%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU816^2 : 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 : n005.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 10:48:56 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 7
% Syntax : Number of formulae : 200 ( 81 unt; 0 typ; 6 def)
% Number of atoms : 2434 ( 651 equ; 0 cnn)
% Maximal formula atoms : 6 ( 12 avg)
% Number of connectives : 5653 (1304 ~;1133 |; 54 &;3027 @)
% ( 0 <=>; 135 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 7 con; 0-2 aty)
% Number of variables : 778 ( 5 ^; 764 !; 9 ?; 778 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binintTransitive,type,
binintTransitive: $o ).
thf(tp_binintersect,type,
binintersect: $i > $i > $i ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_nonempty,type,
nonempty: $i > $o ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY93,type,
sK2_SY93: $i ).
thf(tp_sK3_SY79,type,
sK3_SY79: $i > $i ).
thf(tp_sK4_SY115,type,
sK4_SY115: $i ).
thf(tp_sK5_SY116,type,
sK5_SY116: $i > $i > $i ).
thf(tp_sK6_SY118,type,
sK6_SY118: $i > $i > $i ).
thf(tp_sK7_SY120,type,
sK7_SY120: $i > $i ).
thf(tp_sK8_SY122,type,
sK8_SY122: $i > $i ).
thf(tp_stricttotalorderedByIn,type,
stricttotalorderedByIn: $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_transitiveset,type,
transitiveset: $i > $o ).
thf(tp_wellorderedByIn,type,
wellorderedByIn: $i > $o ).
thf(binintTransitive,definition,
( binintTransitive
= ( ! [X: $i] :
( ( transitiveset @ X )
=> ! [Y: $i] :
( ( transitiveset @ Y )
=> ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintTransitive) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(ordinal,definition,
( ordinal
= ( ^ [Xx: $i] :
( ( transitiveset @ Xx )
& ( wellorderedByIn @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal) ).
thf(stricttotalorderedByIn,definition,
( stricttotalorderedByIn
= ( ^ [A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( ( in @ Xx @ X )
& ( in @ X @ Y ) )
=> ( in @ Xx @ Y ) ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( X = Y )
| ( in @ X @ Y )
| ( in @ Y @ X ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ~ ( in @ X @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricttotalorderedByIn) ).
thf(transitiveset,definition,
( transitiveset
= ( ^ [A: $i] :
! [X: $i] :
( ( in @ X @ A )
=> ( subset @ X @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitiveset) ).
thf(wellorderedByIn,definition,
( wellorderedByIn
= ( ^ [A: $i] :
( ( stricttotalorderedByIn @ A )
& ! [X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( ( nonempty @ X )
=> ? [Xx: $i] :
( ( in @ Xx @ X )
& ! [Y: $i] :
( ( in @ Y @ X )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderedByIn) ).
thf(1,conjecture,
( binintTransitive
=> ! [X: $i] :
( ( ordinal @ X )
=> ! [Y: $i] :
( ( ordinal @ Y )
=> ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalMinLem1) ).
thf(2,negated_conjecture,
( ( binintTransitive
=> ! [X: $i] :
( ( ordinal @ X )
=> ! [Y: $i] :
( ( ordinal @ Y )
=> ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY23: $i] :
( ! [SY24: $i] :
( ( in @ SY24 @ SY23 )
=> ( subset @ SY24 @ SY23 ) )
=> ! [SY25: $i] :
( ! [SY26: $i] :
( ( in @ SY26 @ SY25 )
=> ( subset @ SY26 @ SY25 ) )
=> ! [SY27: $i] :
( ( in @ SY27 @ ( binintersect @ SY23 @ SY25 ) )
=> ( subset @ SY27 @ ( binintersect @ SY23 @ SY25 ) ) ) ) )
=> ! [SY0: $i] :
( ( ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ( subset @ SY1 @ SY0 ) )
& ! [SY2: $i] :
( ( in @ SY2 @ SY0 )
=> ! [SY3: $i] :
( ( in @ SY3 @ SY0 )
=> ! [SY4: $i] :
( ( in @ SY4 @ SY0 )
=> ( ( ( in @ SY2 @ SY3 )
& ( in @ SY3 @ SY4 ) )
=> ( in @ SY2 @ SY4 ) ) ) ) )
& ! [SY5: $i] :
( ( in @ SY5 @ SY0 )
=> ! [SY6: $i] :
( ( in @ SY6 @ SY0 )
=> ( ( SY5 = SY6 )
| ( in @ SY5 @ SY6 )
| ( in @ SY6 @ SY5 ) ) ) )
& ! [SY7: $i] :
( ( in @ SY7 @ SY0 )
=> ~ ( in @ SY7 @ SY7 ) )
& ! [SY8: $i] :
( ( in @ SY8 @ ( powerset @ SY0 ) )
=> ( ( SY8 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY8 )
& ! [Y: $i] :
( ( in @ Y @ SY8 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) )
=> ! [SY11: $i] :
( ( ! [SY12: $i] :
( ( in @ SY12 @ SY11 )
=> ( subset @ SY12 @ SY11 ) )
& ! [SY13: $i] :
( ( in @ SY13 @ SY11 )
=> ! [SY14: $i] :
( ( in @ SY14 @ SY11 )
=> ! [SY15: $i] :
( ( in @ SY15 @ SY11 )
=> ( ( ( in @ SY13 @ SY14 )
& ( in @ SY14 @ SY15 ) )
=> ( in @ SY13 @ SY15 ) ) ) ) )
& ! [SY16: $i] :
( ( in @ SY16 @ SY11 )
=> ! [SY17: $i] :
( ( in @ SY17 @ SY11 )
=> ( ( SY16 = SY17 )
| ( in @ SY16 @ SY17 )
| ( in @ SY17 @ SY16 ) ) ) )
& ! [SY18: $i] :
( ( in @ SY18 @ SY11 )
=> ~ ( in @ SY18 @ SY18 ) )
& ! [SY19: $i] :
( ( in @ SY19 @ ( powerset @ SY11 ) )
=> ( ( SY19 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY19 )
& ! [Y: $i] :
( ( in @ Y @ SY19 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) )
=> ! [SY22: $i] :
( ( in @ SY22 @ ( binintersect @ SY0 @ SY11 ) )
=> ( subset @ SY22 @ ( binintersect @ SY0 @ SY11 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binintTransitive,nonempty,ordinal,stricttotalorderedByIn,transitiveset,wellorderedByIn]) ).
thf(4,plain,
( ( ! [SY23: $i] :
( ! [SY24: $i] :
( ( in @ SY24 @ SY23 )
=> ( subset @ SY24 @ SY23 ) )
=> ! [SY25: $i] :
( ! [SY26: $i] :
( ( in @ SY26 @ SY25 )
=> ( subset @ SY26 @ SY25 ) )
=> ! [SY27: $i] :
( ( in @ SY27 @ ( binintersect @ SY23 @ SY25 ) )
=> ( subset @ SY27 @ ( binintersect @ SY23 @ SY25 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i] :
( ( ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ( subset @ SY1 @ SY0 ) )
& ! [SY2: $i] :
( ( in @ SY2 @ SY0 )
=> ! [SY3: $i] :
( ( in @ SY3 @ SY0 )
=> ! [SY4: $i] :
( ( in @ SY4 @ SY0 )
=> ( ( ( in @ SY2 @ SY3 )
& ( in @ SY3 @ SY4 ) )
=> ( in @ SY2 @ SY4 ) ) ) ) )
& ! [SY5: $i] :
( ( in @ SY5 @ SY0 )
=> ! [SY6: $i] :
( ( in @ SY6 @ SY0 )
=> ( ( SY5 = SY6 )
| ( in @ SY5 @ SY6 )
| ( in @ SY6 @ SY5 ) ) ) )
& ! [SY7: $i] :
( ( in @ SY7 @ SY0 )
=> ~ ( in @ SY7 @ SY7 ) )
& ! [SY8: $i] :
( ( in @ SY8 @ ( powerset @ SY0 ) )
=> ( ( SY8 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY8 )
& ! [Y: $i] :
( ( in @ Y @ SY8 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) )
=> ! [SY11: $i] :
( ( ! [SY12: $i] :
( ( in @ SY12 @ SY11 )
=> ( subset @ SY12 @ SY11 ) )
& ! [SY13: $i] :
( ( in @ SY13 @ SY11 )
=> ! [SY14: $i] :
( ( in @ SY14 @ SY11 )
=> ! [SY15: $i] :
( ( in @ SY15 @ SY11 )
=> ( ( ( in @ SY13 @ SY14 )
& ( in @ SY14 @ SY15 ) )
=> ( in @ SY13 @ SY15 ) ) ) ) )
& ! [SY16: $i] :
( ( in @ SY16 @ SY11 )
=> ! [SY17: $i] :
( ( in @ SY17 @ SY11 )
=> ( ( SY16 = SY17 )
| ( in @ SY16 @ SY17 )
| ( in @ SY17 @ SY16 ) ) ) )
& ! [SY18: $i] :
( ( in @ SY18 @ SY11 )
=> ~ ( in @ SY18 @ SY18 ) )
& ! [SY19: $i] :
( ( in @ SY19 @ ( powerset @ SY11 ) )
=> ( ( SY19 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY19 )
& ! [Y: $i] :
( ( in @ Y @ SY19 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) )
=> ! [SY22: $i] :
( ( in @ SY22 @ ( binintersect @ SY0 @ SY11 ) )
=> ( subset @ SY22 @ ( binintersect @ SY0 @ SY11 ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $i] :
( ( ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ( subset @ SY1 @ SY0 ) )
& ! [SY2: $i] :
( ( in @ SY2 @ SY0 )
=> ! [SY3: $i] :
( ( in @ SY3 @ SY0 )
=> ! [SY4: $i] :
( ( in @ SY4 @ SY0 )
=> ( ( ( in @ SY2 @ SY3 )
& ( in @ SY3 @ SY4 ) )
=> ( in @ SY2 @ SY4 ) ) ) ) )
& ! [SY5: $i] :
( ( in @ SY5 @ SY0 )
=> ! [SY6: $i] :
( ( in @ SY6 @ SY0 )
=> ( ( SY5 = SY6 )
| ( in @ SY5 @ SY6 )
| ( in @ SY6 @ SY5 ) ) ) )
& ! [SY7: $i] :
( ( in @ SY7 @ SY0 )
=> ~ ( in @ SY7 @ SY7 ) )
& ! [SY8: $i] :
( ( in @ SY8 @ ( powerset @ SY0 ) )
=> ( ( SY8 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY8 )
& ! [Y: $i] :
( ( in @ Y @ SY8 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) )
=> ! [SY11: $i] :
( ( ! [SY12: $i] :
( ( in @ SY12 @ SY11 )
=> ( subset @ SY12 @ SY11 ) )
& ! [SY13: $i] :
( ( in @ SY13 @ SY11 )
=> ! [SY14: $i] :
( ( in @ SY14 @ SY11 )
=> ! [SY15: $i] :
( ( in @ SY15 @ SY11 )
=> ( ( ( in @ SY13 @ SY14 )
& ( in @ SY14 @ SY15 ) )
=> ( in @ SY13 @ SY15 ) ) ) ) )
& ! [SY16: $i] :
( ( in @ SY16 @ SY11 )
=> ! [SY17: $i] :
( ( in @ SY17 @ SY11 )
=> ( ( SY16 = SY17 )
| ( in @ SY16 @ SY17 )
| ( in @ SY17 @ SY16 ) ) ) )
& ! [SY18: $i] :
( ( in @ SY18 @ SY11 )
=> ~ ( in @ SY18 @ SY18 ) )
& ! [SY19: $i] :
( ( in @ SY19 @ ( powerset @ SY11 ) )
=> ( ( SY19 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY19 )
& ! [Y: $i] :
( ( in @ Y @ SY19 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) )
=> ! [SY22: $i] :
( ( in @ SY22 @ ( binintersect @ SY0 @ SY11 ) )
=> ( subset @ SY22 @ ( binintersect @ SY0 @ SY11 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY23: $i] :
( ! [SY24: $i] :
( ( in @ SY24 @ SY23 )
=> ( subset @ SY24 @ SY23 ) )
=> ! [SY25: $i] :
( ! [SY26: $i] :
( ( in @ SY26 @ SY25 )
=> ( subset @ SY26 @ SY25 ) )
=> ! [SY27: $i] :
( ( in @ SY27 @ ( binintersect @ SY23 @ SY25 ) )
=> ( subset @ SY27 @ ( binintersect @ SY23 @ SY25 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ! [SY0: $i] :
( ( ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ( subset @ SY1 @ SY0 ) )
& ! [SY2: $i] :
