TSTP Solution File: SEU682^2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU682^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:13:54 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 16
% Syntax : Number of formulae : 88 ( 35 unt; 13 typ; 2 def)
% Number of atoms : 587 ( 155 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 1938 ( 273 ~; 216 |; 12 &;1386 @)
% ( 0 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 68 ( 68 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 283 ( 3 ^ 280 !; 0 ?; 283 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_breln,type,
breln: $i > $i > $i > $o ).
thf(tp_brelnall1,type,
brelnall1: $o ).
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY41,type,
sK2_SY41: $i ).
thf(tp_sK3_SY47,type,
sK3_SY47: $i ).
thf(tp_sK4_SY52,type,
sK4_SY52: $i > $o ).
thf(tp_sK5_SY58,type,
sK5_SY58: $i ).
thf(tp_sK6_Xx,type,
sK6_Xx: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK7_SY59,type,
sK7_SY59: ( $i > $o ) > $i > $i > $i > $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(brelnall1,definition,
( brelnall1
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(1,conjecture,
( brelnall1
=> ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2) ).
thf(2,negated_conjecture,
( ( brelnall1
=> ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY10: $i,SY11: $i,SY12: $i] :
( ( subset @ SY12 @ ( cartprod @ SY10 @ SY11 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY10 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY11 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY12 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY12 )
=> ( Xphi @ Xx ) ) ) )
=> ! [SY0: $i,SY1: $i,SY2: $i] :
( ( subset @ SY2 @ ( cartprod @ SY0 @ SY1 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY1 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY2 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY2 )
=> ( Xphi @ Xx ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,breln,brelnall1]) ).
thf(4,plain,
( ( ! [SY10: $i,SY11: $i,SY12: $i] :
( ( subset @ SY12 @ ( cartprod @ SY10 @ SY11 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY10 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY11 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY12 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY12 )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i,SY1: $i,SY2: $i] :
( ( subset @ SY2 @ ( cartprod @ SY0 @ SY1 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY1 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY2 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY2 )
=> ( Xphi @ Xx ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $i,SY1: $i,SY2: $i] :
( ( subset @ SY2 @ ( cartprod @ SY0 @ SY1 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY1 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY2 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY2 )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( subset @ sK3_SY47 @ ( cartprod @ sK1_SY0 @ sK2_SY41 ) )
& ! [SY56: $i] :
( ~ ( in @ SY56 @ sK1_SY0 )
| ! [SY57: $i] :
( ~ ( in @ SY57 @ sK2_SY41 )
| ~ ( in @ ( kpair @ SY56 @ SY57 ) @ sK3_SY47 )
| ( sK4_SY52 @ ( kpair @ SY56 @ SY57 ) ) ) )
& ( in @ sK5_SY58 @ sK3_SY47 )
& ~ ( sK4_SY52 @ sK5_SY58 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [SY10: $i,SY11: $i,SY12: $i] :
( ~ ( subset @ SY12 @ ( cartprod @ SY10 @ SY11 ) )
| ! [Xphi: $i > $o] :
( ( ( in @ ( sK6_Xx @ Xphi @ SY12 @ SY11 @ SY10 ) @ SY10 )
& ( in @ ( sK7_SY59 @ Xphi @ SY12 @ SY11 @ SY10 ) @ SY11 )
& ( in @ ( kpair @ ( sK6_Xx @ Xphi @ SY12 @ SY11 @ SY10 ) @ ( sK7_SY59 @ Xphi @ SY12 @ SY11 @ SY10 ) ) @ SY12 )
& ~ ( Xphi @ ( kpair @ ( sK6_Xx @ Xphi @ SY12 @ SY11 @ SY10 ) @ ( sK7_SY59 @ Xphi @ SY12 @ SY11 @ SY10 ) ) ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY12 )
| ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [SY10: $i,SY11: $i,SY12: $i] :
( ~ ( subset @ SY12 @ ( cartprod @ SY10 @ SY11 ) )
| ! [Xphi: $i > $o] :
( ( ( in @ ( sK6_Xx @ Xphi @ SY12 @ SY11 @ SY10 ) @ SY10 )
