%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU776^2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 10:48:12 AM UTC 2026
% Result : Theorem 6.16s 1.36s
% Output : CNFRefutation 6.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 222 ( 44 unt; 0 typ; 4 def)
% Number of atoms : 2490 ( 853 equ; 0 cnn)
% Maximal formula atoms : 9 ( 11 avg)
% Number of connectives : 6200 ( 139 ~; 549 |; 8 &;5472 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 264 ( 264 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 11 con; 0-7 aty)
% Number of variables : 1445 ( 777 ^; 668 !; 0 ?;1445 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_breln,type,
breln: $i > $i > $i > $o ).
thf(tp_breln1,type,
breln1: $i > $i > $o ).
thf(tp_breln1invset,type,
breln1invset: $i > $i > $i ).
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_dpsetconstr,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_dpsetconstrI,type,
dpsetconstrI: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_sK10_E,type,
sK10_E: ( $i > $i > $o ) > $i > $i > $i ).
thf(tp_sK11_E,type,
sK11_E: $i ).
thf(tp_sK12_E,type,
sK12_E: $i ).
thf(tp_sK13_E,type,
sK13_E: $i ).
thf(tp_sK14_E,type,
sK14_E: $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY26,type,
sK2_SY26: $i ).
thf(tp_sK3_SY31,type,
sK3_SY31: $i ).
thf(tp_sK4_SY35,type,
sK4_SY35: $i ).
thf(tp_sK5_E,type,
sK5_E: ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $i > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK6_E,type,
sK6_E: ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $i > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK7_E,type,
sK7_E: ( $i > $i > $o ) > $i ).
thf(tp_sK8_E,type,
sK8_E: ( $i > $i > $o ) > $i ).
thf(tp_sK9_E,type,
sK9_E: $i > $i > ( $i > $i > $o ) > $i ).
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/sandbox/benchmark/theBenchmark.p',breln) ).
thf(breln1,definition,
( breln1
= ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1) ).
thf(breln1invset,definition,
( breln1invset
= ( ^ [A: $i,R: $i] :
( dpsetconstr @ A @ A
@ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invset) ).
thf(dpsetconstrI,definition,
( dpsetconstrI
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xphi @ Xx @ Xy )
=> ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(1,conjecture,
( dpsetconstrI
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invI) ).
thf(2,negated_conjecture,
( ( dpsetconstrI
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xphi @ Xx @ Xy )
=> ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) )
=> ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [SY6: $i] :
( ( in @ SY6 @ SY0 )
=> ! [SY7: $i] :
( ( in @ SY7 @ SY0 )
=> ( ( in @ ( kpair @ SY6 @ SY7 ) @ SY1 )
=> ( in @ ( kpair @ SY7 @ SY6 )
@ ( dpsetconstr @ SY0 @ SY0
@ ^ [SY11: $i,SY12: $i] : ( in @ ( kpair @ SY12 @ SY11 ) @ SY1 ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,breln,breln1,breln1invset,dpsetconstrI]) ).
thf(4,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xphi @ Xx @ Xy )
=> ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [SY6: $i] :
( ( in @ SY6 @ SY0 )
=> ! [SY7: $i] :
( ( in @ SY7 @ SY0 )
=> ( ( in @ ( kpair @ SY6 @ SY7 ) @ SY1 )
=> ( in @ ( kpair @ SY7 @ SY6 )
@ ( dpsetconstr @ SY0 @ SY0
@ ^ [SY11: $i,SY12: $i] : ( in @ ( kpair @ SY12 @ SY11 ) @ SY1 ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [SY6: $i] :
( ( in @ SY6 @ SY0 )
=> ! [SY7: $i] :
( ( in @ SY7 @ SY0 )
=> ( ( in @ ( kpair @ SY6 @ SY7 ) @ SY1 )
=> ( in @ ( kpair @ SY7 @ SY6 )
@ ( dpsetconstr @ SY0 @ SY0
@ ^ [SY11: $i,SY12: $i] : ( in @ ( kpair @ SY12 @ SY11 ) @ SY1 ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( subset @ sK2_SY26 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
& ( in @ sK3_SY31 @ sK1_SY0 )
& ( in @ sK4_SY35 @ sK1_SY0 )
& ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
& ~ ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SY33: $i,SY34: $i] : ( in @ ( kpair @ SY34 @ SY33 ) @ sK2_SY26 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ~ ( Xphi @ Xx @ Xy )
| ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ~ ( Xphi @ Xx @ Xy )
| ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ( subset @ sK2_SY26 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
& ( in @ sK3_SY31 @ sK1_SY0 )
& ( in @ sK4_SY35 @ sK1_SY0 )
& ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
& ~ ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SY33: $i,SY34: $i] : ( in @ ( kpair @ SY34 @ SY33 ) @ sK2_SY26 ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ( ~ ( subset @ sK2_SY26 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
| ~ ~ ( ~ ( in @ sK3_SY31 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK4_SY35 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
| ~ ~ ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,breln,breln1,breln1invset,dpsetconstrI]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY40: $i,SY41: $i > $i > $o,SY42: $i] :
( ~ ( in @ SY42 @ SV1 )
| ! [SY43: $i] :
( ~ ( in @ SY43 @ SY40 )
| ~ ( SY41 @ SY42 @ SY43 )
| ( in @ ( kpair @ SY42 @ SY43 )
@ ( dpsetconstr @ SV1 @ SY40
@ ^ [Xz: $i,Xu: $i] : ( SY41 @ Xz @ Xu ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ( subset @ sK2_SY26 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
| ~ ~ ( ~ ( in @ sK3_SY31 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK4_SY35 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
| ~ ~ ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY46: $i > $i > $o,SY47: $i] :
( ~ ( in @ SY47 @ SV1 )
| ! [SY48: $i] :
( ~ ( in @ SY48 @ SV2 )
| ~ ( SY46 @ SY47 @ SY48 )
| ( in @ ( kpair @ SY47 @ SY48 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [Xz: $i,Xu: $i] : ( SY46 @ Xz @ Xu ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( subset @ sK2_SY26 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY31 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK4_SY35 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
| ~ ~ ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i] :
( ( ! [SY51: $i] :
( ~ ( in @ SY51 @ SV1 )
| ! [SY52: $i] :
( ~ ( in @ SY52 @ SV2 )
| ~ ( SV3 @ SY51 @ SY52 )
| ( in @ ( kpair @ SY51 @ SY52 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY53: $i,SY54: $i] : ( SV3 @ SY53 @ SY54 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( subset @ sK2_SY26 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ( ~ ( in @ sK3_SY31 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK4_SY35 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
| ~ ~ ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ SV1 )
| ! [SY55: $i] :
( ~ ( in @ SY55 @ SV2 )
| ~ ( SV3 @ SV4 @ SY55 )
| ( in @ ( kpair @ SV4 @ SY55 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY53: $i,SY54: $i] : ( SV3 @ SY53 @ SY54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ( in @ sK3_SY31 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK4_SY35 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
| ~ ~ ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV1 ) )
= $true )
| ( ( ! [SY55: $i] :
( ~ ( in @ SY55 @ SV2 )
| ~ ( SV3 @ SV4 @ SY55 )
| ( in @ ( kpair @ SV4 @ SY55 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY53: $i,SY54: $i] : ( SV3 @ SY53 @ SY54 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(23,plain,
( ( ~ ( in @ sK3_SY31 @ sK1_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ~ ( ~ ( in @ sK4_SY35 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
| ~ ~ ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV4: $i] :
( ( ( in @ SV4 @ SV1 )
= $false )
| ( ( ! [SY55: $i] :
( ~ ( in @ SY55 @ SV2 )
| ~ ( SV3 @ SV4 @ SY55 )
| ( in @ ( kpair @ SV4 @ SY55 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY53: $i,SY54: $i] : ( SV3 @ SY53 @ SY54 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( in @ sK3_SY31 @ sK1_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ( ~ ( in @ sK4_SY35 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
| ~ ~ ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV1: $i,SV4: $i,SV3: $i > $i > $o,SV2: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV2 )
| ~ ( SV3 @ SV4 @ SV5 )
| ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY53: $i,SY54: $i] : ( SV3 @ SY53 @ SY54 ) ) ) )
= $true )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(29,plain,
( ( ~ ( in @ sK4_SY35 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
| ~ ~ ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV1: $i,SV4: $i,SV3: $i > $i > $o,SV2: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV2 ) )
= $true )
| ( ( ~ ( SV3 @ SV4 @ SV5 )
| ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY53: $i,SY54: $i] : ( SV3 @ SY53 @ SY54 ) ) ) )
= $true )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(31,plain,
( ( ~ ( in @ sK4_SY35 @ sK1_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(32,plain,
( ( ~ ~ ( ~ ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
| ~ ~ ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV1: $i,SV4: $i,SV3: $i > $i > $o,SV2: $i,SV5: $i] :
( ( ( in @ SV5 @ SV2 )
= $false )
| ( ( ~ ( SV3 @ SV4 @ SV5 )
| ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY53: $i,SY54: $i] : ( SV3 @ SY53 @ SY54 ) ) ) )
= $true )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
( ( in @ sK4_SY35 @ sK1_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(35,plain,
( ( ~ ( ~ ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
| ~ ~ ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i,SV3: $i > $i > $o] :
( ( ( ~ ( SV3 @ SV4 @ SV5 ) )
= $true )
| ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY53: $i,SY54: $i] : ( SV3 @ SY53 @ SY54 ) ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(37,plain,
( ( ~ ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
| ~ ~ ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i,SV3: $i > $i > $o] :
( ( ( SV3 @ SV4 @ SV5 )
= $false )
| ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY53: $i,SY54: $i] : ( SV3 @ SY53 @ SY54 ) ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
( ( ~ ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(40,plain,
( ( ~ ~ ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(41,plain,
( ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(42,plain,
( ( ~ ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(43,plain,
( ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(44,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( $true = $false )
| ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX0: $i,SX1: $i] : $true ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV3,$thf( ^ [SV13: $i] : ^ [SV14: $i] : $true ))]]) ).
