%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU690^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:46:16 AM UTC 2026
% Result : Theorem 0.11s 0.25s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 4
% Syntax : Number of formulae : 88 ( 47 unt; 0 typ; 3 def)
% Number of atoms : 831 ( 208 equ; 0 cnn)
% Maximal formula atoms : 13 ( 9 avg)
% Number of connectives : 2615 ( 386 ~; 297 |; 14 &;1838 @)
% ( 0 <=>; 80 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 281 ( 3 ^; 278 !; 0 ?; 281 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_breln,type,
breln: $i > $i > $i > $o ).
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY52,type,
sK2_SY52: $i ).
thf(tp_sK3_SY59,type,
sK3_SY59: $i ).
thf(tp_sK4_SY65,type,
sK4_SY65: $i ).
thf(tp_sK5_Xx,type,
sK5_Xx: $i > $i > $i > $i > $i ).
thf(tp_sK6_SY74,type,
sK6_SY74: $i > $i > $i > $i > $i ).
thf(tp_setextsub,type,
setextsub: $o ).
thf(tp_subbreln,type,
subbreln: $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(breln,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(setextsub,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(subbreln,definition,
( subbreln
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subbreln) ).
thf(1,conjecture,
( setextsub
=> ( subbreln
=> ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqbreln) ).
thf(2,negated_conjecture,
( ( setextsub
=> ( subbreln
=> ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) )
=> ( ! [SY16: $i,SY17: $i,SY18: $i] :
( ( subset @ SY18 @ ( cartprod @ SY16 @ SY17 ) )
=> ! [SY22: $i] :
( ( subset @ SY22 @ ( cartprod @ SY16 @ SY17 ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY16 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY17 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY18 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY22 ) ) ) )
=> ( subset @ SY18 @ SY22 ) ) ) )
=> ! [SY0: $i,SY1: $i,SY2: $i] :
( ( subset @ SY2 @ ( cartprod @ SY0 @ SY1 ) )
=> ! [SY6: $i] :
( ( subset @ SY6 @ ( cartprod @ SY0 @ SY1 ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY1 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY2 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY6 ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY1 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY6 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY2 ) ) ) )
=> ( SY2 = SY6 ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,breln,setextsub,subbreln]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY16: $i,SY17: $i,SY18: $i] :
( ( subset @ SY18 @ ( cartprod @ SY16 @ SY17 ) )
=> ! [SY22: $i] :
( ( subset @ SY22 @ ( cartprod @ SY16 @ SY17 ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY16 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY17 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY18 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY22 ) ) ) )
=> ( subset @ SY18 @ SY22 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [SY0: $i,SY1: $i,SY2: $i] :
( ( subset @ SY2 @ ( cartprod @ SY0 @ SY1 ) )
=> ! [SY6: $i] :
( ( subset @ SY6 @ ( cartprod @ SY0 @ SY1 ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY1 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY2 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY6 ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY1 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY6 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY2 ) ) ) )
=> ( SY2 = SY6 ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [SY0: $i,SY1: $i,SY2: $i] :
( ( subset @ SY2 @ ( cartprod @ SY0 @ SY1 ) )
=> ! [SY6: $i] :