& ( in @ ( sK7_SY59 @ Xphi @ SY12 @ SY11 @ SY10 ) @ SY11 )
& ( in @ ( kpair @ ( sK6_Xx @ Xphi @ SY12 @ SY11 @ SY10 ) @ ( sK7_SY59 @ Xphi @ SY12 @ SY11 @ SY10 ) ) @ SY12 )
& ~ ( Xphi @ ( kpair @ ( sK6_Xx @ Xphi @ SY12 @ SY11 @ SY10 ) @ ( sK7_SY59 @ Xphi @ SY12 @ SY11 @ SY10 ) ) ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY12 )
| ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ( subset @ sK3_SY47 @ ( cartprod @ sK1_SY0 @ sK2_SY41 ) )
& ! [SY56: $i] :
( ~ ( in @ SY56 @ sK1_SY0 )
| ! [SY57: $i] :
( ~ ( in @ SY57 @ sK2_SY41 )
| ~ ( in @ ( kpair @ SY56 @ SY57 ) @ sK3_SY47 )
| ( sK4_SY52 @ ( kpair @ SY56 @ SY57 ) ) ) )
& ( in @ sK5_SY58 @ sK3_SY47 )
& ~ ( sK4_SY52 @ sK5_SY58 ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i > $o] :
( ~ ( ~ ( in @ ( sK6_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK7_SY59 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK6_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK7_SY59 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ~ ( SX3 @ ( kpair @ ( sK6_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK7_SY59 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,breln,brelnall1]) ).
thf(12,plain,
( ( ~ ( ~ ( subset @ sK3_SY47 @ ( cartprod @ sK1_SY0 @ sK2_SY41 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY41 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY47 )
| ( sK4_SY52 @ ( kpair @ SX0 @ SX1 ) ) ) )
| ~ ~ ( ~ ( in @ sK5_SY58 @ sK3_SY47 )
| ~ ~ ( sK4_SY52 @ sK5_SY58 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,breln,brelnall1]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY60: $i,SY61: $i] :
( ~ ( subset @ SY61 @ ( cartprod @ SV1 @ SY60 ) )
| ! [SY62: $i > $o] :
( ~ ( ~ ( in @ ( sK6_Xx @ SY62 @ SY61 @ SY60 @ SV1 ) @ SV1 )
| ~ ~ ( ~ ( in @ ( sK7_SY59 @ SY62 @ SY61 @ SY60 @ SV1 ) @ SY60 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK6_Xx @ SY62 @ SY61 @ SY60 @ SV1 ) @ ( sK7_SY59 @ SY62 @ SY61 @ SY60 @ SV1 ) ) @ SY61 )
| ~ ~ ( SY62 @ ( kpair @ ( sK6_Xx @ SY62 @ SY61 @ SY60 @ SV1 ) @ ( sK7_SY59 @ SY62 @ SY61 @ SY60 @ SV1 ) ) ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY61 )
| ( SY62 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ( subset @ sK3_SY47 @ ( cartprod @ sK1_SY0 @ sK2_SY41 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY41 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY47 )
| ( sK4_SY52 @ ( kpair @ SX0 @ SX1 ) ) ) )
| ~ ~ ( ~ ( in @ sK5_SY58 @ sK3_SY47 )
| ~ ~ ( sK4_SY52 @ sK5_SY58 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY64: $i] :
( ~ ( subset @ SY64 @ ( cartprod @ SV1 @ SV2 ) )
| ! [SY65: $i > $o] :
( ~ ( ~ ( in @ ( sK6_Xx @ SY65 @ SY64 @ SV2 @ SV1 ) @ SV1 )
| ~ ~ ( ~ ( in @ ( sK7_SY59 @ SY65 @ SY64 @ SV2 @ SV1 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK6_Xx @ SY65 @ SY64 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SY65 @ SY64 @ SV2 @ SV1 ) ) @ SY64 )
| ~ ~ ( SY65 @ ( kpair @ ( sK6_Xx @ SY65 @ SY64 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SY65 @ SY64 @ SV2 @ SV1 ) ) ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY64 )
| ( SY65 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( subset @ sK3_SY47 @ ( cartprod @ sK1_SY0 @ sK2_SY41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY41 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY47 )
| ( sK4_SY52 @ ( kpair @ SX0 @ SX1 ) ) ) )
| ~ ~ ( ~ ( in @ sK5_SY58 @ sK3_SY47 )
| ~ ~ ( sK4_SY52 @ sK5_SY58 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ~ ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
| ! [SY67: $i > $o] :
( ~ ( ~ ( in @ ( sK6_Xx @ SY67 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ~ ( ~ ( in @ ( sK7_SY59 @ SY67 @ SV3 @ SV2 @ SV1 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK6_Xx @ SY67 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SY67 @ SV3 @ SV2 @ SV1 ) ) @ SV3 )
| ~ ~ ( SY67 @ ( kpair @ ( sK6_Xx @ SY67 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SY67 @ SV3 @ SV2 @ SV1 ) ) ) ) ) )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV3 )
