%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO540^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 0.10s 0.22s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 2
% Syntax : Number of formulae : 63 ( 13 unt; 0 typ; 1 def)
% Number of atoms : 965 ( 496 equ; 0 cnn)
% Maximal formula atoms : 4 ( 15 avg)
% Number of connectives : 1445 ( 871 ~; 464 |; 12 &; 98 @)
% ( 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 : 145 ( 95 ^; 50 !; 0 ?; 145 :)
% 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_SY13,type,
sK2_SY13: $i ).
thf(if,definition,
( if
= ( ^ [B: $o,X: $i,Y: $i] :
( eps
@ ^ [Z: $i] :
( ( B
& ( Z = X ) )
| ( ~ B
& ( Z = Y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifd) ).
thf(2,conjecture,
! [B: $o,X: $i] :
( ( if @ B @ X @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(3,negated_conjecture,
( ( ! [B: $o,X: $i] :
( ( if @ B @ X @ X )
= X ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ! [SY0: $o,SY1: $i] :
( ( eps
@ ^ [SY7: $i] :
( ( SY0
& ( SY7 = SY1 ) )
| ( ~ SY0
& ( SY7 = SY1 ) ) ) )
= SY1 ) )
= $false ),
inference(unfold_def,[status(thm)],[3,if]) ).
thf(6,plain,
( ( ! [SY13: $i] :
( ( eps
@ ^ [SY14: $i] :
( ( sK1_SY0
& ( SY14 = SY13 ) )
| ( ~ sK1_SY0
& ( SY14 = SY13 ) ) ) )
= SY13 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(7,plain,
( ( ( eps
@ ^ [SY15: $i] :
( ( sK1_SY0
& ( SY15 = sK2_SY13 ) )
| ( ~ sK1_SY0
& ( SY15 = sK2_SY13 ) ) ) )
= sK2_SY13 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ( eps
@ ^ [SY15: $i] :
( ( sK1_SY0
& ( SY15 = sK2_SY13 ) )
| ( ~ sK1_SY0
& ( SY15 = sK2_SY13 ) ) ) )
!= sK2_SY13 )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(10,plain,
( ( ( eps
@ ^ [SY15: $i] :
( ( sK1_SY0
& ( SY15 = sK2_SY13 ) )
| ( ~ sK1_SY0
& ( SY15 = sK2_SY13 ) ) ) )
!= sK2_SY13 )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 )
= $true ),
inference(unfold_def,[status(thm)],[10,if]) ).
thf(14,plain,
( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(20,plain,
( ( ~ ~ ! [SY17: $i] :
~ ( ~ ( ~ sK1_SY0
| ( SY17 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SY17 != sK2_SY13 ) ) )
| ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ),
inference(choice,[status(thm)],[14]) ).
thf(21,plain,
( ( ( ~ ~ ! [SY17: $i] :
~ ( ~ ( ~ sK1_SY0
| ( SY17 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SY17 != sK2_SY13 ) ) ) )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(22,plain,
( ( ( ~ ! [SY17: $i] :
~ ( ~ ( ~ sK1_SY0
| ( SY17 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SY17 != sK2_SY13 ) ) ) )
= $false )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(23,plain,
( ( ( ! [SY17: $i] :
~ ( ~ ( ~ sK1_SY0
| ( SY17 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SY17 != sK2_SY13 ) ) ) )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(24,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( ~ sK1_SY0
| ( SV4 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SV4 != sK2_SY13 ) ) ) )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(25,plain,
! [SV4: $i] :
( ( ( ~ ( ~ sK1_SY0
| ( SV4 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SV4 != sK2_SY13 ) ) )
= $false )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(26,plain,
! [SV4: $i] :
( ( ( ~ ( ~ sK1_SY0
| ( SV4 != sK2_SY13 ) ) )
= $false )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(27,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ~ sK1_SY0
| ( SV4 != sK2_SY13 ) ) )
= $false )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(28,plain,
! [SV4: $i] :
( ( ( ~ sK1_SY0
| ( SV4 != sK2_SY13 ) )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(29,plain,
! [SV4: $i] :
( ( ( ~ ~ sK1_SY0
| ( SV4 != sK2_SY13 ) )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(30,plain,
! [SV4: $i] :
( ( ( ~ sK1_SY0 ) = $true )
| ( ( SV4 != sK2_SY13 )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(31,plain,
! [SV4: $i] :
( ( ( ~ ~ sK1_SY0 )
= $true )
| ( ( SV4 != sK2_SY13 )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV4: $i] :
( ( sK1_SY0 = $false )
| ( ( SV4 != sK2_SY13 )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV4: $i] :
( ( ( ~ sK1_SY0 ) = $false )
| ( ( SV4 != sK2_SY13 )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV4: $i] :
( ( ( SV4 = sK2_SY13 )
= $false )
| ( sK1_SY0 = $false )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV4: $i] :
( ( sK1_SY0 = $true )
| ( ( SV4 != sK2_SY13 )
= $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(36,plain,
! [SV4: $i] :
( ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV4: $i] :
( ( ( SV4 = sK2_SY13 )
= $false )
| ( sK1_SY0 = $true )
| ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV4: $i] :
( ( ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
= $false )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV4: $i] :
( ( ( ~ ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 )
= $false )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV4: $i] :
( ( ( ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