( ( in @ SY2 @ SY0 )
=> ! [SY3: $i] :
( ( in @ SY3 @ SY0 )
=> ! [SY4: $i] :
( ( in @ SY4 @ SY0 )
=> ( ( ( in @ SY2 @ SY3 )
& ( in @ SY3 @ SY4 ) )
=> ( in @ SY2 @ SY4 ) ) ) ) )
& ! [SY5: $i] :
( ( in @ SY5 @ SY0 )
=> ! [SY6: $i] :
( ( in @ SY6 @ SY0 )
=> ( ( SY5 = SY6 )
| ( in @ SY5 @ SY6 )
| ( in @ SY6 @ SY5 ) ) ) )
& ! [SY7: $i] :
( ( in @ SY7 @ SY0 )
=> ~ ( in @ SY7 @ SY7 ) )
& ! [SY8: $i] :
( ( in @ SY8 @ ( powerset @ SY0 ) )
=> ( ( SY8 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY8 )
& ! [Y: $i] :
( ( in @ Y @ SY8 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) )
=> ! [SY11: $i] :
( ( ! [SY12: $i] :
( ( in @ SY12 @ SY11 )
=> ( subset @ SY12 @ SY11 ) )
& ! [SY13: $i] :
( ( in @ SY13 @ SY11 )
=> ! [SY14: $i] :
( ( in @ SY14 @ SY11 )
=> ! [SY15: $i] :
( ( in @ SY15 @ SY11 )
=> ( ( ( in @ SY13 @ SY14 )
& ( in @ SY14 @ SY15 ) )
=> ( in @ SY13 @ SY15 ) ) ) ) )
& ! [SY16: $i] :
( ( in @ SY16 @ SY11 )
=> ! [SY17: $i] :
( ( in @ SY17 @ SY11 )
=> ( ( SY16 = SY17 )
| ( in @ SY16 @ SY17 )
| ( in @ SY17 @ SY16 ) ) ) )
& ! [SY18: $i] :
( ( in @ SY18 @ SY11 )
=> ~ ( in @ SY18 @ SY18 ) )
& ! [SY19: $i] :
( ( in @ SY19 @ ( powerset @ SY11 ) )
=> ( ( SY19 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY19 )
& ! [Y: $i] :
( ( in @ Y @ SY19 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) )
=> ! [SY22: $i] :
( ( in @ SY22 @ ( binintersect @ SY0 @ SY11 ) )
=> ( subset @ SY22 @ ( binintersect @ SY0 @ SY11 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SX0: $i] :
( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX3 ) )
| ( in @ SX1 @ SX3 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 = SX2 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX1 @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( ( SX1 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) ) )
| ! [SX1: $i] :
( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX1 )
| ~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX4 ) )
| ( in @ SX2 @ SX4 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX1 ) )
| ~ ( ( SX2 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,binintTransitive,nonempty,ordinal,stricttotalorderedByIn,transitiveset,wellorderedByIn]) ).
thf(10,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) )
| ! [SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX1 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,binintTransitive,nonempty,ordinal,stricttotalorderedByIn,transitiveset,wellorderedByIn]) ).
thf(11,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX3 ) )
| ( in @ SX1 @ SX3 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 = SX2 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX1 @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( ( SX1 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) ) )
| ! [SX1: $i] :
( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX1 )
| ~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX4 ) )
| ( in @ SX2 @ SX4 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX1 ) )
| ~ ( ( SX2 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ SV1 )
| ( subset @ SY79 @ SV1 ) )
| ! [SY80: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY80 )
| ( subset @ SX2 @ SY80 ) )
| ! [SY82: $i] :
( ~ ( in @ SY82 @ ( binintersect @ SV1 @ SY80 ) )
| ( subset @ SY82 @ ( binintersect @ SV1 @ SY80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ~ ( ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ sK1_SX0 )
| ( subset @ SY83 @ sK1_SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( in @ SY84 @ sK1_SX0 )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ sK1_SX0 )
| ! [SY86: $i] :
( ~ ( in @ SY86 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY84 @ SY85 )
| ~ ( in @ SY85 @ SY86 ) )
| ( in @ SY84 @ SY86 ) ) ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ sK1_SX0 )
| ! [SY88: $i] :
( ~ ( in @ SY88 @ sK1_SX0 )
| ( SY87 = SY88 )
| ( in @ SY87 @ SY88 )
| ( in @ SY88 @ SY87 ) ) ) )
| ~ ! [SY89: $i] :
( ~ ( in @ SY89 @ sK1_SX0 )
| ~ ( in @ SY89 @ SY89 ) ) )
| ~ ! [SY90: $i] :
( ~ ( in @ SY90 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY90 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY90 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY90 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) ) )
| ! [SY93: $i] :
( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY93 )
| ( subset @ SX2 @ SY93 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY93 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY93 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY93 )
| ~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX4 ) )
| ( in @ SX2 @ SX4 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY93 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY93 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY93 )
| ~ ( in @ SX2 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SY93 ) )
| ~ ( ( SX2 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) )
| ! [SY104: $i] :
( ~ ( in @ SY104 @ ( binintersect @ sK1_SX0 @ SY93 ) )
| ( subset @ SY104 @ ( binintersect @ sK1_SX0 @ SY93 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV1: $i] :
( ( ( ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ SV1 )
| ( subset @ SY79 @ SV1 ) ) )
= $true )
| ( ( ! [SY80: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY80 )
| ( subset @ SX2 @ SY80 ) )
| ! [SY82: $i] :
( ~ ( in @ SY82 @ ( binintersect @ SV1 @ SY80 ) )
| ( subset @ SY82 @ ( binintersect @ SV1 @ SY80 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ~ ( ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ sK1_SX0 )
| ( subset @ SY83 @ sK1_SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( in @ SY84 @ sK1_SX0 )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ sK1_SX0 )
| ! [SY86: $i] :
( ~ ( in @ SY86 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY84 @ SY85 )
| ~ ( in @ SY85 @ SY86 ) )
| ( in @ SY84 @ SY86 ) ) ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ sK1_SX0 )
| ! [SY88: $i] :
( ~ ( in @ SY88 @ sK1_SX0 )
| ( SY87 = SY88 )
| ( in @ SY87 @ SY88 )
| ( in @ SY88 @ SY87 ) ) ) )
| ~ ! [SY89: $i] :
( ~ ( in @ SY89 @ sK1_SX0 )
| ~ ( in @ SY89 @ SY89 ) ) )
| ~ ! [SY90: $i] :
( ~ ( in @ SY90 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY90 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY90 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY90 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [SY93: $i] :
( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY93 )
| ( subset @ SX2 @ SY93 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY93 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY93 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY93 )
| ~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX4 ) )
| ( in @ SX2 @ SX4 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY93 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY93 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY93 )
| ~ ( in @ SX2 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SY93 ) )
| ~ ( ( SX2 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) )
| ! [SY104: $i] :
( ~ ( in @ SY104 @ ( binintersect @ sK1_SX0 @ SY93 ) )
| ( subset @ SY104 @ ( binintersect @ sK1_SX0 @ SY93 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: $i] :
( ( ( ! [SY79: $i] :
( ~ ( in @ SY79 @ SV1 )
| ( subset @ SY79 @ SV1 ) ) )
= $false )
| ( ( ! [SY80: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY80 )
| ( subset @ SX2 @ SY80 ) )
| ! [SY82: $i] :
( ~ ( in @ SY82 @ ( binintersect @ SV1 @ SY80 ) )
| ( subset @ SY82 @ ( binintersect @ SV1 @ SY80 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ( ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ sK1_SX0 )
| ( subset @ SY83 @ sK1_SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( in @ SY84 @ sK1_SX0 )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ sK1_SX0 )
| ! [SY86: $i] :
( ~ ( in @ SY86 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY84 @ SY85 )
| ~ ( in @ SY85 @ SY86 ) )
| ( in @ SY84 @ SY86 ) ) ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ sK1_SX0 )
| ! [SY88: $i] :
( ~ ( in @ SY88 @ sK1_SX0 )
| ( SY87 = SY88 )
| ( in @ SY87 @ SY88 )
| ( in @ SY88 @ SY87 ) ) ) )
| ~ ! [SY89: $i] :
( ~ ( in @ SY89 @ sK1_SX0 )
| ~ ( in @ SY89 @ SY89 ) ) )
| ~ ! [SY90: $i] :
( ~ ( in @ SY90 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY90 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY90 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY90 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ~ ( ~ ! [SY105: $i] :
( ~ ( in @ SY105 @ sK2_SY93 )
| ( subset @ SY105 @ sK2_SY93 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ sK2_SY93 )
| ! [SY107: $i] :
( ~ ( in @ SY107 @ sK2_SY93 )
| ! [SY108: $i] :
( ~ ( in @ SY108 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SY106 @ SY107 )
| ~ ( in @ SY107 @ SY108 ) )
| ( in @ SY106 @ SY108 ) ) ) )
| ~ ! [SY109: $i] :
( ~ ( in @ SY109 @ sK2_SY93 )
| ! [SY110: $i] :
( ~ ( in @ SY110 @ sK2_SY93 )
| ( SY109 = SY110 )
| ( in @ SY109 @ SY110 )
| ( in @ SY110 @ SY109 ) ) ) )
