%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU817^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 10:48:57 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 7
% Syntax : Number of formulae : 106 ( 58 unt; 0 typ; 6 def)
% Number of atoms : 1145 ( 303 equ; 0 cnn)
% Maximal formula atoms : 6 ( 10 avg)
% Number of connectives : 2547 ( 609 ~; 511 |; 30 &;1313 @)
% ( 0 <=>; 84 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 369 ( 5 ^; 359 !; 5 ?; 369 :)
% 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_SY41,type,
sK2_SY41: $i ).
thf(tp_sK3_SY44,type,
sK3_SY44: $i ).
thf(tp_sK4_SY45,type,
sK4_SY45: $i > $i ).
thf(tp_stricttotalorderedByIn,type,
stricttotalorderedByIn: $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subsetE,type,
subsetE: $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/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(ordinal,definition,
( ordinal
= ( ^ [Xx: $i] :
( ( transitiveset @ Xx )
& ( wellorderedByIn @ Xx ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',stricttotalorderedByIn) ).
thf(subsetE,definition,
( subsetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(transitiveset,definition,
( transitiveset
= ( ^ [A: $i] :
! [X: $i] :
( ( in @ X @ A )
=> ( subset @ X @ A ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',wellorderedByIn) ).
thf(1,conjecture,
( subsetE
=> ! [X: $i] :
( ( ordinal @ X )
=> ! [Xx: $i,A: $i] :
( ( in @ A @ X )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinalTransSet) ).
thf(2,negated_conjecture,
( ( subsetE
=> ! [X: $i] :
( ( ordinal @ X )
=> ! [Xx: $i,A: $i] :
( ( in @ A @ X )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ X ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ! [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 ) ) ) ) ) ) )
=> ! [Xx: $i,A: $i] :
( ( in @ A @ SY0 )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ SY0 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,nonempty,ordinal,stricttotalorderedByIn,subsetE,transitiveset,wellorderedByIn]) ).
thf(4,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $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 ) ) ) ) ) ) )
=> ! [Xx: $i,A: $i] :
( ( in @ A @ SY0 )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ SY0 ) ) ) ) )
= $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 ) ) ) ) ) ) )
=> ! [Xx: $i,A: $i] :
( ( in @ A @ SY0 )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ SY0 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $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 ) ) ) ) ) ) )
=> ! [Xx: $i,A: $i] :
( ( in @ A @ SY0 )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ SY0 ) ) ) ) )
= $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 @ SX0 )
| ~ ( in @ SX1 @ SX2 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,nonempty,ordinal,stricttotalorderedByIn,subsetE,transitiveset,wellorderedByIn]) ).
thf(10,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,nonempty,ordinal,stricttotalorderedByIn,subsetE,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 @ SX0 )
| ~ ( in @ SX1 @ SX2 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ( subset @ SV1 @ SY29 )
| ~ ( in @ SY30 @ SV1 )
| ( in @ SY30 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ~ ( ~ ! [SY31: $i] :
( ~ ( in @ SY31 @ sK1_SX0 )
| ( subset @ SY31 @ sK1_SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ sK1_SX0 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY32 @ SY33 )
| ~ ( in @ SY33 @ SY34 ) )
| ( in @ SY32 @ SY34 ) ) ) )
| ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SX0 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ( SY35 = SY36 )
| ( in @ SY35 @ SY36 )
| ( in @ SY36 @ SY35 ) ) ) )
| ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ sK1_SX0 )
| ~ ( in @ SY37 @ SY37 ) ) )
| ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY38 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY38 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) ) )