thf(46,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i,SV10: $i > $i > $o] :
( ( ( ~ ( SV10 @ SV4 @ SV5 ) )
= $false )
| ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX0: $i,SX1: $i] :
~ ( SV10 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV3,$thf( ^ [SV8: $i] : ^ [SV9: $i] : ~ ( SV10 @ SV8 @ SV9 ) ))]]) ).
thf(47,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( SV4 != SV5 )
= $false )
| ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV3,$thf( ^ [SY60: $i] : ^ [SY61: $i] : ( SY60 != SY61 ) ))]]) ).
thf(48,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( SV4 = SV5 )
= $false )
| ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV3,$thf( ^ [SV7: $i] : ^ [SV6: $i] : ( SV7 = SV6 ) ))]]) ).
thf(49,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i,SV10: $i > $i > $o] :
( ( ( SV10 @ SV4 @ SV5 )
= $true )
| ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX0: $i,SX1: $i] :
~ ( SV10 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(50,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( SV4 = SV5 )
= $true )
| ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(51,plain,
! [SV2: $i,SV1: $i,SV5: $i] :
( ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ SV5 @ SV2 )
= $false )
| ( ( in @ ( kpair @ SV5 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[48:[bind(SV4,$thf( SV5 ))]]) ).
thf(52,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX0: $i,SX1: $i] : $true ) )
= $true )
| ( ( in @ SV5 @ SV2 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(sim,[status(thm)],[44]) ).
thf(53,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV19: $i > $i > $o] :
( ( ( SV19 @ SV18 @ SV17 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(rename,[status(thm)],[38]) ).
thf(58,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV19: $i > $i > $o,SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV19: $i > $i > $o] :
( ( ( ( SV19 @ SV18 @ SV17 )
= ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false )
| ( ( SV19 @ SV18 @ SV17 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(res,[status(thm)],[53,53]) ).
thf(60,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV19: $i > $i > $o] :
( ( ( ( in @ SV18 @ SV16 )
= ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 ) )
= $false )
| ( ( SV19 @ SV18 @ SV17 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false ) ),
inference(res,[status(thm)],[53,41]) ).
thf(61,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV19: $i > $i > $o] :
( ( ( ( in @ SV17 @ SV15 )
= ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 ) )
= $false )
| ( ( SV19 @ SV18 @ SV17 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(res,[status(thm)],[53,41]) ).
thf(62,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV19: $i > $i > $o] :
( ( ( ( SV19 @ SV18 @ SV17 )
= ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 ) )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(res,[status(thm)],[53,41]) ).
thf(63,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV19: $i > $i > $o] :
( ( ( ( in @ SV18 @ SV16 )
= ( in @ sK4_SY35 @ sK1_SY0 ) )
= $false )
| ( ( SV19 @ SV18 @ SV17 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false ) ),
inference(res,[status(thm)],[53,34]) ).
thf(64,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV19: $i > $i > $o] :
( ( ( ( in @ SV17 @ SV15 )
= ( in @ sK4_SY35 @ sK1_SY0 ) )
= $false )
| ( ( SV19 @ SV18 @ SV17 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(res,[status(thm)],[53,34]) ).
thf(65,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV19: $i > $i > $o] :
( ( ( ( SV19 @ SV18 @ SV17 )
= ( in @ sK4_SY35 @ sK1_SY0 ) )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(res,[status(thm)],[53,34]) ).
thf(66,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV19: $i > $i > $o] :
( ( ( ( in @ SV18 @ SV16 )
= ( in @ sK3_SY31 @ sK1_SY0 ) )
= $false )
| ( ( SV19 @ SV18 @ SV17 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false ) ),
inference(res,[status(thm)],[53,26]) ).
thf(67,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV19: $i > $i > $o] :
( ( ( ( in @ SV17 @ SV15 )
= ( in @ sK3_SY31 @ sK1_SY0 ) )
= $false )
| ( ( SV19 @ SV18 @ SV17 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(res,[status(thm)],[53,26]) ).
thf(68,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV19: $i > $i > $o] :
( ( ( ( SV19 @ SV18 @ SV17 )
= ( in @ sK3_SY31 @ sK1_SY0 ) )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(res,[status(thm)],[53,26]) ).
thf(71,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV19: $i > $i > $o] :
( ( ( ( SV19 @ SV18 @ SV17 )
= ( subset @ sK2_SY26 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(res,[status(thm)],[53,18]) ).
thf(72,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i] :
( ( $true = $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : $true ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(prim_subst,[status(thm)],[53:[bind(SV19,$thf( ^ [SV37: $i] : ^ [SV38: $i] : $true ))]]) ).
thf(73,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i] :
( ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : $true ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(sim,[status(thm)],[72]) ).
thf(75,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV34: $i > $i > $o] :
( ( ( ~ ( SV34 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] :
~ ( SV34 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(prim_subst,[status(thm)],[53:[bind(SV19,$thf( ^ [SV32: $i] : ^ [SV33: $i] : ~ ( SV34 @ SV32 @ SV33 ) ))]]) ).
thf(76,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i] :
( ( ( SV18 != SV17 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(prim_subst,[status(thm)],[53:[bind(SV19,$thf( ^ [SY75: $i] : ^ [SY76: $i] : ( SY75 != SY76 ) ))]]) ).
thf(77,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i] :
( ( ( SV18 = SV17 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(prim_subst,[status(thm)],[53:[bind(SV19,$thf( ^ [SV31: $i] : ^ [SV30: $i] : ( SV31 = SV30 ) ))]]) ).
thf(78,plain,
! [SV15: $i,SV16: $i,SV29: $i > $i > $o,SV17: $i,SV18: $i,SV28: $i > $i > $o] :
( ( ( ( SV28 @ SV18 @ SV17 )
| ( SV29 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] :
( ( SV28 @ SX0 @ SX1 )
| ( SV29 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(prim_subst,[status(thm)],[53:[bind(SV19,$thf( ^ [SV26: $i] : ^ [SV27: $i] : ( ( SV28 @ SV26 @ SV27 ) | ( SV29 @ SV26 @ SV27 ) ) ))]]) ).
thf(80,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( cartprod @ SX1 @ SX1 ) ) ) )
= $true )
| ( ( sK2_SY26 = sK1_SY0 )
= $false )
| ( ( sK2_SY26 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX1 @ ( cartprod @ SX1 @ SX1 ) ) ))]]) ).
thf(81,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK1_SY0 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK1_SY0 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( cartprod @ SX1 @ SX0 ) ) ) )
= $true )
| ( ( sK2_SY26 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( sK1_SY0 )),bind(SV17,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX1 @ ( cartprod @ SX1 @ SX0 ) ) ))]]) ).
thf(82,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( cartprod @ SX1 @ sK1_SY0 ) ) ) )
= $true )
| ( ( sK2_SY26 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX1 @ ( cartprod @ SX1 @ sK1_SY0 ) ) ))]]) ).
thf(83,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK1_SY0 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK1_SY0 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( cartprod @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( sK2_SY26 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( sK1_SY0 )),bind(SV17,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX1 @ ( cartprod @ SX0 @ SX1 ) ) ))]]) ).
thf(84,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK1_SY0 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK1_SY0 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( cartprod @ SX0 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( sK1_SY0 )),bind(SV17,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX1 @ ( cartprod @ SX0 @ SX0 ) ) ))]]) ).
thf(85,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK1_SY0 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK1_SY0 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( cartprod @ SX0 @ sK1_SY0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( sK1_SY0 )),bind(SV17,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX1 @ ( cartprod @ SX0 @ sK1_SY0 ) ) ))]]) ).
thf(86,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( cartprod @ sK1_SY0 @ SX1 ) ) ) )
= $true )
| ( ( sK2_SY26 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX1 @ ( cartprod @ sK1_SY0 @ SX1 ) ) ))]]) ).
thf(87,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK1_SY0 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK1_SY0 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( cartprod @ sK1_SY0 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( sK1_SY0 )),bind(SV17,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX1 @ ( cartprod @ sK1_SY0 @ SX0 ) ) ))]]) ).