| ~ ! [SY111: $i] :
( ~ ( in @ SY111 @ sK2_SY93 )
| ~ ( in @ SY111 @ SY111 ) ) )
| ~ ! [SY112: $i] :
( ~ ( in @ SY112 @ ( powerset @ sK2_SY93 ) )
| ~ ( ( SY112 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY112 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY112 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) )
| ! [SY115: $i] :
( ~ ( in @ SY115 @ ( binintersect @ sK1_SX0 @ sK2_SY93 ) )
| ( subset @ SY115 @ ( binintersect @ sK1_SX0 @ sK2_SY93 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(20,plain,
! [SV1: $i] :
( ( ( ~ ( in @ ( sK3_SY79 @ SV1 ) @ SV1 )
| ( subset @ ( sK3_SY79 @ SV1 ) @ SV1 ) )
= $false )
| ( ( ! [SY80: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY80 )
| ( subset @ SX2 @ SY80 ) )
| ! [SY82: $i] :
( ~ ( in @ SY82 @ ( binintersect @ SV1 @ SY80 ) )
| ( subset @ SY82 @ ( binintersect @ SV1 @ SY80 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(21,plain,
( ( ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ sK1_SX0 )
| ( subset @ SY83 @ sK1_SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( in @ SY84 @ sK1_SX0 )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ sK1_SX0 )
| ! [SY86: $i] :
( ~ ( in @ SY86 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY84 @ SY85 )
| ~ ( in @ SY85 @ SY86 ) )
| ( in @ SY84 @ SY86 ) ) ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ sK1_SX0 )
| ! [SY88: $i] :
( ~ ( in @ SY88 @ sK1_SX0 )
| ( SY87 = SY88 )
| ( in @ SY87 @ SY88 )
| ( in @ SY88 @ SY87 ) ) ) )
| ~ ! [SY89: $i] :
( ~ ( in @ SY89 @ sK1_SX0 )
| ~ ( in @ SY89 @ SY89 ) ) )
| ~ ! [SY90: $i] :
( ~ ( in @ SY90 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY90 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY90 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY90 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ~ ( ~ ! [SY105: $i] :
( ~ ( in @ SY105 @ sK2_SY93 )
| ( subset @ SY105 @ sK2_SY93 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ sK2_SY93 )
| ! [SY107: $i] :
( ~ ( in @ SY107 @ sK2_SY93 )
| ! [SY108: $i] :
( ~ ( in @ SY108 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SY106 @ SY107 )
| ~ ( in @ SY107 @ SY108 ) )
| ( in @ SY106 @ SY108 ) ) ) )
| ~ ! [SY109: $i] :
( ~ ( in @ SY109 @ sK2_SY93 )
| ! [SY110: $i] :
( ~ ( in @ SY110 @ sK2_SY93 )
| ( SY109 = SY110 )
| ( in @ SY109 @ SY110 )
| ( in @ SY110 @ SY109 ) ) ) )
| ~ ! [SY111: $i] :
( ~ ( in @ SY111 @ sK2_SY93 )
| ~ ( in @ SY111 @ SY111 ) ) )
| ~ ! [SY112: $i] :
( ~ ( in @ SY112 @ ( powerset @ sK2_SY93 ) )
| ~ ( ( SY112 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY112 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY112 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ! [SY115: $i] :
( ~ ( in @ SY115 @ ( binintersect @ sK1_SX0 @ sK2_SY93 ) )
| ( subset @ SY115 @ ( binintersect @ sK1_SX0 @ sK2_SY93 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(24,plain,
! [SV1: $i] :
( ( ( ~ ( in @ ( sK3_SY79 @ SV1 ) @ SV1 ) )
= $false )
| ( ( ! [SY80: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY80 )
| ( subset @ SX2 @ SY80 ) )
| ! [SY82: $i] :
( ~ ( in @ SY82 @ ( binintersect @ SV1 @ SY80 ) )
| ( subset @ SY82 @ ( binintersect @ SV1 @ SY80 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(25,plain,
! [SV1: $i] :
( ( ( subset @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $false )
| ( ( ! [SY80: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY80 )
| ( subset @ SX2 @ SY80 ) )
| ! [SY82: $i] :
( ~ ( in @ SY82 @ ( binintersect @ SV1 @ SY80 ) )
| ( subset @ SY82 @ ( binintersect @ SV1 @ SY80 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(26,plain,
( ( ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ sK1_SX0 )
| ( subset @ SY83 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(27,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( in @ SY84 @ sK1_SX0 )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ sK1_SX0 )
| ! [SY86: $i] :
( ~ ( in @ SY86 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY84 @ SY85 )
| ~ ( in @ SY85 @ SY86 ) )
| ( in @ SY84 @ SY86 ) ) ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ sK1_SX0 )
| ! [SY88: $i] :
( ~ ( in @ SY88 @ sK1_SX0 )
| ( SY87 = SY88 )
| ( in @ SY87 @ SY88 )
| ( in @ SY88 @ SY87 ) ) ) )
| ~ ! [SY89: $i] :
( ~ ( in @ SY89 @ sK1_SX0 )
| ~ ( in @ SY89 @ SY89 ) ) )
| ~ ! [SY90: $i] :
( ~ ( in @ SY90 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY90 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY90 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY90 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(28,plain,
( ( ~ ( ~ ! [SY105: $i] :
( ~ ( in @ SY105 @ sK2_SY93 )
| ( subset @ SY105 @ sK2_SY93 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ sK2_SY93 )
| ! [SY107: $i] :
( ~ ( in @ SY107 @ sK2_SY93 )
| ! [SY108: $i] :
( ~ ( in @ SY108 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SY106 @ SY107 )
| ~ ( in @ SY107 @ SY108 ) )
| ( in @ SY106 @ SY108 ) ) ) )
| ~ ! [SY109: $i] :
( ~ ( in @ SY109 @ sK2_SY93 )
| ! [SY110: $i] :
( ~ ( in @ SY110 @ sK2_SY93 )
| ( SY109 = SY110 )
| ( in @ SY109 @ SY110 )
| ( in @ SY110 @ SY109 ) ) ) )
| ~ ! [SY111: $i] :
( ~ ( in @ SY111 @ sK2_SY93 )
| ~ ( in @ SY111 @ SY111 ) ) )
| ~ ! [SY112: $i] :
( ~ ( in @ SY112 @ ( powerset @ sK2_SY93 ) )
| ~ ( ( SY112 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY112 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY112 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(29,plain,
( ( ~ ( in @ sK4_SY115 @ ( binintersect @ sK1_SX0 @ sK2_SY93 ) )
| ( subset @ sK4_SY115 @ ( binintersect @ sK1_SX0 @ sK2_SY93 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(30,plain,
! [SV1: $i] :
( ( ( in @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $true )
| ( ( ! [SY80: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY80 )
| ( subset @ SX2 @ SY80 ) )
| ! [SY82: $i] :
( ~ ( in @ SY82 @ ( binintersect @ SV1 @ SY80 ) )
| ( subset @ SY82 @ ( binintersect @ SV1 @ SY80 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(31,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ! [SY116: $i] :
( ~ ( in @ SY116 @ SV2 )
| ( subset @ SY116 @ SV2 ) )
| ! [SY117: $i] :
( ~ ( in @ SY117 @ ( binintersect @ SV1 @ SV2 ) )
| ( subset @ SY117 @ ( binintersect @ SV1 @ SV2 ) ) ) )
= $true )
| ( ( subset @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(32,plain,
( ( ! [SY83: $i] :
( ~ ( in @ SY83 @ sK1_SX0 )
| ( subset @ SY83 @ sK1_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(33,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( in @ SY84 @ sK1_SX0 )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ sK1_SX0 )
| ! [SY86: $i] :
( ~ ( in @ SY86 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY84 @ SY85 )
| ~ ( in @ SY85 @ SY86 ) )
| ( in @ SY84 @ SY86 ) ) ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ sK1_SX0 )
| ! [SY88: $i] :
( ~ ( in @ SY88 @ sK1_SX0 )
| ( SY87 = SY88 )
| ( in @ SY87 @ SY88 )
| ( in @ SY88 @ SY87 ) ) ) )
| ~ ! [SY89: $i] :
( ~ ( in @ SY89 @ sK1_SX0 )
| ~ ( in @ SY89 @ SY89 ) ) )
| ~ ! [SY90: $i] :
( ~ ( in @ SY90 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY90 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY90 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY90 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(34,plain,
( ( ~ ! [SY105: $i] :
( ~ ( in @ SY105 @ sK2_SY93 )
| ( subset @ SY105 @ sK2_SY93 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ sK2_SY93 )
| ! [SY107: $i] :
( ~ ( in @ SY107 @ sK2_SY93 )
| ! [SY108: $i] :
( ~ ( in @ SY108 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SY106 @ SY107 )
| ~ ( in @ SY107 @ SY108 ) )
| ( in @ SY106 @ SY108 ) ) ) )
| ~ ! [SY109: $i] :
( ~ ( in @ SY109 @ sK2_SY93 )
| ! [SY110: $i] :
( ~ ( in @ SY110 @ sK2_SY93 )
| ( SY109 = SY110 )
| ( in @ SY109 @ SY110 )
| ( in @ SY110 @ SY109 ) ) ) )
| ~ ! [SY111: $i] :
( ~ ( in @ SY111 @ sK2_SY93 )
| ~ ( in @ SY111 @ SY111 ) ) )
| ~ ! [SY112: $i] :
( ~ ( in @ SY112 @ ( powerset @ sK2_SY93 ) )
| ~ ( ( SY112 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY112 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY112 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(35,plain,
( ( ~ ( in @ sK4_SY115 @ ( binintersect @ sK1_SX0 @ sK2_SY93 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(36,plain,
( ( subset @ sK4_SY115 @ ( binintersect @ sK1_SX0 @ sK2_SY93 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(37,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ! [SY118: $i] :
( ~ ( in @ SY118 @ SV3 )
| ( subset @ SY118 @ SV3 ) )
| ! [SY119: $i] :
( ~ ( in @ SY119 @ ( binintersect @ SV1 @ SV3 ) )
| ( subset @ SY119 @ ( binintersect @ SV1 @ SV3 ) ) ) )
= $true )
| ( ( in @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(38,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ! [SY116: $i] :
( ~ ( in @ SY116 @ SV2 )
| ( subset @ SY116 @ SV2 ) ) )
= $true )
| ( ( ! [SY117: $i] :
( ~ ( in @ SY117 @ ( binintersect @ SV1 @ SV2 ) )
| ( subset @ SY117 @ ( binintersect @ SV1 @ SV2 ) ) ) )
= $true )
| ( ( subset @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(39,plain,
