ^ [SX2: $i] :
~ ( SV27 @ SX1 @ SX2 ) ) ) )
@ SX0 ) ) )
= $false )
| ( ( ~ ( SV27
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ( sK1_SX0
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV27
@ ( sK3_E
@ ^ [SX1: $i,SX2: $i] :
~ ( SV27 @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(104,plain,
! [SV3: $i,SV52: $i > $o] :
( ( ( SV52 @ SV3 )
= $true )
| ( ( ~ ( SV52 @ SV3 ) )
= $false )
| ( ( ~ ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV52 @ SX0 ) )
@ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(107,plain,
! [SV56: $i > $i,SV3: $i,SV55: $i > $i] :
( ( ( sK1_SX0 @ ( SV55 @ SV3 ) @ ( SV56 @ SV3 ) )
= $true )
| ( ( sK1_SX0 @ ( SV55 @ SV3 ) @ ( SV56 @ SV3 ) )
= $true )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ ( SV55 @ SX0 ) @ ( SV56 @ SX0 ) ) )
@ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(108,plain,
( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ SX0 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(109,plain,
! [SV62: $i > $i > $o] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV62 @ SX0 ) ) ) )
@ ( sK2_SY5
@ ( SV62
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV62 @ SX0 ) ) ) ) ) ) )
= $true )
| ( ( ( sK2_SY5
@ ( SV62
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV62 @ SX0 ) ) ) ) ) )
= ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0 @ ( sK2_SY5 @ ( SV62 @ SX0 ) ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(110,plain,
! [SV67: $i > $i > $o] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV67
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( sK1_SX0 @ SX1
@ ( sK2_SY5
@ ^ [SX2: $i] :
~ ( SV67 @ SX1 @ SX2 ) ) ) )
@ SX0 ) ) )
= $true )
| ( ( ~ ( SV67
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ( sK1_SX0
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV67
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] :
~ ( SV67 @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(111,plain,
! [SV67: $i > $i > $o] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV67
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( sK1_SX0 @ SX1
@ ( sK2_SY5
@ ^ [SX2: $i] :
~ ( SV67 @ SX1 @ SX2 ) ) ) )
@ SX0 ) ) )
= $true )
| ( ( ~ ( SV67
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ( sK1_SX0
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV67
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] :
~ ( SV67 @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(113,plain,
! [SV3: $i,SV12: $i > $o] :
( ( ( SV12 @ SV3 )
= $false )
| ( ( SV12 @ SV3 )
= $false )
| ( ( ~ ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) )
@ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(114,plain,
! [SV27: $i > $i > $o] :
( ( ( SV27
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) )
= $true )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV27
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( sK1_SX0 @ SX1
@ ( sK2_SY5
@ ^ [SX2: $i] :
~ ( SV27 @ SX1 @ SX2 ) ) ) )
@ SX0 ) ) )
= $false )
| ( ( ~ ( sK1_SX0
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV27
@ ( sK3_E
@ ^ [SX1: $i,SX2: $i] :
~ ( SV27 @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(115,plain,
! [SV27: $i > $i > $o] :
( ( ( SV27
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) )
= $false )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV27
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( sK1_SX0 @ SX1
@ ( sK2_SY5
@ ^ [SX2: $i] :
~ ( SV27 @ SX1 @ SX2 ) ) ) )
@ SX0 ) ) )
= $false )
| ( ( ~ ( sK1_SX0
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV27
@ ( sK3_E
@ ^ [SX1: $i,SX2: $i] :
~ ( SV27 @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(116,plain,
! [SV3: $i,SV52: $i > $o] :
( ( ( SV52 @ SV3 )
= $true )
| ( ( SV52 @ SV3 )
= $true )
| ( ( ~ ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV52 @ SX0 ) )
@ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(118,plain,
! [SV67: $i > $i > $o] :
( ( ( SV67
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) )
= $true )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV67
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( sK1_SX0 @ SX1
@ ( sK2_SY5
@ ^ [SX2: $i] :
~ ( SV67 @ SX1 @ SX2 ) ) ) )
@ SX0 ) ) )
= $true )
| ( ( ~ ( sK1_SX0
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV67
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] :
~ ( SV67 @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(119,plain,
! [SV67: $i > $i > $o] :
( ( ( SV67
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) )
= $false )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV67
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( sK1_SX0 @ SX1
@ ( sK2_SY5
@ ^ [SX2: $i] :
~ ( SV67 @ SX1 @ SX2 ) ) ) )
@ SX0 ) ) )
= $true )
| ( ( ~ ( sK1_SX0
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV67
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] :
~ ( SV67 @ SX1 @ SX2 ) )
@ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(121,plain,
! [SV3: $i,SV12: $i > $o] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) )
@ SV3 )
= $false )
| ( ( SV12 @ SV3 )
= $false )
| ( ( SV12 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(122,plain,
! [SV27: $i > $i > $o] :
( ( ( sK1_SX0
