%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO362^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n020.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 11:08:07 AM UTC 2026
% Result : Theorem 1.01s 0.42s
% Output : CNFRefutation 1.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 1
% Syntax : Number of formulae : 116 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 802 ( 221 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 1403 ( 137 ~; 317 |; 4 &; 927 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 191 ( 191 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-3 aty)
% Number of variables : 397 ( 110 ^; 287 !; 0 ?; 397 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cK,type,
cK: ( $i > $o ) > $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i > $o ).
thf(tp_sK2_SY8,type,
sK2_SY8: $i > $o ).
thf(tp_sK3_SY12,type,
sK3_SY12: $i ).
thf(tp_sK4_E,type,
sK4_E: $i ).
thf(tp_sK5_E,type,
sK5_E: $i ).
thf(tp_sK6_E,type,
sK6_E: $i ).
thf(tp_sK7_E,type,
sK7_E: $i ).
thf(tp_sK8_E,type,
sK8_E: $i ).
thf(tp_sK9_E,type,
sK9_E: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(1,conjecture,
( ! [X: $i > $o,Y: $i > $o] :
( ( cK
@ ^ [Xz: $i] :
( ( X @ Xz )
| ( Y @ Xz ) ) )
= ( ^ [Xw: $i] :
( ( cK @ X @ Xw )
| ( cK @ Y @ Xw ) ) ) )
=> ! [X: $i > $o,Y: $i > $o] :
( ! [Xx: $i] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: $i] :
( ( cK @ X @ Xx )
=> ( cK @ Y @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM631A_pme) ).
thf(2,negated_conjecture,
( ( ! [X: $i > $o,Y: $i > $o] :
( ( cK
@ ^ [Xz: $i] :
( ( X @ Xz )
| ( Y @ Xz ) ) )
= ( ^ [Xw: $i] :
( ( cK @ X @ Xw )
| ( cK @ Y @ Xw ) ) ) )
=> ! [X: $i > $o,Y: $i > $o] :
( ! [Xx: $i] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: $i] :
( ( cK @ X @ Xx )
=> ( cK @ Y @ Xx ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: $i > $o,Y: $i > $o] :
( ( cK
@ ^ [Xz: $i] :
( ( X @ Xz )
| ( Y @ Xz ) ) )
= ( ^ [Xw: $i] :
( ( cK @ X @ Xw )
| ( cK @ Y @ Xw ) ) ) )
=> ! [X: $i > $o,Y: $i > $o] :
( ! [Xx: $i] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: $i] :
( ( cK @ X @ Xx )
=> ( cK @ Y @ Xx ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [X: $i > $o,Y: $i > $o] :
( ( cK
@ ^ [Xz: $i] :
( ( X @ Xz )
| ( Y @ Xz ) ) )
= ( ^ [Xw: $i] :
( ( cK @ X @ Xw )
| ( cK @ Y @ Xw ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [X: $i > $o,Y: $i > $o] :
( ! [Xx: $i] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: $i] :
( ( cK @ X @ Xx )
=> ( cK @ Y @ Xx ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [X: $i > $o,Y: $i > $o] :
( ! [Xx: $i] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: $i] :
( ( cK @ X @ Xx )
=> ( cK @ Y @ Xx ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY11: $i] :
( ~ ( sK1_X @ SY11 )
| ( sK2_SY8 @ SY11 ) )
& ( cK @ sK1_X @ sK3_SY12 )
& ~ ( cK @ sK2_SY8 @ sK3_SY12 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [X: $i > $o,Y: $i > $o] :
( ( cK
@ ^ [Xz: $i] :
( ( X @ Xz )
| ( Y @ Xz ) ) )
= ( ^ [Xw: $i] :
( ( cK @ X @ Xw )
| ( cK @ Y @ Xw ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(9,plain,
( ( ! [SY11: $i] :
( ~ ( sK1_X @ SY11 )
| ( sK2_SY8 @ SY11 ) )
& ( cK @ sK1_X @ sK3_SY12 )
& ~ ( cK @ sK2_SY8 @ sK3_SY12 ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( sK1_X @ SX0 )
| ( sK2_SY8 @ SX0 ) )
| ~ ~ ( ~ ( cK @ sK1_X @ sK3_SY12 )
| ~ ~ ( cK @ sK2_SY8 @ sK3_SY12 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: $i > $o] :
( ( ! [SY13: $i > $o] :
( ( cK
@ ^ [SY14: $i] :
( ( SV1 @ SY14 )