! [SV4: $i] :
( ( ~ ( in @ SV4 @ sK1_SX0 )
| ( subset @ SV4 @ sK1_SX0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(40,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( in @ SY84 @ sK1_SX0 )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ sK1_SX0 )
| ! [SY86: $i] :
( ~ ( in @ SY86 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY84 @ SY85 )
| ~ ( in @ SY85 @ SY86 ) )
| ( in @ SY84 @ SY86 ) ) ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ sK1_SX0 )
| ! [SY88: $i] :
( ~ ( in @ SY88 @ sK1_SX0 )
| ( SY87 = SY88 )
| ( in @ SY87 @ SY88 )
| ( in @ SY88 @ SY87 ) ) ) )
| ~ ! [SY89: $i] :
( ~ ( in @ SY89 @ sK1_SX0 )
| ~ ( in @ SY89 @ SY89 ) ) )
| ~ ! [SY90: $i] :
( ~ ( in @ SY90 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY90 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY90 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY90 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(41,plain,
( ( ~ ! [SY105: $i] :
( ~ ( in @ SY105 @ sK2_SY93 )
| ( subset @ SY105 @ sK2_SY93 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(42,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ sK2_SY93 )
| ! [SY107: $i] :
( ~ ( in @ SY107 @ sK2_SY93 )
| ! [SY108: $i] :
( ~ ( in @ SY108 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SY106 @ SY107 )
| ~ ( in @ SY107 @ SY108 ) )
| ( in @ SY106 @ SY108 ) ) ) )
| ~ ! [SY109: $i] :
( ~ ( in @ SY109 @ sK2_SY93 )
| ! [SY110: $i] :
( ~ ( in @ SY110 @ sK2_SY93 )
| ( SY109 = SY110 )
| ( in @ SY109 @ SY110 )
| ( in @ SY110 @ SY109 ) ) ) )
| ~ ! [SY111: $i] :
( ~ ( in @ SY111 @ sK2_SY93 )
| ~ ( in @ SY111 @ SY111 ) ) )
| ~ ! [SY112: $i] :
( ~ ( in @ SY112 @ ( powerset @ sK2_SY93 ) )
| ~ ( ( SY112 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY112 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY112 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(43,plain,
( ( in @ sK4_SY115 @ ( binintersect @ sK1_SX0 @ sK2_SY93 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(44,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ! [SY118: $i] :
( ~ ( in @ SY118 @ SV3 )
| ( subset @ SY118 @ SV3 ) ) )
= $true )
| ( ( ! [SY119: $i] :
( ~ ( in @ SY119 @ ( binintersect @ SV1 @ SV3 ) )
| ( subset @ SY119 @ ( binintersect @ SV1 @ SV3 ) ) ) )
= $true )
| ( ( in @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV1: $i,SV2: $i] :
( ( ( ! [SY116: $i] :
( ~ ( in @ SY116 @ SV2 )
| ( subset @ SY116 @ SV2 ) ) )
= $false )
| ( ( ! [SY117: $i] :
( ~ ( in @ SY117 @ ( binintersect @ SV1 @ SV2 ) )
| ( subset @ SY117 @ ( binintersect @ SV1 @ SV2 ) ) ) )
= $true )
| ( ( subset @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV4: $i] :
( ( ( ~ ( in @ SV4 @ sK1_SX0 ) )
= $true )
| ( ( subset @ SV4 @ sK1_SX0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(47,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( in @ SY84 @ sK1_SX0 )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ sK1_SX0 )
| ! [SY86: $i] :
( ~ ( in @ SY86 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY84 @ SY85 )
| ~ ( in @ SY85 @ SY86 ) )
| ( in @ SY84 @ SY86 ) ) ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ sK1_SX0 )
| ! [SY88: $i] :
( ~ ( in @ SY88 @ sK1_SX0 )
| ( SY87 = SY88 )
| ( in @ SY87 @ SY88 )
| ( in @ SY88 @ SY87 ) ) ) )
| ~ ! [SY89: $i] :
( ~ ( in @ SY89 @ sK1_SX0 )
| ~ ( in @ SY89 @ SY89 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(48,plain,
( ( ~ ! [SY90: $i] :
( ~ ( in @ SY90 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY90 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY90 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY90 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(49,plain,
( ( ! [SY105: $i] :
( ~ ( in @ SY105 @ sK2_SY93 )
| ( subset @ SY105 @ sK2_SY93 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(50,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ sK2_SY93 )
| ! [SY107: $i] :
( ~ ( in @ SY107 @ sK2_SY93 )
| ! [SY108: $i] :
( ~ ( in @ SY108 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SY106 @ SY107 )
| ~ ( in @ SY107 @ SY108 ) )
| ( in @ SY106 @ SY108 ) ) ) )
| ~ ! [SY109: $i] :
( ~ ( in @ SY109 @ sK2_SY93 )
| ! [SY110: $i] :
( ~ ( in @ SY110 @ sK2_SY93 )
| ( SY109 = SY110 )
| ( in @ SY109 @ SY110 )
| ( in @ SY110 @ SY109 ) ) ) )
| ~ ! [SY111: $i] :
( ~ ( in @ SY111 @ sK2_SY93 )
| ~ ( in @ SY111 @ SY111 ) ) )
| ~ ! [SY112: $i] :
( ~ ( in @ SY112 @ ( powerset @ sK2_SY93 ) )
| ~ ( ( SY112 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY112 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY112 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(51,plain,
! [SV1: $i,SV3: $i] :
( ( ( ! [SY118: $i] :
( ~ ( in @ SY118 @ SV3 )
| ( subset @ SY118 @ SV3 ) ) )
= $false )
| ( ( ! [SY119: $i] :
( ~ ( in @ SY119 @ ( binintersect @ SV1 @ SV3 ) )
| ( subset @ SY119 @ ( binintersect @ SV1 @ SV3 ) ) ) )
= $true )
| ( ( in @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(52,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( in @ ( sK5_SY116 @ SV1 @ SV2 ) @ SV2 )
| ( subset @ ( sK5_SY116 @ SV1 @ SV2 ) @ SV2 ) )
= $false )
| ( ( ! [SY117: $i] :
( ~ ( in @ SY117 @ ( binintersect @ SV1 @ SV2 ) )
| ( subset @ SY117 @ ( binintersect @ SV1 @ SV2 ) ) ) )
= $true )
| ( ( subset @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[45]) ).
thf(53,plain,
! [SV4: $i] :
( ( ( in @ SV4 @ sK1_SX0 )
= $false )
| ( ( subset @ SV4 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(54,plain,
( ( ~ ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( in @ SY84 @ sK1_SX0 )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ sK1_SX0 )
| ! [SY86: $i] :
( ~ ( in @ SY86 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY84 @ SY85 )
| ~ ( in @ SY85 @ SY86 ) )
| ( in @ SY84 @ SY86 ) ) ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ sK1_SX0 )
| ! [SY88: $i] :
( ~ ( in @ SY88 @ sK1_SX0 )
| ( SY87 = SY88 )
| ( in @ SY87 @ SY88 )
| ( in @ SY88 @ SY87 ) ) ) )
| ~ ! [SY89: $i] :
( ~ ( in @ SY89 @ sK1_SX0 )
| ~ ( in @ SY89 @ SY89 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(55,plain,
( ( ! [SY90: $i] :
( ~ ( in @ SY90 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY90 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY90 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY90 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(56,plain,
! [SV5: $i] :
( ( ~ ( in @ SV5 @ sK2_SY93 )
| ( subset @ SV5 @ sK2_SY93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(57,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ sK2_SY93 )
| ! [SY107: $i] :
( ~ ( in @ SY107 @ sK2_SY93 )
| ! [SY108: $i] :
( ~ ( in @ SY108 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SY106 @ SY107 )
| ~ ( in @ SY107 @ SY108 ) )
| ( in @ SY106 @ SY108 ) ) ) )
| ~ ! [SY109: $i] :
( ~ ( in @ SY109 @ sK2_SY93 )
| ! [SY110: $i] :
( ~ ( in @ SY110 @ sK2_SY93 )
| ( SY109 = SY110 )
| ( in @ SY109 @ SY110 )
| ( in @ SY110 @ SY109 ) ) ) )
| ~ ! [SY111: $i] :
( ~ ( in @ SY111 @ sK2_SY93 )
| ~ ( in @ SY111 @ SY111 ) ) )
| ~ ! [SY112: $i] :
( ~ ( in @ SY112 @ ( powerset @ sK2_SY93 ) )
| ~ ( ( SY112 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY112 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY112 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(58,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( in @ ( sK6_SY118 @ SV1 @ SV3 ) @ SV3 )
| ( subset @ ( sK6_SY118 @ SV1 @ SV3 ) @ SV3 ) )
= $false )
| ( ( ! [SY119: $i] :
( ~ ( in @ SY119 @ ( binintersect @ SV1 @ SV3 ) )
| ( subset @ SY119 @ ( binintersect @ SV1 @ SV3 ) ) ) )
= $true )
| ( ( in @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(59,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( in @ ( sK5_SY116 @ SV1 @ SV2 ) @ SV2 ) )
= $false )
| ( ( ! [SY117: $i] :
( ~ ( in @ SY117 @ ( binintersect @ SV1 @ SV2 ) )
| ( subset @ SY117 @ ( binintersect @ SV1 @ SV2 ) ) ) )
= $true )
| ( ( subset @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(60,plain,
! [SV2: $i,SV1: $i] :
( ( ( subset @ ( sK5_SY116 @ SV1 @ SV2 ) @ SV2 )
= $false )
| ( ( ! [SY117: $i] :
( ~ ( in @ SY117 @ ( binintersect @ SV1 @ SV2 ) )
| ( subset @ SY117 @ ( binintersect @ SV1 @ SV2 ) ) ) )
= $true )
| ( ( subset @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(61,plain,
( ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( in @ SY84 @ sK1_SX0 )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ sK1_SX0 )
| ! [SY86: $i] :
( ~ ( in @ SY86 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY84 @ SY85 )
| ~ ( in @ SY85 @ SY86 ) )
| ( in @ SY84 @ SY86 ) ) ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ sK1_SX0 )
| ! [SY88: $i] :
( ~ ( in @ SY88 @ sK1_SX0 )
| ( SY87 = SY88 )
| ( in @ SY87 @ SY88 )
| ( in @ SY88 @ SY87 ) ) ) )
| ~ ! [SY89: $i] :
( ~ ( in @ SY89 @ sK1_SX0 )
| ~ ( in @ SY89 @ SY89 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(62,plain,
! [SV6: $i] :
( ( ~ ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SV6 != emptyset ) )
| ~ ! [SY120: $i] :
~ ~ ( ~ ( in @ SY120 @ SV6 )
| ~ ! [SY121: $i] :
( ~ ( in @ SY121 @ SV6 )
| ( SY120 = SY121 )
