%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO539^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:08:41 AM UTC 2026
% Result : Theorem 0.09s 0.30s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 2
% Syntax : Number of formulae : 114 ( 21 unt; 0 typ; 1 def)
% Number of atoms : 1881 ( 970 equ; 0 cnn)
% Maximal formula atoms : 4 ( 16 avg)
% Number of connectives : 2896 (1745 ~; 922 |; 32 &; 197 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-3 aty)
% Number of variables : 282 ( 188 ^; 94 !; 0 ?; 282 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_eps,type,
eps: ( $i > $o ) > $i ).
thf(tp_if,type,
if: $o > $i > $i > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $o ).
thf(tp_sK2_SY22,type,
sK2_SY22: $i ).
thf(tp_sK3_SY26,type,
sK3_SY26: $i ).
thf(if,definition,
( if
= ( ^ [B: $o,X: $i,Y: $i] :
( eps
@ ^ [Z: $i] :
( ( B
& ( Z = X ) )
| ( ~ B
& ( Z = Y ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifd) ).
thf(2,conjecture,
! [B: $o,X: $i,Y: $i] :
( ( ( if @ B @ X @ Y )
= X )
| ( ( if @ B @ X @ Y )
= Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(3,negated_conjecture,
( ( ! [B: $o,X: $i,Y: $i] :
( ( ( if @ B @ X @ Y )
= X )
| ( ( if @ B @ X @ Y )
= Y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ! [SY0: $o,SY1: $i,SY2: $i] :
( ( ( eps
@ ^ [SY8: $i] :
( ( SY0
& ( SY8 = SY1 ) )
| ( ~ SY0
& ( SY8 = SY2 ) ) ) )
= SY1 )
| ( ( eps
@ ^ [SY14: $i] :
( ( SY0
& ( SY14 = SY1 ) )
| ( ~ SY0
& ( SY14 = SY2 ) ) ) )
= SY2 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[3,if]) ).
thf(6,plain,
( ( ! [SY22: $i,SY23: $i] :
( ( ( eps
@ ^ [SY24: $i] :
( ( sK1_SY0
& ( SY24 = SY22 ) )
| ( ~ sK1_SY0
& ( SY24 = SY23 ) ) ) )
= SY22 )
| ( ( eps
@ ^ [SY25: $i] :
( ( sK1_SY0
& ( SY25 = SY22 ) )
| ( ~ sK1_SY0
& ( SY25 = SY23 ) ) ) )
= SY23 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(7,plain,
( ( ! [SY26: $i] :
( ( ( eps
@ ^ [SY27: $i] :
( ( sK1_SY0
& ( SY27 = sK2_SY22 ) )
| ( ~ sK1_SY0
& ( SY27 = SY26 ) ) ) )
= sK2_SY22 )
| ( ( eps
@ ^ [SY28: $i] :
( ( sK1_SY0
& ( SY28 = sK2_SY22 ) )
| ( ~ sK1_SY0
& ( SY28 = SY26 ) ) ) )
= SY26 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ( ( eps
@ ^ [SY29: $i] :
( ( sK1_SY0
& ( SY29 = sK2_SY22 ) )
| ( ~ sK1_SY0
& ( SY29 = sK3_SY26 ) ) ) )
= sK2_SY22 )
| ( ( eps
@ ^ [SY30: $i] :
( ( sK1_SY0
& ( SY30 = sK2_SY22 ) )
| ( ~ sK1_SY0
& ( SY30 = sK3_SY26 ) ) ) )
= sK3_SY26 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(9,plain,
( ( ~ ( ( ( eps
@ ^ [SY29: $i] :
( ( sK1_SY0
& ( SY29 = sK2_SY22 ) )
| ( ~ sK1_SY0
& ( SY29 = sK3_SY26 ) ) ) )
= sK2_SY22 )
| ( ( eps
@ ^ [SY30: $i] :
( ( sK1_SY0
& ( SY30 = sK2_SY22 ) )
| ( ~ sK1_SY0
& ( SY30 = sK3_SY26 ) ) ) )
= sK3_SY26 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ( ( eps
@ ^ [SY29: $i] :
( ( sK1_SY0
& ( SY29 = sK2_SY22 ) )
| ( ~ sK1_SY0
& ( SY29 = sK3_SY26 ) ) ) )
!= sK2_SY22 )
& ( ( eps
@ ^ [SY30: $i] :
( ( sK1_SY0
& ( SY30 = sK2_SY22 ) )
| ( ~ sK1_SY0
& ( SY30 = sK3_SY26 ) ) ) )
!= sK3_SY26 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(13,plain,
( ( ( ( eps
@ ^ [SY29: $i] :
( ( sK1_SY0
& ( SY29 = sK2_SY22 ) )
| ( ~ sK1_SY0
& ( SY29 = sK3_SY26 ) ) ) )
!= sK2_SY22 )
& ( ( eps
@ ^ [SY30: $i] :
( ( sK1_SY0
& ( SY30 = sK2_SY22 ) )
| ( ~ sK1_SY0
& ( SY30 = sK3_SY26 ) ) ) )
!= sK3_SY26 ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(14,plain,
( ( ~ ( ~ ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,if]) ).