| ! [SY41: $i,SY42: $i] :
( ~ ( in @ SY42 @ sK1_SX0 )
| ~ ( in @ SY41 @ SY42 )
| ( in @ SY41 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY43: $i] :
( ~ ( subset @ SV1 @ SV2 )
| ~ ( in @ SY43 @ SV1 )
| ( in @ SY43 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ~ ( ~ ! [SY31: $i] :
( ~ ( in @ SY31 @ sK1_SX0 )
| ( subset @ SY31 @ sK1_SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ sK1_SX0 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY32 @ SY33 )
| ~ ( in @ SY33 @ SY34 ) )
| ( in @ SY32 @ SY34 ) ) ) )
| ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SX0 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ( SY35 = SY36 )
| ( in @ SY35 @ SY36 )
| ( in @ SY36 @ SY35 ) ) ) )
| ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ sK1_SX0 )
| ~ ( in @ SY37 @ SY37 ) ) )
| ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY38 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY38 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [SY41: $i,SY42: $i] :
( ~ ( in @ SY42 @ sK1_SX0 )
| ~ ( in @ SY41 @ SY42 )
| ( in @ SY41 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ( subset @ SV1 @ SV2 )
| ~ ( in @ SV3 @ SV1 )
| ( in @ SV3 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ( ~ ! [SY31: $i] :
( ~ ( in @ SY31 @ sK1_SX0 )
| ( subset @ SY31 @ sK1_SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ sK1_SX0 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY32 @ SY33 )
| ~ ( in @ SY33 @ SY34 ) )
| ( in @ SY32 @ SY34 ) ) ) )
| ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SX0 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ( SY35 = SY36 )
| ( in @ SY35 @ SY36 )
| ( in @ SY36 @ SY35 ) ) ) )
| ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ sK1_SX0 )
| ~ ( in @ SY37 @ SY37 ) ) )
| ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY38 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY38 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [SY44: $i] :
( ~ ( in @ SY44 @ sK1_SX0 )
| ~ ( in @ sK2_SY41 @ SY44 )
| ( in @ sK2_SY41 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(20,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( subset @ SV1 @ SV2 ) )
= $true )
| ( ( ~ ( in @ SV3 @ SV1 )
| ( in @ SV3 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ! [SY31: $i] :
( ~ ( in @ SY31 @ sK1_SX0 )
| ( subset @ SY31 @ sK1_SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ sK1_SX0 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY32 @ SY33 )
| ~ ( in @ SY33 @ SY34 ) )
| ( in @ SY32 @ SY34 ) ) ) )
| ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SX0 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ( SY35 = SY36 )
| ( in @ SY35 @ SY36 )
| ( in @ SY36 @ SY35 ) ) ) )
| ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ sK1_SX0 )
| ~ ( in @ SY37 @ SY37 ) ) )
| ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY38 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY38 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ( in @ sK3_SY44 @ sK1_SX0 )
| ~ ( in @ sK2_SY41 @ sK3_SY44 )
| ( in @ sK2_SY41 @ sK1_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(23,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( subset @ SV1 @ SV2 )
= $false )
| ( ( ~ ( in @ SV3 @ SV1 )
| ( in @ SV3 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ! [SY31: $i] :
( ~ ( in @ SY31 @ sK1_SX0 )
| ( subset @ SY31 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ sK1_SX0 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY32 @ SY33 )
| ~ ( in @ SY33 @ SY34 ) )
| ( in @ SY32 @ SY34 ) ) ) )
| ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SX0 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ( SY35 = SY36 )
| ( in @ SY35 @ SY36 )
| ( in @ SY36 @ SY35 ) ) ) )
| ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ sK1_SX0 )
| ~ ( in @ SY37 @ SY37 ) ) )
| ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY38 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY38 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ( in @ sK3_SY44 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( ~ ( in @ sK2_SY41 @ sK3_SY44 )
| ( in @ sK2_SY41 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(28,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( ( in @ SV3 @ SV2 )
= $true )
| ( ( subset @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(29,plain,
( ( ! [SY31: $i] :
( ~ ( in @ SY31 @ sK1_SX0 )
| ( subset @ SY31 @ sK1_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(30,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ sK1_SX0 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY32 @ SY33 )
| ~ ( in @ SY33 @ SY34 ) )
| ( in @ SY32 @ SY34 ) ) ) )
| ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SX0 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ( SY35 = SY36 )
| ( in @ SY35 @ SY36 )
| ( in @ SY36 @ SY35 ) ) ) )
| ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ sK1_SX0 )
| ~ ( in @ SY37 @ SY37 ) ) )
| ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY38 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY38 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(31,plain,
( ( in @ sK3_SY44 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(32,plain,
( ( ~ ( in @ sK2_SY41 @ sK3_SY44 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(33,plain,
( ( in @ sK2_SY41 @ sK1_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(34,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( ( in @ SV3 @ SV2 )
= $true )
| ( ( subset @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV4: $i] :
( ( ~ ( in @ SV4 @ sK1_SX0 )
| ( subset @ SV4 @ sK1_SX0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ sK1_SX0 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY32 @ SY33 )
| ~ ( in @ SY33 @ SY34 ) )
| ( in @ SY32 @ SY34 ) ) ) )
| ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SX0 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ( SY35 = SY36 )
| ( in @ SY35 @ SY36 )
| ( in @ SY36 @ SY35 ) ) ) )
| ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ sK1_SX0 )
| ~ ( in @ SY37 @ SY37 ) ) )
| ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY38 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY38 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(37,plain,
( ( in @ sK2_SY41 @ sK3_SY44 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(38,plain,
! [SV4: $i] :
( ( ( ~ ( in @ SV4 @ sK1_SX0 ) )
= $true )
| ( ( subset @ SV4 @ sK1_SX0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(39,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ sK1_SX0 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY32 @ SY33 )
| ~ ( in @ SY33 @ SY34 ) )
| ( in @ SY32 @ SY34 ) ) ) )
| ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SX0 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ( SY35 = SY36 )
| ( in @ SY35 @ SY36 )
| ( in @ SY36 @ SY35 ) ) ) )
| ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ sK1_SX0 )
| ~ ( in @ SY37 @ SY37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(40,plain,
( ( ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY38 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY38 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(41,plain,
! [SV4: $i] :
( ( ( in @ SV4 @ sK1_SX0 )
= $false )
| ( ( subset @ SV4 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(42,plain,
( ( ~ ( ~ ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ sK1_SX0 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY32 @ SY33 )
| ~ ( in @ SY33 @ SY34 ) )
| ( in @ SY32 @ SY34 ) ) ) )
| ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SX0 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ( SY35 = SY36 )
| ( in @ SY35 @ SY36 )
| ( in @ SY36 @ SY35 ) ) ) )
| ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ sK1_SX0 )
| ~ ( in @ SY37 @ SY37 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(43,plain,
( ( ! [SY38: $i] :