| ( in @ SY120 @ SY121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(63,plain,
! [SV5: $i] :
( ( ( ~ ( in @ SV5 @ sK2_SY93 ) )
= $true )
| ( ( subset @ SV5 @ sK2_SY93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(64,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ sK2_SY93 )
| ! [SY107: $i] :
( ~ ( in @ SY107 @ sK2_SY93 )
| ! [SY108: $i] :
( ~ ( in @ SY108 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SY106 @ SY107 )
| ~ ( in @ SY107 @ SY108 ) )
| ( in @ SY106 @ SY108 ) ) ) )
| ~ ! [SY109: $i] :
( ~ ( in @ SY109 @ sK2_SY93 )
| ! [SY110: $i] :
( ~ ( in @ SY110 @ sK2_SY93 )
| ( SY109 = SY110 )
| ( in @ SY109 @ SY110 )
| ( in @ SY110 @ SY109 ) ) ) )
| ~ ! [SY111: $i] :
( ~ ( in @ SY111 @ sK2_SY93 )
| ~ ( in @ SY111 @ SY111 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(65,plain,
( ( ~ ! [SY112: $i] :
( ~ ( in @ SY112 @ ( powerset @ sK2_SY93 ) )
| ~ ( ( SY112 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY112 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY112 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(66,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( in @ ( sK6_SY118 @ SV1 @ SV3 ) @ SV3 ) )
= $false )
| ( ( ! [SY119: $i] :
( ~ ( in @ SY119 @ ( binintersect @ SV1 @ SV3 ) )
| ( subset @ SY119 @ ( binintersect @ SV1 @ SV3 ) ) ) )
= $true )
| ( ( in @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(67,plain,
! [SV3: $i,SV1: $i] :
( ( ( subset @ ( sK6_SY118 @ SV1 @ SV3 ) @ SV3 )
= $false )
| ( ( ! [SY119: $i] :
( ~ ( in @ SY119 @ ( binintersect @ SV1 @ SV3 ) )
| ( subset @ SY119 @ ( binintersect @ SV1 @ SV3 ) ) ) )
= $true )
| ( ( in @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(68,plain,
! [SV2: $i,SV1: $i] :
( ( ( in @ ( sK5_SY116 @ SV1 @ SV2 ) @ SV2 )
= $true )
| ( ( ! [SY117: $i] :
( ~ ( in @ SY117 @ ( binintersect @ SV1 @ SV2 ) )
| ( subset @ SY117 @ ( binintersect @ SV1 @ SV2 ) ) ) )
= $true )
| ( ( subset @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(69,plain,
! [SV2: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( binintersect @ SV1 @ SV2 ) )
| ( subset @ SV7 @ ( binintersect @ SV1 @ SV2 ) ) )
= $true )
| ( ( subset @ ( sK5_SY116 @ SV1 @ SV2 ) @ SV2 )
= $false )
| ( ( subset @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(70,plain,
( ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( in @ SY84 @ sK1_SX0 )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ sK1_SX0 )
| ! [SY86: $i] :
( ~ ( in @ SY86 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY84 @ SY85 )
| ~ ( in @ SY85 @ SY86 ) )
| ( in @ SY84 @ SY86 ) ) ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ sK1_SX0 )
| ! [SY88: $i] :
( ~ ( in @ SY88 @ sK1_SX0 )
| ( SY87 = SY88 )
| ( in @ SY87 @ SY88 )
| ( in @ SY88 @ SY87 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(71,plain,
( ( ~ ! [SY89: $i] :
( ~ ( in @ SY89 @ sK1_SX0 )
| ~ ( in @ SY89 @ SY89 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(72,plain,
! [SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( powerset @ sK1_SX0 ) ) )
= $true )
| ( ( ~ ( ( SV6 != emptyset ) )
| ~ ! [SY120: $i] :
~ ~ ( ~ ( in @ SY120 @ SV6 )
| ~ ! [SY121: $i] :
( ~ ( in @ SY121 @ SV6 )
| ( SY120 = SY121 )
| ( in @ SY120 @ SY121 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(73,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ sK2_SY93 )
= $false )
| ( ( subset @ SV5 @ sK2_SY93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(74,plain,
( ( ~ ( ~ ~ ( ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ sK2_SY93 )
| ! [SY107: $i] :
( ~ ( in @ SY107 @ sK2_SY93 )
| ! [SY108: $i] :
( ~ ( in @ SY108 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SY106 @ SY107 )
| ~ ( in @ SY107 @ SY108 ) )
| ( in @ SY106 @ SY108 ) ) ) )
| ~ ! [SY109: $i] :
( ~ ( in @ SY109 @ sK2_SY93 )
| ! [SY110: $i] :
( ~ ( in @ SY110 @ sK2_SY93 )
| ( SY109 = SY110 )
| ( in @ SY109 @ SY110 )
| ( in @ SY110 @ SY109 ) ) ) )
| ~ ! [SY111: $i] :
( ~ ( in @ SY111 @ sK2_SY93 )
| ~ ( in @ SY111 @ SY111 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(75,plain,
( ( ! [SY112: $i] :
( ~ ( in @ SY112 @ ( powerset @ sK2_SY93 ) )
| ~ ( ( SY112 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY112 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY112 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(76,plain,
! [SV3: $i,SV1: $i] :
( ( ( in @ ( sK6_SY118 @ SV1 @ SV3 ) @ SV3 )
= $true )
| ( ( ! [SY119: $i] :
( ~ ( in @ SY119 @ ( binintersect @ SV1 @ SV3 ) )
| ( subset @ SY119 @ ( binintersect @ SV1 @ SV3 ) ) ) )
= $true )
| ( ( in @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(77,plain,
! [SV3: $i,SV1: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( binintersect @ SV1 @ SV3 ) )
| ( subset @ SV8 @ ( binintersect @ SV1 @ SV3 ) ) )
= $true )
| ( ( subset @ ( sK6_SY118 @ SV1 @ SV3 ) @ SV3 )
= $false )
| ( ( in @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(78,plain,
! [SV2: $i,SV1: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( binintersect @ SV1 @ SV2 ) )
| ( subset @ SV9 @ ( binintersect @ SV1 @ SV2 ) ) )
= $true )
| ( ( in @ ( sK5_SY116 @ SV1 @ SV2 ) @ SV2 )
= $true )
| ( ( subset @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(79,plain,
! [SV2: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( binintersect @ SV1 @ SV2 ) ) )
= $true )
| ( ( subset @ SV7 @ ( binintersect @ SV1 @ SV2 ) )
= $true )
| ( ( subset @ ( sK5_SY116 @ SV1 @ SV2 ) @ SV2 )
= $false )
| ( ( subset @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(80,plain,
( ( ~ ( ~ ! [SY84: $i] :
( ~ ( in @ SY84 @ sK1_SX0 )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ sK1_SX0 )
| ! [SY86: $i] :
( ~ ( in @ SY86 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY84 @ SY85 )
| ~ ( in @ SY85 @ SY86 ) )
| ( in @ SY84 @ SY86 ) ) ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ sK1_SX0 )
| ! [SY88: $i] :
( ~ ( in @ SY88 @ sK1_SX0 )
| ( SY87 = SY88 )
| ( in @ SY87 @ SY88 )
| ( in @ SY88 @ SY87 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(81,plain,
( ( ! [SY89: $i] :
( ~ ( in @ SY89 @ sK1_SX0 )
| ~ ( in @ SY89 @ SY89 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(82,plain,
! [SV6: $i] :
( ( ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
= $false )
| ( ( ~ ( ( SV6 != emptyset ) )
| ~ ! [SY120: $i] :
~ ~ ( ~ ( in @ SY120 @ SV6 )
| ~ ! [SY121: $i] :
( ~ ( in @ SY121 @ SV6 )
| ( SY120 = SY121 )
| ( in @ SY120 @ SY121 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(83,plain,
( ( ~ ~ ( ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ sK2_SY93 )
| ! [SY107: $i] :
( ~ ( in @ SY107 @ sK2_SY93 )
| ! [SY108: $i] :
( ~ ( in @ SY108 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SY106 @ SY107 )
| ~ ( in @ SY107 @ SY108 ) )
| ( in @ SY106 @ SY108 ) ) ) )
| ~ ! [SY109: $i] :
( ~ ( in @ SY109 @ sK2_SY93 )
| ! [SY110: $i] :
( ~ ( in @ SY110 @ sK2_SY93 )
| ( SY109 = SY110 )
| ( in @ SY109 @ SY110 )
| ( in @ SY110 @ SY109 ) ) ) )
| ~ ! [SY111: $i] :
( ~ ( in @ SY111 @ sK2_SY93 )
| ~ ( in @ SY111 @ SY111 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(84,plain,
! [SV10: $i] :
( ( ~ ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
| ~ ( ( SV10 != emptyset ) )
| ~ ! [SY122: $i] :
~ ~ ( ~ ( in @ SY122 @ SV10 )
| ~ ! [SY123: $i] :
( ~ ( in @ SY123 @ SV10 )
| ( SY122 = SY123 )
| ( in @ SY122 @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(85,plain,
! [SV3: $i,SV1: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ ( binintersect @ SV1 @ SV3 ) )
| ( subset @ SV11 @ ( binintersect @ SV1 @ SV3 ) ) )
= $true )
| ( ( in @ ( sK6_SY118 @ SV1 @ SV3 ) @ SV3 )
= $true )
| ( ( in @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV3: $i,SV1: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( binintersect @ SV1 @ SV3 ) ) )
= $true )
| ( ( subset @ SV8 @ ( binintersect @ SV1 @ SV3 ) )
= $true )
| ( ( subset @ ( sK6_SY118 @ SV1 @ SV3 ) @ SV3 )
= $false )
| ( ( in @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV2: $i,SV1: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( binintersect @ SV1 @ SV2 ) ) )
= $true )
| ( ( subset @ SV9 @ ( binintersect @ SV1 @ SV2 ) )
= $true )
| ( ( in @ ( sK5_SY116 @ SV1 @ SV2 ) @ SV2 )
= $true )
| ( ( subset @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV2: $i,SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ ( binintersect @ SV1 @ SV2 ) )
= $false )
| ( ( subset @ SV7 @ ( binintersect @ SV1 @ SV2 ) )
= $true )
| ( ( subset @ ( sK5_SY116 @ SV1 @ SV2 ) @ SV2 )
= $false )
| ( ( subset @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(89,plain,
( ( ~ ! [SY84: $i] :
( ~ ( in @ SY84 @ sK1_SX0 )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ sK1_SX0 )
| ! [SY86: $i] :
( ~ ( in @ SY86 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY84 @ SY85 )
| ~ ( in @ SY85 @ SY86 ) )
| ( in @ SY84 @ SY86 ) ) ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ sK1_SX0 )
| ! [SY88: $i] :
( ~ ( in @ SY88 @ sK1_SX0 )
| ( SY87 = SY88 )
| ( in @ SY87 @ SY88 )
| ( in @ SY88 @ SY87 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV12: $i] :
( ( ~ ( in @ SV12 @ sK1_SX0 )
| ~ ( in @ SV12 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV6: $i] :