thf(88,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX1 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) ))]]) ).
thf(89,plain,
! [SV98: $i > $i > $i,SV97: $i > $i > $i,SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( cartprod @ ( SV97 @ SX0 @ SX1 ) @ ( SV98 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( ( cartprod @ ( SV97 @ SV18 @ sK2_SY26 ) @ ( SV98 @ SV18 @ sK2_SY26 ) )
= ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
= $false ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX1 @ ( cartprod @ ( SV97 @ SX0 @ SX1 ) @ ( SV98 @ SX0 @ SX1 ) ) ) ))]]) ).
thf(90,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX1 @ SX1 ) ) )
= $true )
| ( ( sK2_SY26
= ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
= $false ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX1 @ SX1 ) ))]]) ).
thf(91,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( cartprod @ sK1_SY0 @ sK1_SY0 )),bind(SV17,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX1 @ SX0 ) ))]]) ).
thf(92,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ sK1_SY0 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ sK1_SY0 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX0 @ ( cartprod @ SX1 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( sK1_SY0 )),bind(SV18,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX0 @ ( cartprod @ SX1 @ SX1 ) ) ))]]) ).
thf(93,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ sK1_SY0 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ sK1_SY0 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX0 @ ( cartprod @ SX1 @ SX0 ) ) ) )
= $true )
| ( ( sK2_SY26 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( sK1_SY0 )),bind(SV18,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX0 @ ( cartprod @ SX1 @ SX0 ) ) ))]]) ).
thf(94,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ sK1_SY0 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ sK1_SY0 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX0 @ ( cartprod @ SX1 @ sK1_SY0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( sK1_SY0 )),bind(SV18,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX0 @ ( cartprod @ SX1 @ sK1_SY0 ) ) ))]]) ).
thf(95,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ sK1_SY0 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ sK1_SY0 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX0 @ ( cartprod @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( sK2_SY26 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( sK1_SY0 )),bind(SV18,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX0 @ ( cartprod @ SX0 @ SX1 ) ) ))]]) ).
thf(96,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX0 @ ( cartprod @ SX0 @ SX0 ) ) ) )
= $true )
| ( ( sK2_SY26 = sK1_SY0 )
= $false )
| ( ( sK2_SY26 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX0 @ ( cartprod @ SX0 @ SX0 ) ) ))]]) ).
thf(97,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX0 @ ( cartprod @ SX0 @ sK1_SY0 ) ) ) )
= $true )
| ( ( sK2_SY26 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX0 @ ( cartprod @ SX0 @ sK1_SY0 ) ) ))]]) ).
thf(98,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ sK1_SY0 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ sK1_SY0 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX0 @ ( cartprod @ sK1_SY0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( sK1_SY0 )),bind(SV18,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX0 @ ( cartprod @ sK1_SY0 @ SX1 ) ) ))]]) ).
thf(99,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX0 @ ( cartprod @ sK1_SY0 @ SX0 ) ) ) )
= $true )
| ( ( sK2_SY26 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX0 @ ( cartprod @ sK1_SY0 @ SX0 ) ) ))]]) ).
thf(100,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX0 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX0 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) ))]]) ).
thf(101,plain,
! [SV76: $i > $i > $i,SV75: $i > $i > $i,SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX0 @ ( cartprod @ ( SV75 @ SX0 @ SX1 ) @ ( SV76 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( ( cartprod @ ( SV75 @ sK2_SY26 @ SV17 ) @ ( SV76 @ sK2_SY26 @ SV17 ) )
= ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
= $false ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX0 @ ( cartprod @ ( SV75 @ SX0 @ SX1 ) @ ( SV76 @ SX0 @ SX1 ) ) ) ))]]) ).
thf(102,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX0 @ SX1 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( cartprod @ sK1_SY0 @ sK1_SY0 )),bind(SV18,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX0 @ SX1 ) ))]]) ).
thf(103,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX0 @ SX0 ) ) )
= $true )
| ( ( sK2_SY26
= ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
= $false ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ SX0 @ SX0 ) ))]]) ).
thf(104,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK1_SY0 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK1_SY0 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ SX1 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ SX1 @ SX1 ) ) ))]]) ).
thf(105,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK1_SY0 @ SV16 )
= $false )
| ( ( in @ sK1_SY0 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK1_SY0 @ sK1_SY0 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ SX1 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( sK1_SY0 )),bind(SV17,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ SX1 @ SX0 ) ) ))]]) ).
thf(106,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK1_SY0 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK1_SY0 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ SX1 @ sK1_SY0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ SX1 @ sK1_SY0 ) ) ))]]) ).
thf(107,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK1_SY0 @ SV16 )
= $false )
| ( ( in @ sK1_SY0 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK1_SY0 @ sK1_SY0 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( sK1_SY0 )),bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ SX0 @ SX1 ) ) ))]]) ).
thf(108,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK1_SY0 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK1_SY0 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ SX0 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ SX0 @ SX0 ) ) ))]]) ).
thf(109,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK1_SY0 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK1_SY0 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ SX0 @ sK1_SY0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ SX0 @ sK1_SY0 ) ) ))]]) ).
thf(110,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK1_SY0 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK1_SY0 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ sK1_SY0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ sK1_SY0 @ SX1 ) ) ))]]) ).
thf(111,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK1_SY0 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK1_SY0 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ sK1_SY0 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ sK1_SY0 @ SX0 ) ) ))]]) ).
thf(112,plain,
! [SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) ))]]) ).
thf(113,plain,
! [SV54: $i > $i > $i,SV53: $i > $i > $i,SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( ( cartprod @ ( SV53 @ SV18 @ SV17 ) @ ( SV54 @ SV18 @ SV17 ) )
= ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
= $false ) ),
inference(extuni,[status(esa)],[71:[bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ sK2_SY26 @ ( cartprod @ ( SV53 @ SX0 @ SX1 ) @ ( SV54 @ SX0 @ SX1 ) ) ) ))]]) ).
thf(114,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ sK2_SY26 @ SX1 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV17,$thf( cartprod @ sK1_SY0 @ sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ sK2_SY26 @ SX1 ) ))]]) ).
thf(115,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ sK2_SY26 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV18,$thf( cartprod @ sK1_SY0 @ sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ sK2_SY26 @ SX0 ) ))]]) ).
thf(116,plain,
! [SV44: $i > $i > $i,SV43: $i > $i > $i,SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ ( SV43 @ SX0 @ SX1 ) @ ( SV44 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( subset @ ( SV43 @ SV18 @ SV17 ) @ ( SV44 @ SV18 @ SV17 ) )
= $true )
| ( ( subset @ sK2_SY26 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
= $true ) ),
inference(extuni,[status(esa)],[71:[bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ ( SV43 @ SX0 @ SX1 ) @ ( SV44 @ SX0 @ SX1 ) ) ))]]) ).
thf(117,plain,
! [SV44: $i > $i > $i,SV43: $i > $i > $i,SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ ( SV43 @ SX0 @ SX1 ) @ ( SV44 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( subset @ ( SV43 @ SV18 @ SV17 ) @ ( SV44 @ SV18 @ SV17 ) )
= $false )
| ( ( subset @ sK2_SY26 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
= $false ) ),
inference(extuni,[status(esa)],[71:[bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( subset @ ( SV43 @ SX0 @ SX1 ) @ ( SV44 @ SX0 @ SX1 ) ) ))]]) ).
thf(118,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK3_SY31 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK3_SY31 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX1 @ SX1 ) ) )
= $true )
| ( ( sK3_SY31 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[68:[bind(SV17,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX1 @ SX1 ) ))]]) ).
thf(119,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK1_SY0 @ SV16 )
= $false )
| ( ( in @ sK3_SY31 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK1_SY0 @ sK3_SY31 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[68:[bind(SV18,$thf( sK1_SY0 )),bind(SV17,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX1 @ SX0 ) ))]]) ).
thf(120,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK3_SY31 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK3_SY31 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX1 @ sK1_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[68:[bind(SV17,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX1 @ sK1_SY0 ) ))]]) ).
thf(121,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK3_SY31 @ SV16 )
= $false )
| ( ( in @ sK1_SY0 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ sK1_SY0 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX0 @ SX1 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[68:[bind(SV17,$thf( sK1_SY0 )),bind(SV18,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX0 @ SX1 ) ))]]) ).
thf(122,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK3_SY31 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX0 @ SX0 ) ) )
= $true )
| ( ( sK3_SY31 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[68:[bind(SV18,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX0 @ SX0 ) ))]]) ).
thf(123,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK3_SY31 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX0 @ sK1_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[68:[bind(SV18,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX0 @ sK1_SY0 ) ))]]) ).
thf(124,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK1_SY0 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK1_SY0 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ sK3_SY31 @ SX1 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[68:[bind(SV17,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ sK3_SY31 @ SX1 ) ))]]) ).
thf(125,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK1_SY0 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK1_SY0 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ sK3_SY31 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[68:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ sK3_SY31 @ SX0 ) ))]]) ).
