%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU819^2 : 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 : n012.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 10:49:01 AM UTC 2026
% Result : Theorem 0.07s 0.14s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 7
% Syntax : Number of formulae : 118 ( 28 unt; 0 typ; 6 def)
% Number of atoms : 1529 ( 413 equ; 0 cnn)
% Maximal formula atoms : 7 ( 12 avg)
% Number of connectives : 3309 ( 729 ~; 677 |; 30 &;1785 @)
% ( 0 <=>; 88 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 498 ( 5 ^; 488 !; 5 ?; 498 :)
% Comments :
%------------------------------------------------------------------------------
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_SY61,type,
sK2_SY61: $i ).
thf(tp_sK3_SY47,type,
sK3_SY47: $i > $i ).
thf(tp_sK4_SY62,type,
sK4_SY62: $i > $i ).
thf(tp_sK5_SY73,type,
sK5_SY73: $i > $i > $i ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionTransitive,type,
setunionTransitive: $o ).
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(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(setunionTransitive,definition,
( setunionTransitive
= ( ! [X: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( transitiveset @ Xx ) )
=> ( transitiveset @ ( setunion @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionTransitive) ).
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,
( setunionTransitive
=> ! [X: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ordinal @ Xx ) )
=> ( transitiveset @ ( setunion @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionOrdinalLem1) ).
thf(2,negated_conjecture,
( ( setunionTransitive
=> ! [X: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ordinal @ Xx ) )
=> ( transitiveset @ ( setunion @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY13: $i] :
( ! [SY14: $i] :
( ( in @ SY14 @ SY13 )
=> ! [SY15: $i] :
( ( in @ SY15 @ SY14 )
=> ( subset @ SY15 @ SY14 ) ) )
=> ! [SY16: $i] :
( ( in @ SY16 @ ( setunion @ SY13 ) )
=> ( subset @ SY16 @ ( setunion @ SY13 ) ) ) )
=> ! [SY0: $i] :
( ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ( ! [SY2: $i] :
( ( in @ SY2 @ SY1 )
=> ( subset @ SY2 @ SY1 ) )
& ! [SY3: $i] :
( ( in @ SY3 @ SY1 )
=> ! [SY4: $i] :
( ( in @ SY4 @ SY1 )
=> ! [SY5: $i] :
( ( in @ SY5 @ SY1 )
=> ( ( ( in @ SY3 @ SY4 )
& ( in @ SY4 @ SY5 ) )
=> ( in @ SY3 @ SY5 ) ) ) ) )
& ! [SY6: $i] :
( ( in @ SY6 @ SY1 )
=> ! [SY7: $i] :
( ( in @ SY7 @ SY1 )
=> ( ( SY6 = SY7 )
| ( in @ SY6 @ SY7 )
| ( in @ SY7 @ SY6 ) ) ) )
& ! [SY8: $i] :
( ( in @ SY8 @ SY1 )
=> ~ ( in @ SY8 @ SY8 ) )
& ! [SY9: $i] :
( ( in @ SY9 @ ( powerset @ SY1 ) )
=> ( ( SY9 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY9 )
& ! [Y: $i] :
( ( in @ Y @ SY9 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) ) )
=> ! [SY12: $i] :
( ( in @ SY12 @ ( setunion @ SY0 ) )
=> ( subset @ SY12 @ ( setunion @ SY0 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,nonempty,ordinal,setunionTransitive,stricttotalorderedByIn,transitiveset,wellorderedByIn]) ).
thf(4,plain,
( ( ! [SY13: $i] :
( ! [SY14: $i] :
( ( in @ SY14 @ SY13 )
=> ! [SY15: $i] :
( ( in @ SY15 @ SY14 )
=> ( subset @ SY15 @ SY14 ) ) )
=> ! [SY16: $i] :
( ( in @ SY16 @ ( setunion @ SY13 ) )
=> ( subset @ SY16 @ ( setunion @ SY13 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i] :
( ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ( ! [SY2: $i] :
( ( in @ SY2 @ SY1 )
=> ( subset @ SY2 @ SY1 ) )
& ! [SY3: $i] :
( ( in @ SY3 @ SY1 )
=> ! [SY4: $i] :
( ( in @ SY4 @ SY1 )
=> ! [SY5: $i] :
( ( in @ SY5 @ SY1 )
=> ( ( ( in @ SY3 @ SY4 )
& ( in @ SY4 @ SY5 ) )
=> ( in @ SY3 @ SY5 ) ) ) ) )
& ! [SY6: $i] :
( ( in @ SY6 @ SY1 )
=> ! [SY7: $i] :
( ( in @ SY7 @ SY1 )
=> ( ( SY6 = SY7 )
| ( in @ SY6 @ SY7 )
| ( in @ SY7 @ SY6 ) ) ) )
& ! [SY8: $i] :
( ( in @ SY8 @ SY1 )
=> ~ ( in @ SY8 @ SY8 ) )
& ! [SY9: $i] :
( ( in @ SY9 @ ( powerset @ SY1 ) )
=> ( ( SY9 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY9 )
& ! [Y: $i] :
( ( in @ Y @ SY9 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) ) )
=> ! [SY12: $i] :
( ( in @ SY12 @ ( setunion @ SY0 ) )
=> ( subset @ SY12 @ ( setunion @ SY0 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $i] :
( ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ( ! [SY2: $i] :
( ( in @ SY2 @ SY1 )
=> ( subset @ SY2 @ SY1 ) )
& ! [SY3: $i] :
( ( in @ SY3 @ SY1 )
=> ! [SY4: $i] :
( ( in @ SY4 @ SY1 )
=> ! [SY5: $i] :
( ( in @ SY5 @ SY1 )
=> ( ( ( in @ SY3 @ SY4 )
& ( in @ SY4 @ SY5 ) )
=> ( in @ SY3 @ SY5 ) ) ) ) )
& ! [SY6: $i] :
( ( in @ SY6 @ SY1 )
=> ! [SY7: $i] :
( ( in @ SY7 @ SY1 )
=> ( ( SY6 = SY7 )
| ( in @ SY6 @ SY7 )
| ( in @ SY7 @ SY6 ) ) ) )
& ! [SY8: $i] :
( ( in @ SY8 @ SY1 )
=> ~ ( in @ SY8 @ SY8 ) )
& ! [SY9: $i] :
( ( in @ SY9 @ ( powerset @ SY1 ) )
=> ( ( SY9 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY9 )
