%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO538^1 : 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 : 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 11:08:41 AM UTC 2026
% Result : Theorem 0.37s 0.35s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 2
% Syntax : Number of formulae : 76 ( 22 unt; 0 typ; 1 def)
% Number of atoms : 1155 ( 599 equ; 0 cnn)
% Maximal formula atoms : 4 ( 15 avg)
% Number of connectives : 1824 (1101 ~; 563 |; 31 &; 129 @)
% ( 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 : 7 ( 4 usr; 4 con; 0-3 aty)
% Number of variables : 176 ( 120 ^; 56 !; 0 ?; 176 :)
% 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: $i ).
thf(tp_sK2_SY20,type,
sK2_SY20: $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,
! [X: $i,Y: $i] :
( ( ( if @ $true @ X @ Y )
= X )
& ( ( if @ $false @ X @ Y )
= Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(3,negated_conjecture,
( ( ! [X: $i,Y: $i] :
( ( ( if @ $true @ X @ Y )
= X )
& ( ( if @ $false @ X @ Y )
= Y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ! [SY0: $i,SY1: $i] :
( ( ( eps
@ ^ [SY7: $i] :
( ( $true
& ( SY7 = SY0 ) )
| ( ~ $true
& ( SY7 = SY1 ) ) ) )
= SY0 )
& ( ( eps
@ ^ [SY13: $i] :
( ( $false
& ( SY13 = SY0 ) )
| ( ~ $false
& ( SY13 = SY1 ) ) ) )
= SY1 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[3,if]) ).
thf(6,plain,
( ( ! [SY20: $i] :
( ( ( eps
@ ^ [SY21: $i] :
( ( $true
& ( SY21 = sK1_SY0 ) )
| ( ~ $true
& ( SY21 = SY20 ) ) ) )
= sK1_SY0 )
& ( ( eps
@ ^ [SY22: $i] :
( ( $false
& ( SY22 = sK1_SY0 ) )
| ( ~ $false
& ( SY22 = SY20 ) ) ) )
= SY20 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(7,plain,
( ( ( ( eps
@ ^ [SY23: $i] :
( ( $true
& ( SY23 = sK1_SY0 ) )
| ( ~ $true
& ( SY23 = sK2_SY20 ) ) ) )
= sK1_SY0 )
& ( ( eps
@ ^ [SY24: $i] :
( ( $false
& ( SY24 = sK1_SY0 ) )
| ( ~ $false
& ( SY24 = sK2_SY20 ) ) ) )
= sK2_SY20 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ( eps
@ ^ [SY23: $i] :
( ( $true
& ( SY23 = sK1_SY0 ) )
| ( ~ $true
& ( SY23 = sK2_SY20 ) ) ) )
= sK1_SY0 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(9,plain,
( ( ( eps
@ ^ [SY24: $i] :
( ( $false
& ( SY24 = sK1_SY0 ) )
| ( ~ $false
& ( SY24 = sK2_SY20 ) ) ) )
= sK2_SY20 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(10,plain,
( ( ( eps
@ ^ [SY23: $i] :
( ( $true
& ( SY23 = sK1_SY0 ) )
| ( ~ $true
& ( SY23 = sK2_SY20 ) ) ) )
!= sK1_SY0 )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ( eps
@ ^ [SY24: $i] :
( ( $false
& ( SY24 = sK1_SY0 ) )
| ( ~ $false
& ( SY24 = sK2_SY20 ) ) ) )
!= sK2_SY20 )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(13,plain,
( ( ( eps
@ ^ [SY23: $i] :
( ( $true
& ( SY23 = sK1_SY0 ) )
| ( ~ $true
& ( SY23 = sK2_SY20 ) ) ) )
!= sK1_SY0 )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(14,plain,
( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 )
= $true ),
inference(unfold_def,[status(thm)],[13,if]) ).
thf(16,plain,
( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(23,plain,
( ( ~ ~ ! [SY26: $i] :
~ ( ~ ( ~ $true
| ( SY26 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SY26 != sK2_SY20 ) ) )
| ~ ( ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ),
inference(choice,[status(thm)],[16]) ).