| ( SY67 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( subset @ sK3_SY47 @ ( cartprod @ sK1_SY0 @ sK2_SY41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY41 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY47 )
| ( sK4_SY52 @ ( kpair @ SX0 @ SX1 ) ) ) )
| ~ ~ ( ~ ( in @ sK5_SY58 @ sK3_SY47 )
| ~ ~ ( sK4_SY52 @ sK5_SY58 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) ) )
= $true )
| ( ( ! [SY67: $i > $o] :
( ~ ( ~ ( in @ ( sK6_Xx @ SY67 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ~ ( ~ ( in @ ( sK7_SY59 @ SY67 @ SV3 @ SV2 @ SV1 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK6_Xx @ SY67 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SY67 @ SV3 @ SV2 @ SV1 ) ) @ SV3 )
| ~ ~ ( SY67 @ ( kpair @ ( sK6_Xx @ SY67 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SY67 @ SV3 @ SV2 @ SV1 ) ) ) ) ) )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV3 )
| ( SY67 @ SY68 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY41 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY47 )
| ( sK4_SY52 @ ( kpair @ SX0 @ SX1 ) ) ) )
| ~ ~ ( ~ ( in @ sK5_SY58 @ sK3_SY47 )
| ~ ~ ( sK4_SY52 @ sK5_SY58 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false )
| ( ( ! [SY67: $i > $o] :
( ~ ( ~ ( in @ ( sK6_Xx @ SY67 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ~ ( ~ ( in @ ( sK7_SY59 @ SY67 @ SV3 @ SV2 @ SV1 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK6_Xx @ SY67 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SY67 @ SV3 @ SV2 @ SV1 ) ) @ SV3 )
| ~ ~ ( SY67 @ ( kpair @ ( sK6_Xx @ SY67 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SY67 @ SV3 @ SV2 @ SV1 ) ) ) ) ) )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV3 )
| ( SY67 @ SY68 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY41 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY47 )
| ( sK4_SY52 @ ( kpair @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( ~ ~ ( ~ ( in @ sK5_SY58 @ sK3_SY47 )
| ~ ~ ( sK4_SY52 @ sK5_SY58 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ~ ( ~ ( in @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV3 )
| ~ ~ ( SV4 @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) ) ) ) )
| ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY41 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY47 )
| ( sK4_SY52 @ ( kpair @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( ~ ( ~ ( in @ sK5_SY58 @ sK3_SY47 )
| ~ ~ ( sK4_SY52 @ sK5_SY58 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ~ ( ~ ( in @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV3 )
| ~ ~ ( SV4 @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV5: $i] :
( ( ~ ( in @ SV5 @ sK1_SY0 )
| ! [SY70: $i] :
( ~ ( in @ SY70 @ sK2_SY41 )
| ~ ( in @ ( kpair @ SV5 @ SY70 ) @ sK3_SY47 )
| ( sK4_SY52 @ ( kpair @ SV5 @ SY70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ~ ( in @ sK5_SY58 @ sK3_SY47 )
| ~ ~ ( sK4_SY52 @ sK5_SY58 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( ~ ( in @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ~ ( ~ ( in @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV3 )
| ~ ~ ( SV4 @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) ) ) ) )
= $false )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV5: $i] :
( ( ( ~ ( in @ SV5 @ sK1_SY0 ) )
= $true )
| ( ( ! [SY70: $i] :
( ~ ( in @ SY70 @ sK2_SY41 )
| ~ ( in @ ( kpair @ SV5 @ SY70 ) @ sK3_SY47 )
| ( sK4_SY52 @ ( kpair @ SV5 @ SY70 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(34,plain,
( ( ~ ( in @ sK5_SY58 @ sK3_SY47 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(35,plain,
( ( ~ ~ ( sK4_SY52 @ sK5_SY58 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(36,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( ~ ( in @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 ) )
= $false )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV3 )
| ~ ~ ( SV4 @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) ) ) ) )
= $false )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(38,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ sK1_SY0 )