& ! [Y: $i] :
( ( in @ Y @ SY9 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) ) )
=> ! [SY12: $i] :
( ( in @ SY12 @ ( setunion @ SY0 ) )
=> ( subset @ SY12 @ ( setunion @ SY0 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY13: $i] :
( ! [SY14: $i] :
( ( in @ SY14 @ SY13 )
=> ! [SY15: $i] :
( ( in @ SY15 @ SY14 )
=> ( subset @ SY15 @ SY14 ) ) )
=> ! [SY16: $i] :
( ( in @ SY16 @ ( setunion @ SY13 ) )
=> ( subset @ SY16 @ ( setunion @ SY13 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ! [SY0: $i] :
( ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ( ! [SY2: $i] :
( ( in @ SY2 @ SY1 )
=> ( subset @ SY2 @ SY1 ) )
& ! [SY3: $i] :
( ( in @ SY3 @ SY1 )
=> ! [SY4: $i] :
( ( in @ SY4 @ SY1 )
=> ! [SY5: $i] :
( ( in @ SY5 @ SY1 )
=> ( ( ( in @ SY3 @ SY4 )
& ( in @ SY4 @ SY5 ) )
=> ( in @ SY3 @ SY5 ) ) ) ) )
& ! [SY6: $i] :
( ( in @ SY6 @ SY1 )
=> ! [SY7: $i] :
( ( in @ SY7 @ SY1 )
=> ( ( SY6 = SY7 )
| ( in @ SY6 @ SY7 )
| ( in @ SY7 @ SY6 ) ) ) )
& ! [SY8: $i] :
( ( in @ SY8 @ SY1 )
=> ~ ( in @ SY8 @ SY8 ) )
& ! [SY9: $i] :
( ( in @ SY9 @ ( powerset @ SY1 ) )
=> ( ( SY9 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY9 )
& ! [Y: $i] :
( ( in @ Y @ SY9 )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) ) ) ) ) ) )
=> ! [SY12: $i] :
( ( in @ SY12 @ ( setunion @ SY0 ) )
=> ( subset @ SY12 @ ( setunion @ SY0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ~ ( ~ ! [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 ) ) ) ) ) ) )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ( subset @ SX1 @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,nonempty,ordinal,setunionTransitive,stricttotalorderedByIn,transitiveset,wellorderedByIn]) ).
thf(10,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX1 ) ) )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ( subset @ SX1 @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,nonempty,ordinal,setunionTransitive,stricttotalorderedByIn,transitiveset,wellorderedByIn]) ).
thf(11,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ~ ( ~ ! [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 ) ) ) ) ) ) )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ( subset @ SX1 @ ( setunion @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ~ ! [SY47: $i] :
( ~ ( in @ SY47 @ SV1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SY47 )
| ( subset @ SX2 @ SY47 ) ) )
| ! [SY49: $i] :
( ~ ( in @ SY49 @ ( setunion @ SV1 ) )
| ( subset @ SY49 @ ( setunion @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ! [SY50: $i] :
( ~ ( in @ SY50 @ sK1_SX0 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY50 )
| ( subset @ SX2 @ SY50 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY50 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY50 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY50 )
| ~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX4 ) )
| ( in @ SX2 @ SX4 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY50 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY50 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY50 )
| ~ ( in @ SX2 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SY50 ) )
| ~ ( ( SX2 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) ) )
| ! [SY61: $i] :
( ~ ( in @ SY61 @ ( setunion @ sK1_SX0 ) )
| ( subset @ SY61 @ ( setunion @ sK1_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV1: $i] :
( ( ( ~ ! [SY47: $i] :
( ~ ( in @ SY47 @ SV1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SY47 )
| ( subset @ SX2 @ SY47 ) ) ) )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ ( setunion @ SV1 ) )
| ( subset @ SY49 @ ( setunion @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ! [SY50: $i] :
( ~ ( in @ SY50 @ sK1_SX0 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY50 )
| ( subset @ SX2 @ SY50 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY50 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY50 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY50 )
| ~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX4 ) )
| ( in @ SX2 @ SX4 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY50 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY50 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY50 )
| ~ ( in @ SX2 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SY50 ) )
| ~ ( ( SX2 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [SY61: $i] :
( ~ ( in @ SY61 @ ( setunion @ sK1_SX0 ) )
| ( subset @ SY61 @ ( setunion @ sK1_SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: $i] :
( ( ( ! [SY47: $i] :
( ~ ( in @ SY47 @ SV1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SY47 )
| ( subset @ SX2 @ SY47 ) ) ) )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ ( setunion @ SV1 ) )
| ( subset @ SY49 @ ( setunion @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( ! [SY50: $i] :
