TSTP Solution File: SEU762^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU762^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:14:31 EDT 2022
% Result : Theorem 0.13s 0.34s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 18
% Syntax : Number of formulae : 114 ( 63 unt; 13 typ; 4 def)
% Number of atoms : 782 ( 185 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 1849 ( 323 ~; 252 |; 12 &;1215 @)
% ( 0 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 223 ( 0 ^ 223 !; 0 ?; 223 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binintersect,type,
binintersect: $i > $i > $i ).
thf(tp_binintersectT_lem,type,
binintersectT_lem: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY0,type,
sK2_SY0: $i ).
thf(tp_sK3_SY4,type,
sK3_SY4: $i ).
thf(tp_sK4_SY7,type,
sK4_SY7: $i ).
thf(tp_sK5_SY9,type,
sK5_SY9: $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_woz13rule1,type,
woz13rule1: $o ).
thf(tp_woz13rule2,type,
woz13rule2: $o ).
thf(tp_woz13rule3,type,
woz13rule3: $o ).
thf(binintersectT_lem,definition,
( binintersectT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(woz13rule1,definition,
( woz13rule1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ X @ Z )
=> ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule1) ).
thf(woz13rule2,definition,
( woz13rule2
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ Y @ Z )
=> ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule2) ).
thf(woz13rule3,definition,
( woz13rule3
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ X @ Y )
=> ( ( subset @ X @ Z )
=> ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule3) ).
thf(1,conjecture,
( binintersectT_lem
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( subset @ X @ Z )
=> ( ( subset @ Y @ W )
=> ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule4) ).
thf(2,negated_conjecture,
( ( binintersectT_lem
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( subset @ X @ Z )
=> ( ( subset @ Y @ W )
=> ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
binintersectT_lem = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(4,plain,
woz13rule1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(5,plain,
woz13rule2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(6,plain,
woz13rule3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(7,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( subset @ X @ Z )
=> ( ( subset @ Y @ W )
=> ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(8,plain,
( ( ~ ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( subset @ X @ Z )
=> ( ( subset @ Y @ W )
=> ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY4 @ ( powerset @ sK1_A ) )
& ( in @ sK4_SY7 @ ( powerset @ sK1_A ) )
& ( in @ sK5_SY9 @ ( powerset @ sK1_A ) )
& ( subset @ sK2_SY0 @ sK4_SY7 )
& ( subset @ sK3_SY4 @ sK5_SY9 )
& ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
woz13rule3 = $true,
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
woz13rule2 = $true,
inference(copy,[status(thm)],[5]) ).
thf(12,plain,
woz13rule1 = $true,
inference(copy,[status(thm)],[4]) ).
thf(13,plain,
binintersectT_lem = $true,
inference(copy,[status(thm)],[3]) ).
thf(14,plain,
( ( ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY4 @ ( powerset @ sK1_A ) )
& ( in @ sK4_SY7 @ ( powerset @ sK1_A ) )
& ( in @ sK5_SY9 @ ( powerset @ sK1_A ) )
& ( subset @ sK2_SY0 @ sK4_SY7 )
& ( subset @ sK3_SY4 @ sK5_SY9 )
& ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(15,plain,
( ( ~ ( ~ ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY4 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY7 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK5_SY9 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( subset @ sK2_SY0 @ sK4_SY7 )
| ~ ~ ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,binintersectT_lem,woz13rule1,woz13rule2,woz13rule3]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( binintersect @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,binintersectT_lem,woz13rule1,woz13rule2,woz13rule3]) ).
thf(17,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ SX3 )
| ( subset @ ( binintersect @ SX1 @ SX2 ) @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,binintersectT_lem,woz13rule1,woz13rule2,woz13rule3]) ).
thf(18,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX2 @ SX3 )
| ( subset @ ( binintersect @ SX1 @ SX2 ) @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,binintersectT_lem,woz13rule1,woz13rule2,woz13rule3]) ).
thf(19,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ SX2 )
| ~ ( subset @ SX1 @ SX3 )
| ( subset @ SX1 @ ( binintersect @ SX2 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,binintersectT_lem,woz13rule1,woz13rule2,woz13rule3]) ).