( ( subset @ SY6 @ ( cartprod @ SY0 @ SY1 ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY1 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY2 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY6 ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY1 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY6 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY2 ) ) ) )
=> ( SY2 = SY6 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( subset @ sK3_SY59 @ ( cartprod @ sK1_SY0 @ sK2_SY52 ) )
& ( subset @ sK4_SY65 @ ( cartprod @ sK1_SY0 @ sK2_SY52 ) )
& ! [SY70: $i] :
( ~ ( in @ SY70 @ sK1_SY0 )
| ! [SY71: $i] :
( ~ ( in @ SY71 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SY70 @ SY71 ) @ sK3_SY59 )
| ( in @ ( kpair @ SY70 @ SY71 ) @ sK4_SY65 ) ) )
& ! [SY72: $i] :
( ~ ( in @ SY72 @ sK1_SY0 )
| ! [SY73: $i] :
( ~ ( in @ SY73 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SY72 @ SY73 ) @ sK4_SY65 )
| ( in @ ( kpair @ SY72 @ SY73 ) @ sK3_SY59 ) ) )
& ( sK3_SY59 != sK4_SY65 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [SY16: $i,SY17: $i,SY18: $i] :
( ~ ( subset @ SY18 @ ( cartprod @ SY16 @ SY17 ) )
| ! [SY22: $i] :
( ~ ( subset @ SY22 @ ( cartprod @ SY16 @ SY17 ) )
| ( ( in @ ( sK5_Xx @ SY22 @ SY18 @ SY17 @ SY16 ) @ SY16 )
& ( in @ ( sK6_SY74 @ SY22 @ SY18 @ SY17 @ SY16 ) @ SY17 )
& ( in @ ( kpair @ ( sK5_Xx @ SY22 @ SY18 @ SY17 @ SY16 ) @ ( sK6_SY74 @ SY22 @ SY18 @ SY17 @ SY16 ) ) @ SY18 )
& ~ ( in @ ( kpair @ ( sK5_Xx @ SY22 @ SY18 @ SY17 @ SY16 ) @ ( sK6_SY74 @ SY22 @ SY18 @ SY17 @ SY16 ) ) @ SY22 ) )
| ( subset @ SY18 @ SY22 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(11,plain,
( ( ! [SY16: $i,SY17: $i,SY18: $i] :
( ~ ( subset @ SY18 @ ( cartprod @ SY16 @ SY17 ) )
| ! [SY22: $i] :
( ~ ( subset @ SY22 @ ( cartprod @ SY16 @ SY17 ) )
| ( ( in @ ( sK5_Xx @ SY22 @ SY18 @ SY17 @ SY16 ) @ SY16 )
& ( in @ ( sK6_SY74 @ SY22 @ SY18 @ SY17 @ SY16 ) @ SY17 )
& ( in @ ( kpair @ ( sK5_Xx @ SY22 @ SY18 @ SY17 @ SY16 ) @ ( sK6_SY74 @ SY22 @ SY18 @ SY17 @ SY16 ) ) @ SY18 )
& ~ ( in @ ( kpair @ ( sK5_Xx @ SY22 @ SY18 @ SY17 @ SY16 ) @ ( sK6_SY74 @ SY22 @ SY18 @ SY17 @ SY16 ) ) @ SY22 ) )
| ( subset @ SY18 @ SY22 ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ( subset @ sK3_SY59 @ ( cartprod @ sK1_SY0 @ sK2_SY52 ) )
& ( subset @ sK4_SY65 @ ( cartprod @ sK1_SY0 @ sK2_SY52 ) )
& ! [SY70: $i] :
( ~ ( in @ SY70 @ sK1_SY0 )
| ! [SY71: $i] :
( ~ ( in @ SY71 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SY70 @ SY71 ) @ sK3_SY59 )
| ( in @ ( kpair @ SY70 @ SY71 ) @ sK4_SY65 ) ) )
& ! [SY72: $i] :
( ~ ( in @ SY72 @ sK1_SY0 )
| ! [SY73: $i] :
( ~ ( in @ SY73 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SY72 @ SY73 ) @ sK4_SY65 )
| ( in @ ( kpair @ SY72 @ SY73 ) @ sK3_SY59 ) ) )
& ( sK3_SY59 != sK4_SY65 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ( ~ ( subset @ sK3_SY59 @ ( cartprod @ sK1_SY0 @ sK2_SY52 ) )
| ~ ~ ( ~ ( subset @ sK4_SY65 @ ( cartprod @ sK1_SY0 @ sK2_SY52 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 ) ) )
| ~ ( ( sK3_SY59 != sK4_SY65 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,breln,setextsub,subbreln]) ).
thf(15,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( subset @ SX3 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ ( sK5_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK6_SY74 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK5_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK6_SY74 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK6_SY74 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX3 ) ) ) )
| ( subset @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,breln,setextsub,subbreln]) ).