( ~ ( in @ SY50 @ sK1_SX0 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY50 )
| ( subset @ SX2 @ SY50 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY50 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY50 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY50 )
| ~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX4 ) )
| ( in @ SX2 @ SX4 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY50 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY50 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY50 )
| ~ ( in @ SX2 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SY50 ) )
| ~ ( ( SX2 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ( in @ sK2_SY61 @ ( setunion @ sK1_SX0 ) )
| ( subset @ sK2_SY61 @ ( setunion @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(20,plain,
! [SV1: $i] :
( ( ( ~ ( in @ ( sK3_SY47 @ SV1 ) @ SV1 )
| ! [SY62: $i] :
( ~ ( in @ SY62 @ ( sK3_SY47 @ SV1 ) )
| ( subset @ SY62 @ ( sK3_SY47 @ SV1 ) ) ) )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ ( setunion @ SV1 ) )
| ( subset @ SY49 @ ( setunion @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(21,plain,
! [SV2: $i] :
( ( ~ ( in @ SV2 @ sK1_SX0 )
| ~ ( ~ ! [SY63: $i] :
( ~ ( in @ SY63 @ SV2 )
| ( subset @ SY63 @ SV2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV2 )
| ! [SY65: $i] :
( ~ ( in @ SY65 @ SV2 )
| ! [SY66: $i] :
( ~ ( in @ SY66 @ SV2 )
| ~ ~ ( ~ ( in @ SY64 @ SY65 )
| ~ ( in @ SY65 @ SY66 ) )
| ( in @ SY64 @ SY66 ) ) ) )
| ~ ! [SY67: $i] :
( ~ ( in @ SY67 @ SV2 )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV2 )
| ( SY67 = SY68 )
| ( in @ SY67 @ SY68 )
| ( in @ SY68 @ SY67 ) ) ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SV2 )
| ~ ( in @ SY69 @ SY69 ) ) )
| ~ ! [SY70: $i] :
( ~ ( in @ SY70 @ ( powerset @ SV2 ) )
| ~ ( ( SY70 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY70 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY70 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ( in @ sK2_SY61 @ ( setunion @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( subset @ sK2_SY61 @ ( setunion @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(24,plain,
! [SV1: $i] :
( ( ( ~ ( in @ ( sK3_SY47 @ SV1 ) @ SV1 ) )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ ( setunion @ SV1 ) )
| ( subset @ SY49 @ ( setunion @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(25,plain,
! [SV1: $i] :
( ( ( ! [SY62: $i] :
( ~ ( in @ SY62 @ ( sK3_SY47 @ SV1 ) )
| ( subset @ SY62 @ ( sK3_SY47 @ SV1 ) ) ) )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ ( setunion @ SV1 ) )
| ( subset @ SY49 @ ( setunion @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(26,plain,
! [SV2: $i] :
( ( ( ~ ( in @ SV2 @ sK1_SX0 ) )
= $true )
| ( ( ~ ( ~ ! [SY63: $i] :
( ~ ( in @ SY63 @ SV2 )
| ( subset @ SY63 @ SV2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV2 )
| ! [SY65: $i] :
( ~ ( in @ SY65 @ SV2 )
| ! [SY66: $i] :
( ~ ( in @ SY66 @ SV2 )
| ~ ~ ( ~ ( in @ SY64 @ SY65 )
| ~ ( in @ SY65 @ SY66 ) )
| ( in @ SY64 @ SY66 ) ) ) )
| ~ ! [SY67: $i] :
( ~ ( in @ SY67 @ SV2 )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV2 )
| ( SY67 = SY68 )
| ( in @ SY67 @ SY68 )
| ( in @ SY68 @ SY67 ) ) ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SV2 )
| ~ ( in @ SY69 @ SY69 ) ) )
| ~ ! [SY70: $i] :
( ~ ( in @ SY70 @ ( powerset @ SV2 ) )
| ~ ( ( SY70 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY70 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY70 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(27,plain,
( ( in @ sK2_SY61 @ ( setunion @ sK1_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(28,plain,
! [SV1: $i] :
( ( ( in @ ( sK3_SY47 @ SV1 ) @ SV1 )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ ( setunion @ SV1 ) )
| ( subset @ SY49 @ ( setunion @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
! [SV1: $i] :
( ( ( ~ ( in @ ( sK4_SY62 @ SV1 ) @ ( sK3_SY47 @ SV1 ) )
| ( subset @ ( sK4_SY62 @ SV1 ) @ ( sK3_SY47 @ SV1 ) ) )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ ( setunion @ SV1 ) )
| ( subset @ SY49 @ ( setunion @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(30,plain,
! [SV2: $i] :
( ( ( in @ SV2 @ sK1_SX0 )
= $false )
| ( ( ~ ( ~ ! [SY63: $i] :
( ~ ( in @ SY63 @ SV2 )
| ( subset @ SY63 @ SV2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV2 )
| ! [SY65: $i] :
( ~ ( in @ SY65 @ SV2 )
| ! [SY66: $i] :
( ~ ( in @ SY66 @ SV2 )
| ~ ~ ( ~ ( in @ SY64 @ SY65 )
| ~ ( in @ SY65 @ SY66 ) )
| ( in @ SY64 @ SY66 ) ) ) )
| ~ ! [SY67: $i] :
( ~ ( in @ SY67 @ SV2 )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV2 )
| ( SY67 = SY68 )
| ( in @ SY67 @ SY68 )
| ( in @ SY68 @ SY67 ) ) ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SV2 )
| ~ ( in @ SY69 @ SY69 ) ) )
| ~ ! [SY70: $i] :
( ~ ( in @ SY70 @ ( powerset @ SV2 ) )