| ( SY13 @ SY14 ) ) )
= ( ^ [SY15: $i] :
( ( cK @ SV1 @ SY15 )
| ( cK @ SY13 @ SY15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_X @ SX0 )
| ( sK2_SY8 @ SX0 ) )
| ~ ~ ( ~ ( cK @ sK1_X @ sK3_SY12 )
| ~ ~ ( cK @ sK2_SY8 @ sK3_SY12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(13,plain,
! [SV2: $i > $o,SV1: $i > $o] :
( ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) ) )
= ( ^ [SY17: $i] :
( ( cK @ SV1 @ SY17 )
| ( cK @ SV2 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_X @ SX0 )
| ( sK2_SY8 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ~ ( ~ ( cK @ sK1_X @ sK3_SY12 )
| ~ ~ ( cK @ sK2_SY8 @ sK3_SY12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(16,plain,
! [SV2: $i > $o,SV1: $i > $o] :
( ( ! [SV3: $i] :
( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV3 )
= ( ( cK @ SV1 @ SV3 )
| ( cK @ SV2 @ SV3 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV2: $i > $o,SV1: $i > $o] :
( ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) ) )
= ( ^ [SY17: $i] :
( ( cK @ SV1 @ SY17 )
| ( cK @ SV2 @ SY17 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[13]) ).
thf(18,plain,
( ( ! [SX0: $i] :
( ~ ( sK1_X @ SX0 )
| ( sK2_SY8 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(19,plain,
( ( ~ ( ~ ( cK @ sK1_X @ sK3_SY12 )
| ~ ~ ( cK @ sK2_SY8 @ sK3_SY12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(20,plain,
! [SV4: $i,SV2: $i > $o,SV1: $i > $o] :
( ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
= ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
! [SV5: $i] :
( ( ~ ( sK1_X @ SV5 )
| ( sK2_SY8 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ( cK @ sK1_X @ sK3_SY12 )
| ~ ~ ( cK @ sK2_SY8 @ sK3_SY12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV4: $i,SV2: $i > $o,SV1: $i > $o] :
( ( ~ ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
| ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) )
| ~ ( ~ ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
| ~ ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV4: $i,SV2: $i > $o,SV1: $i > $o] :
( ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
= ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV5: $i] :
( ( ( ~ ( sK1_X @ SV5 ) )
= $true )
| ( ( sK2_SY8 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ( cK @ sK1_X @ sK3_SY12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( ~ ~ ( cK @ sK2_SY8 @ sK3_SY12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(28,plain,
! [SV4: $i,SV2: $i > $o,SV1: $i > $o] :
( ( ( ~ ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
| ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
| ~ ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV5: $i] :
( ( ( sK1_X @ SV5 )
= $false )
| ( ( sK2_SY8 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(30,plain,
( ( cK @ sK1_X @ sK3_SY12 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(31,plain,
( ( ~ ( cK @ sK2_SY8 @ sK3_SY12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(32,plain,
! [SV4: $i,SV2: $i > $o,SV1: $i > $o] :
( ( ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
| ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
| ~ ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( cK @ sK2_SY8 @ sK3_SY12 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV4: $i,SV2: $i > $o,SV1: $i > $o] :
( ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
= $false )
| ( ( ~ ( ~ ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
| ~ ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(35,plain,
! [SV2: $i > $o,SV4: $i,SV1: $i > $o] :
( ( ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
| ~ ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV4: $i,SV2: $i > $o,SV1: $i > $o] :
( ( ( ~ ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
| ~ ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) ) )
= $false )
| ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV2: $i > $o,SV4: $i,SV1: $i > $o] :
( ( ( cK @ SV1 @ SV4 )
= $false )
| ( ( ~ ( ~ ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
| ~ ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(38,plain,
! [SV1: $i > $o,SV4: $i,SV2: $i > $o] :
( ( ( cK @ SV2 @ SV4 )
= $false )
| ( ( ~ ( ~ ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
| ~ ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
! [SV2: $i > $o,SV4: $i,SV1: $i > $o] :
( ( ( ~ ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) ) )
= $false )
| ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(41,plain,
! [SV4: $i,SV2: $i > $o,SV1: $i > $o] :
( ( ( ~ ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
| ~ ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) ) )
= $false )
| ( ( cK @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV4: $i,SV2: $i > $o,SV1: $i > $o] :
( ( ( ~ ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
| ~ ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) ) )
= $false )
| ( ( cK @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV2: $i > $o,SV4: $i,SV1: $i > $o] :
( ( ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) )
= $true )
| ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV4: $i,SV2: $i > $o,SV1: $i > $o] :
( ( ( ~ ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 ) )
= $false )
| ( ( cK @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV4: $i,SV2: $i > $o,SV1: $i > $o] :
( ( ( ~ ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 ) )
= $false )
| ( ( cK @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(49,plain,
! [SV2: $i > $o,SV4: $i,SV1: $i > $o] :
( ( ( cK @ SV1 @ SV4 )
= $true )
| ( ( cK @ SV2 @ SV4 )
= $true )
| ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV4: $i,SV2: $i > $o,SV1: $i > $o] :
( ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
= $true )
| ( ( cK @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(52,plain,
! [SV4: $i,SV2: $i > $o,SV1: $i > $o] :
( ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
= $true )
| ( ( cK @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(56,plain,
! [SV2: $i > $o,SV1: $i > $o,SV6: $i] :
( ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV6 )
= ( ( cK @ SV1 @ SV6 )
| ( cK @ SV2 @ SV6 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[17]) ).
thf(57,plain,
! [SV2: $i > $o,SV1: $i > $o,SV6: $i] :
( ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV6 )
= $true )
| ( ( ( cK @ SV1 @ SV6 )
| ( cK @ SV2 @ SV6 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[56]) ).
thf(58,plain,
! [SV2: $i > $o,SV1: $i > $o,SV6: $i] :
( ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV6 )
= $false )
| ( ( ( cK @ SV1 @ SV6 )
| ( cK @ SV2 @ SV6 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV4: $i,SV2: $i > $o,SV1: $i > $o] :
( ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
= $true )
| ( ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[24]) ).
thf(60,plain,
! [SV4: $i,SV2: $i > $o,SV1: $i > $o] :
( ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
= $false )
| ( ( ( cK @ SV1 @ SV4 )
| ( cK @ SV2 @ SV4 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[24]) ).