thf(16,plain,
! [SV1: $i] :
( ( ! [SY75: $i] :
( ~ ( subset @ SV1 @ SY75 )
| ~ ( subset @ SY75 @ SV1 )
| ( SV1 = SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(17,plain,
( ( ~ ( subset @ sK3_SY59 @ ( cartprod @ sK1_SY0 @ sK2_SY52 ) )
| ~ ~ ( ~ ( subset @ sK4_SY65 @ ( cartprod @ sK1_SY0 @ sK2_SY52 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 ) ) )
| ~ ( ( sK3_SY59 != sK4_SY65 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: $i] :
( ( ! [SY76: $i,SY77: $i] :
( ~ ( subset @ SY77 @ ( cartprod @ SV2 @ SY76 ) )
| ! [SY78: $i] :
( ~ ( subset @ SY78 @ ( cartprod @ SV2 @ SY76 ) )
| ~ ( ~ ( in @ ( sK5_Xx @ SY78 @ SY77 @ SY76 @ SV2 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( sK6_SY74 @ SY78 @ SY77 @ SY76 @ SV2 ) @ SY76 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK5_Xx @ SY78 @ SY77 @ SY76 @ SV2 ) @ ( sK6_SY74 @ SY78 @ SY77 @ SY76 @ SV2 ) ) @ SY77 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SY78 @ SY77 @ SY76 @ SV2 ) @ ( sK6_SY74 @ SY78 @ SY77 @ SY76 @ SV2 ) ) @ SY78 ) ) ) )
| ( subset @ SY77 @ SY78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( subset @ SV1 @ SV3 )
| ~ ( subset @ SV3 @ SV1 )
| ( SV1 = SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( subset @ sK3_SY59 @ ( cartprod @ sK1_SY0 @ sK2_SY52 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ~ ( ~ ( subset @ sK4_SY65 @ ( cartprod @ sK1_SY0 @ sK2_SY52 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 ) ) )
| ~ ( ( sK3_SY59 != sK4_SY65 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY79: $i] :
( ~ ( subset @ SY79 @ ( cartprod @ SV2 @ SV4 ) )
| ! [SY80: $i] :
( ~ ( subset @ SY80 @ ( cartprod @ SV2 @ SV4 ) )
| ~ ( ~ ( in @ ( sK5_Xx @ SY80 @ SY79 @ SV4 @ SV2 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( sK6_SY74 @ SY80 @ SY79 @ SV4 @ SV2 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK5_Xx @ SY80 @ SY79 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SY80 @ SY79 @ SV4 @ SV2 ) ) @ SY79 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SY80 @ SY79 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SY80 @ SY79 @ SV4 @ SV2 ) ) @ SY80 ) ) ) )
| ( subset @ SY79 @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( subset @ SV1 @ SV3 ) )
= $true )
| ( ( ~ ( subset @ SV3 @ SV1 )
| ( SV1 = SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( subset @ sK3_SY59 @ ( cartprod @ sK1_SY0 @ sK2_SY52 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( ~ ( subset @ sK4_SY65 @ ( cartprod @ sK1_SY0 @ sK2_SY52 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 ) ) )
| ~ ( ( sK3_SY59 != sK4_SY65 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ~ ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
| ! [SY81: $i] :
( ~ ( subset @ SY81 @ ( cartprod @ SV2 @ SV4 ) )
| ~ ( ~ ( in @ ( sK5_Xx @ SY81 @ SV5 @ SV4 @ SV2 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( sK6_SY74 @ SY81 @ SV5 @ SV4 @ SV2 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK5_Xx @ SY81 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SY81 @ SV5 @ SV4 @ SV2 ) ) @ SV5 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SY81 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SY81 @ SV5 @ SV4 @ SV2 ) ) @ SY81 ) ) ) )
| ( subset @ SV5 @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV3: $i,SV1: $i] :
( ( ( subset @ SV1 @ SV3 )
= $false )
| ( ( ~ ( subset @ SV3 @ SV1 )
| ( SV1 = SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ~ ( subset @ sK4_SY65 @ ( cartprod @ sK1_SY0 @ sK2_SY52 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 ) ) )
| ~ ( ( sK3_SY59 != sK4_SY65 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) ) )
= $true )
| ( ( ! [SY81: $i] :
( ~ ( subset @ SY81 @ ( cartprod @ SV2 @ SV4 ) )
| ~ ( ~ ( in @ ( sK5_Xx @ SY81 @ SV5 @ SV4 @ SV2 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( sK6_SY74 @ SY81 @ SV5 @ SV4 @ SV2 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK5_Xx @ SY81 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SY81 @ SV5 @ SV4 @ SV2 ) ) @ SV5 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SY81 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SY81 @ SV5 @ SV4 @ SV2 ) ) @ SY81 ) ) ) )
| ( subset @ SV5 @ SY81 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV1 ) )
= $true )
| ( ( SV1 = SV3 )
= $true )
| ( ( subset @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ~ ( subset @ sK4_SY65 @ ( cartprod @ sK1_SY0 @ sK2_SY52 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(32,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 ) ) )
| ~ ( ( sK3_SY59 != sK4_SY65 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(33,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( ! [SY81: $i] :
( ~ ( subset @ SY81 @ ( cartprod @ SV2 @ SV4 ) )
| ~ ( ~ ( in @ ( sK5_Xx @ SY81 @ SV5 @ SV4 @ SV2 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( sK6_SY74 @ SY81 @ SV5 @ SV4 @ SV2 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK5_Xx @ SY81 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SY81 @ SV5 @ SV4 @ SV2 ) ) @ SV5 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SY81 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SY81 @ SV5 @ SV4 @ SV2 ) ) @ SY81 ) ) ) )
| ( subset @ SV5 @ SY81 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV1: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV1 )