| ~ ( ( SY70 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY70 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY70 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ ( setunion @ SV1 ) )
| ( subset @ SV3 @ ( setunion @ SV1 ) ) )
= $true )
| ( ( in @ ( sK3_SY47 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: $i] :
( ( ( ~ ( in @ ( sK4_SY62 @ SV1 ) @ ( sK3_SY47 @ SV1 ) ) )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ ( setunion @ SV1 ) )
| ( subset @ SY49 @ ( setunion @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV1: $i] :
( ( ( subset @ ( sK4_SY62 @ SV1 ) @ ( sK3_SY47 @ SV1 ) )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ ( setunion @ SV1 ) )
| ( subset @ SY49 @ ( setunion @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV2: $i] :
( ( ( ~ ! [SY63: $i] :
( ~ ( in @ SY63 @ SV2 )
| ( subset @ SY63 @ SV2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV2 )
| ! [SY65: $i] :
( ~ ( in @ SY65 @ SV2 )
| ! [SY66: $i] :
( ~ ( in @ SY66 @ SV2 )
| ~ ~ ( ~ ( in @ SY64 @ SY65 )
| ~ ( in @ SY65 @ SY66 ) )
| ( in @ SY64 @ SY66 ) ) ) )
| ~ ! [SY67: $i] :
( ~ ( in @ SY67 @ SV2 )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV2 )
| ( SY67 = SY68 )
| ( in @ SY67 @ SY68 )
| ( in @ SY68 @ SY67 ) ) ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SV2 )
| ~ ( in @ SY69 @ SY69 ) ) )
| ~ ! [SY70: $i] :
( ~ ( in @ SY70 @ ( powerset @ SV2 ) )
| ~ ( ( SY70 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY70 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY70 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ ( setunion @ SV1 ) ) )
= $true )
| ( ( subset @ SV3 @ ( setunion @ SV1 ) )
= $true )
| ( ( in @ ( sK3_SY47 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV1: $i] :
( ( ( in @ ( sK4_SY62 @ SV1 ) @ ( sK3_SY47 @ SV1 ) )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ ( setunion @ SV1 ) )
| ( subset @ SY49 @ ( setunion @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ ( setunion @ SV1 ) )
| ( subset @ SV4 @ ( setunion @ SV1 ) ) )
= $true )
| ( ( subset @ ( sK4_SY62 @ SV1 ) @ ( sK3_SY47 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV2: $i] :
( ( ( ~ ! [SY63: $i] :
( ~ ( in @ SY63 @ SV2 )
| ( subset @ SY63 @ SV2 ) ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(39,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV2 )
| ! [SY65: $i] :
( ~ ( in @ SY65 @ SV2 )
| ! [SY66: $i] :
( ~ ( in @ SY66 @ SV2 )
| ~ ~ ( ~ ( in @ SY64 @ SY65 )
| ~ ( in @ SY65 @ SY66 ) )
| ( in @ SY64 @ SY66 ) ) ) )
| ~ ! [SY67: $i] :
( ~ ( in @ SY67 @ SV2 )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV2 )
| ( SY67 = SY68 )
| ( in @ SY67 @ SY68 )
| ( in @ SY68 @ SY67 ) ) ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SV2 )
| ~ ( in @ SY69 @ SY69 ) ) )
| ~ ! [SY70: $i] :
( ~ ( in @ SY70 @ ( powerset @ SV2 ) )
| ~ ( ( SY70 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY70 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY70 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(40,plain,
! [SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ ( setunion @ SV1 ) )
= $false )
| ( ( subset @ SV3 @ ( setunion @ SV1 ) )
= $true )
| ( ( in @ ( sK3_SY47 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV1: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ ( setunion @ SV1 ) )
| ( subset @ SV5 @ ( setunion @ SV1 ) ) )
= $true )
| ( ( in @ ( sK4_SY62 @ SV1 ) @ ( sK3_SY47 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ ( setunion @ SV1 ) ) )
= $true )
| ( ( subset @ SV4 @ ( setunion @ SV1 ) )
= $true )
| ( ( subset @ ( sK4_SY62 @ SV1 ) @ ( sK3_SY47 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV2: $i] :
( ( ( ! [SY63: $i] :
( ~ ( in @ SY63 @ SV2 )
| ( subset @ SY63 @ SV2 ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(44,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV2 )
| ! [SY65: $i] :
( ~ ( in @ SY65 @ SV2 )
| ! [SY66: $i] :
( ~ ( in @ SY66 @ SV2 )
| ~ ~ ( ~ ( in @ SY64 @ SY65 )
| ~ ( in @ SY65 @ SY66 ) )
| ( in @ SY64 @ SY66 ) ) ) )
| ~ ! [SY67: $i] :
( ~ ( in @ SY67 @ SV2 )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV2 )
| ( SY67 = SY68 )
| ( in @ SY67 @ SY68 )
| ( in @ SY68 @ SY67 ) ) ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SV2 )
| ~ ( in @ SY69 @ SY69 ) ) )
| ~ ! [SY70: $i] :
( ~ ( in @ SY70 @ ( powerset @ SV2 ) )
| ~ ( ( SY70 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY70 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY70 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(45,plain,
! [SV1: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ ( setunion @ SV1 ) ) )
= $true )
| ( ( subset @ SV5 @ ( setunion @ SV1 ) )
= $true )
| ( ( in @ ( sK4_SY62 @ SV1 ) @ ( sK3_SY47 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV1: $i,SV4: $i] :
( ( ( in @ SV4 @ ( setunion @ SV1 ) )
= $false )
| ( ( subset @ SV4 @ ( setunion @ SV1 ) )
= $true )