thf(20,plain,
( ( ~ ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY4 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY7 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK5_SY9 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( subset @ sK2_SY0 @ sK4_SY7 )
| ~ ~ ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(21,plain,
! [SV1: $i] :
( ( ! [SY10: $i] :
( ~ ( in @ SY10 @ ( powerset @ SV1 ) )
| ! [SY11: $i] :
( ~ ( in @ SY11 @ ( powerset @ SV1 ) )
| ( in @ ( binintersect @ SY10 @ SY11 ) @ ( powerset @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(22,plain,
! [SV2: $i] :
( ( ! [SY12: $i] :
( ~ ( in @ SY12 @ ( powerset @ SV2 ) )
| ! [SY13: $i] :
( ~ ( in @ SY13 @ ( powerset @ SV2 ) )
| ! [SY14: $i] :
( ~ ( in @ SY14 @ ( powerset @ SV2 ) )
| ~ ( subset @ SY12 @ SY14 )
| ( subset @ ( binintersect @ SY12 @ SY13 ) @ SY14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(23,plain,
! [SV3: $i] :
( ( ! [SY15: $i] :
( ~ ( in @ SY15 @ ( powerset @ SV3 ) )
| ! [SY16: $i] :
( ~ ( in @ SY16 @ ( powerset @ SV3 ) )
| ! [SY17: $i] :
( ~ ( in @ SY17 @ ( powerset @ SV3 ) )
| ~ ( subset @ SY16 @ SY17 )
| ( subset @ ( binintersect @ SY15 @ SY16 ) @ SY17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(24,plain,
! [SV4: $i] :
( ( ! [SY18: $i] :
( ~ ( in @ SY18 @ ( powerset @ SV4 ) )
| ! [SY19: $i] :
( ~ ( in @ SY19 @ ( powerset @ SV4 ) )
| ! [SY20: $i] :
( ~ ( in @ SY20 @ ( powerset @ SV4 ) )
| ~ ( subset @ SY18 @ SY19 )
| ~ ( subset @ SY18 @ SY20 )
| ( subset @ SY18 @ ( binintersect @ SY19 @ SY20 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(25,plain,
( ( ~ ( in @ sK2_SY0 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(26,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY4 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY7 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK5_SY9 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( subset @ sK2_SY0 @ sK4_SY7 )
| ~ ~ ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(27,plain,
! [SV1: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ ( powerset @ SV1 ) )
| ! [SY21: $i] :
( ~ ( in @ SY21 @ ( powerset @ SV1 ) )
| ( in @ ( binintersect @ SV5 @ SY21 ) @ ( powerset @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
! [SV2: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ ( powerset @ SV2 ) )
| ! [SY22: $i] :
( ~ ( in @ SY22 @ ( powerset @ SV2 ) )
| ! [SY23: $i] :
( ~ ( in @ SY23 @ ( powerset @ SV2 ) )
| ~ ( subset @ SV6 @ SY23 )
| ( subset @ ( binintersect @ SV6 @ SY22 ) @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV3: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ ( powerset @ SV3 ) )
| ! [SY24: $i] :
( ~ ( in @ SY24 @ ( powerset @ SV3 ) )
| ! [SY25: $i] :
( ~ ( in @ SY25 @ ( powerset @ SV3 ) )
| ~ ( subset @ SY24 @ SY25 )
| ( subset @ ( binintersect @ SV7 @ SY24 ) @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV4: $i,SV8: $i] :
( ( ~ ( in @ SV8 @ ( powerset @ SV4 ) )
| ! [SY26: $i] :
( ~ ( in @ SY26 @ ( powerset @ SV4 ) )
| ! [SY27: $i] :
( ~ ( in @ SY27 @ ( powerset @ SV4 ) )
| ~ ( subset @ SV8 @ SY26 )
| ~ ( subset @ SV8 @ SY27 )
| ( subset @ SV8 @ ( binintersect @ SY26 @ SY27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(31,plain,
( ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(32,plain,
( ( ~ ( ~ ( in @ sK3_SY4 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY7 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK5_SY9 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( subset @ sK2_SY0 @ sK4_SY7 )
| ~ ~ ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(33,plain,
! [SV1: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( ! [SY21: $i] :
( ~ ( in @ SY21 @ ( powerset @ SV1 ) )
| ( in @ ( binintersect @ SV5 @ SY21 ) @ ( powerset @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( powerset @ SV2 ) ) )