( ( ( ~ ( ( SV6 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY120: $i] :
~ ~ ( ~ ( in @ SY120 @ SV6 )
| ~ ! [SY121: $i] :
( ~ ( in @ SY121 @ SV6 )
| ( SY120 = SY121 )
| ( in @ SY120 @ SY121 ) ) ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(92,plain,
( ( ~ ~ ( ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ sK2_SY93 )
| ! [SY107: $i] :
( ~ ( in @ SY107 @ sK2_SY93 )
| ! [SY108: $i] :
( ~ ( in @ SY108 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SY106 @ SY107 )
| ~ ( in @ SY107 @ SY108 ) )
| ( in @ SY106 @ SY108 ) ) ) )
| ~ ! [SY109: $i] :
( ~ ( in @ SY109 @ sK2_SY93 )
| ! [SY110: $i] :
( ~ ( in @ SY110 @ sK2_SY93 )
| ( SY109 = SY110 )
| ( in @ SY109 @ SY110 )
| ( in @ SY110 @ SY109 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(93,plain,
( ( ~ ! [SY111: $i] :
( ~ ( in @ SY111 @ sK2_SY93 )
| ~ ( in @ SY111 @ SY111 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(94,plain,
! [SV10: $i] :
( ( ( ~ ( in @ SV10 @ ( powerset @ sK2_SY93 ) ) )
= $true )
| ( ( ~ ( ( SV10 != emptyset ) )
| ~ ! [SY122: $i] :
~ ~ ( ~ ( in @ SY122 @ SV10 )
| ~ ! [SY123: $i] :
( ~ ( in @ SY123 @ SV10 )
| ( SY122 = SY123 )
| ( in @ SY122 @ SY123 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(95,plain,
! [SV3: $i,SV1: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ ( binintersect @ SV1 @ SV3 ) ) )
= $true )
| ( ( subset @ SV11 @ ( binintersect @ SV1 @ SV3 ) )
= $true )
| ( ( in @ ( sK6_SY118 @ SV1 @ SV3 ) @ SV3 )
= $true )
| ( ( in @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(96,plain,
! [SV3: $i,SV1: $i,SV8: $i] :
( ( ( in @ SV8 @ ( binintersect @ SV1 @ SV3 ) )
= $false )
| ( ( subset @ SV8 @ ( binintersect @ SV1 @ SV3 ) )
= $true )
| ( ( subset @ ( sK6_SY118 @ SV1 @ SV3 ) @ SV3 )
= $false )
| ( ( in @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(97,plain,
! [SV2: $i,SV1: $i,SV9: $i] :
( ( ( in @ SV9 @ ( binintersect @ SV1 @ SV2 ) )
= $false )
| ( ( subset @ SV9 @ ( binintersect @ SV1 @ SV2 ) )
= $true )
| ( ( in @ ( sK5_SY116 @ SV1 @ SV2 ) @ SV2 )
= $true )
| ( ( subset @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(98,plain,
( ( ~ ! [SY84: $i] :
( ~ ( in @ SY84 @ sK1_SX0 )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ sK1_SX0 )
| ! [SY86: $i] :
( ~ ( in @ SY86 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY84 @ SY85 )
| ~ ( in @ SY85 @ SY86 ) )
| ( in @ SY84 @ SY86 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(99,plain,
( ( ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ sK1_SX0 )
| ! [SY88: $i] :
( ~ ( in @ SY88 @ sK1_SX0 )
| ( SY87 = SY88 )
| ( in @ SY87 @ SY88 )
| ( in @ SY88 @ SY87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(100,plain,
! [SV12: $i] :
( ( ( ~ ( in @ SV12 @ sK1_SX0 ) )
= $true )
| ( ( ~ ( in @ SV12 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(101,plain,
! [SV6: $i] :
( ( ( SV6 != emptyset )
= $false )
| ( ( ~ ! [SY120: $i] :
~ ~ ( ~ ( in @ SY120 @ SV6 )
| ~ ! [SY121: $i] :
( ~ ( in @ SY121 @ SV6 )
| ( SY120 = SY121 )
| ( in @ SY120 @ SY121 ) ) ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(102,plain,
( ( ~ ( ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ sK2_SY93 )
| ! [SY107: $i] :
( ~ ( in @ SY107 @ sK2_SY93 )
| ! [SY108: $i] :
( ~ ( in @ SY108 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SY106 @ SY107 )
| ~ ( in @ SY107 @ SY108 ) )
| ( in @ SY106 @ SY108 ) ) ) )
| ~ ! [SY109: $i] :
( ~ ( in @ SY109 @ sK2_SY93 )
| ! [SY110: $i] :
( ~ ( in @ SY110 @ sK2_SY93 )
| ( SY109 = SY110 )
| ( in @ SY109 @ SY110 )
| ( in @ SY110 @ SY109 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(103,plain,
( ( ! [SY111: $i] :
( ~ ( in @ SY111 @ sK2_SY93 )
| ~ ( in @ SY111 @ SY111 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(104,plain,
! [SV10: $i] :
( ( ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
= $false )
| ( ( ~ ( ( SV10 != emptyset ) )
| ~ ! [SY122: $i] :
~ ~ ( ~ ( in @ SY122 @ SV10 )
| ~ ! [SY123: $i] :
( ~ ( in @ SY123 @ SV10 )
| ( SY122 = SY123 )
| ( in @ SY122 @ SY123 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(105,plain,
! [SV3: $i,SV1: $i,SV11: $i] :
( ( ( in @ SV11 @ ( binintersect @ SV1 @ SV3 ) )
= $false )
| ( ( subset @ SV11 @ ( binintersect @ SV1 @ SV3 ) )
= $true )
| ( ( in @ ( sK6_SY118 @ SV1 @ SV3 ) @ SV3 )
= $true )
| ( ( in @ ( sK3_SY79 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(106,plain,
( ( ! [SY84: $i] :
( ~ ( in @ SY84 @ sK1_SX0 )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ sK1_SX0 )
| ! [SY86: $i] :
( ~ ( in @ SY86 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY84 @ SY85 )
| ~ ( in @ SY85 @ SY86 ) )
| ( in @ SY84 @ SY86 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(107,plain,
( ( ! [SY87: $i] :
( ~ ( in @ SY87 @ sK1_SX0 )
| ! [SY88: $i] :
( ~ ( in @ SY88 @ sK1_SX0 )
| ( SY87 = SY88 )
| ( in @ SY87 @ SY88 )
| ( in @ SY88 @ SY87 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(108,plain,
! [SV12: $i] :
( ( ( in @ SV12 @ sK1_SX0 )
= $false )
| ( ( ~ ( in @ SV12 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(109,plain,
! [SV6: $i] :
( ( ( SV6 = emptyset )
= $true )
| ( ( ~ ! [SY120: $i] :
~ ~ ( ~ ( in @ SY120 @ SV6 )
| ~ ! [SY121: $i] :
( ~ ( in @ SY121 @ SV6 )
| ( SY120 = SY121 )
| ( in @ SY120 @ SY121 ) ) ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(110,plain,
( ( ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ sK2_SY93 )
| ! [SY107: $i] :
( ~ ( in @ SY107 @ sK2_SY93 )
| ! [SY108: $i] :
( ~ ( in @ SY108 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SY106 @ SY107 )
| ~ ( in @ SY107 @ SY108 ) )
| ( in @ SY106 @ SY108 ) ) ) )
| ~ ! [SY109: $i] :
( ~ ( in @ SY109 @ sK2_SY93 )
| ! [SY110: $i] :
( ~ ( in @ SY110 @ sK2_SY93 )
| ( SY109 = SY110 )
| ( in @ SY109 @ SY110 )
| ( in @ SY110 @ SY109 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(111,plain,
! [SV13: $i] :
( ( ~ ( in @ SV13 @ sK2_SY93 )
| ~ ( in @ SV13 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(112,plain,
! [SV10: $i] :
( ( ( ~ ( ( SV10 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY122: $i] :
~ ~ ( ~ ( in @ SY122 @ SV10 )
| ~ ! [SY123: $i] :
( ~ ( in @ SY123 @ SV10 )
| ( SY122 = SY123 )
| ( in @ SY122 @ SY123 ) ) ) )
= $true )
| ( ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(113,plain,
! [SV14: $i] :
( ( ~ ( in @ SV14 @ sK1_SX0 )
| ! [SY124: $i] :
( ~ ( in @ SY124 @ sK1_SX0 )
| ! [SY125: $i] :
( ~ ( in @ SY125 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SV14 @ SY124 )
| ~ ( in @ SY124 @ SY125 ) )
| ( in @ SV14 @ SY125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(114,plain,
! [SV15: $i] :
( ( ~ ( in @ SV15 @ sK1_SX0 )
| ! [SY126: $i] :
( ~ ( in @ SY126 @ sK1_SX0 )
| ( SV15 = SY126 )
| ( in @ SV15 @ SY126 )
| ( in @ SY126 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(115,plain,
! [SV12: $i] :
( ( ( in @ SV12 @ SV12 )
= $false )
| ( ( in @ SV12 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(116,plain,
! [SV6: $i] :
( ( ( ! [SY120: $i] :
~ ~ ( ~ ( in @ SY120 @ SV6 )
| ~ ! [SY121: $i] :
( ~ ( in @ SY121 @ SV6 )
| ( SY120 = SY121 )
| ( in @ SY120 @ SY121 ) ) ) )
= $false )
| ( ( SV6 = emptyset )
= $true )
| ( ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(117,plain,
( ( ~ ! [SY106: $i] :
( ~ ( in @ SY106 @ sK2_SY93 )
| ! [SY107: $i] :
( ~ ( in @ SY107 @ sK2_SY93 )
| ! [SY108: $i] :
( ~ ( in @ SY108 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SY106 @ SY107 )
| ~ ( in @ SY107 @ SY108 ) )
| ( in @ SY106 @ SY108 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(118,plain,
( ( ~ ! [SY109: $i] :
( ~ ( in @ SY109 @ sK2_SY93 )
| ! [SY110: $i] :
( ~ ( in @ SY110 @ sK2_SY93 )
| ( SY109 = SY110 )
| ( in @ SY109 @ SY110 )
| ( in @ SY110 @ SY109 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(119,plain,
! [SV13: $i] :
( ( ( ~ ( in @ SV13 @ sK2_SY93 ) )
= $true )
| ( ( ~ ( in @ SV13 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(120,plain,
! [SV10: $i] :
( ( ( SV10 != emptyset )
= $false )
| ( ( ~ ! [SY122: $i] :
~ ~ ( ~ ( in @ SY122 @ SV10 )
| ~ ! [SY123: $i] :
( ~ ( in @ SY123 @ SV10 )
| ( SY122 = SY123 )
| ( in @ SY122 @ SY123 ) ) ) )
= $true )
| ( ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(121,plain,
! [SV14: $i] :
( ( ( ~ ( in @ SV14 @ sK1_SX0 ) )
= $true )
| ( ( ! [SY124: $i] :
( ~ ( in @ SY124 @ sK1_SX0 )
| ! [SY125: $i] :
( ~ ( in @ SY125 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SV14 @ SY124 )
| ~ ( in @ SY124 @ SY125 ) )
| ( in @ SV14 @ SY125 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(122,plain,
! [SV15: $i] :
( ( ( ~ ( in @ SV15 @ sK1_SX0 ) )
= $true )
| ( ( ! [SY126: $i] :
( ~ ( in @ SY126 @ sK1_SX0 )
| ( SV15 = SY126 )
| ( in @ SV15 @ SY126 )
| ( in @ SY126 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(123,plain,
! [SV6: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_SY120 @ SV6 ) @ SV6 )
| ~ ! [SY127: $i] :
( ~ ( in @ SY127 @ SV6 )
| ( ( sK7_SY120 @ SV6 )
= SY127 )
| ( in @ ( sK7_SY120 @ SV6 ) @ SY127 ) ) ) )
= $false )
| ( ( SV6 = emptyset )
= $true )
| ( ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[116]) ).