thf(126,plain,
! [SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ sK3_SY31 @ sK1_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[68:[bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ sK3_SY31 @ sK1_SY0 ) ))]]) ).
thf(127,plain,
! [SV120: $i > $i > $i,SV119: $i > $i > $i,SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV119 @ SX0 @ SX1 ) @ ( SV120 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( in @ ( SV119 @ SV18 @ SV17 ) @ ( SV120 @ SV18 @ SV17 ) )
= $true )
| ( ( in @ sK3_SY31 @ sK1_SY0 )
= $true ) ),
inference(extuni,[status(esa)],[68:[bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( SV119 @ SX0 @ SX1 ) @ ( SV120 @ SX0 @ SX1 ) ) ))]]) ).
thf(128,plain,
! [SV120: $i > $i > $i,SV119: $i > $i > $i,SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV119 @ SX0 @ SX1 ) @ ( SV120 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( in @ ( SV119 @ SV18 @ SV17 ) @ ( SV120 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ sK3_SY31 @ sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[68:[bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( SV119 @ SX0 @ SX1 ) @ ( SV120 @ SX0 @ SX1 ) ) ))]]) ).
thf(129,plain,
! [SV19: $i > $i > $o,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK3_SY31 )
@ ( dpsetconstr @ SV16 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( SV19 @ SV18 @ sK3_SY31 )
= $false ) ),
inference(extuni,[status(esa)],[67:[bind(SV15,$thf( sK1_SY0 )),bind(SV17,$thf( sK3_SY31 ))]]) ).
thf(130,plain,
! [SV19: $i > $i > $o,SV15: $i,SV17: $i] :
( ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ SV17 )
@ ( dpsetconstr @ sK1_SY0 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( SV19 @ sK3_SY31 @ SV17 )
= $false ) ),
inference(extuni,[status(esa)],[66:[bind(SV16,$thf( sK1_SY0 )),bind(SV18,$thf( sK3_SY31 ))]]) ).
thf(131,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK4_SY35 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK4_SY35 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX1 @ SX1 ) ) )
= $true )
| ( ( sK4_SY35 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[65:[bind(SV17,$thf( sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX1 @ SX1 ) ))]]) ).
thf(132,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK1_SY0 @ SV16 )
= $false )
| ( ( in @ sK4_SY35 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK1_SY0 @ sK4_SY35 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[65:[bind(SV18,$thf( sK1_SY0 )),bind(SV17,$thf( sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX1 @ SX0 ) ))]]) ).
thf(133,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK4_SY35 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK4_SY35 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX1 @ sK1_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[65:[bind(SV17,$thf( sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX1 @ sK1_SY0 ) ))]]) ).
thf(134,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK4_SY35 @ SV16 )
= $false )
| ( ( in @ sK1_SY0 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK4_SY35 @ sK1_SY0 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX0 @ SX1 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[65:[bind(SV17,$thf( sK1_SY0 )),bind(SV18,$thf( sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX0 @ SX1 ) ))]]) ).
thf(135,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK4_SY35 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK4_SY35 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX0 @ SX0 ) ) )
= $true )
| ( ( sK4_SY35 = sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[65:[bind(SV18,$thf( sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX0 @ SX0 ) ))]]) ).
thf(136,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK4_SY35 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK4_SY35 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX0 @ sK1_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[65:[bind(SV18,$thf( sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX0 @ sK1_SY0 ) ))]]) ).
thf(137,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK1_SY0 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK1_SY0 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ sK4_SY35 @ SX1 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[65:[bind(SV17,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ sK4_SY35 @ SX1 ) ))]]) ).
thf(138,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK1_SY0 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK1_SY0 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ sK4_SY35 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[65:[bind(SV18,$thf( sK1_SY0 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ sK4_SY35 @ SX0 ) ))]]) ).
thf(139,plain,
! [SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ sK4_SY35 @ sK1_SY0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[65:[bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ sK4_SY35 @ sK1_SY0 ) ))]]) ).
thf(140,plain,
! [SV142: $i > $i > $i,SV141: $i > $i > $i,SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV141 @ SX0 @ SX1 ) @ ( SV142 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( in @ ( SV141 @ SV18 @ SV17 ) @ ( SV142 @ SV18 @ SV17 ) )
= $true )
| ( ( in @ sK4_SY35 @ sK1_SY0 )
= $true ) ),
inference(extuni,[status(esa)],[65:[bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( SV141 @ SX0 @ SX1 ) @ ( SV142 @ SX0 @ SX1 ) ) ))]]) ).
thf(141,plain,
! [SV142: $i > $i > $i,SV141: $i > $i > $i,SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV141 @ SX0 @ SX1 ) @ ( SV142 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( in @ ( SV141 @ SV18 @ SV17 ) @ ( SV142 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ sK4_SY35 @ sK1_SY0 )
= $false ) ),
inference(extuni,[status(esa)],[65:[bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( SV141 @ SX0 @ SX1 ) @ ( SV142 @ SX0 @ SX1 ) ) ))]]) ).
thf(142,plain,
! [SV19: $i > $i > $o,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK4_SY35 )
@ ( dpsetconstr @ SV16 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( SV19 @ SV18 @ sK4_SY35 )
= $false ) ),
inference(extuni,[status(esa)],[64:[bind(SV15,$thf( sK1_SY0 )),bind(SV17,$thf( sK4_SY35 ))]]) ).
thf(143,plain,
! [SV19: $i > $i > $o,SV15: $i,SV17: $i] :
( ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK4_SY35 @ SV17 )
@ ( dpsetconstr @ sK1_SY0 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( SV19 @ sK4_SY35 @ SV17 )
= $false ) ),
inference(extuni,[status(esa)],[63:[bind(SV16,$thf( sK1_SY0 )),bind(SV18,$thf( sK4_SY35 ))]]) ).
thf(144,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK3_SY31 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK3_SY31 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX1 ) @ SX1 ) ) )
= $true )
| ( ( sK3_SY31 = sK2_SY26 )
= $false )
| ( ( sK3_SY31 = sK4_SY35 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX1 @ SX1 ) @ SX1 ) ))]]) ).
thf(145,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ sK3_SY31 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ sK3_SY31 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX1 ) @ SX0 ) ) )
= $true )
| ( ( sK3_SY31 = sK4_SY35 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( sK2_SY26 )),bind(SV17,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX1 @ SX1 ) @ SX0 ) ))]]) ).
thf(146,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK3_SY31 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK3_SY31 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX1 ) @ sK2_SY26 ) ) )
= $true )
| ( ( sK3_SY31 = sK4_SY35 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX1 @ SX1 ) @ sK2_SY26 ) ))]]) ).
thf(147,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK4_SY35 @ SV16 )
= $false )
| ( ( in @ sK3_SY31 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ SX1 ) ) )
= $true )
| ( ( sK3_SY31 = sK2_SY26 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( sK4_SY35 )),bind(SV17,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ SX1 ) ))]]) ).
thf(148,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK4_SY35 @ SV16 )
= $false )
| ( ( in @ sK3_SY31 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ SX0 ) ) )
= $true )
| ( ( sK4_SY35 = sK2_SY26 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( sK4_SY35 )),bind(SV17,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ SX0 ) ))]]) ).
thf(149,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK4_SY35 @ SV16 )
= $false )
| ( ( in @ sK3_SY31 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( sK4_SY35 )),bind(SV17,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ))]]) ).
thf(150,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK3_SY31 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK3_SY31 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ sK4_SY35 ) @ SX1 ) ) )
= $true )
| ( ( sK3_SY31 = sK2_SY26 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX1 @ sK4_SY35 ) @ SX1 ) ))]]) ).
thf(151,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ sK3_SY31 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ sK3_SY31 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ sK4_SY35 ) @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( sK2_SY26 )),bind(SV17,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX1 @ sK4_SY35 ) @ SX0 ) ))]]) ).
thf(152,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK3_SY31 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK3_SY31 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ sK4_SY35 ) @ sK2_SY26 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX1 @ sK4_SY35 ) @ sK2_SY26 ) ))]]) ).
thf(153,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK3_SY31 @ SV16 )
= $false )
| ( ( in @ sK4_SY35 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX0 @ SX1 ) @ SX1 ) ) )
= $true )
| ( ( sK4_SY35 = sK2_SY26 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( sK4_SY35 )),bind(SV18,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX0 @ SX1 ) @ SX1 ) ))]]) ).
thf(154,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK3_SY31 @ SV16 )
= $false )
| ( ( in @ sK4_SY35 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX0 @ SX1 ) @ SX0 ) ) )
= $true )
| ( ( sK3_SY31 = sK2_SY26 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( sK4_SY35 )),bind(SV18,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX0 @ SX1 ) @ SX0 ) ))]]) ).
thf(155,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK3_SY31 @ SV16 )
= $false )
| ( ( in @ sK4_SY35 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX0 @ SX1 ) @ sK2_SY26 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( sK4_SY35 )),bind(SV18,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX0 @ SX1 ) @ sK2_SY26 ) ))]]) ).