thf(24,plain,
( ( ( ~ ~ ! [SY26: $i] :
~ ( ~ ( ~ $true
| ( SY26 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SY26 != sK2_SY20 ) ) ) )
= $true )
| ( ( ~ ( ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(25,plain,
( ( ( ~ ! [SY26: $i] :
~ ( ~ ( ~ $true
| ( SY26 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SY26 != sK2_SY20 ) ) ) )
= $false )
| ( ( ~ ( ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(26,plain,
( ( ( ! [SY26: $i] :
~ ( ~ ( ~ $true
| ( SY26 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SY26 != sK2_SY20 ) ) ) )
= $true )
| ( ( ~ ( ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(27,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( ~ $true
| ( SV4 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SV4 != sK2_SY20 ) ) ) )
= $true )
| ( ( ~ ( ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(28,plain,
! [SV4: $i] :
( ( ( ~ ( ~ $true
| ( SV4 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SV4 != sK2_SY20 ) ) )
= $false )
| ( ( ~ ( ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(29,plain,
! [SV4: $i] :
( ( ( ~ ( ~ $true
| ( SV4 != sK1_SY0 ) ) )
= $false )
| ( ( ~ ( ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(31,plain,
! [SV4: $i] :
( ( ( ~ $true
| ( SV4 != sK1_SY0 ) )
= $true )
| ( ( ~ ( ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV4: $i] :
( ( ( ~ $true ) = $true )
| ( ( SV4 != sK1_SY0 )
= $true )
| ( ( ~ ( ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV4: $i] :
( ( $true = $false )
| ( ( SV4 != sK1_SY0 )
= $true )
| ( ( ~ ( ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV4: $i] :
( ( ( SV4 = sK1_SY0 )
= $false )
| ( $true = $false )
| ( ( ~ ( ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV4: $i] :
( ( ( ~ ( ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) ) )
= $true )
| ( ( ~ ( ~ ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true )
| ( $true = $false )
| ( ( SV4 = sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV4: $i] :
( ( ( ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
= $false )
| ( ( ~ ( ~ ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true )
| ( $true = $false )
| ( ( SV4 = sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 )
= $false )
| ( ( ~ ( ~ ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true )
| ( $true = $false )
| ( ( SV4 = sK1_SY0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( ( ~ ( ~ ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true )
| ( $true = $false )
| ( ( SV4 = sK1_SY0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(51,plain,
! [SV4: $i] :
( ( ( ~ ~ $true
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( $true = $false )
| ( ( SV4 = sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(56,plain,
! [SV4: $i] :
( ( ( ~ ~ $true )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( $true = $false )
| ( ( SV4 = sK1_SY0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(57,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( $true = $false )
| ( ( SV4 = sK1_SY0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(62,plain,
! [SV4: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( $true = $false )
| ( ( SV4 = sK1_SY0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(63,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK2_SY20 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( $true = $false )
| ( ( SV4 = sK1_SY0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(69,plain,
! [SV4: $i] :
( ( $true = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( $true = $false )
| ( ( SV4 = sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(78,plain,
( ( $true = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( $true = $false ) ),
inference(extuni,[status(esa)],[69:[bind(SV4,$thf( sK1_SY0 ))]]) ).
thf(79,plain,
( ( $true = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK2_SY20 )
= $true ) ),
inference(extuni,[status(esa)],[63:[bind(SV4,$thf( sK1_SY0 ))]]) ).
thf(84,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( ( SV4 = sK1_SY0 )
= $false ) ),
inference(sim,[status(thm)],[69]) ).
thf(85,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK2_SY20 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( ( SV4 = sK1_SY0 )
= $false ) ),
inference(sim,[status(thm)],[63]) ).
thf(86,plain,
( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true ),
inference(sim,[status(thm)],[78]) ).
thf(87,plain,
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $true
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $true
| ( SX0 != sK2_SY20 ) ) ) )
= sK2_SY20 )
= $true ) ),
inference(sim,[status(thm)],[79]) ).
thf(88,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,87,86,85,84]) ).
thf(90,plain,
( ( ( eps
@ ^ [SY24: $i] :
( ( $false
& ( SY24 = sK1_SY0 ) )
| ( ~ $false
& ( SY24 = sK2_SY20 ) ) ) )
!= sK2_SY20 )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(91,plain,
( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 )
= $true ),
inference(unfold_def,[status(thm)],[90,if]) ).
thf(93,plain,
( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
= sK2_SY20 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(100,plain,
( ( ~ ~ ! [SY29: $i] :
~ ( ~ ( ~ $false
| ( SY29 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SY29 != sK2_SY20 ) ) )
| ~ ( ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ),
inference(choice,[status(thm)],[93]) ).