( ~ ( in @ SY38 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SY38 != emptyset ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY38 )
| ( SX2 = SX3 )
| ( in @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(44,plain,
( ( ~ ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ sK1_SX0 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY32 @ SY33 )
| ~ ( in @ SY33 @ SY34 ) )
| ( in @ SY32 @ SY34 ) ) ) )
| ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SX0 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ( SY35 = SY36 )
| ( in @ SY35 @ SY36 )
| ( in @ SY36 @ SY35 ) ) ) )
| ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ sK1_SX0 )
| ~ ( in @ SY37 @ SY37 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV5: $i] :
( ( ~ ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
| ~ ( ( SV5 != emptyset ) )
| ~ ! [SY45: $i] :
~ ~ ( ~ ( in @ SY45 @ SV5 )
| ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SV5 )
| ( SY45 = SY46 )
| ( in @ SY45 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(46,plain,
( ( ~ ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ sK1_SX0 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY32 @ SY33 )
| ~ ( in @ SY33 @ SY34 ) )
| ( in @ SY32 @ SY34 ) ) ) )
| ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SX0 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ( SY35 = SY36 )
| ( in @ SY35 @ SY36 )
| ( in @ SY36 @ SY35 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(47,plain,
( ( ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ sK1_SX0 )
| ~ ( in @ SY37 @ SY37 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(48,plain,
! [SV5: $i] :
( ( ( ~ ( in @ SV5 @ ( powerset @ sK1_SX0 ) ) )
= $true )
| ( ( ~ ( ( SV5 != emptyset ) )
| ~ ! [SY45: $i] :
~ ~ ( ~ ( in @ SY45 @ SV5 )
| ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SV5 )
| ( SY45 = SY46 )
| ( in @ SY45 @ SY46 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(49,plain,
( ( ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ sK1_SX0 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY32 @ SY33 )
| ~ ( in @ SY33 @ SY34 ) )
| ( in @ SY32 @ SY34 ) ) ) )
| ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SX0 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ( SY35 = SY36 )
| ( in @ SY35 @ SY36 )
| ( in @ SY36 @ SY35 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(50,plain,
( ( ! [SY37: $i] :
( ~ ( in @ SY37 @ sK1_SX0 )
| ~ ( in @ SY37 @ SY37 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(51,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
= $false )
| ( ( ~ ( ( SV5 != emptyset ) )
| ~ ! [SY45: $i] :
~ ~ ( ~ ( in @ SY45 @ SV5 )
| ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SV5 )
| ( SY45 = SY46 )
| ( in @ SY45 @ SY46 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(52,plain,
( ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ sK1_SX0 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY32 @ SY33 )
| ~ ( in @ SY33 @ SY34 ) )
| ( in @ SY32 @ SY34 ) ) ) )
| ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SX0 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ( SY35 = SY36 )
| ( in @ SY35 @ SY36 )
| ( in @ SY36 @ SY35 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV6: $i] :
( ( ~ ( in @ SV6 @ sK1_SX0 )
| ~ ( in @ SV6 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV5: $i] :
( ( ( ~ ( ( SV5 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY45: $i] :
~ ~ ( ~ ( in @ SY45 @ SV5 )
| ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SV5 )
| ( SY45 = SY46 )
| ( in @ SY45 @ SY46 ) ) ) )
= $true )
| ( ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(55,plain,
( ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ sK1_SX0 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY32 @ SY33 )
| ~ ( in @ SY33 @ SY34 ) )
| ( in @ SY32 @ SY34 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(56,plain,
( ( ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SX0 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ( SY35 = SY36 )