thf(156,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK3_SY31 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX0 @ SX0 ) @ SX1 ) ) )
= $true )
| ( ( sK3_SY31 = sK4_SY35 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( sK2_SY26 )),bind(SV18,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX0 @ SX0 ) @ SX1 ) ))]]) ).
thf(157,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK3_SY31 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX0 @ SX0 ) @ SX0 ) ) )
= $true )
| ( ( sK3_SY31 = sK2_SY26 )
= $false )
| ( ( sK3_SY31 = sK4_SY35 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX0 @ SX0 ) @ SX0 ) ))]]) ).
thf(158,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK3_SY31 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX0 @ SX0 ) @ sK2_SY26 ) ) )
= $true )
| ( ( sK3_SY31 = sK4_SY35 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX0 @ SX0 ) @ sK2_SY26 ) ))]]) ).
thf(159,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK3_SY31 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX0 @ sK4_SY35 ) @ SX1 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( sK2_SY26 )),bind(SV18,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX0 @ sK4_SY35 ) @ SX1 ) ))]]) ).
thf(160,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK3_SY31 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX0 @ sK4_SY35 ) @ SX0 ) ) )
= $true )
| ( ( sK3_SY31 = sK2_SY26 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX0 @ sK4_SY35 ) @ SX0 ) ))]]) ).
thf(161,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK3_SY31 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX0 @ sK4_SY35 ) @ sK2_SY26 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( sK3_SY31 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX0 @ sK4_SY35 ) @ sK2_SY26 ) ))]]) ).
thf(162,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK4_SY35 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK4_SY35 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ SX1 ) @ SX1 ) ) )
= $true )
| ( ( sK4_SY35 = sK2_SY26 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ SX1 ) @ SX1 ) ))]]) ).
thf(163,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ sK4_SY35 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ sK4_SY35 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ SX1 ) @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( sK2_SY26 )),bind(SV17,$thf( sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ SX1 ) @ SX0 ) ))]]) ).
thf(164,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK4_SY35 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK4_SY35 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ SX1 ) @ sK2_SY26 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ SX1 ) @ sK2_SY26 ) ))]]) ).
thf(165,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK4_SY35 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK4_SY35 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ SX0 ) @ SX1 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( sK2_SY26 )),bind(SV18,$thf( sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ SX0 ) @ SX1 ) ))]]) ).
thf(166,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK4_SY35 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK4_SY35 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ SX0 ) @ SX0 ) ) )
= $true )
| ( ( sK4_SY35 = sK2_SY26 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ SX0 ) @ SX0 ) ))]]) ).
thf(167,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK4_SY35 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK4_SY35 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ SX0 ) @ sK2_SY26 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ SX0 ) @ sK2_SY26 ) ))]]) ).
thf(168,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ SX1 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ SX1 ) ))]]) ).
thf(169,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ SX0 ) ))]]) ).
thf(170,plain,
! [SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 ) ))]]) ).
thf(171,plain,
! [SV170: $i > $i > $i,SV169: $i > $i > $i,SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV169 @ SX0 @ SX1 ) @ ( SV170 @ SX0 @ SX1 ) ) @ SX1 ) ) )
= $true )
| ( ( ( kpair @ ( SV169 @ SV18 @ sK2_SY26 ) @ ( SV170 @ SV18 @ sK2_SY26 ) )
= ( kpair @ sK3_SY31 @ sK4_SY35 ) )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ ( SV169 @ SX0 @ SX1 ) @ ( SV170 @ SX0 @ SX1 ) ) @ SX1 ) ))]]) ).
thf(172,plain,
! [SV170: $i > $i > $i,SV169: $i > $i > $i,SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV169 @ SX0 @ SX1 ) @ ( SV170 @ SX0 @ SX1 ) ) @ SX0 ) ) )
= $true )
| ( ( ( kpair @ ( SV169 @ sK2_SY26 @ SV17 ) @ ( SV170 @ sK2_SY26 @ SV17 ) )
= ( kpair @ sK3_SY31 @ sK4_SY35 ) )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( sK2_SY26 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ ( SV169 @ SX0 @ SX1 ) @ ( SV170 @ SX0 @ SX1 ) ) @ SX0 ) ))]]) ).
thf(173,plain,
! [SV170: $i > $i > $i,SV169: $i > $i > $i,SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV169 @ SX0 @ SX1 ) @ ( SV170 @ SX0 @ SX1 ) ) @ sK2_SY26 ) ) )
= $true )
| ( ( ( kpair @ ( SV169 @ SV18 @ SV17 ) @ ( SV170 @ SV18 @ SV17 ) )
= ( kpair @ sK3_SY31 @ sK4_SY35 ) )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ ( SV169 @ SX0 @ SX1 ) @ ( SV170 @ SX0 @ SX1 ) ) @ sK2_SY26 ) ))]]) ).
thf(174,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ ( kpair @ sK3_SY31 @ sK4_SY35 ) )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX1 @ SX1 ) ) )
= $true )
| ( ( ( kpair @ sK3_SY31 @ sK4_SY35 )
= sK2_SY26 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( kpair @ sK3_SY31 @ sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX1 @ SX1 ) ))]]) ).
thf(175,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ ( kpair @ sK3_SY31 @ sK4_SY35 ) )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( sK2_SY26 )),bind(SV17,$thf( kpair @ sK3_SY31 @ sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX1 @ SX0 ) ))]]) ).
thf(176,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ ( kpair @ sK3_SY31 @ sK4_SY35 ) )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX1 @ sK2_SY26 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( kpair @ sK3_SY31 @ sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX1 @ sK2_SY26 ) ))]]) ).
thf(177,plain,
! [SV15: $i,SV16: $i] :
( ( ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX0 @ SX1 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV17,$thf( sK2_SY26 )),bind(SV18,$thf( kpair @ sK3_SY31 @ sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX0 @ SX1 ) ))]]) ).
thf(178,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX0 @ SX0 ) ) )
= $true )
| ( ( ( kpair @ sK3_SY31 @ sK4_SY35 )
= sK2_SY26 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( kpair @ sK3_SY31 @ sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX0 @ SX0 ) ))]]) ).
thf(179,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ SX0 @ sK2_SY26 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV18,$thf( kpair @ sK3_SY31 @ sK4_SY35 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ SX0 @ sK2_SY26 ) ))]]) ).
thf(180,plain,
! [SV164: $i > $i > $i,SV163: $i > $i > $i,SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV163 @ SX0 @ SX1 ) @ ( SV164 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( in @ ( SV163 @ SV18 @ SV17 ) @ ( SV164 @ SV18 @ SV17 ) )
= $true )
| ( ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
= $true ) ),
inference(extuni,[status(esa)],[62:[bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( SV163 @ SX0 @ SX1 ) @ ( SV164 @ SX0 @ SX1 ) ) ))]]) ).
thf(181,plain,
! [SV164: $i > $i > $i,SV163: $i > $i > $i,SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV163 @ SX0 @ SX1 ) @ ( SV164 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( in @ ( SV163 @ SV18 @ SV17 ) @ ( SV164 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( SV163 @ SX0 @ SX1 ) @ ( SV164 @ SX0 @ SX1 ) ) ))]]) ).
thf(182,plain,
! [SV19: $i > $i > $o,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ ( kpair @ SV18 @ ( kpair @ sK3_SY31 @ sK4_SY35 ) )
@ ( dpsetconstr @ SV16 @ sK2_SY26
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( SV19 @ SV18 @ ( kpair @ sK3_SY31 @ sK4_SY35 ) )
= $false ) ),
inference(extuni,[status(esa)],[61:[bind(SV15,$thf( sK2_SY26 )),bind(SV17,$thf( kpair @ sK3_SY31 @ sK4_SY35 ))]]) ).
thf(183,plain,
! [SV19: $i > $i > $o,SV15: $i,SV17: $i] :
( ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ SV17 )
@ ( dpsetconstr @ sK2_SY26 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $true )
| ( ( SV19 @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ SV17 )
= $false ) ),
inference(extuni,[status(esa)],[60:[bind(SV16,$thf( sK2_SY26 )),bind(SV18,$thf( kpair @ sK3_SY31 @ sK4_SY35 ))]]) ).