= $true )
| ( ( ! [SY22: $i] :
( ~ ( in @ SY22 @ ( powerset @ SV2 ) )
| ! [SY23: $i] :
( ~ ( in @ SY23 @ ( powerset @ SV2 ) )
| ~ ( subset @ SV6 @ SY23 )
| ( subset @ ( binintersect @ SV6 @ SY22 ) @ SY23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( ! [SY24: $i] :
( ~ ( in @ SY24 @ ( powerset @ SV3 ) )
| ! [SY25: $i] :
( ~ ( in @ SY25 @ ( powerset @ SV3 ) )
| ~ ( subset @ SY24 @ SY25 )
| ( subset @ ( binintersect @ SV7 @ SY24 ) @ SY25 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( powerset @ SV4 ) ) )
= $true )
| ( ( ! [SY26: $i] :
( ~ ( in @ SY26 @ ( powerset @ SV4 ) )
| ! [SY27: $i] :
( ~ ( in @ SY27 @ ( powerset @ SV4 ) )
| ~ ( subset @ SV8 @ SY26 )
| ~ ( subset @ SV8 @ SY27 )
| ( subset @ SV8 @ ( binintersect @ SY26 @ SY27 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(37,plain,
( ( ~ ( in @ sK3_SY4 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY7 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK5_SY9 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( subset @ sK2_SY0 @ sK4_SY7 )
| ~ ~ ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV1: $i,SV5: $i] :
( ( ( in @ SV5 @ ( powerset @ SV1 ) )
= $false )
| ( ( ! [SY21: $i] :
( ~ ( in @ SY21 @ ( powerset @ SV1 ) )
| ( in @ ( binintersect @ SV5 @ SY21 ) @ ( powerset @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV2: $i,SV6: $i] :
( ( ( in @ SV6 @ ( powerset @ SV2 ) )
= $false )
| ( ( ! [SY22: $i] :
( ~ ( in @ SY22 @ ( powerset @ SV2 ) )
| ! [SY23: $i] :
( ~ ( in @ SY23 @ ( powerset @ SV2 ) )
| ~ ( subset @ SV6 @ SY23 )
| ( subset @ ( binintersect @ SV6 @ SY22 ) @ SY23 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV3: $i,SV7: $i] :
( ( ( in @ SV7 @ ( powerset @ SV3 ) )
= $false )
| ( ( ! [SY24: $i] :
( ~ ( in @ SY24 @ ( powerset @ SV3 ) )
| ! [SY25: $i] :
( ~ ( in @ SY25 @ ( powerset @ SV3 ) )
| ~ ( subset @ SY24 @ SY25 )
| ( subset @ ( binintersect @ SV7 @ SY24 ) @ SY25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV4: $i,SV8: $i] :
( ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false )
| ( ( ! [SY26: $i] :
( ~ ( in @ SY26 @ ( powerset @ SV4 ) )
| ! [SY27: $i] :
( ~ ( in @ SY27 @ ( powerset @ SV4 ) )
| ~ ( subset @ SV8 @ SY26 )
| ~ ( subset @ SV8 @ SY27 )
| ( subset @ SV8 @ ( binintersect @ SY26 @ SY27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(42,plain,
( ( ~ ( in @ sK3_SY4 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(43,plain,
( ( ~ ~ ( ~ ( in @ sK4_SY7 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK5_SY9 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( subset @ sK2_SY0 @ sK4_SY7 )
| ~ ~ ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(44,plain,
! [SV5: $i,SV1: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( powerset @ SV1 ) )
| ( in @ ( binintersect @ SV5 @ SV9 ) @ ( powerset @ SV1 ) ) )
= $true )
| ( ( in @ SV5 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(45,plain,
! [SV6: $i,SV2: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ ( powerset @ SV2 ) )
| ! [SY28: $i] :
( ~ ( in @ SY28 @ ( powerset @ SV2 ) )
| ~ ( subset @ SV6 @ SY28 )
| ( subset @ ( binintersect @ SV6 @ SV10 ) @ SY28 ) ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV7: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ ( powerset @ SV3 ) )
| ! [SY29: $i] :
( ~ ( in @ SY29 @ ( powerset @ SV3 ) )
| ~ ( subset @ SV11 @ SY29 )
| ( subset @ ( binintersect @ SV7 @ SV11 ) @ SY29 ) ) )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV8: $i,SV4: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ ( powerset @ SV4 ) )
| ! [SY30: $i] :
( ~ ( in @ SY30 @ ( powerset @ SV4 ) )
| ~ ( subset @ SV8 @ SV12 )
| ~ ( subset @ SV8 @ SY30 )
| ( subset @ SV8 @ ( binintersect @ SV12 @ SY30 ) ) ) )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(48,plain,