thf(124,plain,
( ( ! [SY106: $i] :
( ~ ( in @ SY106 @ sK2_SY93 )
| ! [SY107: $i] :
( ~ ( in @ SY107 @ sK2_SY93 )
| ! [SY108: $i] :
( ~ ( in @ SY108 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SY106 @ SY107 )
| ~ ( in @ SY107 @ SY108 ) )
| ( in @ SY106 @ SY108 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(125,plain,
( ( ! [SY109: $i] :
( ~ ( in @ SY109 @ sK2_SY93 )
| ! [SY110: $i] :
( ~ ( in @ SY110 @ sK2_SY93 )
| ( SY109 = SY110 )
| ( in @ SY109 @ SY110 )
| ( in @ SY110 @ SY109 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(126,plain,
! [SV13: $i] :
( ( ( in @ SV13 @ sK2_SY93 )
= $false )
| ( ( ~ ( in @ SV13 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(127,plain,
! [SV10: $i] :
( ( ( SV10 = emptyset )
= $true )
| ( ( ~ ! [SY122: $i] :
~ ~ ( ~ ( in @ SY122 @ SV10 )
| ~ ! [SY123: $i] :
( ~ ( in @ SY123 @ SV10 )
| ( SY122 = SY123 )
| ( in @ SY122 @ SY123 ) ) ) )
= $true )
| ( ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(128,plain,
! [SV14: $i] :
( ( ( in @ SV14 @ sK1_SX0 )
= $false )
| ( ( ! [SY124: $i] :
( ~ ( in @ SY124 @ sK1_SX0 )
| ! [SY125: $i] :
( ~ ( in @ SY125 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SV14 @ SY124 )
| ~ ( in @ SY124 @ SY125 ) )
| ( in @ SV14 @ SY125 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(129,plain,
! [SV15: $i] :
( ( ( in @ SV15 @ sK1_SX0 )
= $false )
| ( ( ! [SY126: $i] :
( ~ ( in @ SY126 @ sK1_SX0 )
| ( SV15 = SY126 )
| ( in @ SV15 @ SY126 )
| ( in @ SY126 @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(130,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY120 @ SV6 ) @ SV6 )
| ~ ! [SY127: $i] :
( ~ ( in @ SY127 @ SV6 )
| ( ( sK7_SY120 @ SV6 )
= SY127 )
| ( in @ ( sK7_SY120 @ SV6 ) @ SY127 ) ) ) )
= $true )
| ( ( SV6 = emptyset )
= $true )
| ( ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(131,plain,
! [SV16: $i] :
( ( ~ ( in @ SV16 @ sK2_SY93 )
| ! [SY128: $i] :
( ~ ( in @ SY128 @ sK2_SY93 )
| ! [SY129: $i] :
( ~ ( in @ SY129 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SV16 @ SY128 )
| ~ ( in @ SY128 @ SY129 ) )
| ( in @ SV16 @ SY129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(132,plain,
! [SV17: $i] :
( ( ~ ( in @ SV17 @ sK2_SY93 )
| ! [SY130: $i] :
( ~ ( in @ SY130 @ sK2_SY93 )
| ( SV17 = SY130 )
| ( in @ SV17 @ SY130 )
| ( in @ SY130 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(133,plain,
! [SV13: $i] :
( ( ( in @ SV13 @ SV13 )
= $false )
| ( ( in @ SV13 @ sK2_SY93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(134,plain,
! [SV10: $i] :
( ( ( ! [SY122: $i] :
~ ~ ( ~ ( in @ SY122 @ SV10 )
| ~ ! [SY123: $i] :
( ~ ( in @ SY123 @ SV10 )
| ( SY122 = SY123 )
| ( in @ SY122 @ SY123 ) ) ) )
= $false )
| ( ( SV10 = emptyset )
= $true )
| ( ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(135,plain,
! [SV14: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ sK1_SX0 )
| ! [SY131: $i] :
( ~ ( in @ SY131 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SV14 @ SV18 )
| ~ ( in @ SV18 @ SY131 ) )
| ( in @ SV14 @ SY131 ) ) )
= $true )
| ( ( in @ SV14 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(136,plain,
! [SV15: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ sK1_SX0 )
| ( SV15 = SV19 )
| ( in @ SV15 @ SV19 )
| ( in @ SV19 @ SV15 ) )
= $true )
| ( ( in @ SV15 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(137,plain,
! [SV6: $i] :
( ( ( ~ ( in @ ( sK7_SY120 @ SV6 ) @ SV6 )
| ~ ! [SY127: $i] :
( ~ ( in @ SY127 @ SV6 )
| ( ( sK7_SY120 @ SV6 )
= SY127 )
| ( in @ ( sK7_SY120 @ SV6 ) @ SY127 ) ) )
= $false )
| ( ( SV6 = emptyset )
= $true )
| ( ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(138,plain,
! [SV16: $i] :
( ( ( ~ ( in @ SV16 @ sK2_SY93 ) )
= $true )
| ( ( ! [SY128: $i] :
( ~ ( in @ SY128 @ sK2_SY93 )
| ! [SY129: $i] :
( ~ ( in @ SY129 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SV16 @ SY128 )
| ~ ( in @ SY128 @ SY129 ) )
| ( in @ SV16 @ SY129 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(139,plain,
! [SV17: $i] :
( ( ( ~ ( in @ SV17 @ sK2_SY93 ) )
= $true )
| ( ( ! [SY130: $i] :
( ~ ( in @ SY130 @ sK2_SY93 )
| ( SV17 = SY130 )
| ( in @ SV17 @ SY130 )
| ( in @ SY130 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(140,plain,
! [SV10: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY122 @ SV10 ) @ SV10 )
| ~ ! [SY132: $i] :
( ~ ( in @ SY132 @ SV10 )
| ( ( sK8_SY122 @ SV10 )
= SY132 )
| ( in @ ( sK8_SY122 @ SV10 ) @ SY132 ) ) ) )
= $false )
| ( ( SV10 = emptyset )
= $true )
| ( ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[134]) ).
thf(141,plain,
! [SV14: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ sK1_SX0 ) )
= $true )
| ( ( ! [SY131: $i] :
( ~ ( in @ SY131 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SV14 @ SV18 )
| ~ ( in @ SV18 @ SY131 ) )
| ( in @ SV14 @ SY131 ) ) )
= $true )
| ( ( in @ SV14 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(142,plain,
! [SV15: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ sK1_SX0 ) )
= $true )
| ( ( ( SV15 = SV19 )
| ( in @ SV15 @ SV19 )
| ( in @ SV19 @ SV15 ) )
= $true )
| ( ( in @ SV15 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(143,plain,
! [SV6: $i] :
( ( ( ~ ( in @ ( sK7_SY120 @ SV6 ) @ SV6 ) )
= $false )
| ( ( SV6 = emptyset )
= $true )
| ( ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(144,plain,
! [SV6: $i] :
( ( ( ~ ! [SY127: $i] :
( ~ ( in @ SY127 @ SV6 )
| ( ( sK7_SY120 @ SV6 )
= SY127 )
| ( in @ ( sK7_SY120 @ SV6 ) @ SY127 ) ) )
= $false )
| ( ( SV6 = emptyset )
= $true )
| ( ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(145,plain,
! [SV16: $i] :
( ( ( in @ SV16 @ sK2_SY93 )
= $false )
| ( ( ! [SY128: $i] :
( ~ ( in @ SY128 @ sK2_SY93 )
| ! [SY129: $i] :
( ~ ( in @ SY129 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SV16 @ SY128 )
| ~ ( in @ SY128 @ SY129 ) )
| ( in @ SV16 @ SY129 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(146,plain,
! [SV17: $i] :
( ( ( in @ SV17 @ sK2_SY93 )
= $false )
| ( ( ! [SY130: $i] :
( ~ ( in @ SY130 @ sK2_SY93 )
| ( SV17 = SY130 )
| ( in @ SV17 @ SY130 )
| ( in @ SY130 @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(147,plain,
! [SV10: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY122 @ SV10 ) @ SV10 )
| ~ ! [SY132: $i] :
( ~ ( in @ SY132 @ SV10 )
| ( ( sK8_SY122 @ SV10 )
= SY132 )
| ( in @ ( sK8_SY122 @ SV10 ) @ SY132 ) ) ) )
= $true )
| ( ( SV10 = emptyset )
= $true )
| ( ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(148,plain,
! [SV14: $i,SV18: $i] :
( ( ( in @ SV18 @ sK1_SX0 )
= $false )
| ( ( ! [SY131: $i] :
( ~ ( in @ SY131 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SV14 @ SV18 )
| ~ ( in @ SV18 @ SY131 ) )
| ( in @ SV14 @ SY131 ) ) )
= $true )
| ( ( in @ SV14 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(149,plain,
! [SV15: $i,SV19: $i] :
( ( ( in @ SV19 @ sK1_SX0 )
= $false )
| ( ( ( SV15 = SV19 )
| ( in @ SV15 @ SV19 )
| ( in @ SV19 @ SV15 ) )
= $true )
| ( ( in @ SV15 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(150,plain,
! [SV6: $i] :
( ( ( in @ ( sK7_SY120 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6 = emptyset )
= $true )
| ( ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(151,plain,
! [SV6: $i] :
( ( ( ! [SY127: $i] :
( ~ ( in @ SY127 @ SV6 )
| ( ( sK7_SY120 @ SV6 )
= SY127 )
| ( in @ ( sK7_SY120 @ SV6 ) @ SY127 ) ) )
= $true )
| ( ( SV6 = emptyset )
= $true )
| ( ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(152,plain,
! [SV16: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ sK2_SY93 )
| ! [SY133: $i] :
( ~ ( in @ SY133 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SV16 @ SV20 )
| ~ ( in @ SV20 @ SY133 ) )
| ( in @ SV16 @ SY133 ) ) )
= $true )
| ( ( in @ SV16 @ sK2_SY93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(153,plain,
! [SV17: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ sK2_SY93 )
| ( SV17 = SV21 )
| ( in @ SV17 @ SV21 )
| ( in @ SV21 @ SV17 ) )
= $true )
| ( ( in @ SV17 @ sK2_SY93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(154,plain,
! [SV10: $i] :
( ( ( ~ ( in @ ( sK8_SY122 @ SV10 ) @ SV10 )
| ~ ! [SY132: $i] :
( ~ ( in @ SY132 @ SV10 )
| ( ( sK8_SY122 @ SV10 )
= SY132 )
| ( in @ ( sK8_SY122 @ SV10 ) @ SY132 ) ) )
= $false )
| ( ( SV10 = emptyset )
= $true )
| ( ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(155,plain,
! [SV18: $i,SV14: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SV14 @ SV18 )
| ~ ( in @ SV18 @ SV22 ) )
| ( in @ SV14 @ SV22 ) )
= $true )
| ( ( in @ SV18 @ sK1_SX0 )
= $false )
| ( ( in @ SV14 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(156,plain,
! [SV19: $i,SV15: $i] :
( ( ( ( SV15 = SV19 )
| ( in @ SV15 @ SV19 ) )
= $true )
| ( ( in @ SV19 @ SV15 )
= $true )
| ( ( in @ SV19 @ sK1_SX0 )
= $false )
| ( ( in @ SV15 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(157,plain,
! [SV6: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV6 )
| ( ( sK7_SY120 @ SV6 )
= SV23 )
| ( in @ ( sK7_SY120 @ SV6 ) @ SV23 ) )
= $true )
| ( ( SV6 = emptyset )
= $true )
| ( ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(158,plain,
! [SV16: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ sK2_SY93 ) )
= $true )
| ( ( ! [SY133: $i] :
( ~ ( in @ SY133 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SV16 @ SV20 )
| ~ ( in @ SV20 @ SY133 ) )
| ( in @ SV16 @ SY133 ) ) )
= $true )
| ( ( in @ SV16 @ sK2_SY93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(159,plain,
! [SV17: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ sK2_SY93 ) )
= $true )
| ( ( ( SV17 = SV21 )
| ( in @ SV17 @ SV21 )
| ( in @ SV21 @ SV17 ) )
= $true )
| ( ( in @ SV17 @ sK2_SY93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(160,plain,
! [SV10: $i] :
( ( ( ~ ( in @ ( sK8_SY122 @ SV10 ) @ SV10 ) )
= $false )
| ( ( SV10 = emptyset )
= $true )
| ( ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(161,plain,
! [SV10: $i] :
( ( ( ~ ! [SY132: $i] :
( ~ ( in @ SY132 @ SV10 )
| ( ( sK8_SY122 @ SV10 )
= SY132 )
| ( in @ ( sK8_SY122 @ SV10 ) @ SY132 ) ) )
= $false )
| ( ( SV10 = emptyset )
= $true )
| ( ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(162,plain,