| ( in @ SY35 @ SY36 )
| ( in @ SY36 @ SY35 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(57,plain,
! [SV6: $i] :
( ( ( ~ ( in @ SV6 @ sK1_SX0 ) )
= $true )
| ( ( ~ ( in @ SV6 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV5: $i] :
( ( ( SV5 != emptyset )
= $false )
| ( ( ~ ! [SY45: $i] :
~ ~ ( ~ ( in @ SY45 @ SV5 )
| ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SV5 )
| ( SY45 = SY46 )
| ( in @ SY45 @ SY46 ) ) ) )
= $true )
| ( ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(59,plain,
( ( ! [SY32: $i] :
( ~ ( in @ SY32 @ sK1_SX0 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SY32 @ SY33 )
| ~ ( in @ SY33 @ SY34 ) )
| ( in @ SY32 @ SY34 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(60,plain,
( ( ! [SY35: $i] :
( ~ ( in @ SY35 @ sK1_SX0 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ( SY35 = SY36 )
| ( in @ SY35 @ SY36 )
| ( in @ SY36 @ SY35 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(61,plain,
! [SV6: $i] :
( ( ( in @ SV6 @ sK1_SX0 )
= $false )
| ( ( ~ ( in @ SV6 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV5: $i] :
( ( ( SV5 = emptyset )
= $true )
| ( ( ~ ! [SY45: $i] :
~ ~ ( ~ ( in @ SY45 @ SV5 )
| ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SV5 )
| ( SY45 = SY46 )
| ( in @ SY45 @ SY46 ) ) ) )
= $true )
| ( ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(63,plain,
! [SV7: $i] :
( ( ~ ( in @ SV7 @ sK1_SX0 )
| ! [SY47: $i] :
( ~ ( in @ SY47 @ sK1_SX0 )
| ! [SY48: $i] :
( ~ ( in @ SY48 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SV7 @ SY47 )
| ~ ( in @ SY47 @ SY48 ) )
| ( in @ SV7 @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV8: $i] :
( ( ~ ( in @ SV8 @ sK1_SX0 )
| ! [SY49: $i] :
( ~ ( in @ SY49 @ sK1_SX0 )
| ( SV8 = SY49 )
| ( in @ SV8 @ SY49 )
| ( in @ SY49 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV6: $i] :
( ( ( in @ SV6 @ SV6 )
= $false )
| ( ( in @ SV6 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV5: $i] :
( ( ( ! [SY45: $i] :
~ ~ ( ~ ( in @ SY45 @ SV5 )
| ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SV5 )
| ( SY45 = SY46 )
| ( in @ SY45 @ SY46 ) ) ) )
= $false )
| ( ( SV5 = emptyset )
= $true )
| ( ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV7: $i] :
( ( ( ~ ( in @ SV7 @ sK1_SX0 ) )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( in @ SY47 @ sK1_SX0 )
| ! [SY48: $i] :
( ~ ( in @ SY48 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SV7 @ SY47 )
| ~ ( in @ SY47 @ SY48 ) )
| ( in @ SV7 @ SY48 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV8: $i] :
( ( ( ~ ( in @ SV8 @ sK1_SX0 ) )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ sK1_SX0 )
| ( SV8 = SY49 )
| ( in @ SV8 @ SY49 )
| ( in @ SY49 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK4_SY45 @ SV5 ) @ SV5 )
| ~ ! [SY50: $i] :
( ~ ( in @ SY50 @ SV5 )
| ( ( sK4_SY45 @ SV5 )
= SY50 )
| ( in @ ( sK4_SY45 @ SV5 ) @ SY50 ) ) ) )
= $false )
| ( ( SV5 = emptyset )
= $true )
| ( ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[66]) ).
thf(70,plain,
! [SV7: $i] :
( ( ( in @ SV7 @ sK1_SX0 )
= $false )
| ( ( ! [SY47: $i] :
( ~ ( in @ SY47 @ sK1_SX0 )
| ! [SY48: $i] :
( ~ ( in @ SY48 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SV7 @ SY47 )
| ~ ( in @ SY47 @ SY48 ) )
| ( in @ SV7 @ SY48 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(71,plain,
! [SV8: $i] :
( ( ( in @ SV8 @ sK1_SX0 )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ sK1_SX0 )
| ( SV8 = SY49 )
| ( in @ SV8 @ SY49 )
| ( in @ SY49 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_SY45 @ SV5 ) @ SV5 )
| ~ ! [SY50: $i] :
( ~ ( in @ SY50 @ SV5 )
| ( ( sK4_SY45 @ SV5 )
= SY50 )
| ( in @ ( sK4_SY45 @ SV5 ) @ SY50 ) ) ) )
= $true )
| ( ( SV5 = emptyset )
= $true )
| ( ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(73,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ sK1_SX0 )
| ! [SY51: $i] :