thf(184,plain,
! [SV263: $i > $i > $i > $i > $i,SV262: $i > $i > $i > $i > $i,SV246: $i > $i > $i,SV245: $i > $i > $i,SV252: $i > $i > $i,SV17: $i,SV251: $i > $i > $i,SV18: $i] :
( ( ( in @ SV18 @ ( SV251 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ SV17 @ ( SV252 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ ( kpair @ ( SV245 @ SV18 @ SV17 ) @ ( SV246 @ SV18 @ SV17 ) )
@ ( dpsetconstr @ ( SV251 @ SV18 @ SV17 ) @ ( SV252 @ SV18 @ SV17 )
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV262 @ SV18 @ SV17 @ SX0 @ SX1 ) @ ( SV263 @ SV18 @ SV17 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( in @ SV18 @ ( SV251 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ SV17 @ ( SV252 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ ( SV251 @ SV18 @ SV17 ) @ ( SV252 @ SV18 @ SV17 )
@ ^ [SX0: $i,SX1: $i] :
( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) )
@ ( dpsetconstr @ ( SV251 @ SX0 @ SX1 ) @ ( SV252 @ SX0 @ SX1 )
@ ^ [SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) ) )
= $true )
| ( ( in
@ ( SV262 @ SV18 @ SV17
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV263 @ SV18 @ SV17
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $true )
| ( ( in
@ ( kpair
@ ( SV245
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV246
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
@ ( dpsetconstr
@ ( SV251
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV252
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ^ [SX0: $i,SX1: $i] :
( in
@ ( SV262
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( in @ ( SV262 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV263 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( in @ ( SV262 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV263 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV263
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( in @ ( SV262 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV263 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( in @ ( SV262 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV263 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) ) ) )
= $true )
| ( ( ( kpair @ ( SV245 @ SV18 @ SV17 ) @ ( SV246 @ SV18 @ SV17 ) )
= ( kpair @ SV18 @ SV17 ) )
= $false ) ),
inference(extuni,[status(esa)],[58:[bind(SV15,$thf( SV252 @ SV18 @ SV17 )),bind(SV16,$thf( SV251 @ SV18 @ SV17 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ ( dpsetconstr @ ( SV251 @ SX0 @ SX1 ) @ ( SV252 @ SX0 @ SX1 ) @ ^ [SX2: $i] : ^ [SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) ))]]) ).
thf(185,plain,
! [SV263: $i > $i > $i > $i > $i,SV262: $i > $i > $i > $i > $i,SV246: $i > $i > $i,SV245: $i > $i > $i,SV252: $i > $i > $i,SV17: $i,SV251: $i > $i > $i,SV18: $i] :
( ( ( in @ SV18 @ ( SV251 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ SV17 @ ( SV252 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ ( kpair @ ( SV245 @ SV18 @ SV17 ) @ ( SV246 @ SV18 @ SV17 ) )
@ ( dpsetconstr @ ( SV251 @ SV18 @ SV17 ) @ ( SV252 @ SV18 @ SV17 )
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV262 @ SV18 @ SV17 @ SX0 @ SX1 ) @ ( SV263 @ SV18 @ SV17 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( in @ SV18 @ ( SV251 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ SV17 @ ( SV252 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ ( SV251 @ SV18 @ SV17 ) @ ( SV252 @ SV18 @ SV17 )
@ ^ [SX0: $i,SX1: $i] :
( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) )
@ ( dpsetconstr @ ( SV251 @ SX0 @ SX1 ) @ ( SV252 @ SX0 @ SX1 )
@ ^ [SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) ) )
= $true )
| ( ( in
@ ( SV262 @ SV18 @ SV17
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV263 @ SV18 @ SV17
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $false )
| ( ( in
@ ( kpair
@ ( SV245
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV246
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
@ ( dpsetconstr
@ ( SV251
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV252
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ^ [SX0: $i,SX1: $i] :
( in
@ ( SV262
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( in @ ( SV262 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV263 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( in @ ( SV262 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV263 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV263
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( in @ ( SV262 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV263 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( in @ ( SV262 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV263 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) ) ) )
= $false )
| ( ( ( kpair @ ( SV245 @ SV18 @ SV17 ) @ ( SV246 @ SV18 @ SV17 ) )
= ( kpair @ SV18 @ SV17 ) )
= $false ) ),
inference(extuni,[status(esa)],[58:[bind(SV15,$thf( SV252 @ SV18 @ SV17 )),bind(SV16,$thf( SV251 @ SV18 @ SV17 )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ ( dpsetconstr @ ( SV251 @ SX0 @ SX1 ) @ ( SV252 @ SX0 @ SX1 ) @ ^ [SX2: $i] : ^ [SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) ))]]) ).
thf(186,plain,
! [SV253: $i > $i > $i > $i > $o,SV252: $i > $i > $i,SV251: $i > $i > $i,SV246: $i > $i > $i,SV245: $i > $i > $i,SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ ( SV245 @ SV18 @ SV17 ) @ ( SV246 @ SV18 @ SV17 ) ) @ ( dpsetconstr @ ( SV251 @ SV18 @ SV17 ) @ ( SV252 @ SV18 @ SV17 ) @ ( SV253 @ SV18 @ SV17 ) ) )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ ( dpsetconstr @ ( SV251 @ SX0 @ SX1 ) @ ( SV252 @ SX0 @ SX1 ) @ ( SV253 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( ( dpsetconstr @ ( SV251 @ SV18 @ SV17 ) @ ( SV252 @ SV18 @ SV17 ) @ ( SV253 @ SV18 @ SV17 ) )
= ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ ( dpsetconstr @ ( SV251 @ SX0 @ SX1 ) @ ( SV252 @ SX0 @ SX1 ) @ ( SV253 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( ( kpair @ ( SV245 @ SV18 @ SV17 ) @ ( SV246 @ SV18 @ SV17 ) )
= ( kpair @ SV18 @ SV17 ) )
= $false ) ),
inference(extuni,[status(esa)],[58:[bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ ( dpsetconstr @ ( SV251 @ SX0 @ SX1 ) @ ( SV252 @ SX0 @ SX1 ) @ ( SV253 @ SX0 @ SX1 ) ) ) ))]]) ).
thf(187,plain,
! [SV246: $i > $i > $i,SV245: $i > $i > $i,SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) )
@ SV15 )
= $false )
| ( ( in
@ ( kpair
@ ( SV245 @ SV18
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ) )
@ ( SV246 @ SV18
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ) ) )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ) )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) )
@ SV15 )
= $false )
| ( ( in
@ ( kpair @ SV18
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ) )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ) )
= $true )
| ( ( ( kpair
@ ( SV245 @ SV18
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ) )
@ ( SV246 @ SV18
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ) ) )
= ( kpair @ SV18
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[58:[bind(SV17,$thf( dpsetconstr @ SV16 @ SV15 @ ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ))]]) ).
thf(188,plain,
! [SV17: $i,SV246: $i > $i > $i,SV245: $i > $i > $i,SV15: $i,SV16: $i] :
( ( ( in
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) )
@ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in
@ ( kpair
@ ( SV245
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) )
@ SV17 )
@ ( SV246
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) )
@ SV17 ) )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) ) )
= $false )
| ( ( in
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) )
@ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in
@ ( kpair
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) )
@ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) ) )
= $true )
| ( ( ( kpair
@ ( SV245
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) )
@ SV17 )
@ ( SV246
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) )
@ SV17 ) )
= ( kpair
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) )
@ SV17 ) )
= $false ) ),
inference(extuni,[status(esa)],[58:[bind(SV18,$thf( dpsetconstr @ SV16 @ SV15 @ ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) )),bind(SV19,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) ))]]) ).
thf(191,plain,
! [SV15: $i,SV16: $i,SV17: $i] :
( ( ( in @ SV17 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV17 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[77:[bind(SV18,$thf( SV17 ))]]) ).
thf(192,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV34: $i > $i > $o] :
( ( ( SV34 @ SV18 @ SV17 )
= $true )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] :
~ ( SV34 @ SX0 @ SX1 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(193,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i] :
( ( ( SV18 = SV17 )
= $true )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(194,plain,
! [SV29: $i > $i > $o,SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV28: $i > $i > $o] :
( ( ( SV28 @ SV18 @ SV17 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] :
( ( SV28 @ SX0 @ SX1 )
| ( SV29 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(195,plain,
! [SV28: $i > $i > $o,SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV29: $i > $i > $o] :
( ( ( SV29 @ SV18 @ SV17 )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] :
( ( SV28 @ SX0 @ SX1 )
| ( SV29 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(196,plain,
! [SV15: $i,SV17: $i,SV16: $i] :
( ( ( in @ sK2_SY26 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ sK2_SY26 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX0 @ ( cartprod @ SX0 @ SX0 ) ) ) )
= $true )
| ( ( sK2_SY26 = sK1_SY0 )
= $false ) ),
inference(sim,[status(thm)],[96]) ).
thf(197,plain,
! [SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ sK2_SY26 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV18 @ sK2_SY26 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( cartprod @ SX1 @ SX1 ) ) ) )
= $true )
| ( ( sK2_SY26 = sK1_SY0 )
= $false ) ),
inference(sim,[status(thm)],[80]) ).
thf(198,plain,
! [SV17: $i,SV246: $i > $i > $i,SV245: $i > $i > $i,SV15: $i,SV16: $i] :
( ( ( in
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) )
@ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in
@ ( kpair
@ ( SV245
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) )
@ SV17 )
@ ( SV246
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) )
@ SV17 ) )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) ) )
= $false )
| ( ( in
@ ( kpair
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) )
@ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) ) )
= $true )
| ( ( ( kpair
@ ( SV245
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) )
@ SV17 )
@ ( SV246
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) )
@ SV17 ) )
= ( kpair
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX0 ) )
@ SV17 ) )
= $false ) ),
inference(sim,[status(thm)],[188]) ).