! [SV18: $i,SV14: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ sK1_SX0 ) )
= $true )
| ( ( ~ ~ ( ~ ( in @ SV14 @ SV18 )
| ~ ( in @ SV18 @ SV22 ) )
| ( in @ SV14 @ SV22 ) )
= $true )
| ( ( in @ SV18 @ sK1_SX0 )
= $false )
| ( ( in @ SV14 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(163,plain,
! [SV19: $i,SV15: $i] :
( ( ( SV15 = SV19 )
= $true )
| ( ( in @ SV15 @ SV19 )
= $true )
| ( ( in @ SV19 @ SV15 )
= $true )
| ( ( in @ SV19 @ sK1_SX0 )
= $false )
| ( ( in @ SV15 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(164,plain,
! [SV6: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV6 ) )
= $true )
| ( ( ( ( sK7_SY120 @ SV6 )
= SV23 )
| ( in @ ( sK7_SY120 @ SV6 ) @ SV23 ) )
= $true )
| ( ( SV6 = emptyset )
= $true )
| ( ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(165,plain,
! [SV16: $i,SV20: $i] :
( ( ( in @ SV20 @ sK2_SY93 )
= $false )
| ( ( ! [SY133: $i] :
( ~ ( in @ SY133 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SV16 @ SV20 )
| ~ ( in @ SV20 @ SY133 ) )
| ( in @ SV16 @ SY133 ) ) )
= $true )
| ( ( in @ SV16 @ sK2_SY93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(166,plain,
! [SV17: $i,SV21: $i] :
( ( ( in @ SV21 @ sK2_SY93 )
= $false )
| ( ( ( SV17 = SV21 )
| ( in @ SV17 @ SV21 )
| ( in @ SV21 @ SV17 ) )
= $true )
| ( ( in @ SV17 @ sK2_SY93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(167,plain,
! [SV10: $i] :
( ( ( in @ ( sK8_SY122 @ SV10 ) @ SV10 )
= $true )
| ( ( SV10 = emptyset )
= $true )
| ( ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(168,plain,
! [SV10: $i] :
( ( ( ! [SY132: $i] :
( ~ ( in @ SY132 @ SV10 )
| ( ( sK8_SY122 @ SV10 )
= SY132 )
| ( in @ ( sK8_SY122 @ SV10 ) @ SY132 ) ) )
= $true )
| ( ( SV10 = emptyset )
= $true )
| ( ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(169,plain,
! [SV18: $i,SV14: $i,SV22: $i] :
( ( ( in @ SV22 @ sK1_SX0 )
= $false )
| ( ( ~ ~ ( ~ ( in @ SV14 @ SV18 )
| ~ ( in @ SV18 @ SV22 ) )
| ( in @ SV14 @ SV22 ) )
= $true )
| ( ( in @ SV18 @ sK1_SX0 )
= $false )
| ( ( in @ SV14 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(170,plain,
! [SV6: $i,SV23: $i] :
( ( ( in @ SV23 @ SV6 )
= $false )
| ( ( ( ( sK7_SY120 @ SV6 )
= SV23 )
| ( in @ ( sK7_SY120 @ SV6 ) @ SV23 ) )
= $true )
| ( ( SV6 = emptyset )
= $true )
| ( ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(171,plain,
! [SV20: $i,SV16: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ sK2_SY93 )
| ~ ~ ( ~ ( in @ SV16 @ SV20 )
| ~ ( in @ SV20 @ SV24 ) )
| ( in @ SV16 @ SV24 ) )
= $true )
| ( ( in @ SV20 @ sK2_SY93 )
= $false )
| ( ( in @ SV16 @ sK2_SY93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(172,plain,
! [SV21: $i,SV17: $i] :
( ( ( ( SV17 = SV21 )
| ( in @ SV17 @ SV21 ) )
= $true )
| ( ( in @ SV21 @ SV17 )
= $true )
| ( ( in @ SV21 @ sK2_SY93 )
= $false )
| ( ( in @ SV17 @ sK2_SY93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(173,plain,
! [SV10: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV10 )
| ( ( sK8_SY122 @ SV10 )
= SV25 )
| ( in @ ( sK8_SY122 @ SV10 ) @ SV25 ) )
= $true )
| ( ( SV10 = emptyset )
= $true )
| ( ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(174,plain,
! [SV22: $i,SV18: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ SV14 @ SV18 )
| ~ ( in @ SV18 @ SV22 ) ) )
= $true )
| ( ( in @ SV14 @ SV22 )
= $true )
| ( ( in @ SV22 @ sK1_SX0 )
= $false )
| ( ( in @ SV18 @ sK1_SX0 )
= $false )
| ( ( in @ SV14 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(175,plain,
! [SV23: $i,SV6: $i] :
( ( ( ( sK7_SY120 @ SV6 )
= SV23 )
= $true )
| ( ( in @ ( sK7_SY120 @ SV6 ) @ SV23 )
= $true )
| ( ( in @ SV23 @ SV6 )
= $false )
| ( ( SV6 = emptyset )
= $true )
| ( ( in @ SV6 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(176,plain,
! [SV20: $i,SV16: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ sK2_SY93 ) )
= $true )
| ( ( ~ ~ ( ~ ( in @ SV16 @ SV20 )
| ~ ( in @ SV20 @ SV24 ) )
| ( in @ SV16 @ SV24 ) )
= $true )
| ( ( in @ SV20 @ sK2_SY93 )
= $false )
| ( ( in @ SV16 @ sK2_SY93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(177,plain,
! [SV21: $i,SV17: $i] :
( ( ( SV17 = SV21 )
= $true )
| ( ( in @ SV17 @ SV21 )
= $true )
| ( ( in @ SV21 @ SV17 )
= $true )
| ( ( in @ SV21 @ sK2_SY93 )
= $false )
| ( ( in @ SV17 @ sK2_SY93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(178,plain,
! [SV10: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV10 ) )
= $true )
| ( ( ( ( sK8_SY122 @ SV10 )
= SV25 )
| ( in @ ( sK8_SY122 @ SV10 ) @ SV25 ) )
= $true )
| ( ( SV10 = emptyset )
= $true )
| ( ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(179,plain,
! [SV22: $i,SV18: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ SV14 @ SV18 )
| ~ ( in @ SV18 @ SV22 ) ) )
= $false )
| ( ( in @ SV14 @ SV22 )
= $true )
| ( ( in @ SV22 @ sK1_SX0 )
= $false )
| ( ( in @ SV18 @ sK1_SX0 )
= $false )
| ( ( in @ SV14 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(180,plain,
! [SV20: $i,SV16: $i,SV24: $i] :
( ( ( in @ SV24 @ sK2_SY93 )
= $false )
| ( ( ~ ~ ( ~ ( in @ SV16 @ SV20 )
| ~ ( in @ SV20 @ SV24 ) )
| ( in @ SV16 @ SV24 ) )
= $true )
| ( ( in @ SV20 @ sK2_SY93 )
= $false )
| ( ( in @ SV16 @ sK2_SY93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(181,plain,
! [SV10: $i,SV25: $i] :
( ( ( in @ SV25 @ SV10 )
= $false )
| ( ( ( ( sK8_SY122 @ SV10 )
= SV25 )
| ( in @ ( sK8_SY122 @ SV10 ) @ SV25 ) )
= $true )
| ( ( SV10 = emptyset )
= $true )
| ( ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(182,plain,
! [SV22: $i,SV18: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV18 )
| ~ ( in @ SV18 @ SV22 ) )
= $true )
| ( ( in @ SV14 @ SV22 )
= $true )
| ( ( in @ SV22 @ sK1_SX0 )
= $false )
| ( ( in @ SV18 @ sK1_SX0 )
= $false )
| ( ( in @ SV14 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(183,plain,
! [SV24: $i,SV20: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( in @ SV16 @ SV20 )
| ~ ( in @ SV20 @ SV24 ) ) )
= $true )
| ( ( in @ SV16 @ SV24 )
= $true )
| ( ( in @ SV24 @ sK2_SY93 )
= $false )
| ( ( in @ SV20 @ sK2_SY93 )
= $false )
| ( ( in @ SV16 @ sK2_SY93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(184,plain,
! [SV25: $i,SV10: $i] :
( ( ( ( sK8_SY122 @ SV10 )
= SV25 )
= $true )
| ( ( in @ ( sK8_SY122 @ SV10 ) @ SV25 )
= $true )
| ( ( in @ SV25 @ SV10 )
= $false )
| ( ( SV10 = emptyset )
= $true )
| ( ( in @ SV10 @ ( powerset @ sK2_SY93 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(185,plain,
! [SV22: $i,SV18: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV18 ) )
= $true )
| ( ( ~ ( in @ SV18 @ SV22 ) )
= $true )
| ( ( in @ SV14 @ SV22 )
= $true )
| ( ( in @ SV22 @ sK1_SX0 )
= $false )
| ( ( in @ SV18 @ sK1_SX0 )
= $false )
| ( ( in @ SV14 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(186,plain,
! [SV24: $i,SV20: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ SV16 @ SV20 )
| ~ ( in @ SV20 @ SV24 ) ) )
= $false )
| ( ( in @ SV16 @ SV24 )
= $true )
| ( ( in @ SV24 @ sK2_SY93 )
= $false )
| ( ( in @ SV20 @ sK2_SY93 )
= $false )
| ( ( in @ SV16 @ sK2_SY93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(187,plain,
! [SV22: $i,SV18: $i,SV14: $i] :
( ( ( in @ SV14 @ SV18 )
= $false )
| ( ( ~ ( in @ SV18 @ SV22 ) )
= $true )
| ( ( in @ SV14 @ SV22 )
= $true )
| ( ( in @ SV22 @ sK1_SX0 )
= $false )
| ( ( in @ SV18 @ sK1_SX0 )
= $false )
| ( ( in @ SV14 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(188,plain,
! [SV24: $i,SV20: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV20 )
| ~ ( in @ SV20 @ SV24 ) )
= $true )
| ( ( in @ SV16 @ SV24 )
= $true )
| ( ( in @ SV24 @ sK2_SY93 )
= $false )
| ( ( in @ SV20 @ sK2_SY93 )
= $false )
| ( ( in @ SV16 @ sK2_SY93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(189,plain,
! [SV14: $i,SV22: $i,SV18: $i] :
( ( ( in @ SV18 @ SV22 )
= $false )
| ( ( in @ SV14 @ SV18 )
= $false )
| ( ( in @ SV14 @ SV22 )
= $true )
| ( ( in @ SV22 @ sK1_SX0 )
= $false )
| ( ( in @ SV18 @ sK1_SX0 )
= $false )
| ( ( in @ SV14 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(190,plain,
! [SV24: $i,SV20: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV20 ) )
= $true )
| ( ( ~ ( in @ SV20 @ SV24 ) )
= $true )
| ( ( in @ SV16 @ SV24 )
= $true )
| ( ( in @ SV24 @ sK2_SY93 )
= $false )
| ( ( in @ SV20 @ sK2_SY93 )
= $false )
| ( ( in @ SV16 @ sK2_SY93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(191,plain,
! [SV24: $i,SV20: $i,SV16: $i] :
( ( ( in @ SV16 @ SV20 )
= $false )
| ( ( ~ ( in @ SV20 @ SV24 ) )
= $true )
| ( ( in @ SV16 @ SV24 )
= $true )
| ( ( in @ SV24 @ sK2_SY93 )
= $false )
| ( ( in @ SV20 @ sK2_SY93 )
= $false )
| ( ( in @ SV16 @ sK2_SY93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(192,plain,
! [SV16: $i,SV24: $i,SV20: $i] :
( ( ( in @ SV20 @ SV24 )
= $false )
| ( ( in @ SV16 @ SV20 )
= $false )
| ( ( in @ SV16 @ SV24 )
= $true )
| ( ( in @ SV24 @ sK2_SY93 )
= $false )
| ( ( in @ SV20 @ sK2_SY93 )
= $false )
| ( ( in @ SV16 @ sK2_SY93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(193,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[36,192,189,184,177,175,167,163,150,133,115,105,97,96,88,73,53,43]) ).
thf(194,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU816^2 : 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
% 0.08/0.17 % Computer : n005.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 15:36:38 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.25
% 0.08/0.25 No.of.Axioms: 0
% 0.08/0.25
% 0.08/0.25 Length.of.Defs: 1442
% 0.08/0.25
% 0.08/0.25 Contains.Choice.Funs: false
% 0.08/0.25 .........
% 0.08/0.25
% 0.08/0.25 ********************************
% 0.08/0.25 * All subproblems solved! *
% 0.08/0.25 ********************************
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:193,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.25
% 0.08/0.25 %**** Beginning of derivation protocol ****
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25
% 0.08/0.25 %**** End of derivation protocol ****
% 0.08/0.25 %**** no. of clauses in derivation: 194 ****
% 0.08/0.25 %**** clause counter: 193 ****
% 0.08/0.25
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:193,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------