( ( in @ sK3_SY4 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(49,plain,
( ( ~ ( ~ ( in @ sK4_SY7 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK5_SY9 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( subset @ sK2_SY0 @ sK4_SY7 )
| ~ ~ ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(50,plain,
! [SV5: $i,SV1: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV5 @ SV9 ) @ ( powerset @ SV1 ) )
= $true )
| ( ( in @ SV5 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV6: $i,SV2: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ ( powerset @ SV2 ) ) )
= $true )
| ( ( ! [SY28: $i] :
( ~ ( in @ SY28 @ ( powerset @ SV2 ) )
| ~ ( subset @ SV6 @ SY28 )
| ( subset @ ( binintersect @ SV6 @ SV10 ) @ SY28 ) ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(52,plain,
! [SV7: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( ! [SY29: $i] :
( ~ ( in @ SY29 @ ( powerset @ SV3 ) )
| ~ ( subset @ SV11 @ SY29 )
| ( subset @ ( binintersect @ SV7 @ SV11 ) @ SY29 ) ) )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV8: $i,SV4: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ ( powerset @ SV4 ) ) )
= $true )
| ( ( ! [SY30: $i] :
( ~ ( in @ SY30 @ ( powerset @ SV4 ) )
| ~ ( subset @ SV8 @ SV12 )
| ~ ( subset @ SV8 @ SY30 )
| ( subset @ SV8 @ ( binintersect @ SV12 @ SY30 ) ) ) )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(54,plain,
( ( ~ ( in @ sK4_SY7 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK5_SY9 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( subset @ sK2_SY0 @ sK4_SY7 )
| ~ ~ ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV5: $i,SV1: $i,SV9: $i] :
( ( ( in @ SV9 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ ( binintersect @ SV5 @ SV9 ) @ ( powerset @ SV1 ) )
= $true )
| ( ( in @ SV5 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV6: $i,SV2: $i,SV10: $i] :
( ( ( in @ SV10 @ ( powerset @ SV2 ) )
= $false )
| ( ( ! [SY28: $i] :
( ~ ( in @ SY28 @ ( powerset @ SV2 ) )
| ~ ( subset @ SV6 @ SY28 )
| ( subset @ ( binintersect @ SV6 @ SV10 ) @ SY28 ) ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV7: $i,SV3: $i,SV11: $i] :
( ( ( in @ SV11 @ ( powerset @ SV3 ) )
= $false )
| ( ( ! [SY29: $i] :
( ~ ( in @ SY29 @ ( powerset @ SV3 ) )
| ~ ( subset @ SV11 @ SY29 )
| ( subset @ ( binintersect @ SV7 @ SV11 ) @ SY29 ) ) )
= $true )
| ( ( in @ SV7 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV8: $i,SV4: $i,SV12: $i] :
( ( ( in @ SV12 @ ( powerset @ SV4 ) )
= $false )
| ( ( ! [SY30: $i] :
( ~ ( in @ SY30 @ ( powerset @ SV4 ) )
| ~ ( subset @ SV8 @ SV12 )
| ~ ( subset @ SV8 @ SY30 )
| ( subset @ SV8 @ ( binintersect @ SV12 @ SY30 ) ) ) )
= $true )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(59,plain,
( ( ~ ( in @ sK4_SY7 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(60,plain,
( ( ~ ~ ( ~ ( in @ sK5_SY9 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( subset @ sK2_SY0 @ sK4_SY7 )
| ~ ~ ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(61,plain,
! [SV10: $i,SV6: $i,SV2: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ ( powerset @ SV2 ) )
| ~ ( subset @ SV6 @ SV13 )
| ( subset @ ( binintersect @ SV6 @ SV10 ) @ SV13 ) )
= $true )
| ( ( in @ SV10 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV7: $i,SV11: $i,SV3: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ ( powerset @ SV3 ) )
| ~ ( subset @ SV11 @ SV14 )
| ( subset @ ( binintersect @ SV7 @ SV11 ) @ SV14 ) )
= $true )
| ( ( in @ SV11 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV7 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV12: $i,SV8: $i,SV4: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ ( powerset @ SV4 ) )
| ~ ( subset @ SV8 @ SV12 )
| ~ ( subset @ SV8 @ SV15 )