( ~ ( in @ SY51 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SV7 @ SV9 )
| ~ ( in @ SV9 @ SY51 ) )
| ( in @ SV7 @ SY51 ) ) )
= $true )
| ( ( in @ SV7 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(74,plain,
! [SV8: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ sK1_SX0 )
| ( SV8 = SV10 )
| ( in @ SV8 @ SV10 )
| ( in @ SV10 @ SV8 ) )
= $true )
| ( ( in @ SV8 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV5: $i] :
( ( ( ~ ( in @ ( sK4_SY45 @ SV5 ) @ SV5 )
| ~ ! [SY50: $i] :
( ~ ( in @ SY50 @ SV5 )
| ( ( sK4_SY45 @ SV5 )
= SY50 )
| ( in @ ( sK4_SY45 @ SV5 ) @ SY50 ) ) )
= $false )
| ( ( SV5 = emptyset )
= $true )
| ( ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(76,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ sK1_SX0 ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( in @ SY51 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SV7 @ SV9 )
| ~ ( in @ SV9 @ SY51 ) )
| ( in @ SV7 @ SY51 ) ) )
= $true )
| ( ( in @ SV7 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(77,plain,
! [SV8: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ sK1_SX0 ) )
= $true )
| ( ( ( SV8 = SV10 )
| ( in @ SV8 @ SV10 )
| ( in @ SV10 @ SV8 ) )
= $true )
| ( ( in @ SV8 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(78,plain,
! [SV5: $i] :
( ( ( ~ ( in @ ( sK4_SY45 @ SV5 ) @ SV5 ) )
= $false )
| ( ( SV5 = emptyset )
= $true )
| ( ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(79,plain,
! [SV5: $i] :
( ( ( ~ ! [SY50: $i] :
( ~ ( in @ SY50 @ SV5 )
| ( ( sK4_SY45 @ SV5 )
= SY50 )
| ( in @ ( sK4_SY45 @ SV5 ) @ SY50 ) ) )
= $false )
| ( ( SV5 = emptyset )
= $true )
| ( ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(80,plain,
! [SV7: $i,SV9: $i] :
( ( ( in @ SV9 @ sK1_SX0 )
= $false )
| ( ( ! [SY51: $i] :
( ~ ( in @ SY51 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SV7 @ SV9 )
| ~ ( in @ SV9 @ SY51 ) )
| ( in @ SV7 @ SY51 ) ) )
= $true )
| ( ( in @ SV7 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV8: $i,SV10: $i] :
( ( ( in @ SV10 @ sK1_SX0 )
= $false )
| ( ( ( SV8 = SV10 )
| ( in @ SV8 @ SV10 )
| ( in @ SV10 @ SV8 ) )
= $true )
| ( ( in @ SV8 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV5: $i] :
( ( ( in @ ( sK4_SY45 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = emptyset )
= $true )
| ( ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(83,plain,
! [SV5: $i] :
( ( ( ! [SY50: $i] :
( ~ ( in @ SY50 @ SV5 )
| ( ( sK4_SY45 @ SV5 )
= SY50 )
| ( in @ ( sK4_SY45 @ SV5 ) @ SY50 ) ) )
= $true )
| ( ( SV5 = emptyset )
= $true )
| ( ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(84,plain,
! [SV9: $i,SV7: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ sK1_SX0 )
| ~ ~ ( ~ ( in @ SV7 @ SV9 )
| ~ ( in @ SV9 @ SV11 ) )
| ( in @ SV7 @ SV11 ) )
= $true )
| ( ( in @ SV9 @ sK1_SX0 )
= $false )
| ( ( in @ SV7 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV10: $i,SV8: $i] :
( ( ( ( SV8 = SV10 )
| ( in @ SV8 @ SV10 ) )
= $true )
| ( ( in @ SV10 @ SV8 )
= $true )
| ( ( in @ SV10 @ sK1_SX0 )
= $false )
| ( ( in @ SV8 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV5: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV5 )
| ( ( sK4_SY45 @ SV5 )
= SV12 )
| ( in @ ( sK4_SY45 @ SV5 ) @ SV12 ) )
= $true )
| ( ( SV5 = emptyset )
= $true )
| ( ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(87,plain,
! [SV9: $i,SV7: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ sK1_SX0 ) )
= $true )
| ( ( ~ ~ ( ~ ( in @ SV7 @ SV9 )
| ~ ( in @ SV9 @ SV11 ) )
| ( in @ SV7 @ SV11 ) )
= $true )
| ( ( in @ SV9 @ sK1_SX0 )
= $false )
| ( ( in @ SV7 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(88,plain,
! [SV10: $i,SV8: $i] :
( ( ( SV8 = SV10 )
= $true )
| ( ( in @ SV8 @ SV10 )
= $true )
| ( ( in @ SV10 @ SV8 )
= $true )
| ( ( in @ SV10 @ sK1_SX0 )
= $false )
| ( ( in @ SV8 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(89,plain,
! [SV5: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV5 ) )
= $true )