thf(61,plain,
! [SV2: $i > $o,SV6: $i,SV1: $i > $o] :
( ( ( cK @ SV1 @ SV6 )
= $true )
| ( ( cK @ SV2 @ SV6 )
= $true )
| ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV2: $i > $o,SV6: $i,SV1: $i > $o] :
( ( ( cK @ SV1 @ SV6 )
= $false )
| ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(63,plain,
! [SV1: $i > $o,SV6: $i,SV2: $i > $o] :
( ( ( cK @ SV2 @ SV6 )
= $false )
| ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(64,plain,
! [SV2: $i > $o,SV4: $i,SV1: $i > $o] :
( ( ( cK @ SV1 @ SV4 )
= $true )
| ( ( cK @ SV2 @ SV4 )
= $true )
| ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV2: $i > $o,SV4: $i,SV1: $i > $o] :
( ( ( cK @ SV1 @ SV4 )
= $false )
| ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(66,plain,
! [SV1: $i > $o,SV4: $i,SV2: $i > $o] :
( ( ( cK @ SV2 @ SV4 )
= $false )
| ( ( cK
@ ^ [SY16: $i] :
( ( SV1 @ SY16 )
| ( SV2 @ SY16 ) )
@ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(67,plain,
! [SV7: $i > $o,SV8: $i > $o] :
( ( ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) ) )
= ( ^ [SX0: $i] :
( ( cK @ SV8 @ SX0 )
| ( cK @ SV7 @ SX0 ) ) ) )
= $true ),
inference(rename,[status(thm)],[17]) ).
thf(68,plain,
! [SV7: $i > $o,SV8: $i > $o] :
( ( ! [SV9: $i] :
( ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV9 )
= ( ( cK @ SV8 @ SV9 )
| ( cK @ SV7 @ SV9 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[67]) ).
thf(70,plain,
! [SV10: $i,SV7: $i > $o,SV8: $i > $o] :
( ( ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
= ( ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(71,plain,
! [SV10: $i,SV7: $i > $o,SV8: $i > $o] :
( ( ~ ( ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
| ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) )
| ~ ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
| ~ ( ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[70]) ).
thf(73,plain,
! [SV10: $i,SV7: $i > $o,SV8: $i > $o] :
( ( ( ~ ( ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
| ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) ) )
= $true )
| ( ( ~ ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
| ~ ( ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(74,plain,
! [SV10: $i,SV7: $i > $o,SV8: $i > $o] :
( ( ( ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
| ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) )
= $false )
| ( ( ~ ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
| ~ ( ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(75,plain,
! [SV10: $i,SV7: $i > $o,SV8: $i > $o] :
( ( ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
= $false )
| ( ( ~ ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
| ~ ( ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(76,plain,
! [SV7: $i > $o,SV10: $i,SV8: $i > $o] :
( ( ( ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) )
= $false )
| ( ( ~ ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
| ~ ( ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(77,plain,
! [SV10: $i,SV7: $i > $o,SV8: $i > $o] :
( ( ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
| ~ ( ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) ) )
= $false )
| ( ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(78,plain,
! [SV7: $i > $o,SV10: $i,SV8: $i > $o] :
( ( ( cK @ SV8 @ SV10 )
= $false )
| ( ( ~ ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
| ~ ( ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(79,plain,
! [SV8: $i > $o,SV10: $i,SV7: $i > $o] :
( ( ( cK @ SV7 @ SV10 )
= $false )
| ( ( ~ ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
| ~ ( ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(81,plain,
! [SV7: $i > $o,SV10: $i,SV8: $i > $o] :
( ( ( ~ ( ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) ) )
= $false )
| ( ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(82,plain,
! [SV10: $i,SV7: $i > $o,SV8: $i > $o] :
( ( ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
| ~ ( ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) ) )
= $false )
| ( ( cK @ SV8 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV10: $i,SV7: $i > $o,SV8: $i > $o] :
( ( ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
| ~ ( ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) ) )
= $false )
| ( ( cK @ SV7 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(85,plain,
! [SV7: $i > $o,SV10: $i,SV8: $i > $o] :
( ( ( ( cK @ SV8 @ SV10 )
| ( cK @ SV7 @ SV10 ) )
= $true )
| ( ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(86,plain,
! [SV10: $i,SV7: $i > $o,SV8: $i > $o] :
( ( ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 ) )
= $false )
| ( ( cK @ SV8 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(88,plain,
! [SV10: $i,SV7: $i > $o,SV8: $i > $o] :
( ( ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 ) )
= $false )
| ( ( cK @ SV7 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(90,plain,
! [SV7: $i > $o,SV10: $i,SV8: $i > $o] :
( ( ( cK @ SV8 @ SV10 )
= $true )
| ( ( cK @ SV7 @ SV10 )
= $true )
| ( ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(91,plain,
! [SV10: $i,SV7: $i > $o,SV8: $i > $o] :
( ( ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
= $true )
| ( ( cK @ SV8 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(93,plain,
! [SV10: $i,SV7: $i > $o,SV8: $i > $o] :
( ( ( cK
@ ^ [SX0: $i] :
( ( SV8 @ SX0 )
| ( SV7 @ SX0 ) )
@ SV10 )
= $true )
| ( ( cK @ SV7 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(97,plain,
! [SV11: $i,SV12: $i > $o,SV13: $i > $o] :
( ( ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
= ( ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) ) )
= $true ),
inference(rename,[status(thm)],[24]) ).