| ( subset @ SV8 @ ( binintersect @ SV12 @ SV15 ) ) )
= $true )
| ( ( in @ SV12 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(64,plain,
( ( in @ sK4_SY7 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(65,plain,
( ( ~ ( ~ ( in @ sK5_SY9 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( subset @ sK2_SY0 @ sK4_SY7 )
| ~ ~ ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(66,plain,
! [SV10: $i,SV6: $i,SV2: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ ( powerset @ SV2 ) ) )
= $true )
| ( ( ~ ( subset @ SV6 @ SV13 )
| ( subset @ ( binintersect @ SV6 @ SV10 ) @ SV13 ) )
= $true )
| ( ( in @ SV10 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV7: $i,SV11: $i,SV3: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( ~ ( subset @ SV11 @ SV14 )
| ( subset @ ( binintersect @ SV7 @ SV11 ) @ SV14 ) )
= $true )
| ( ( in @ SV11 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV7 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(68,plain,
! [SV12: $i,SV8: $i,SV4: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ ( powerset @ SV4 ) ) )
= $true )
| ( ( ~ ( subset @ SV8 @ SV12 )
| ~ ( subset @ SV8 @ SV15 )
| ( subset @ SV8 @ ( binintersect @ SV12 @ SV15 ) ) )
= $true )
| ( ( in @ SV12 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(69,plain,
( ( ~ ( in @ sK5_SY9 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( subset @ sK2_SY0 @ sK4_SY7 )
| ~ ~ ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV10: $i,SV6: $i,SV2: $i,SV13: $i] :
( ( ( in @ SV13 @ ( powerset @ SV2 ) )
= $false )
| ( ( ~ ( subset @ SV6 @ SV13 )
| ( subset @ ( binintersect @ SV6 @ SV10 ) @ SV13 ) )
= $true )
| ( ( in @ SV10 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV7: $i,SV11: $i,SV3: $i,SV14: $i] :
( ( ( in @ SV14 @ ( powerset @ SV3 ) )
= $false )
| ( ( ~ ( subset @ SV11 @ SV14 )
| ( subset @ ( binintersect @ SV7 @ SV11 ) @ SV14 ) )
= $true )
| ( ( in @ SV11 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV7 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(72,plain,
! [SV12: $i,SV8: $i,SV4: $i,SV15: $i] :
( ( ( in @ SV15 @ ( powerset @ SV4 ) )
= $false )
| ( ( ~ ( subset @ SV8 @ SV12 )
| ~ ( subset @ SV8 @ SV15 )
| ( subset @ SV8 @ ( binintersect @ SV12 @ SV15 ) ) )
= $true )
| ( ( in @ SV12 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(73,plain,
( ( ~ ( in @ sK5_SY9 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(74,plain,
( ( ~ ~ ( ~ ( subset @ sK2_SY0 @ sK4_SY7 )
| ~ ~ ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(75,plain,
! [SV2: $i,SV10: $i,SV13: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV13 ) )
= $true )
| ( ( subset @ ( binintersect @ SV6 @ SV10 ) @ SV13 )
= $true )
| ( ( in @ SV13 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV10 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV3: $i,SV7: $i,SV14: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV14 ) )
= $true )
| ( ( subset @ ( binintersect @ SV7 @ SV11 ) @ SV14 )
= $true )
| ( ( in @ SV14 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV11 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV7 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV4: $i,SV15: $i,SV12: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV12 ) )
= $true )
| ( ( ~ ( subset @ SV8 @ SV15 )
| ( subset @ SV8 @ ( binintersect @ SV12 @ SV15 ) ) )
= $true )
| ( ( in @ SV15 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV12 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(78,plain,
( ( in @ sK5_SY9 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(79,plain,
( ( ~ ( ~ ( subset @ sK2_SY0 @ sK4_SY7 )
| ~ ~ ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(80,plain,
! [SV2: $i,SV10: $i,SV13: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV13 )
= $false )