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV27
@ ( sK3_E
@ ^ [SX1: $i,SX2: $i] :
~ ( SV27 @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV27
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( sK1_SX0 @ SX1
@ ( sK2_SY5
@ ^ [SX2: $i] :
~ ( SV27 @ SX1 @ SX2 ) ) ) )
@ SX0 ) ) )
= $false )
| ( ( SV27
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(123,plain,
! [SV27: $i > $i > $o] :
( ( ( sK1_SX0
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV27
@ ( sK3_E
@ ^ [SX1: $i,SX2: $i] :
~ ( SV27 @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $false )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV27
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( sK1_SX0 @ SX1
@ ( sK2_SY5
@ ^ [SX2: $i] :
~ ( SV27 @ SX1 @ SX2 ) ) ) )
@ SX0 ) ) )
= $false )
| ( ( SV27
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) ) )
@ ( sK3_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(124,plain,
! [SV3: $i,SV52: $i > $o] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV52 @ SX0 ) )
@ SV3 )
= $true )
| ( ( SV52 @ SV3 )
= $true )
| ( ( SV52 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(126,plain,
! [SV67: $i > $i > $o] :
( ( ( sK1_SX0
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV67
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] :
~ ( SV67 @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $true )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV67
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( sK1_SX0 @ SX1
@ ( sK2_SY5
@ ^ [SX2: $i] :
~ ( SV67 @ SX1 @ SX2 ) ) ) )
@ SX0 ) ) )
= $true )
| ( ( SV67
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(127,plain,
! [SV67: $i > $i > $o] :
( ( ( sK1_SX0
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV67
@ ( sK5_E
@ ^ [SX1: $i,SX2: $i] :
~ ( SV67 @ SX1 @ SX2 ) )
@ SX0 ) ) )
= $false )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV67
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( sK1_SX0 @ SX1
@ ( sK2_SY5
@ ^ [SX2: $i] :
~ ( SV67 @ SX1 @ SX2 ) ) ) )
@ SX0 ) ) )
= $true )
| ( ( SV67
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ SX0
@ ( sK2_SY5
@ ^ [SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) ) )
@ ( sK5_E
@ ^ [SX0: $i,SX1: $i] :
~ ( SV67 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(128,plain,
! [SV90: $i] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $true )
@ SV90 )
= $true )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[34]) ).
thf(129,plain,
! [SV91: $i] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $false )
@ SV91 )
= $false )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[35]) ).
thf(130,plain,
! [SV6: $i > $o,SV92: $i] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV92 )
= ( ~ ( SV6 @ SV92 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[36]) ).
thf(131,plain,
! [SV90: $i] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $true )
@ SV90 )
= $true )
| ( $true = $false ) ),
inference(extcnf_equal_pos,[status(thm)],[128]) ).
thf(134,plain,
! [SV91: $i] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $false )
@ SV91 )
= $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[129]) ).
thf(135,plain,
! [SV6: $i > $o,SV92: $i] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV92 )
= $true )
| ( ( ~ ( SV6 @ SV92 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[130]) ).
thf(136,plain,
! [SV6: $i > $o,SV92: $i] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV92 )
= $false )
| ( ( ~ ( SV6 @ SV92 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[130]) ).
thf(137,plain,
! [SV3: $i] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $true )
@ SV3 )
= $true )
| ( $true = $false ) ),
inference(extcnf_equal_pos,[status(thm)],[37]) ).
thf(140,plain,
! [SV3: $i] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $false )
@ SV3 )
= $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[38]) ).
thf(141,plain,
! [SV3: $i,SV6: $i > $o] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV3 )
= $true )
| ( ( ~ ( SV6 @ SV3 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[39]) ).
thf(142,plain,
! [SV3: $i,SV6: $i > $o] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV3 )
= $false )
| ( ( ~ ( SV6 @ SV3 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[39]) ).
thf(143,plain,
! [SV92: $i,SV6: $i > $o] :
( ( ( SV6 @ SV92 )
= $false )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(144,plain,
! [SV92: $i,SV6: $i > $o] :
( ( ( SV6 @ SV92 )
= $true )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(145,plain,
! [SV3: $i,SV6: $i > $o] :
( ( ( SV6 @ SV3 )
= $false )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(146,plain,
! [SV3: $i,SV6: $i > $o] :
( ( ( SV6 @ SV3 )
= $true )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(147,plain,
! [SV3: $i,SV6: $i > $o] :
( ( ( SV6 @ SV3 )
= $false )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(148,plain,
! [SV3: $i,SV6: $i > $o] :
( ( ( SV6 @ SV3 )
= $true )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV6 @ SX0 ) )
@ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(149,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
= $false )
| ( ( SV1 @ SV3 )
= $true ) ),
inference(sim,[status(thm)],[72]) ).