| ( ( subset @ ( sK4_SY62 @ SV1 ) @ ( sK3_SY47 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV2 )
| ( subset @ SV6 @ SV2 ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV2 )
| ! [SY65: $i] :
( ~ ( in @ SY65 @ SV2 )
| ! [SY66: $i] :
( ~ ( in @ SY66 @ SV2 )
| ~ ~ ( ~ ( in @ SY64 @ SY65 )
| ~ ( in @ SY65 @ SY66 ) )
| ( in @ SY64 @ SY66 ) ) ) )
| ~ ! [SY67: $i] :
( ~ ( in @ SY67 @ SV2 )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV2 )
| ( SY67 = SY68 )
| ( in @ SY67 @ SY68 )
| ( in @ SY68 @ SY67 ) ) ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SV2 )
| ~ ( in @ SY69 @ SY69 ) ) )
| ~ ! [SY70: $i] :
( ~ ( in @ SY70 @ ( powerset @ SV2 ) )
| ~ ( ( SY70 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY70 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY70 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV1: $i,SV5: $i] :
( ( ( in @ SV5 @ ( setunion @ SV1 ) )
= $false )
| ( ( subset @ SV5 @ ( setunion @ SV1 ) )
= $true )
| ( ( in @ ( sK4_SY62 @ SV1 ) @ ( sK3_SY47 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV2 ) )
= $true )
| ( ( subset @ SV6 @ SV2 )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV2 )
| ! [SY65: $i] :
( ~ ( in @ SY65 @ SV2 )
| ! [SY66: $i] :
( ~ ( in @ SY66 @ SV2 )
| ~ ~ ( ~ ( in @ SY64 @ SY65 )
| ~ ( in @ SY65 @ SY66 ) )
| ( in @ SY64 @ SY66 ) ) ) )
| ~ ! [SY67: $i] :
( ~ ( in @ SY67 @ SV2 )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV2 )
| ( SY67 = SY68 )
| ( in @ SY67 @ SY68 )
| ( in @ SY68 @ SY67 ) ) ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SV2 )
| ~ ( in @ SY69 @ SY69 ) ) ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(52,plain,
! [SV2: $i] :
( ( ( ~ ! [SY70: $i] :
( ~ ( in @ SY70 @ ( powerset @ SV2 ) )
| ~ ( ( SY70 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY70 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY70 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(53,plain,
! [SV2: $i,SV6: $i] :
( ( ( in @ SV6 @ SV2 )
= $false )
| ( ( subset @ SV6 @ SV2 )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV2 )
| ! [SY65: $i] :
( ~ ( in @ SY65 @ SV2 )
| ! [SY66: $i] :
( ~ ( in @ SY66 @ SV2 )
| ~ ~ ( ~ ( in @ SY64 @ SY65 )
| ~ ( in @ SY65 @ SY66 ) )
| ( in @ SY64 @ SY66 ) ) ) )
| ~ ! [SY67: $i] :
( ~ ( in @ SY67 @ SV2 )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV2 )
| ( SY67 = SY68 )
| ( in @ SY67 @ SY68 )
| ( in @ SY68 @ SY67 ) ) ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SV2 )
| ~ ( in @ SY69 @ SY69 ) ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(55,plain,
! [SV2: $i] :
( ( ( ! [SY70: $i] :
( ~ ( in @ SY70 @ ( powerset @ SV2 ) )
| ~ ( ( SY70 != emptyset ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SY70 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY70 )
| ( SX3 = SX4 )
| ( in @ SX3 @ SX4 ) ) ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(56,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV2 )
| ! [SY65: $i] :
( ~ ( in @ SY65 @ SV2 )
| ! [SY66: $i] :
( ~ ( in @ SY66 @ SV2 )
| ~ ~ ( ~ ( in @ SY64 @ SY65 )
| ~ ( in @ SY65 @ SY66 ) )
| ( in @ SY64 @ SY66 ) ) ) )
| ~ ! [SY67: $i] :
( ~ ( in @ SY67 @ SV2 )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV2 )
| ( SY67 = SY68 )
| ( in @ SY67 @ SY68 )
| ( in @ SY68 @ SY67 ) ) ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SV2 )
| ~ ( in @ SY69 @ SY69 ) ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( powerset @ SV2 ) )
| ~ ( ( SV7 != emptyset ) )
| ~ ! [SY73: $i] :
~ ~ ( ~ ( in @ SY73 @ SV7 )
| ~ ! [SY74: $i] :
( ~ ( in @ SY74 @ SV7 )
| ( SY73 = SY74 )
| ( in @ SY73 @ SY74 ) ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV2 )
| ! [SY65: $i] :
( ~ ( in @ SY65 @ SV2 )
| ! [SY66: $i] :
( ~ ( in @ SY66 @ SV2 )
| ~ ~ ( ~ ( in @ SY64 @ SY65 )
| ~ ( in @ SY65 @ SY66 ) )
| ( in @ SY64 @ SY66 ) ) ) )
| ~ ! [SY67: $i] :
( ~ ( in @ SY67 @ SV2 )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV2 )
| ( SY67 = SY68 )
| ( in @ SY67 @ SY68 )
| ( in @ SY68 @ SY67 ) ) ) ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(59,plain,
! [SV2: $i] :
( ( ( ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SV2 )
| ~ ( in @ SY69 @ SY69 ) ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(60,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( powerset @ SV2 ) ) )
= $true )
| ( ( ~ ( ( SV7 != emptyset ) )
| ~ ! [SY73: $i] :
~ ~ ( ~ ( in @ SY73 @ SV7 )
| ~ ! [SY74: $i] :
( ~ ( in @ SY74 @ SV7 )
| ( SY73 = SY74 )
| ( in @ SY73 @ SY74 ) ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(61,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV2 )
| ! [SY65: $i] :
( ~ ( in @ SY65 @ SV2 )
| ! [SY66: $i] :
( ~ ( in @ SY66 @ SV2 )
| ~ ~ ( ~ ( in @ SY64 @ SY65 )
| ~ ( in @ SY65 @ SY66 ) )
| ( in @ SY64 @ SY66 ) ) ) )
| ~ ! [SY67: $i] :
( ~ ( in @ SY67 @ SV2 )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV2 )
| ( SY67 = SY68 )