= $false )
| ( ( SV1 = SV3 )
= $true )
| ( ( subset @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(35,plain,
( ( subset @ sK4_SY65 @ ( cartprod @ sK1_SY0 @ sK2_SY52 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(36,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 ) ) )
| ~ ( ( sK3_SY59 != sK4_SY65 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV5: $i,SV4: $i,SV2: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
| ~ ( ~ ( in @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV5 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV6 ) ) ) )
| ( subset @ SV5 @ SV6 ) )
= $true )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 ) ) )
| ~ ( ( sK3_SY59 != sK4_SY65 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV5: $i,SV4: $i,SV2: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV5 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV6 ) ) ) )
| ( subset @ SV5 @ SV6 ) )
= $true )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(40,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(41,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 ) ) )
| ~ ( ( sK3_SY59 != sK4_SY65 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV5: $i,SV4: $i,SV2: $i,SV6: $i] :
( ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV5 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV6 ) ) ) )
| ( subset @ SV5 @ SV6 ) )
= $true )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(44,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 ) ) )
| ~ ( ( sK3_SY59 != sK4_SY65 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV5 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV6 ) ) ) ) )
= $true )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV7: $i] :
( ( ~ ( in @ SV7 @ sK1_SY0 )
| ! [SY82: $i] :
( ~ ( in @ SY82 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SV7 @ SY82 ) @ sK3_SY59 )
| ( in @ ( kpair @ SV7 @ SY82 ) @ sK4_SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(47,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 ) ) )
| ~ ( ( sK3_SY59 != sK4_SY65 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV5 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV6 ) ) ) )
= $false )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV7: $i] :
( ( ( ~ ( in @ SV7 @ sK1_SY0 ) )
= $true )
| ( ( ! [SY82: $i] :
( ~ ( in @ SY82 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SV7 @ SY82 ) @ sK3_SY59 )
| ( in @ ( kpair @ SV7 @ SY82 ) @ sK4_SY65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(50,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(51,plain,
( ( ~ ( ( sK3_SY59 != sK4_SY65 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(52,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV2 ) )
= $false )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(53,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV5 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV6 ) ) ) )
= $false )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV7: $i] :
( ( ( in @ SV7 @ sK1_SY0 )
= $false )
| ( ( ! [SY82: $i] :
( ~ ( in @ SY82 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SV7 @ SY82 ) @ sK3_SY59 )
| ( in @ ( kpair @ SV7 @ SY82 ) @ sK4_SY65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(55,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK4_SY65 )
| ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY59 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(56,plain,
( ( sK3_SY59 != sK4_SY65 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(57,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( in @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV2 )
= $true )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(58,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV5 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV6 ) ) ) )
= $true )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(59,plain,
! [SV7: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SV7 @ SV8 ) @ sK3_SY59 )
| ( in @ ( kpair @ SV7 @ SV8 ) @ sK4_SY65 ) )
= $true )
| ( ( in @ SV7 @ sK1_SY0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV9: $i] :
( ( ~ ( in @ SV9 @ sK1_SY0 )
| ! [SY83: $i] :
( ~ ( in @ SY83 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SV9 @ SY83 ) @ sK4_SY65 )
| ( in @ ( kpair @ SV9 @ SY83 ) @ sK3_SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(61,plain,
( ( sK3_SY59 = sK4_SY65 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV4 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV5 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV6 ) ) )
= $false )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV7: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ sK2_SY52 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV7 @ SV8 ) @ sK3_SY59 )
| ( in @ ( kpair @ SV7 @ SV8 ) @ sK4_SY65 ) )
= $true )
| ( ( in @ SV7 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV9: $i] :
( ( ( ~ ( in @ SV9 @ sK1_SY0 ) )
= $true )
| ( ( ! [SY83: $i] :
( ~ ( in @ SY83 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SV9 @ SY83 ) @ sK4_SY65 )
| ( in @ ( kpair @ SV9 @ SY83 ) @ sK3_SY59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(66,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV5 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV6 ) ) )