thf(150,plain,
! [SV3: $i,SV12: $i > $o] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV12 @ SX0 ) )
@ SV3 )
= $false )
| ( ( SV12 @ SV3 )
= $false ) ),
inference(sim,[status(thm)],[121]) ).
thf(151,plain,
! [SV16: $i > $i,SV3: $i,SV15: $i > $i] :
( ( ( sK1_SX0 @ ( SV15 @ SV3 ) @ ( SV16 @ SV3 ) )
= $false )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ ( SV15 @ SX0 ) @ ( SV16 @ SX0 ) ) )
@ SV3 )
= $false ) ),
inference(sim,[status(thm)],[98]) ).
thf(152,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( sK1_SX0 @ ( sK2_SY5 @ SV1 ) @ SV3 )
= $true )
| ( ( SV1 @ SV3 )
= $false ) ),
inference(sim,[status(thm)],[79]) ).
thf(153,plain,
! [SV3: $i,SV52: $i > $o] :
( ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( SV52 @ SX0 ) )
@ SV3 )
= $true )
| ( ( SV52 @ SV3 )
= $true ) ),
inference(sim,[status(thm)],[124]) ).
thf(154,plain,
! [SV56: $i > $i,SV3: $i,SV55: $i > $i] :
( ( ( sK1_SX0 @ ( SV55 @ SV3 ) @ ( SV56 @ SV3 ) )
= $true )
| ( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] :
~ ( sK1_SX0 @ ( SV55 @ SX0 ) @ ( SV56 @ SX0 ) ) )
@ SV3 )
= $true ) ),
inference(sim,[status(thm)],[107]) ).
thf(155,plain,
! [SV90: $i] :
( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $true )
@ SV90 )
= $true ),
inference(sim,[status(thm)],[131]) ).
thf(156,plain,
! [SV91: $i] :
( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $false )
@ SV91 )
= $false ),
inference(sim,[status(thm)],[134]) ).
thf(157,plain,
! [SV3: $i] :
( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $true )
@ SV3 )
= $true ),
inference(sim,[status(thm)],[137]) ).
thf(158,plain,
! [SV3: $i] :
( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $false )
@ SV3 )
= $false ),
inference(sim,[status(thm)],[140]) ).
thf(159,plain,
! [SV3: $i] :
( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $false )
@ SV3 )
= $false ),
inference(sim,[status(thm)],[44]) ).
thf(160,plain,
! [SV3: $i] :
( ( sK1_SX0
@ ( sK2_SY5
@ ^ [SX0: $i] : $true )
@ SV3 )
= $true ),
inference(sim,[status(thm)],[46]) ).
thf(161,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,127,126,123,122,109,108,101,100,55,54,53,52,31,30,18]) ).
thf(162,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET557^1 : TPTP v9.3.1. Released v3.6.0.
% 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
% 0.05/0.17 % Computer : n007.cluster.edu
% 0.05/0.17 % Model : x86_64 x86_64
% 0.05/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.17 % Memory : 8046.5625MB
% 0.05/0.17 % OS : Linux 6.8.0-71-generic
% 0.05/0.17 % CPULimit : 300
% 0.05/0.17 % WCLimit : 300
% 0.05/0.17 % DateTime : Tue Oct 6 14:44:15 UTC 2026
% 0.05/0.17 % CPUTime :
% 0.05/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.27
% 0.05/0.27 No.of.Axioms: 0
% 0.05/0.27
% 0.05/0.27 Length.of.Defs: 0
% 0.05/0.27
% 0.05/0.27 Contains.Choice.Funs: false
% 0.05/0.27 ..
% 0.05/0.27
% 0.05/0.27 ********************************
% 0.05/0.27 * All subproblems solved! *
% 0.05/0.27 ********************************
% 0.05/0.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:161,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.05/0.27
% 0.05/0.27 %**** Beginning of derivation protocol ****
% 0.05/0.27 % SZS output start CNFRefutation
% See solution above
% 0.05/0.27
% 0.05/0.27 %**** End of derivation protocol ****
% 0.05/0.27 %**** no. of clauses in derivation: 126 ****
% 0.05/0.27 %**** clause counter: 161 ****
% 0.05/0.27
% 0.05/0.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:161,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------