| ( in @ SY67 @ SY68 )
| ( in @ SY68 @ SY67 ) ) ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(62,plain,
! [SV2: $i] :
( ( ( ! [SY69: $i] :
( ~ ( in @ SY69 @ SV2 )
| ~ ( in @ SY69 @ SY69 ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(63,plain,
! [SV2: $i,SV7: $i] :
( ( ( in @ SV7 @ ( powerset @ SV2 ) )
= $false )
| ( ( ~ ( ( SV7 != emptyset ) )
| ~ ! [SY73: $i] :
~ ~ ( ~ ( in @ SY73 @ SV7 )
| ~ ! [SY74: $i] :
( ~ ( in @ SY74 @ SV7 )
| ( SY73 = SY74 )
| ( in @ SY73 @ SY74 ) ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV2: $i] :
( ( ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV2 )
| ! [SY65: $i] :
( ~ ( in @ SY65 @ SV2 )
| ! [SY66: $i] :
( ~ ( in @ SY66 @ SV2 )
| ~ ~ ( ~ ( in @ SY64 @ SY65 )
| ~ ( in @ SY65 @ SY66 ) )
| ( in @ SY64 @ SY66 ) ) ) )
| ~ ! [SY67: $i] :
( ~ ( in @ SY67 @ SV2 )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV2 )
| ( SY67 = SY68 )
| ( in @ SY67 @ SY68 )
| ( in @ SY68 @ SY67 ) ) ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV2 )
| ~ ( in @ SV8 @ SV8 ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( ( SV7 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY73: $i] :
~ ~ ( ~ ( in @ SY73 @ SV7 )
| ~ ! [SY74: $i] :
( ~ ( in @ SY74 @ SV7 )
| ( SY73 = SY74 )
| ( in @ SY73 @ SY74 ) ) ) )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(67,plain,
! [SV2: $i] :
( ( ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV2 )
| ! [SY65: $i] :
( ~ ( in @ SY65 @ SV2 )
| ! [SY66: $i] :
( ~ ( in @ SY66 @ SV2 )
| ~ ~ ( ~ ( in @ SY64 @ SY65 )
| ~ ( in @ SY65 @ SY66 ) )
| ( in @ SY64 @ SY66 ) ) ) ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(68,plain,
! [SV2: $i] :
( ( ( ~ ! [SY67: $i] :
( ~ ( in @ SY67 @ SV2 )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV2 )
| ( SY67 = SY68 )
| ( in @ SY67 @ SY68 )
| ( in @ SY68 @ SY67 ) ) ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(69,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV2 ) )
= $true )
| ( ( ~ ( in @ SV8 @ SV8 ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV2: $i,SV7: $i] :
( ( ( SV7 != emptyset )
= $false )
| ( ( ~ ! [SY73: $i] :
~ ~ ( ~ ( in @ SY73 @ SV7 )
| ~ ! [SY74: $i] :
( ~ ( in @ SY74 @ SV7 )
| ( SY73 = SY74 )
| ( in @ SY73 @ SY74 ) ) ) )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV2: $i] :
( ( ( ! [SY64: $i] :
( ~ ( in @ SY64 @ SV2 )
| ! [SY65: $i] :
( ~ ( in @ SY65 @ SV2 )
| ! [SY66: $i] :
( ~ ( in @ SY66 @ SV2 )
| ~ ~ ( ~ ( in @ SY64 @ SY65 )
| ~ ( in @ SY65 @ SY66 ) )
| ( in @ SY64 @ SY66 ) ) ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(72,plain,
! [SV2: $i] :
( ( ( ! [SY67: $i] :
( ~ ( in @ SY67 @ SV2 )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ SV2 )
| ( SY67 = SY68 )
| ( in @ SY67 @ SY68 )
| ( in @ SY68 @ SY67 ) ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(73,plain,
! [SV2: $i,SV8: $i] :
( ( ( in @ SV8 @ SV2 )
= $false )
| ( ( ~ ( in @ SV8 @ SV8 ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(74,plain,
! [SV2: $i,SV7: $i] :
( ( ( SV7 = emptyset )
= $true )
| ( ( ~ ! [SY73: $i] :
~ ~ ( ~ ( in @ SY73 @ SV7 )
| ~ ! [SY74: $i] :
( ~ ( in @ SY74 @ SV7 )
| ( SY73 = SY74 )
| ( in @ SY73 @ SY74 ) ) ) )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(75,plain,
! [SV2: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV2 )
| ! [SY75: $i] :
( ~ ( in @ SY75 @ SV2 )
| ! [SY76: $i] :
( ~ ( in @ SY76 @ SV2 )
| ~ ~ ( ~ ( in @ SV9 @ SY75 )
| ~ ( in @ SY75 @ SY76 ) )
| ( in @ SV9 @ SY76 ) ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV2: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV2 )
| ! [SY77: $i] :
( ~ ( in @ SY77 @ SV2 )
| ( SV10 = SY77 )
| ( in @ SV10 @ SY77 )
| ( in @ SY77 @ SV10 ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV2: $i,SV8: $i] :
( ( ( in @ SV8 @ SV8 )
= $false )
| ( ( in @ SV8 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV2: $i,SV7: $i] :
( ( ( ! [SY73: $i] :
~ ~ ( ~ ( in @ SY73 @ SV7 )
| ~ ! [SY74: $i] :
( ~ ( in @ SY74 @ SV7 )
| ( SY73 = SY74 )
| ( in @ SY73 @ SY74 ) ) ) )
= $false )
| ( ( SV7 = emptyset )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV2: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV2 ) )
= $true )
| ( ( ! [SY75: $i] :
( ~ ( in @ SY75 @ SV2 )
| ! [SY76: $i] :
( ~ ( in @ SY76 @ SV2 )
| ~ ~ ( ~ ( in @ SV9 @ SY75 )
| ~ ( in @ SY75 @ SY76 ) )
| ( in @ SV9 @ SY76 ) ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV2: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV2 ) )
= $true )
| ( ( ! [SY77: $i] :
( ~ ( in @ SY77 @ SV2 )
| ( SV10 = SY77 )
| ( in @ SV10 @ SY77 )
| ( in @ SY77 @ SV10 ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY73 @ SV2 @ SV7 ) @ SV7 )
| ~ ! [SY78: $i] :
( ~ ( in @ SY78 @ SV7 )
| ( ( sK5_SY73 @ SV2 @ SV7 )
= SY78 )
| ( in @ ( sK5_SY73 @ SV2 @ SV7 ) @ SY78 ) ) ) )
= $false )
| ( ( SV7 = emptyset )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[78]) ).