thf(199,plain,
! [SV246: $i > $i > $i,SV245: $i > $i > $i,SV15: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) )
@ SV15 )
= $false )
| ( ( in
@ ( kpair
@ ( SV245 @ SV18
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ) )
@ ( SV246 @ SV18
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ) ) )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ) )
= $false )
| ( ( in
@ ( kpair @ SV18
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ) )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ) )
= $true )
| ( ( ( kpair
@ ( SV245 @ SV18
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ) )
@ ( SV246 @ SV18
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ) ) )
= ( kpair @ SV18
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ SX1 ) ) ) )
= $false ) ),
inference(sim,[status(thm)],[187]) ).
thf(200,plain,
! [SV253: $i > $i > $i > $i > $o,SV252: $i > $i > $i,SV251: $i > $i > $i,SV246: $i > $i > $i,SV245: $i > $i > $i,SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ ( kpair @ ( SV245 @ SV18 @ SV17 ) @ ( SV246 @ SV18 @ SV17 ) ) @ ( dpsetconstr @ ( SV251 @ SV18 @ SV17 ) @ ( SV252 @ SV18 @ SV17 ) @ ( SV253 @ SV18 @ SV17 ) ) )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ ( dpsetconstr @ ( SV251 @ SX0 @ SX1 ) @ ( SV252 @ SX0 @ SX1 ) @ ( SV253 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( ( dpsetconstr @ ( SV251 @ SV18 @ SV17 ) @ ( SV252 @ SV18 @ SV17 ) @ ( SV253 @ SV18 @ SV17 ) )
= ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) ) @ ( dpsetconstr @ ( SV251 @ SX0 @ SX1 ) @ ( SV252 @ SX0 @ SX1 ) @ ( SV253 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( ( kpair @ ( SV245 @ SV18 @ SV17 ) @ ( SV246 @ SV18 @ SV17 ) )
= ( kpair @ SV18 @ SV17 ) )
= $false ) ),
inference(sim,[status(thm)],[186]) ).
thf(201,plain,
! [SV263: $i > $i > $i > $i > $i,SV262: $i > $i > $i > $i > $i,SV246: $i > $i > $i,SV245: $i > $i > $i,SV252: $i > $i > $i,SV17: $i,SV251: $i > $i > $i,SV18: $i] :
( ( ( in @ SV18 @ ( SV251 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ SV17 @ ( SV252 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ ( kpair @ ( SV245 @ SV18 @ SV17 ) @ ( SV246 @ SV18 @ SV17 ) )
@ ( dpsetconstr @ ( SV251 @ SV18 @ SV17 ) @ ( SV252 @ SV18 @ SV17 )
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV262 @ SV18 @ SV17 @ SX0 @ SX1 ) @ ( SV263 @ SV18 @ SV17 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ ( SV251 @ SV18 @ SV17 ) @ ( SV252 @ SV18 @ SV17 )
@ ^ [SX0: $i,SX1: $i] :
( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) )
@ ( dpsetconstr @ ( SV251 @ SX0 @ SX1 ) @ ( SV252 @ SX0 @ SX1 )
@ ^ [SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) ) )
= $true )
| ( ( in
@ ( SV262 @ SV18 @ SV17
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV263 @ SV18 @ SV17
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $false )
| ( ( in
@ ( kpair
@ ( SV245
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV246
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
@ ( dpsetconstr
@ ( SV251
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV252
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ^ [SX0: $i,SX1: $i] :
( in
@ ( SV262
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( in @ ( SV262 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV263 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( in @ ( SV262 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV263 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV263
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( in @ ( SV262 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV263 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( in @ ( SV262 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV263 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) ) ) )
= $false )
| ( ( ( kpair @ ( SV245 @ SV18 @ SV17 ) @ ( SV246 @ SV18 @ SV17 ) )
= ( kpair @ SV18 @ SV17 ) )
= $false ) ),
inference(sim,[status(thm)],[185]) ).
thf(202,plain,
! [SV263: $i > $i > $i > $i > $i,SV262: $i > $i > $i > $i > $i,SV246: $i > $i > $i,SV245: $i > $i > $i,SV252: $i > $i > $i,SV17: $i,SV251: $i > $i > $i,SV18: $i] :
( ( ( in @ SV18 @ ( SV251 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ SV17 @ ( SV252 @ SV18 @ SV17 ) )
= $false )
| ( ( in @ ( kpair @ ( SV245 @ SV18 @ SV17 ) @ ( SV246 @ SV18 @ SV17 ) )
@ ( dpsetconstr @ ( SV251 @ SV18 @ SV17 ) @ ( SV252 @ SV18 @ SV17 )
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV262 @ SV18 @ SV17 @ SX0 @ SX1 ) @ ( SV263 @ SV18 @ SV17 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ ( SV251 @ SV18 @ SV17 ) @ ( SV252 @ SV18 @ SV17 )
@ ^ [SX0: $i,SX1: $i] :
( in @ ( kpair @ ( SV245 @ SX0 @ SX1 ) @ ( SV246 @ SX0 @ SX1 ) )
@ ( dpsetconstr @ ( SV251 @ SX0 @ SX1 ) @ ( SV252 @ SX0 @ SX1 )
@ ^ [SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) ) )
= $true )
| ( ( in
@ ( SV262 @ SV18 @ SV17
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV263 @ SV18 @ SV17
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $true )
| ( ( in
@ ( kpair
@ ( SV245
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV246
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
@ ( dpsetconstr
@ ( SV251
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV252
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX0: $i,SX1: $i,SX2: $i,SX3: $i] : ( in @ ( SV262 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV263 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ^ [SX0: $i,SX1: $i] :
( in
@ ( SV262
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( in @ ( SV262 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV263 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( in @ ( SV262 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV263 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV263
@ ( sK5_E @ SV252 @ SV251 @ SV246 @ SV245 @ SV17 @ SV18
@ ^ [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( in @ ( SV262 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV263 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK6_E @ SV245 @ SV246 @ SV251 @ SV252 @ SV17 @ SV18
@ ^ [SX2: $i,SX3: $i,SX4: $i,SX5: $i] : ( in @ ( SV262 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV263 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) ) ) )
= $true )
| ( ( ( kpair @ ( SV245 @ SV18 @ SV17 ) @ ( SV246 @ SV18 @ SV17 ) )
= ( kpair @ SV18 @ SV17 ) )
= $false ) ),
inference(sim,[status(thm)],[184]) ).
thf(203,plain,
! [SV15: $i,SV16: $i,SV17: $i,SV18: $i,SV19: $i > $i > $o] :
( ( ( ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) )
= ( in @ ( kpair @ SV18 @ SV17 )
@ ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( SV19 @ SV18 @ SV17 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV18 @ SV16 )
= $false ) ),
inference(res,[status(thm)],[43,53]) ).
thf(204,plain,
( ( ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) )
= ( in @ ( kpair @ sK3_SY31 @ sK4_SY35 ) @ sK2_SY26 ) )
= $false ),
inference(res,[status(thm)],[43,41]) ).
thf(205,plain,
( ( ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) )
= ( in @ sK4_SY35 @ sK1_SY0 ) )
= $false ),
inference(res,[status(thm)],[43,34]) ).
thf(206,plain,
( ( ( in @ ( kpair @ sK4_SY35 @ sK3_SY31 )
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) ) )
= ( in @ sK3_SY31 @ sK1_SY0 ) )
= $false ),
inference(res,[status(thm)],[43,26]) ).
thf(208,plain,
( ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= sK1_SY0 )
= $false )
| ( ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= sK3_SY31 )
= $false ) ),
inference(extuni,[status(esa)],[206]) ).
thf(209,plain,
( ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= sK1_SY0 )
= $false )
| ( ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= sK4_SY35 )
= $false ) ),
inference(extuni,[status(esa)],[205]) ).
thf(210,plain,
( ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= sK2_SY26 )
= $false )
| ( ( sK3_SY31 = sK4_SY35 )
= $false )
| ( ( sK4_SY35 = sK3_SY31 )
= $false ) ),
inference(extuni,[status(esa)],[204]) ).
thf(211,plain,
( ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= sK2_SY26 )
= $false )
| ( ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= ( kpair @ sK3_SY31 @ sK4_SY35 ) )
= $false ) ),
inference(extuni,[status(esa)],[204]) ).
thf(212,plain,
! [SV19: $i > $i > $o] :
( ( ( in @ sK4_SY35 @ sK1_SY0 )
= $false )
| ( ( in @ sK3_SY31 @ sK1_SY0 )
= $false )
| ( ( SV19 @ sK4_SY35 @ sK3_SY31 )
= $false )
| ( ( in @ ( kpair @ ( sK8_E @ SV19 ) @ ( sK7_E @ SV19 ) ) @ sK2_SY26 )
= $true )
| ( ( SV19 @ ( sK7_E @ SV19 ) @ ( sK8_E @ SV19 ) )
= $true ) ),
inference(extuni,[status(esa)],[203:[bind(SV15,$thf( sK1_SY0 )),bind(SV16,$thf( sK1_SY0 )),bind(SV17,$thf( sK3_SY31 )),bind(SV18,$thf( sK4_SY35 ))]]) ).