= $false )
| ( ( ! [SY70: $i] :
( ~ ( in @ SY70 @ sK2_SY41 )
| ~ ( in @ ( kpair @ SV5 @ SY70 ) @ sK3_SY47 )
| ( sK4_SY52 @ ( kpair @ SV5 @ SY70 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(39,plain,
( ( in @ sK5_SY58 @ sK3_SY47 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(40,plain,
( ( ~ ( sK4_SY52 @ sK5_SY58 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(41,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( in @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
= $true )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(42,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV3 )
| ~ ~ ( SV4 @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) ) ) ) )
= $true )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(43,plain,
! [SV5: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ sK2_SY41 )
| ~ ( in @ ( kpair @ SV5 @ SV6 ) @ sK3_SY47 )
| ( sK4_SY52 @ ( kpair @ SV5 @ SV6 ) ) )
= $true )
| ( ( in @ SV5 @ sK1_SY0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(44,plain,
( ( sK4_SY52 @ sK5_SY58 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV1: $i,SV2: $i,SV4: $i > $o,SV3: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV3 )
| ( SV4 @ SV7 ) )
= $true )
| ( ( in @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( ~ ( in @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV2 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV3 )
| ~ ~ ( SV4 @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) ) ) )
= $false )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV5: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ sK2_SY41 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV5 @ SV6 ) @ sK3_SY47 )
| ( sK4_SY52 @ ( kpair @ SV5 @ SV6 ) ) )
= $true )
| ( ( in @ SV5 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV1: $i,SV2: $i,SV4: $i > $o,SV3: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV3 ) )
= $true )
| ( ( SV4 @ SV7 )
= $true )
| ( ( in @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( ~ ( in @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV2 ) )
= $false )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(50,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV3 )
| ~ ~ ( SV4 @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) ) ) )
= $false )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(51,plain,
! [SV5: $i,SV6: $i] :
( ( ( in @ SV6 @ sK2_SY41 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV5 @ SV6 ) @ sK3_SY47 )
| ( sK4_SY52 @ ( kpair @ SV5 @ SV6 ) ) )
= $true )
| ( ( in @ SV5 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV1: $i,SV2: $i,SV4: $i > $o,SV3: $i,SV7: $i] :
( ( ( in @ SV7 @ SV3 )
= $false )
| ( ( SV4 @ SV7 )
= $true )
| ( ( in @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( in @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV2 )
= $true )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(54,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( ~ ( ~ ( in @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV3 )
| ~ ~ ( SV4 @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) ) ) )
= $true )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(55,plain,
! [SV6: $i,SV5: $i] :
( ( ( ~ ( in @ ( kpair @ SV5 @ SV6 ) @ sK3_SY47 ) )
= $true )
| ( ( sK4_SY52 @ ( kpair @ SV5 @ SV6 ) )
= $true )
| ( ( in @ SV6 @ sK2_SY41 )
= $false )
| ( ( in @ SV5 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV1: $i,SV2: $i,SV4: $i > $o,SV3: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV3 )
| ( SV4 @ SV8 ) )
= $true )
| ( ( in @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV2 )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV3 )
| ~ ~ ( SV4 @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) ) )
= $false )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV6: $i,SV5: $i] :
( ( ( in @ ( kpair @ SV5 @ SV6 ) @ sK3_SY47 )
= $false )
| ( ( sK4_SY52 @ ( kpair @ SV5 @ SV6 ) )
= $true )
| ( ( in @ SV6 @ sK2_SY41 )
= $false )