thf(82,plain,
! [SV2: $i,SV9: $i] :
( ( ( in @ SV9 @ SV2 )
= $false )
| ( ( ! [SY75: $i] :
( ~ ( in @ SY75 @ SV2 )
| ! [SY76: $i] :
( ~ ( in @ SY76 @ SV2 )
| ~ ~ ( ~ ( in @ SV9 @ SY75 )
| ~ ( in @ SY75 @ SY76 ) )
| ( in @ SV9 @ SY76 ) ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV2: $i,SV10: $i] :
( ( ( in @ SV10 @ SV2 )
= $false )
| ( ( ! [SY77: $i] :
( ~ ( in @ SY77 @ SV2 )
| ( SV10 = SY77 )
| ( in @ SV10 @ SY77 )
| ( in @ SY77 @ SV10 ) ) )
= $true )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(84,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY73 @ SV2 @ SV7 ) @ SV7 )
| ~ ! [SY78: $i] :
( ~ ( in @ SY78 @ SV7 )
| ( ( sK5_SY73 @ SV2 @ SV7 )
= SY78 )
| ( in @ ( sK5_SY73 @ SV2 @ SV7 ) @ SY78 ) ) ) )
= $true )
| ( ( SV7 = emptyset )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(85,plain,
! [SV9: $i,SV2: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV2 )
| ! [SY79: $i] :
( ~ ( in @ SY79 @ SV2 )
| ~ ~ ( ~ ( in @ SV9 @ SV11 )
| ~ ( in @ SV11 @ SY79 ) )
| ( in @ SV9 @ SY79 ) ) )
= $true )
| ( ( in @ SV9 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(86,plain,
! [SV10: $i,SV2: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV2 )
| ( SV10 = SV12 )
| ( in @ SV10 @ SV12 )
| ( in @ SV12 @ SV10 ) )
= $true )
| ( ( in @ SV10 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(87,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK5_SY73 @ SV2 @ SV7 ) @ SV7 )
| ~ ! [SY78: $i] :
( ~ ( in @ SY78 @ SV7 )
| ( ( sK5_SY73 @ SV2 @ SV7 )
= SY78 )
| ( in @ ( sK5_SY73 @ SV2 @ SV7 ) @ SY78 ) ) )
= $false )
| ( ( SV7 = emptyset )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(88,plain,
! [SV9: $i,SV2: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV2 ) )
= $true )
| ( ( ! [SY79: $i] :
( ~ ( in @ SY79 @ SV2 )
| ~ ~ ( ~ ( in @ SV9 @ SV11 )
| ~ ( in @ SV11 @ SY79 ) )
| ( in @ SV9 @ SY79 ) ) )
= $true )
| ( ( in @ SV9 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(89,plain,
! [SV10: $i,SV2: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV2 ) )
= $true )
| ( ( ( SV10 = SV12 )
| ( in @ SV10 @ SV12 )
| ( in @ SV12 @ SV10 ) )
= $true )
| ( ( in @ SV10 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(90,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK5_SY73 @ SV2 @ SV7 ) @ SV7 ) )
= $false )
| ( ( SV7 = emptyset )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(91,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ! [SY78: $i] :
( ~ ( in @ SY78 @ SV7 )
| ( ( sK5_SY73 @ SV2 @ SV7 )
= SY78 )
| ( in @ ( sK5_SY73 @ SV2 @ SV7 ) @ SY78 ) ) )
= $false )
| ( ( SV7 = emptyset )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(92,plain,
! [SV9: $i,SV2: $i,SV11: $i] :
( ( ( in @ SV11 @ SV2 )
= $false )
| ( ( ! [SY79: $i] :
( ~ ( in @ SY79 @ SV2 )
| ~ ~ ( ~ ( in @ SV9 @ SV11 )
| ~ ( in @ SV11 @ SY79 ) )
| ( in @ SV9 @ SY79 ) ) )
= $true )
| ( ( in @ SV9 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(93,plain,
! [SV10: $i,SV2: $i,SV12: $i] :
( ( ( in @ SV12 @ SV2 )
= $false )
| ( ( ( SV10 = SV12 )
| ( in @ SV10 @ SV12 )
| ( in @ SV12 @ SV10 ) )
= $true )
| ( ( in @ SV10 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(94,plain,
! [SV7: $i,SV2: $i] :
( ( ( in @ ( sK5_SY73 @ SV2 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7 = emptyset )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(95,plain,
! [SV2: $i,SV7: $i] :
( ( ( ! [SY78: $i] :
( ~ ( in @ SY78 @ SV7 )
| ( ( sK5_SY73 @ SV2 @ SV7 )
= SY78 )
| ( in @ ( sK5_SY73 @ SV2 @ SV7 ) @ SY78 ) ) )
= $true )
| ( ( SV7 = emptyset )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(96,plain,
! [SV11: $i,SV9: $i,SV2: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV2 )
| ~ ~ ( ~ ( in @ SV9 @ SV11 )
| ~ ( in @ SV11 @ SV13 ) )
| ( in @ SV9 @ SV13 ) )
= $true )
| ( ( in @ SV11 @ SV2 )
= $false )
| ( ( in @ SV9 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(97,plain,
! [SV2: $i,SV12: $i,SV10: $i] :
( ( ( ( SV10 = SV12 )
| ( in @ SV10 @ SV12 ) )
= $true )
| ( ( in @ SV12 @ SV10 )
= $true )
| ( ( in @ SV12 @ SV2 )
= $false )
| ( ( in @ SV10 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(98,plain,
! [SV2: $i,SV7: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV7 )
| ( ( sK5_SY73 @ SV2 @ SV7 )
= SV14 )
| ( in @ ( sK5_SY73 @ SV2 @ SV7 ) @ SV14 ) )
= $true )
| ( ( SV7 = emptyset )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(99,plain,
! [SV11: $i,SV9: $i,SV2: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV2 ) )
= $true )
| ( ( ~ ~ ( ~ ( in @ SV9 @ SV11 )