thf(16,plain,
( ( ~ ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(21,plain,
( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ~ ! [SY32: $i] :
~ ( ~ ( ~ sK1_SY0
| ( SY32 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SY32 != sK3_SY26 ) ) )
| ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ),
inference(choice,[status(thm)],[24]) ).
thf(27,plain,
( ( ~ ~ ! [SY34: $i] :
~ ( ~ ( ~ sK1_SY0
| ( SY34 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SY34 != sK3_SY26 ) ) )
| ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ),
inference(choice,[status(thm)],[25]) ).
thf(28,plain,
( ( ( ~ ~ ! [SY32: $i] :
~ ( ~ ( ~ sK1_SY0
| ( SY32 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SY32 != sK3_SY26 ) ) ) )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(29,plain,
( ( ( ~ ~ ! [SY34: $i] :
~ ( ~ ( ~ sK1_SY0
| ( SY34 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SY34 != sK3_SY26 ) ) ) )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(30,plain,
( ( ( ~ ! [SY32: $i] :
~ ( ~ ( ~ sK1_SY0
| ( SY32 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SY32 != sK3_SY26 ) ) ) )
= $false )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(31,plain,
( ( ( ~ ! [SY34: $i] :
~ ( ~ ( ~ sK1_SY0
| ( SY34 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SY34 != sK3_SY26 ) ) ) )
= $false )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(32,plain,
( ( ( ! [SY32: $i] :
~ ( ~ ( ~ sK1_SY0
| ( SY32 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SY32 != sK3_SY26 ) ) ) )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(33,plain,
( ( ( ! [SY34: $i] :
~ ( ~ ( ~ sK1_SY0
| ( SY34 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SY34 != sK3_SY26 ) ) ) )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(34,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( ~ sK1_SY0
| ( SV5 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SV5 != sK3_SY26 ) ) ) )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ( ~ sK1_SY0
| ( SV6 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SV6 != sK3_SY26 ) ) ) )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV5: $i] :
( ( ( ~ ( ~ sK1_SY0
| ( SV5 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SV5 != sK3_SY26 ) ) )
= $false )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV6: $i] :
( ( ( ~ ( ~ sK1_SY0
| ( SV6 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SV6 != sK3_SY26 ) ) )
= $false )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV5: $i] :
( ( ( ~ ( ~ sK1_SY0
| ( SV5 != sK2_SY22 ) ) )
= $false )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(39,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ~ sK1_SY0
| ( SV5 != sK3_SY26 ) ) )
= $false )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(40,plain,
! [SV6: $i] :
( ( ( ~ ( ~ sK1_SY0
| ( SV6 != sK2_SY22 ) ) )
= $false )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(41,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ~ sK1_SY0
| ( SV6 != sK3_SY26 ) ) )
= $false )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(42,plain,
! [SV5: $i] :
( ( ( ~ sK1_SY0
| ( SV5 != sK2_SY22 ) )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(43,plain,
! [SV5: $i] :
( ( ( ~ ~ sK1_SY0
| ( SV5 != sK3_SY26 ) )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(44,plain,
! [SV6: $i] :
( ( ( ~ sK1_SY0
| ( SV6 != sK2_SY22 ) )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV6: $i] :
( ( ( ~ ~ sK1_SY0
| ( SV6 != sK3_SY26 ) )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(46,plain,
! [SV5: $i] :
( ( ( ~ sK1_SY0 ) = $true )
| ( ( SV5 != sK2_SY22 )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV5: $i] :
( ( ( ~ ~ sK1_SY0 )
= $true )
| ( ( SV5 != sK3_SY26 )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV6: $i] :
( ( ( ~ sK1_SY0 ) = $true )
| ( ( SV6 != sK2_SY22 )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV6: $i] :
( ( ( ~ ~ sK1_SY0 )
= $true )
| ( ( SV6 != sK3_SY26 )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV5: $i] :
( ( sK1_SY0 = $false )
| ( ( SV5 != sK2_SY22 )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV5: $i] :
( ( ( ~ sK1_SY0 ) = $false )
| ( ( SV5 != sK3_SY26 )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV6: $i] :
( ( sK1_SY0 = $false )
| ( ( SV6 != sK2_SY22 )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV6: $i] :
( ( ( ~ sK1_SY0 ) = $false )
| ( ( SV6 != sK3_SY26 )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV5: $i] :
( ( ( SV5 = sK2_SY22 )
= $false )
| ( sK1_SY0 = $false )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV5: $i] :
( ( sK1_SY0 = $true )
| ( ( SV5 != sK3_SY26 )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV6: $i] :
( ( ( SV6 = sK2_SY22 )
= $false )
| ( sK1_SY0 = $false )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV6: $i] :
( ( sK1_SY0 = $true )
| ( ( SV6 != sK3_SY26 )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(58,plain,
! [SV5: $i] :
( ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) ) )
= $true )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV5 = sK2_SY22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV5: $i] :
( ( ( SV5 = sK3_SY26 )
= $false )
| ( sK1_SY0 = $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(60,plain,
! [SV6: $i] :
( ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) ) )
= $true )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV6 = sK2_SY22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV6: $i] :
( ( ( SV6 = sK3_SY26 )
= $false )
| ( sK1_SY0 = $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV5: $i] :
( ( ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
= $false )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV5 = sK2_SY22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV5: $i] :
( ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) ) )
= $true )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV5 = sK3_SY26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV6: $i] :
( ( ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
= $false )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV6 = sK2_SY22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV6: $i] :
( ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) ) )
= $true )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV6 = sK3_SY26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV5: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 )
= $false )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV5 = sK2_SY22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(68,plain,