| ( ( in @ SV5 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV1: $i,SV2: $i,SV4: $i > $o,SV3: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV3 ) )
= $true )
| ( ( SV4 @ SV8 )
= $true )
| ( ( in @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV2 )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV3 ) )
= $false )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(61,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( ~ ~ ( SV4 @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) ) )
= $false )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(62,plain,
! [SV1: $i,SV2: $i,SV4: $i > $o,SV3: $i,SV8: $i] :
( ( ( in @ SV8 @ SV3 )
= $false )
| ( ( SV4 @ SV8 )
= $true )
| ( ( in @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV2 )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( in @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV3 )
= $true )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(64,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( ~ ( SV4 @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) ) )
= $true )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(65,plain,
! [SV1: $i,SV2: $i,SV4: $i > $o,SV3: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV3 )
| ( SV4 @ SV9 ) )
= $true )
| ( ( in @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV3 )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(66,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i > $o] :
( ( ( SV4 @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) )
= $false )
| ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV3 )
| ( SV4 @ SY69 ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(67,plain,
! [SV1: $i,SV2: $i,SV4: $i > $o,SV3: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV3 ) )
= $true )
| ( ( SV4 @ SV9 )
= $true )
| ( ( in @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV3 )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(68,plain,
! [SV1: $i,SV2: $i,SV4: $i > $o,SV3: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV3 )
| ( SV4 @ SV10 ) )
= $true )
| ( ( SV4 @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(69,plain,
! [SV1: $i,SV2: $i,SV4: $i > $o,SV3: $i,SV9: $i] :
( ( ( in @ SV9 @ SV3 )
= $false )
| ( ( SV4 @ SV9 )
= $true )
| ( ( in @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV3 )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(70,plain,
! [SV1: $i,SV2: $i,SV4: $i > $o,SV3: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV3 ) )
= $true )
| ( ( SV4 @ SV10 )
= $true )
| ( ( SV4 @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(71,plain,
! [SV1: $i,SV2: $i,SV4: $i > $o,SV3: $i,SV10: $i] :
( ( ( in @ SV10 @ SV3 )
= $false )
| ( ( SV4 @ SV10 )
= $true )
| ( ( SV4 @ ( kpair @ ( sK6_Xx @ SV4 @ SV3 @ SV2 @ SV1 ) @ ( sK7_SY59 @ SV4 @ SV3 @ SV2 @ SV1 ) ) )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(72,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,71,69,62,58,52,44,39]) ).
thf(73,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU682^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 05:00:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 0
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 477
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.19/0.45
% 0.19/0.45 ********************************
% 0.19/0.45 * All subproblems solved! *
% 0.19/0.45 ********************************
% 0.19/0.45 % 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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:72,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.46
% 0.19/0.46 %**** Beginning of derivation protocol ****
% 0.19/0.46 % SZS output start CNFRefutation
% See solution above
% 0.19/0.46
% 0.19/0.46 %**** End of derivation protocol ****
% 0.19/0.46 %**** no. of clauses in derivation: 73 ****
% 0.19/0.46 %**** clause counter: 72 ****
% 0.19/0.46
% 0.19/0.46 % 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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:72,loop_count:0,foatp_calls:1,translation:fof_full)
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