thf(98,plain,
! [SV11: $i,SV12: $i > $o,SV13: $i > $o] :
( ( ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
= $true )
| ( ( ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[97]) ).
thf(99,plain,
! [SV11: $i,SV12: $i > $o,SV13: $i > $o] :
( ( ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
= $false )
| ( ( ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[97]) ).
thf(100,plain,
! [SV11: $i,SV12: $i > $o,SV13: $i > $o] :
( ( ~ ( ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
| ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) )
| ~ ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
| ~ ( ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[97]) ).
thf(102,plain,
! [SV11: $i,SV12: $i > $o,SV13: $i > $o] :
( ( ( ~ ( ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
| ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
| ~ ( ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(103,plain,
! [SV11: $i,SV12: $i > $o,SV13: $i > $o] :
( ( ( ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
| ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) )
= $false )
| ( ( ~ ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
| ~ ( ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(104,plain,
! [SV11: $i,SV12: $i > $o,SV13: $i > $o] :
( ( ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
= $false )
| ( ( ~ ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
| ~ ( ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(105,plain,
! [SV12: $i > $o,SV11: $i,SV13: $i > $o] :
( ( ( ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) )
= $false )
| ( ( ~ ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
| ~ ( ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(106,plain,
! [SV11: $i,SV12: $i > $o,SV13: $i > $o] :
( ( ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
| ~ ( ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) ) )
= $false )
| ( ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(107,plain,
! [SV12: $i > $o,SV11: $i,SV13: $i > $o] :
( ( ( cK @ SV13 @ SV11 )
= $false )
| ( ( ~ ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
| ~ ( ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(108,plain,
! [SV13: $i > $o,SV11: $i,SV12: $i > $o] :
( ( ( cK @ SV12 @ SV11 )
= $false )
| ( ( ~ ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
| ~ ( ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(110,plain,
! [SV12: $i > $o,SV11: $i,SV13: $i > $o] :
( ( ( ~ ( ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) ) )
= $false )
| ( ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(111,plain,
! [SV11: $i,SV12: $i > $o,SV13: $i > $o] :
( ( ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
| ~ ( ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) ) )
= $false )
| ( ( cK @ SV13 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV11: $i,SV12: $i > $o,SV13: $i > $o] :
( ( ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
| ~ ( ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) ) )
= $false )
| ( ( cK @ SV12 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(114,plain,