thf(101,plain,
( ( ( ~ ~ ! [SY29: $i] :
~ ( ~ ( ~ $false
| ( SY29 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SY29 != sK2_SY20 ) ) ) )
= $true )
| ( ( ~ ( ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(102,plain,
( ( ( ~ ! [SY29: $i] :
~ ( ~ ( ~ $false
| ( SY29 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SY29 != sK2_SY20 ) ) ) )
= $false )
| ( ( ~ ( ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(103,plain,
( ( ( ! [SY29: $i] :
~ ( ~ ( ~ $false
| ( SY29 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SY29 != sK2_SY20 ) ) ) )
= $true )
| ( ( ~ ( ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(104,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( ~ $false
| ( SV8 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SV8 != sK2_SY20 ) ) ) )
= $true )
| ( ( ~ ( ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(105,plain,
! [SV8: $i] :
( ( ( ~ ( ~ $false
| ( SV8 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SV8 != sK2_SY20 ) ) )
= $false )
| ( ( ~ ( ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(107,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ~ $false
| ( SV8 != sK2_SY20 ) ) )
= $false )
| ( ( ~ ( ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(109,plain,
! [SV8: $i] :
( ( ( ~ ~ $false
| ( SV8 != sK2_SY20 ) )
= $true )
| ( ( ~ ( ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(111,plain,
! [SV8: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( SV8 != sK2_SY20 )
= $true )
| ( ( ~ ( ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(113,plain,
! [SV8: $i] :
( ( ( ~ $false ) = $false )
| ( ( SV8 != sK2_SY20 )
= $true )
| ( ( ~ ( ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(115,plain,
! [SV8: $i] :
( ( $false = $true )
| ( ( SV8 != sK2_SY20 )
= $true )
| ( ( ~ ( ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(117,plain,
! [SV8: $i] :
( ( ( SV8 = sK2_SY20 )
= $false )
| ( $false = $true )
| ( ( ~ ( ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(119,plain,
! [SV8: $i] :
( ( ( ~ ( ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) ) )
= $true )
| ( ( ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true )
| ( $false = $true )
| ( ( SV8 = sK2_SY20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(122,plain,
! [SV8: $i] :
( ( ( ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 ) )
= $false )
| ( ( ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true )
| ( $false = $true )
| ( ( SV8 = sK2_SY20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(125,plain,
! [SV8: $i] :
( ( ( ~ $false ) = $false )
| ( ( ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true )
| ( $false = $true )
| ( ( SV8 = sK2_SY20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(126,plain,
! [SV8: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK1_SY0 )
= $false )
| ( ( ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true )
| ( $false = $true )
| ( ( SV8 = sK2_SY20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(129,plain,
! [SV8: $i] :
( ( $false = $true )
| ( ( ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true )
| ( $false = $true )
| ( ( SV8 = sK2_SY20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(130,plain,
! [SV8: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( ( ~ ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) ) )
= $true )
| ( $false = $true )
| ( ( SV8 = sK2_SY20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(135,plain,
! [SV8: $i] :
( ( ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) )
= $false )
| ( $false = $true )
| ( $false = $true )
| ( ( SV8 = sK2_SY20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(136,plain,
! [SV8: $i] :
( ( ( ~ ~ $false
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 ) )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( $false = $true )
| ( ( SV8 = sK2_SY20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(142,plain,
! [SV8: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 )
= $false )
| ( $false = $true )
| ( $false = $true )
| ( ( SV8 = sK2_SY20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(144,plain,
! [SV8: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
!= sK2_SY20 )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( $false = $true )
| ( ( SV8 = sK2_SY20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(148,plain,
! [SV8: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
= sK2_SY20 )
= $true )
| ( $false = $true )
| ( $false = $true )
| ( ( SV8 = sK2_SY20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(150,plain,
! [SV8: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
= sK2_SY20 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( $false = $true )
| ( ( SV8 = sK2_SY20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(158,plain,
( ( $false = $true )
| ( $false = $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
= sK2_SY20 )
= $true ) ),
inference(extuni,[status(esa)],[148:[bind(SV8,$thf( sK2_SY20 ))]]) ).
thf(160,plain,
( ( $false = $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
= sK2_SY20 )
= $true ) ),
inference(extuni,[status(esa)],[150:[bind(SV8,$thf( sK2_SY20 ))]]) ).
thf(161,plain,
! [SV8: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
= sK2_SY20 )
= $true )
| ( ( SV8 = sK2_SY20 )
= $false ) ),
inference(sim,[status(thm)],[148]) ).
thf(162,plain,
! [SV8: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
= sK2_SY20 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( ( SV8 = sK2_SY20 )
= $false ) ),
inference(sim,[status(thm)],[150]) ).
thf(163,plain,
( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
= sK2_SY20 )
= $true ),
inference(sim,[status(thm)],[158]) ).
thf(164,plain,
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
= sK1_SY0 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ $false
| ( SX0 != sK1_SY0 ) )
| ~ ( ~ ~ $false
| ( SX0 != sK2_SY20 ) ) ) )
= sK2_SY20 )
= $true ) ),
inference(sim,[status(thm)],[160]) ).
thf(165,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[93,164,163,162,161]) ).
thf(166,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[165,88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO538^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.21 % Computer : n004.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Oct 6 17:42:24 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.37/0.35
% 0.37/0.35 No.of.Axioms: 1
% 0.37/0.35
% 0.37/0.35 Length.of.Defs: 167
% 0.37/0.35
% 0.37/0.35 Contains.Choice.Funs: true
% 0.37/0.35
% 0.37/0.35 *** Modified list of choice operators: eps ***
% 0.37/0.35 .
% 0.37/0.35
% 0.37/0.35 *** Modified list of choice operators: eps ***
% 0.37/0.35 .
% 0.37/0.35
% 0.37/0.35 ********************************
% 0.37/0.35 * All subproblems solved! *
% 0.37/0.35 ********************************
% 0.37/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,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:165,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.37/0.35
% 0.37/0.35 %**** Beginning of derivation protocol ****
% 0.37/0.35 % SZS output start CNFRefutation
% See solution above
% 0.37/0.36
% 0.37/0.36 %**** End of derivation protocol ****
% 0.37/0.36 %**** no. of clauses in derivation: 75 ****
% 0.37/0.36 %**** clause counter: 165 ****
% 0.37/0.36
% 0.37/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,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:165,loop_count:0,foatp_calls:2,translation:fof_full)
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