= $false )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV4: $i] :
( ( ( ~ sK1_SY0 ) = $false )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 )
= $false )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(48,plain,
! [SV4: $i] :
( ( ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV4: $i] :
( ( sK1_SY0 = $true )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(50,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( ( ~ ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) ) )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(53,plain,
! [SV4: $i] :
( ( ( ~ ~ sK1_SY0 )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(55,plain,
! [SV4: $i] :
( ( ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
= $false )
| ( sK1_SY0 = $true )
| ( sK1_SY0 = $true )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV4: $i] :
( ( ( ~ ~ sK1_SY0
| ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 ) )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(59,plain,
! [SV4: $i] :
( ( ( ~ sK1_SY0 ) = $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(60,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(62,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 )
= $false )
| ( sK1_SY0 = $true )
| ( sK1_SY0 = $true )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(64,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
!= sK2_SY13 )
= $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(66,plain,
! [SV4: $i] :
( ( sK1_SY0 = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(68,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( sK1_SY0 = $true )
| ( sK1_SY0 = $true )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(70,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(75,plain,
( ( sK1_SY0 = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( sK1_SY0 = $false ) ),
inference(extuni,[status(esa)],[66:[bind(SV4,$thf( sK2_SY13 ))]]) ).
thf(76,plain,
( ( sK1_SY0 = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true ) ),
inference(extuni,[status(esa)],[60:[bind(SV4,$thf( sK2_SY13 ))]]) ).
thf(78,plain,
( ( sK1_SY0 = $true )
| ( sK1_SY0 = $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true ) ),
inference(extuni,[status(esa)],[68:[bind(SV4,$thf( sK2_SY13 ))]]) ).
thf(80,plain,
( ( sK1_SY0 = $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true ) ),
inference(extuni,[status(esa)],[70:[bind(SV4,$thf( sK2_SY13 ))]]) ).
thf(81,plain,
! [SV4: $i] :
( ( sK1_SY0 = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(sim,[status(thm)],[66]) ).
thf(82,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( sK1_SY0 = $false )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(sim,[status(thm)],[60]) ).
thf(83,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(sim,[status(thm)],[68]) ).
thf(84,plain,
! [SV4: $i] :
( ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true )
| ( sK1_SY0 = $true )
| ( ( SV4 = sK2_SY13 )
= $false ) ),
inference(sim,[status(thm)],[70]) ).
thf(85,plain,
( ( sK1_SY0 = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true ) ),
inference(sim,[status(thm)],[75]) ).
thf(86,plain,
( ( sK1_SY0 = $false )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true ) ),
inference(sim,[status(thm)],[76]) ).
thf(87,plain,
( ( sK1_SY0 = $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true ) ),
inference(sim,[status(thm)],[78]) ).
thf(88,plain,
( ( sK1_SY0 = $true )
| ( ( ( eps
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SY0
| ( SX0 != sK2_SY13 ) )
| ~ ( ~ ~ sK1_SY0
| ( SX0 != sK2_SY13 ) ) ) )
= sK2_SY13 )
= $true ) ),
inference(sim,[status(thm)],[80]) ).
thf(89,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,88,87,86,85,84,83,82,81]) ).
thf(90,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO540^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.16 % Computer : n003.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Oct 6 17:44:24 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.22
% 0.10/0.22 No.of.Axioms: 1
% 0.10/0.22
% 0.10/0.22 Length.of.Defs: 166
% 0.10/0.22
% 0.10/0.22 Contains.Choice.Funs: true
% 0.10/0.22
% 0.10/0.22 *** Modified list of choice operators: eps ***
% 0.10/0.22 .
% 0.10/0.22
% 0.10/0.22 ********************************
% 0.10/0.22 * All subproblems solved! *
% 0.10/0.22 ********************************
% 0.10/0.22 % SZS status Theorem for /export/starexec/sandbox/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:89,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.10/0.22
% 0.10/0.22 %**** Beginning of derivation protocol ****
% 0.10/0.22 % SZS output start CNFRefutation
% See solution above
% 0.10/0.22
% 0.10/0.22 %**** End of derivation protocol ****
% 0.10/0.22 %**** no. of clauses in derivation: 62 ****
% 0.10/0.22 %**** clause counter: 89 ****
% 0.10/0.22
% 0.10/0.22 % SZS status Theorem for /export/starexec/sandbox/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:89,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------