thf(213,plain,
! [SV19: $i > $i > $o] :
( ( ( in @ sK4_SY35 @ sK1_SY0 )
= $false )
| ( ( in @ sK3_SY31 @ sK1_SY0 )
= $false )
| ( ( SV19 @ sK4_SY35 @ sK3_SY31 )
= $false )
| ( ( in @ ( kpair @ ( sK8_E @ SV19 ) @ ( sK7_E @ SV19 ) ) @ sK2_SY26 )
= $false )
| ( ( SV19 @ ( sK7_E @ SV19 ) @ ( sK8_E @ SV19 ) )
= $false ) ),
inference(extuni,[status(esa)],[203:[bind(SV15,$thf( sK1_SY0 )),bind(SV16,$thf( sK1_SY0 )),bind(SV17,$thf( sK3_SY31 )),bind(SV18,$thf( sK4_SY35 ))]]) ).
thf(214,plain,
! [SV19: $i > $i > $o,SV15: $i,SV16: $i] :
( ( ( in @ sK4_SY35 @ SV16 )
= $false )
| ( ( in @ sK3_SY31 @ SV15 )
= $false )
| ( ( SV19 @ sK4_SY35 @ sK3_SY31 )
= $false )
| ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[203:[bind(SV17,$thf( sK3_SY31 )),bind(SV18,$thf( sK4_SY35 ))]]) ).
thf(215,plain,
! [SV19: $i > $i > $o,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ sK1_SY0 )
= $false )
| ( ( in @ SV17 @ sK1_SY0 )
= $false )
| ( ( SV19 @ SV18 @ SV17 )
= $false )
| ( ( in @ ( kpair @ ( sK10_E @ SV19 @ SV18 @ SV17 ) @ ( sK9_E @ SV17 @ SV18 @ SV19 ) ) @ sK2_SY26 )
= $true )
| ( ( SV19 @ ( sK9_E @ SV17 @ SV18 @ SV19 ) @ ( sK10_E @ SV19 @ SV18 @ SV17 ) )
= $true )
| ( ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= ( kpair @ SV18 @ SV17 ) )
= $false ) ),
inference(extuni,[status(esa)],[203:[bind(SV15,$thf( sK1_SY0 )),bind(SV16,$thf( sK1_SY0 ))]]) ).
thf(216,plain,
! [SV19: $i > $i > $o,SV17: $i,SV18: $i] :
( ( ( in @ SV18 @ sK1_SY0 )
= $false )
| ( ( in @ SV17 @ sK1_SY0 )
= $false )
| ( ( SV19 @ SV18 @ SV17 )
= $false )
| ( ( in @ ( kpair @ ( sK10_E @ SV19 @ SV18 @ SV17 ) @ ( sK9_E @ SV17 @ SV18 @ SV19 ) ) @ sK2_SY26 )
= $false )
| ( ( SV19 @ ( sK9_E @ SV17 @ SV18 @ SV19 ) @ ( sK10_E @ SV19 @ SV18 @ SV17 ) )
= $false )
| ( ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= ( kpair @ SV18 @ SV17 ) )
= $false ) ),
inference(extuni,[status(esa)],[203:[bind(SV15,$thf( sK1_SY0 )),bind(SV16,$thf( sK1_SY0 ))]]) ).
thf(217,plain,
! [SV19: $i > $i > $o,SV15: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( in @ SV18 @ SV16 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $false )
| ( ( SV19 @ SV18 @ SV17 )
= $false )
| ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= ( dpsetconstr @ SV16 @ SV15
@ ^ [SX0: $i,SX1: $i] : ( SV19 @ SX0 @ SX1 ) ) )
= $false )
| ( ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= ( kpair @ SV18 @ SV17 ) )
= $false ) ),
inference(extuni,[status(esa)],[203]) ).
thf(228,plain,
( ( ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= sK3_SY31 )
= $false )
| ( ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= sK1_SY0 )
= ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= sK3_SY31 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[208]) ).
thf(229,plain,
( ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= sK3_SY31 )
= $false )
| ( ( sK1_SY0
= ( kpair @ sK4_SY35 @ sK3_SY31 ) )
= $false )
| ( ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= sK3_SY31 )
= $false ) ),
inference(extuni,[status(esa)],[228]) ).
thf(230,plain,
( ( ( sK1_SY0 = sK3_SY31 )
= $false )
| ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= ( kpair @ sK4_SY35 @ sK3_SY31 ) )
= $false )
| ( ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= sK3_SY31 )
= $false ) ),
inference(extuni,[status(esa)],[228]) ).
thf(241,plain,
( ( ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= sK4_SY35 )
= $false )
| ( ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= sK1_SY0 )
= ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= sK4_SY35 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[209]) ).
thf(242,plain,
( ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= sK4_SY35 )
= $false )
| ( ( sK1_SY0
= ( kpair @ sK4_SY35 @ sK3_SY31 ) )
= $false )
| ( ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= sK4_SY35 )
= $false ) ),
inference(extuni,[status(esa)],[241]) ).
thf(243,plain,
( ( ( sK1_SY0 = sK4_SY35 )
= $false )
| ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= ( kpair @ sK4_SY35 @ sK3_SY31 ) )
= $false )
| ( ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= sK4_SY35 )
= $false ) ),
inference(extuni,[status(esa)],[241]) ).
thf(254,plain,
( ( ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= ( kpair @ sK3_SY31 @ sK4_SY35 ) )
= $false )
| ( ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= sK2_SY26 )
= ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= ( kpair @ sK3_SY31 @ sK4_SY35 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[211]) ).
thf(255,plain,
( ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= ( kpair @ sK3_SY31 @ sK4_SY35 ) )
= $false )
| ( ( sK2_SY26
= ( kpair @ sK4_SY35 @ sK3_SY31 ) )
= $false )
| ( ( sK3_SY31 = sK4_SY35 )
= $false )
| ( ( sK4_SY35 = sK3_SY31 )
= $false ) ),
inference(extuni,[status(esa)],[254]) ).
thf(256,plain,
( ( ( sK2_SY26
= ( kpair @ sK3_SY31 @ sK4_SY35 ) )
= $false )
| ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= ( kpair @ sK4_SY35 @ sK3_SY31 ) )
= $false )
| ( ( sK3_SY31 = sK4_SY35 )
= $false )
| ( ( sK4_SY35 = sK3_SY31 )
= $false ) ),
inference(extuni,[status(esa)],[254]) ).
thf(257,plain,
( ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= ( kpair @ sK3_SY31 @ sK4_SY35 ) )
= $false )
| ( ( sK2_SY26
= ( kpair @ sK4_SY35 @ sK3_SY31 ) )
= $false )
| ( ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= ( kpair @ sK3_SY31 @ sK4_SY35 ) )
= $false ) ),
inference(extuni,[status(esa)],[254]) ).
thf(258,plain,
( ( ( sK2_SY26
= ( kpair @ sK3_SY31 @ sK4_SY35 ) )
= $false )
| ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= ( kpair @ sK4_SY35 @ sK3_SY31 ) )
= $false )
| ( ( ( kpair @ sK4_SY35 @ sK3_SY31 )
= ( kpair @ sK3_SY31 @ sK4_SY35 ) )
= $false ) ),
inference(extuni,[status(esa)],[254]) ).
thf(259,plain,
( ( ( sK3_SY31 = sK4_SY35 )
= $false )
| ( ( sK4_SY35 = sK3_SY31 )
= $false )
| ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY26 ) )
= sK2_SY26 )
= $false ) ),
inference(extuni,[status(esa)],[211]) ).
thf(260,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,259,258,257,256,255,243,242,230,229,217,216,215,214,213,212,211,210,209,208,202,201,200,199,198,197,196,195,194,193,192,191,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,73,53,52,51,50,49,43,41,34,26]) ).
thf(261,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU776^2 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 15:36:57 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.16/1.36
% 6.16/1.36 No.of.Axioms: 0
% 6.16/1.36
% 6.16/1.36 Length.of.Defs: 787
% 6.16/1.36
% 6.16/1.36 Contains.Choice.Funs: false
% 6.16/1.36 ......
% 6.16/1.36
% 6.16/1.36 ********************************
% 6.16/1.36 * All subproblems solved! *
% 6.16/1.36 ********************************
% 6.16/1.36 % SZS status Theorem for /export/starexec/sandbox/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:260,loop_count:10,foatp_calls:3,translation:fof_experiment).
% 6.16/1.36
% 6.16/1.36
% 6.16/1.36 %**** Beginning of derivation protocol ****
% 6.16/1.36 % SZS output start CNFRefutation
% See solution above
% 6.16/1.36
% 6.16/1.36 %**** End of derivation protocol ****
% 6.16/1.36 %**** no. of clauses in derivation: 218 ****
% 6.16/1.36 %**** clause counter: 260 ****
% 6.16/1.36
% 6.16/1.36 % SZS status Theorem for /export/starexec/sandbox/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:260,loop_count:10,foatp_calls:3,translation:fof_experiment)
%------------------------------------------------------------------------------