| ( ( subset @ ( binintersect @ SV6 @ SV10 ) @ SV13 )
= $true )
| ( ( in @ SV13 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV10 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV3: $i,SV7: $i,SV14: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV14 )
= $false )
| ( ( subset @ ( binintersect @ SV7 @ SV11 ) @ SV14 )
= $true )
| ( ( in @ SV14 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV11 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ SV7 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV4: $i,SV15: $i,SV12: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV12 )
= $false )
| ( ( ~ ( subset @ SV8 @ SV15 )
| ( subset @ SV8 @ ( binintersect @ SV12 @ SV15 ) ) )
= $true )
| ( ( in @ SV15 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV12 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(83,plain,
( ( ~ ( subset @ sK2_SY0 @ sK4_SY7 )
| ~ ~ ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV4: $i,SV12: $i,SV15: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV15 ) )
= $true )
| ( ( subset @ SV8 @ ( binintersect @ SV12 @ SV15 ) )
= $true )
| ( ( subset @ SV8 @ SV12 )
= $false )
| ( ( in @ SV15 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV12 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(85,plain,
( ( ~ ( subset @ sK2_SY0 @ sK4_SY7 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(86,plain,
( ( ~ ~ ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(87,plain,
! [SV4: $i,SV12: $i,SV15: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV15 )
= $false )
| ( ( subset @ SV8 @ ( binintersect @ SV12 @ SV15 ) )
= $true )
| ( ( subset @ SV8 @ SV12 )
= $false )
| ( ( in @ SV15 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV12 @ ( powerset @ SV4 ) )
= $false )
| ( ( in @ SV8 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(88,plain,
( ( subset @ sK2_SY0 @ sK4_SY7 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(89,plain,
( ( ~ ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(90,plain,
( ( ~ ( subset @ sK3_SY4 @ sK5_SY9 )
| ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(91,plain,
( ( ~ ( subset @ sK3_SY4 @ sK5_SY9 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(92,plain,
( ( ~ ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(93,plain,
( ( subset @ sK3_SY4 @ sK5_SY9 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(94,plain,
( ( ~ ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(95,plain,
( ( subset @ ( binintersect @ sK2_SY0 @ sK3_SY4 ) @ ( binintersect @ sK4_SY7 @ sK5_SY9 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(96,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,95,93,88,87,81,80,78,64,55,48]) ).
thf(97,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU762^2 : TPTP v8.1.0. Released v3.7.0.
% 0.00/0.09 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Sun Jun 19 05:54:47 EDT 2022
% 0.08/0.28 % CPUTime :
% 0.08/0.29
% 0.08/0.29 No.of.Axioms: 0
% 0.08/0.29
% 0.08/0.29 Length.of.Defs: 1138
% 0.08/0.29
% 0.08/0.29 Contains.Choice.Funs: false
% 0.08/0.29 (rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.13/0.34
% 0.13/0.34 ********************************
% 0.13/0.34 * All subproblems solved! *
% 0.13/0.34 ********************************
% 0.13/0.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:96,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.34
% 0.13/0.34 %**** Beginning of derivation protocol ****
% 0.13/0.34 % SZS output start CNFRefutation
% See solution above
% 0.13/0.34
% 0.13/0.34 %**** End of derivation protocol ****
% 0.13/0.34 %**** no. of clauses in derivation: 97 ****
% 0.13/0.34 %**** clause counter: 96 ****
% 0.13/0.34
% 0.13/0.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:96,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------