! [SV12: $i > $o,SV11: $i,SV13: $i > $o] :
( ( ( ( cK @ SV13 @ SV11 )
| ( cK @ SV12 @ SV11 ) )
= $true )
| ( ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(115,plain,
! [SV11: $i,SV12: $i > $o,SV13: $i > $o] :
( ( ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 ) )
= $false )
| ( ( cK @ SV13 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(117,plain,
! [SV11: $i,SV12: $i > $o,SV13: $i > $o] :
( ( ( ~ ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 ) )
= $false )
| ( ( cK @ SV12 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(119,plain,
! [SV12: $i > $o,SV11: $i,SV13: $i > $o] :
( ( ( cK @ SV13 @ SV11 )
= $true )
| ( ( cK @ SV12 @ SV11 )
= $true )
| ( ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(120,plain,
! [SV11: $i,SV12: $i > $o,SV13: $i > $o] :
( ( ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
= $true )
| ( ( cK @ SV13 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(122,plain,
! [SV11: $i,SV12: $i > $o,SV13: $i > $o] :
( ( ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
= $true )
| ( ( cK @ SV12 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(126,plain,
! [SV12: $i > $o,SV11: $i,SV13: $i > $o] :
( ( ( cK @ SV13 @ SV11 )
= $true )
| ( ( cK @ SV12 @ SV11 )
= $true )
| ( ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(127,plain,
! [SV12: $i > $o,SV11: $i,SV13: $i > $o] :
( ( ( cK @ SV13 @ SV11 )
= $false )
| ( ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(128,plain,
! [SV13: $i > $o,SV11: $i,SV12: $i > $o] :
( ( ( cK @ SV12 @ SV11 )
= $false )
| ( ( cK
@ ^ [SX0: $i] :
( ( SV13 @ SX0 )
| ( SV12 @ SX0 ) )
@ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(131,plain,
( ( ( cK @ sK2_SY8 @ sK3_SY12 )
= ( cK @ sK1_X @ sK3_SY12 ) )
= $false ),
inference(res,[status(thm)],[33,30]) ).
thf(132,plain,
( ( ( sK2_SY8 @ sK4_E )
= $true )
| ( ( sK1_X @ sK4_E )
= $true ) ),
inference(extuni,[status(esa)],[131]) ).
thf(133,plain,
( ( ( sK2_SY8 @ sK4_E )
= $false )
| ( ( sK1_X @ sK4_E )
= $false ) ),
inference(extuni,[status(esa)],[131]) ).
thf(134,plain,
! [SV14: $i] :
( ( ( sK1_X @ SV14 )
= $false )
| ( ( sK2_SY8 @ SV14 )
= $true ) ),
inference(rename,[status(thm)],[29]) ).
thf(144,plain,
! [SV23: $i,SV24: $i > $o,SV25: $i > $o] :
( ( ( cK
@ ^ [SX0: $i] :
( ( SV25 @ SX0 )
| ( SV24 @ SX0 ) )
@ SV23 )
= $true )
| ( ( cK @ SV25 @ SV23 )
= $false ) ),
inference(rename,[status(thm)],[50]) ).
thf(151,plain,
! [SV23: $i,SV24: $i > $o,SV25: $i > $o] :
( ( ( ( cK
@ ^ [SX0: $i] :
( ( SV25 @ SX0 )
| ( SV24 @ SX0 ) )
@ SV23 )
= ( cK @ sK2_SY8 @ sK3_SY12 ) )
= $false )
| ( ( cK @ SV25 @ SV23 )
= $false ) ),
inference(res,[status(thm)],[144,33]) ).
thf(152,plain,
! [SV23: $i,SV24: $i > $o,SV25: $i > $o] :
( ( ( ( cK @ SV25 @ SV23 )
= ( cK @ sK1_X @ sK3_SY12 ) )
= $false )
| ( ( cK
@ ^ [SX0: $i] :
( ( SV25 @ SX0 )
| ( SV24 @ SX0 ) )
@ SV23 )
= $true ) ),
inference(res,[status(thm)],[144,30]) ).
thf(153,plain,
! [SV24: $i > $o] :
( ( cK
@ ^ [SX0: $i] :
( ( sK1_X @ SX0 )
| ( SV24 @ SX0 ) )
@ sK3_SY12 )
= $true ),
inference(extuni,[status(esa)],[152:[bind(SV23,$thf( sK3_SY12 )),bind(SV25,$thf( sK1_X ))]]) ).