= $false )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(67,plain,
! [SV7: $i,SV8: $i] :
( ( ( in @ SV8 @ sK2_SY52 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV7 @ SV8 ) @ sK3_SY59 )
| ( in @ ( kpair @ SV7 @ SV8 ) @ sK4_SY65 ) )
= $true )
| ( ( in @ SV7 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV9: $i] :
( ( ( in @ SV9 @ sK1_SY0 )
= $false )
| ( ( ! [SY83: $i] :
( ~ ( in @ SY83 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SV9 @ SY83 ) @ sK4_SY65 )
| ( in @ ( kpair @ SV9 @ SY83 ) @ sK3_SY59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( in @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) @ SV4 )
= $true )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(70,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV5 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV6 ) ) )
= $true )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(71,plain,
! [SV8: $i,SV7: $i] :
( ( ( ~ ( in @ ( kpair @ SV7 @ SV8 ) @ sK3_SY59 ) )
= $true )
| ( ( in @ ( kpair @ SV7 @ SV8 ) @ sK4_SY65 )
= $true )
| ( ( in @ SV8 @ sK2_SY52 )
= $false )
| ( ( in @ SV7 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(72,plain,
! [SV9: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ sK2_SY52 )
| ~ ( in @ ( kpair @ SV9 @ SV10 ) @ sK4_SY65 )
| ( in @ ( kpair @ SV9 @ SV10 ) @ sK3_SY59 ) )
= $true )
| ( ( in @ SV9 @ sK1_SY0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(73,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV5 )
| ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV6 ) )
= $false )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(74,plain,
! [SV8: $i,SV7: $i] :
( ( ( in @ ( kpair @ SV7 @ SV8 ) @ sK3_SY59 )
= $false )
| ( ( in @ ( kpair @ SV7 @ SV8 ) @ sK4_SY65 )
= $true )
| ( ( in @ SV8 @ sK2_SY52 )
= $false )
| ( ( in @ SV7 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV9: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ sK2_SY52 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV9 @ SV10 ) @ sK4_SY65 )
| ( in @ ( kpair @ SV9 @ SV10 ) @ sK3_SY59 ) )
= $true )
| ( ( in @ SV9 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(76,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV5 ) )
= $false )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(77,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( ~ ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV6 ) )
= $false )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(78,plain,
! [SV9: $i,SV10: $i] :
( ( ( in @ SV10 @ sK2_SY52 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV9 @ SV10 ) @ sK4_SY65 )
| ( in @ ( kpair @ SV9 @ SV10 ) @ sK3_SY59 ) )
= $true )
| ( ( in @ SV9 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(79,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV5 )
= $true )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(80,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV6 ) )
= $true )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(81,plain,
! [SV10: $i,SV9: $i] :
( ( ( ~ ( in @ ( kpair @ SV9 @ SV10 ) @ sK4_SY65 ) )
= $true )
| ( ( in @ ( kpair @ SV9 @ SV10 ) @ sK3_SY59 )
= $true )
| ( ( in @ SV10 @ sK2_SY52 )
= $false )
| ( ( in @ SV9 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(82,plain,
! [SV2: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( in @ ( kpair @ ( sK5_Xx @ SV6 @ SV5 @ SV4 @ SV2 ) @ ( sK6_SY74 @ SV6 @ SV5 @ SV4 @ SV2 ) ) @ SV6 )
= $false )
| ( ( subset @ SV5 @ SV6 )
= $true )
| ( ( subset @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( subset @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(83,plain,
! [SV10: $i,SV9: $i] :
( ( ( in @ ( kpair @ SV9 @ SV10 ) @ sK4_SY65 )
= $false )
| ( ( in @ ( kpair @ SV9 @ SV10 ) @ sK3_SY59 )
= $true )
| ( ( in @ SV10 @ sK2_SY52 )
= $false )
| ( ( in @ SV9 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(84,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,83,82,79,74,69,61,57,35,34]) ).
thf(85,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU690^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.14 % Computer : n019.cluster.edu
% 0.11/0.14 % Model : x86_64 x86_64
% 0.11/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.14 % Memory : 8046.5625MB
% 0.11/0.14 % OS : Linux 6.8.0-71-generic
% 0.11/0.14 % CPULimit : 300
% 0.11/0.14 % WCLimit : 300
% 0.11/0.14 % DateTime : Tue Oct 6 15:31:46 UTC 2026
% 0.11/0.15 % CPUTime :
% 0.11/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.25
% 0.11/0.25 No.of.Axioms: 0
% 0.11/0.25
% 0.11/0.25 Length.of.Defs: 644
% 0.11/0.25
% 0.11/0.25 Contains.Choice.Funs: false
% 0.11/0.25 .....
% 0.11/0.25
% 0.11/0.25 ********************************
% 0.11/0.25 * All subproblems solved! *
% 0.11/0.25 ********************************
% 0.11/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:84,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.11/0.25
% 0.11/0.25 %**** Beginning of derivation protocol ****
% 0.11/0.25 % SZS output start CNFRefutation
% See solution above
% 0.11/0.25
% 0.11/0.25 %**** End of derivation protocol ****
% 0.11/0.25 %**** no. of clauses in derivation: 85 ****
% 0.11/0.25 %**** clause counter: 84 ****
% 0.11/0.25
% 0.11/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:84,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------