! [SV5: $i] :
( ( ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
= $false )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV5 = sK3_SY26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV6: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 )
= $false )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV6 = sK2_SY22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(71,plain,
! [SV6: $i] :
( ( ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 ) )
= $false )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV6 = sK3_SY26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(73,plain,
! [SV5: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV5 = sK2_SY22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(74,plain,
! [SV5: $i] :
( ( ( ~ sK1_SY0 ) = $false )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV5 = sK3_SY26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(75,plain,
! [SV5: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 )
= $false )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV5 = sK3_SY26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(77,plain,
! [SV6: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV6 = sK2_SY22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(78,plain,
! [SV6: $i] :
( ( ( ~ sK1_SY0 ) = $false )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV6 = sK3_SY26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(79,plain,
! [SV6: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK2_SY22 )
= $false )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV6 = sK3_SY26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(81,plain,
! [SV5: $i] :
( ( ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV5 = sK2_SY22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(82,plain,
! [SV5: $i] :
( ( sK1_SY0 = $true )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV5 = sK3_SY26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(83,plain,
! [SV5: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV5 = sK3_SY26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(85,plain,
! [SV6: $i] :
( ( ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV6 = sK2_SY22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(86,plain,
! [SV6: $i] :
( ( sK1_SY0 = $true )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV6 = sK3_SY26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(87,plain,
! [SV6: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV6 = sK3_SY26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(90,plain,
! [SV5: $i] :
( ( ( ~ ~ sK1_SY0 )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV5 = sK2_SY22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(91,plain,
! [SV5: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV5 = sK2_SY22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(92,plain,
! [SV5: $i] :
( ( ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) )
= $false )
| ( sK1_SY0 = $true )
| ( sK1_SY0 = $true )
| ( ( SV5 = sK3_SY26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(93,plain,
! [SV5: $i] :
( ( ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV5 = sK3_SY26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(96,plain,
! [SV6: $i] :
( ( ( ~ ~ sK1_SY0 )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV6 = sK2_SY22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(97,plain,
! [SV6: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV6 = sK2_SY22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(98,plain,
! [SV6: $i] :
( ( ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) )
= $false )
| ( sK1_SY0 = $true )
| ( sK1_SY0 = $true )
| ( ( SV6 = sK3_SY26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(99,plain,
! [SV6: $i] :
( ( ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 ) )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV6 = sK3_SY26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(102,plain,
! [SV5: $i] :
( ( ( ~ sK1_SY0 ) = $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV5 = sK2_SY22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(103,plain,
! [SV5: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV5 = sK2_SY22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(105,plain,
! [SV5: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 )
= $false )
| ( sK1_SY0 = $true )
| ( sK1_SY0 = $true )
| ( ( SV5 = sK3_SY26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(107,plain,
! [SV5: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV5 = sK3_SY26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(110,plain,
! [SV6: $i] :
( ( ( ~ sK1_SY0 ) = $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV6 = sK2_SY22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(111,plain,
! [SV6: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV6 = sK2_SY22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(113,plain,
! [SV6: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 )
= $false )
| ( sK1_SY0 = $true )
| ( sK1_SY0 = $true )
| ( ( SV6 = sK3_SY26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(115,plain,
! [SV6: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
!= sK3_SY26 )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV6 = sK3_SY26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(117,plain,
! [SV5: $i] :
( ( sK1_SY0 = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV5 = sK2_SY22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(119,plain,
! [SV5: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $true )
| ( sK1_SY0 = $true )
| ( sK1_SY0 = $true )
| ( ( SV5 = sK3_SY26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(121,plain,
! [SV5: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV5 = sK3_SY26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(123,plain,
! [SV6: $i] :
( ( sK1_SY0 = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV6 = sK2_SY22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(125,plain,
! [SV6: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $true )
| ( sK1_SY0 = $true )
| ( sK1_SY0 = $true )
| ( ( SV6 = sK3_SY26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(127,plain,
! [SV6: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV6 = sK3_SY26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(134,plain,
( ( sK1_SY0 = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $false ) ),
inference(extuni,[status(esa)],[117:[bind(SV5,$thf( sK2_SY22 ))]]) ).