thf(154,plain,
! [SV24: $i > $o,SV25: $i > $o] :
( ( ( cK @ SV25 @ sK3_SY12 )
= $false )
| ( ( ( SV25 @ ( sK9_E @ sK3_SY12 @ SV24 @ SV25 ) )
| ( SV24 @ ( sK9_E @ sK3_SY12 @ SV24 @ SV25 ) ) )
= $true )
| ( ( sK2_SY8 @ ( sK9_E @ sK3_SY12 @ SV24 @ SV25 ) )
= $true ) ),
inference(extuni,[status(esa)],[151:[bind(SV23,$thf( sK3_SY12 ))]]) ).
thf(155,plain,
! [SV24: $i > $o,SV25: $i > $o] :
( ( ( cK @ SV25 @ sK3_SY12 )
= $false )
| ( ( ( SV25 @ ( sK9_E @ sK3_SY12 @ SV24 @ SV25 ) )
| ( SV24 @ ( sK9_E @ sK3_SY12 @ SV24 @ SV25 ) ) )
= $false )
| ( ( sK2_SY8 @ ( sK9_E @ sK3_SY12 @ SV24 @ SV25 ) )
= $false ) ),
inference(extuni,[status(esa)],[151:[bind(SV23,$thf( sK3_SY12 ))]]) ).
thf(156,plain,
! [SV24: $i > $o,SV25: $i > $o] :
( ( ( SV25 @ ( sK9_E @ sK3_SY12 @ SV24 @ SV25 ) )
= $false )
| ( ( cK @ SV25 @ sK3_SY12 )
= $false )
| ( ( sK2_SY8 @ ( sK9_E @ sK3_SY12 @ SV24 @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(157,plain,
! [SV25: $i > $o,SV24: $i > $o] :
( ( ( SV24 @ ( sK9_E @ sK3_SY12 @ SV24 @ SV25 ) )
= $false )
| ( ( cK @ SV25 @ sK3_SY12 )
= $false )
| ( ( sK2_SY8 @ ( sK9_E @ sK3_SY12 @ SV24 @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(158,plain,
! [SV24: $i > $o,SV25: $i > $o] :
( ( ( SV25 @ ( sK9_E @ sK3_SY12 @ SV24 @ SV25 ) )
= $true )
| ( ( SV24 @ ( sK9_E @ sK3_SY12 @ SV24 @ SV25 ) )
= $true )
| ( ( cK @ SV25 @ sK3_SY12 )
= $false )
| ( ( sK2_SY8 @ ( sK9_E @ sK3_SY12 @ SV24 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(159,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,158,157,156,153,144,134,133,132,128,127,126,122,120,119,97,93,91,90,67,66,65,64,63,62,61,52,49,33]) ).
thf(160,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO362^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.12/0.17 % Computer : n020.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Oct 6 17:36:36 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.01/0.42
% 1.01/0.42 No.of.Axioms: 0
% 1.01/0.42
% 1.01/0.42 Length.of.Defs: 0
% 1.01/0.42
% 1.01/0.42 Contains.Choice.Funs: false
% 1.01/0.42 ...
% 1.01/0.42
% 1.01/0.42 ********************************
% 1.01/0.42 * All subproblems solved! *
% 1.01/0.42 ********************************
% 1.01/0.42 % 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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:159,loop_count:10,foatp_calls:4,translation:fof_experiment)
% 1.01/0.42
% 1.01/0.42 %**** Beginning of derivation protocol ****
% 1.01/0.42 % SZS output start CNFRefutation
% See solution above
% 1.01/0.42
% 1.01/0.42 %**** End of derivation protocol ****
% 1.01/0.42 %**** no. of clauses in derivation: 116 ****
% 1.01/0.42 %**** clause counter: 159 ****
% 1.01/0.42
% 1.01/0.42 % 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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:159,loop_count:10,foatp_calls:4,translation:fof_experiment)
%------------------------------------------------------------------------------