| ~ ( in @ SV11 @ SV13 ) )
| ( in @ SV9 @ SV13 ) )
= $true )
| ( ( in @ SV11 @ SV2 )
= $false )
| ( ( in @ SV9 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(100,plain,
! [SV2: $i,SV12: $i,SV10: $i] :
( ( ( SV10 = SV12 )
= $true )
| ( ( in @ SV10 @ SV12 )
= $true )
| ( ( in @ SV12 @ SV10 )
= $true )
| ( ( in @ SV12 @ SV2 )
= $false )
| ( ( in @ SV10 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(101,plain,
! [SV2: $i,SV7: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV7 ) )
= $true )
| ( ( ( ( sK5_SY73 @ SV2 @ SV7 )
= SV14 )
| ( in @ ( sK5_SY73 @ SV2 @ SV7 ) @ SV14 ) )
= $true )
| ( ( SV7 = emptyset )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(102,plain,
! [SV11: $i,SV9: $i,SV2: $i,SV13: $i] :
( ( ( in @ SV13 @ SV2 )
= $false )
| ( ( ~ ~ ( ~ ( in @ SV9 @ SV11 )
| ~ ( in @ SV11 @ SV13 ) )
| ( in @ SV9 @ SV13 ) )
= $true )
| ( ( in @ SV11 @ SV2 )
= $false )
| ( ( in @ SV9 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(103,plain,
! [SV2: $i,SV7: $i,SV14: $i] :
( ( ( in @ SV14 @ SV7 )
= $false )
| ( ( ( ( sK5_SY73 @ SV2 @ SV7 )
= SV14 )
| ( in @ ( sK5_SY73 @ SV2 @ SV7 ) @ SV14 ) )
= $true )
| ( ( SV7 = emptyset )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(104,plain,
! [SV2: $i,SV13: $i,SV11: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( in @ SV9 @ SV11 )
| ~ ( in @ SV11 @ SV13 ) ) )
= $true )
| ( ( in @ SV9 @ SV13 )
= $true )
| ( ( in @ SV13 @ SV2 )
= $false )
| ( ( in @ SV11 @ SV2 )
= $false )
| ( ( in @ SV9 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(105,plain,
! [SV14: $i,SV7: $i,SV2: $i] :
( ( ( ( sK5_SY73 @ SV2 @ SV7 )
= SV14 )
= $true )
| ( ( in @ ( sK5_SY73 @ SV2 @ SV7 ) @ SV14 )
= $true )
| ( ( in @ SV14 @ SV7 )
= $false )
| ( ( SV7 = emptyset )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(106,plain,
! [SV2: $i,SV13: $i,SV11: $i,SV9: $i] :
( ( ( ~ ( ~ ( in @ SV9 @ SV11 )
| ~ ( in @ SV11 @ SV13 ) ) )
= $false )
| ( ( in @ SV9 @ SV13 )
= $true )
| ( ( in @ SV13 @ SV2 )
= $false )
| ( ( in @ SV11 @ SV2 )
= $false )
| ( ( in @ SV9 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(107,plain,
! [SV2: $i,SV13: $i,SV11: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV11 )
| ~ ( in @ SV11 @ SV13 ) )
= $true )
| ( ( in @ SV9 @ SV13 )
= $true )
| ( ( in @ SV13 @ SV2 )
= $false )
| ( ( in @ SV11 @ SV2 )
= $false )
| ( ( in @ SV9 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(108,plain,
! [SV2: $i,SV13: $i,SV11: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV11 ) )
= $true )
| ( ( ~ ( in @ SV11 @ SV13 ) )
= $true )
| ( ( in @ SV9 @ SV13 )
= $true )
| ( ( in @ SV13 @ SV2 )
= $false )
| ( ( in @ SV11 @ SV2 )
= $false )
| ( ( in @ SV9 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(109,plain,
! [SV2: $i,SV13: $i,SV11: $i,SV9: $i] :
( ( ( in @ SV9 @ SV11 )
= $false )
| ( ( ~ ( in @ SV11 @ SV13 ) )
= $true )
| ( ( in @ SV9 @ SV13 )
= $true )
| ( ( in @ SV13 @ SV2 )
= $false )
| ( ( in @ SV11 @ SV2 )
= $false )
| ( ( in @ SV9 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(110,plain,
! [SV2: $i,SV9: $i,SV13: $i,SV11: $i] :
( ( ( in @ SV11 @ SV13 )
= $false )
| ( ( in @ SV9 @ SV11 )
= $false )
| ( ( in @ SV9 @ SV13 )
= $true )
| ( ( in @ SV13 @ SV2 )
= $false )
| ( ( in @ SV11 @ SV2 )
= $false )
| ( ( in @ SV9 @ SV2 )
= $false )
| ( ( in @ SV2 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(111,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,110,105,100,94,77,53,49,46,40,27]) ).
thf(112,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU819^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 15:36:24 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.14
% 0.07/0.14 No.of.Axioms: 0
% 0.07/0.14
% 0.07/0.14 Length.of.Defs: 1436
% 0.07/0.14
% 0.07/0.14 Contains.Choice.Funs: false
% 0.07/0.14 .....
% 0.07/0.14
% 0.07/0.14 ********************************
% 0.07/0.14 * All subproblems solved! *
% 0.07/0.14 ********************************
% 0.07/0.14 % 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:111,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.14
% 0.07/0.14 %**** Beginning of derivation protocol ****
% 0.07/0.14 % SZS output start CNFRefutation
% See solution above
% 0.07/0.14
% 0.07/0.14 %**** End of derivation protocol ****
% 0.07/0.14 %**** no. of clauses in derivation: 112 ****
% 0.07/0.14 %**** clause counter: 111 ****
% 0.07/0.14
% 0.07/0.14 % 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:111,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------