| ( ( ( ( sK4_SY45 @ SV5 )
= SV12 )
| ( in @ ( sK4_SY45 @ SV5 ) @ SV12 ) )
= $true )
| ( ( SV5 = emptyset )
= $true )
| ( ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(90,plain,
! [SV9: $i,SV7: $i,SV11: $i] :
( ( ( in @ SV11 @ sK1_SX0 )
= $false )
| ( ( ~ ~ ( ~ ( in @ SV7 @ SV9 )
| ~ ( in @ SV9 @ SV11 ) )
| ( in @ SV7 @ SV11 ) )
= $true )
| ( ( in @ SV9 @ sK1_SX0 )
= $false )
| ( ( in @ SV7 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(91,plain,
! [SV5: $i,SV12: $i] :
( ( ( in @ SV12 @ SV5 )
= $false )
| ( ( ( ( sK4_SY45 @ SV5 )
= SV12 )
| ( in @ ( sK4_SY45 @ SV5 ) @ SV12 ) )
= $true )
| ( ( SV5 = emptyset )
= $true )
| ( ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(92,plain,
! [SV11: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ SV7 @ SV9 )
| ~ ( in @ SV9 @ SV11 ) ) )
= $true )
| ( ( in @ SV7 @ SV11 )
= $true )
| ( ( in @ SV11 @ sK1_SX0 )
= $false )
| ( ( in @ SV9 @ sK1_SX0 )
= $false )
| ( ( in @ SV7 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(93,plain,
! [SV12: $i,SV5: $i] :
( ( ( ( sK4_SY45 @ SV5 )
= SV12 )
= $true )
| ( ( in @ ( sK4_SY45 @ SV5 ) @ SV12 )
= $true )
| ( ( in @ SV12 @ SV5 )
= $false )
| ( ( SV5 = emptyset )
= $true )
| ( ( in @ SV5 @ ( powerset @ sK1_SX0 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(94,plain,
! [SV11: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ SV7 @ SV9 )
| ~ ( in @ SV9 @ SV11 ) ) )
= $false )
| ( ( in @ SV7 @ SV11 )
= $true )
| ( ( in @ SV11 @ sK1_SX0 )
= $false )
| ( ( in @ SV9 @ sK1_SX0 )
= $false )
| ( ( in @ SV7 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(95,plain,
! [SV11: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV9 )
| ~ ( in @ SV9 @ SV11 ) )
= $true )
| ( ( in @ SV7 @ SV11 )
= $true )
| ( ( in @ SV11 @ sK1_SX0 )
= $false )
| ( ( in @ SV9 @ sK1_SX0 )
= $false )
| ( ( in @ SV7 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(96,plain,
! [SV11: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV9 ) )
= $true )
| ( ( ~ ( in @ SV9 @ SV11 ) )
= $true )
| ( ( in @ SV7 @ SV11 )
= $true )
| ( ( in @ SV11 @ sK1_SX0 )
= $false )
| ( ( in @ SV9 @ sK1_SX0 )
= $false )
| ( ( in @ SV7 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(97,plain,
! [SV11: $i,SV9: $i,SV7: $i] :
( ( ( in @ SV7 @ SV9 )
= $false )
| ( ( ~ ( in @ SV9 @ SV11 ) )
= $true )
| ( ( in @ SV7 @ SV11 )
= $true )
| ( ( in @ SV11 @ sK1_SX0 )
= $false )
| ( ( in @ SV9 @ sK1_SX0 )
= $false )
| ( ( in @ SV7 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(98,plain,
! [SV7: $i,SV11: $i,SV9: $i] :
( ( ( in @ SV9 @ SV11 )
= $false )
| ( ( in @ SV7 @ SV9 )
= $false )
| ( ( in @ SV7 @ SV11 )
= $true )
| ( ( in @ SV11 @ sK1_SX0 )
= $false )
| ( ( in @ SV9 @ sK1_SX0 )
= $false )
| ( ( in @ SV7 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(99,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,98,93,88,82,65,41,37,34,33]) ).
thf(100,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU817^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n005.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 15:36:38 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.24
% 0.08/0.24 No.of.Axioms: 0
% 0.08/0.24
% 0.08/0.24 Length.of.Defs: 1387
% 0.08/0.24
% 0.08/0.24 Contains.Choice.Funs: false
% 0.08/0.24 ....
% 0.08/0.24
% 0.08/0.24 ********************************
% 0.08/0.24 * All subproblems solved! *
% 0.08/0.24 ********************************
% 0.08/0.24 % SZS status Theorem for /export/starexec/sandbox2/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:99,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.24
% 0.08/0.24 %**** Beginning of derivation protocol ****
% 0.08/0.24 % 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: 100 ****
% 0.08/0.25 %**** clause counter: 99 ****
% 0.08/0.25
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox2/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:99,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------