thf(135,plain,
( ( sK1_SY0 = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $true ) ),
inference(extuni,[status(esa)],[103:[bind(SV5,$thf( sK2_SY22 ))]]) ).
thf(137,plain,
( ( sK1_SY0 = $true )
| ( sK1_SY0 = $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $true ) ),
inference(extuni,[status(esa)],[119:[bind(SV5,$thf( sK3_SY26 ))]]) ).
thf(139,plain,
( ( sK1_SY0 = $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $true ) ),
inference(extuni,[status(esa)],[121:[bind(SV5,$thf( sK3_SY26 ))]]) ).
thf(142,plain,
( ( sK1_SY0 = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( sK1_SY0 = $false ) ),
inference(extuni,[status(esa)],[123:[bind(SV6,$thf( sK2_SY22 ))]]) ).
thf(143,plain,
( ( sK1_SY0 = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $true ) ),
inference(extuni,[status(esa)],[111:[bind(SV6,$thf( sK2_SY22 ))]]) ).
thf(145,plain,
( ( sK1_SY0 = $true )
| ( sK1_SY0 = $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $true ) ),
inference(extuni,[status(esa)],[125:[bind(SV6,$thf( sK3_SY26 ))]]) ).
thf(147,plain,
( ( sK1_SY0 = $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $true ) ),
inference(extuni,[status(esa)],[127:[bind(SV6,$thf( sK3_SY26 ))]]) ).
thf(148,plain,
! [SV5: $i] :
( ( sK1_SY0 = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( ( SV5 = sK2_SY22 )
= $false ) ),
inference(sim,[status(thm)],[117]) ).
thf(149,plain,
! [SV5: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV5 = sK3_SY26 )
= $false ) ),
inference(sim,[status(thm)],[119]) ).
thf(150,plain,
! [SV6: $i] :
( ( sK1_SY0 = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true )
| ( ( SV6 = sK2_SY22 )
= $false ) ),
inference(sim,[status(thm)],[123]) ).
thf(151,plain,
! [SV6: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV6 = sK3_SY26 )
= $false ) ),
inference(sim,[status(thm)],[125]) ).
thf(152,plain,
( ( sK1_SY0 = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true ) ),
inference(sim,[status(thm)],[134]) ).
thf(153,plain,
( ( sK1_SY0 = $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $true ) ),
inference(sim,[status(thm)],[137]) ).
thf(154,plain,
( ( sK1_SY0 = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK2_SY22 )
= $true ) ),
inference(sim,[status(thm)],[142]) ).
thf(155,plain,
( ( sK1_SY0 = $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY22 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK3_SY26 ) ) ) )
= sK3_SY26 )
= $true ) ),
inference(sim,[status(thm)],[145]) ).
thf(156,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,155,154,153,152,151,150,149,148,147,143,139,135,127,121,111,103,25]) ).
thf(157,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO539^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n008.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 17:43:09 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.30
% 0.09/0.30 No.of.Axioms: 1
% 0.09/0.30
% 0.09/0.30 Length.of.Defs: 167
% 0.09/0.30
% 0.09/0.30 Contains.Choice.Funs: true
% 0.09/0.30 .
% 0.09/0.30
% 0.09/0.30 *** Modified list of choice operators: eps ***
% 0.09/0.30 .
% 0.09/0.30
% 0.09/0.30 ********************************
% 0.09/0.30 * All subproblems solved! *
% 0.09/0.30 ********************************
% 0.09/0.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:156,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.09/0.30
% 0.09/0.30 %**** Beginning of derivation protocol ****
% 0.09/0.30 % SZS output start CNFRefutation
% See solution above
% 0.09/0.30
% 0.09/0.30 %**** End of derivation protocol ****
% 0.09/0.30 %**** no. of clauses in derivation: 113 ****
% 0.09/0.30 %**** clause counter: 156 ****
% 0.09/0.30
% 0.09/0.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:156,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------