TSTP Solution File: SEU711^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU711^2 : 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 : n016.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 12:14:07 EDT 2022
% Result : Theorem 0.19s 0.53s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of formulae : 132 ( 58 unt; 10 typ; 3 def)
% Number of atoms : 859 ( 240 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 1638 ( 267 ~; 354 |; 12 &; 959 @)
% ( 0 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 414 ( 0 ^ 414 !; 0 ?; 414 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binunion,type,
binunion: $i > $i > $i ).
thf(tp_binunionEcases,type,
binunionEcases: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetE,type,
powersetE: $o ).
thf(tp_powersetI,type,
powersetI: $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY16,type,
sK2_SY16: $i ).
thf(tp_sK3_SY18,type,
sK3_SY18: $i ).
thf(tp_sK4_Xx,type,
sK4_Xx: $i > $i > $i ).
thf(binunionEcases,definition,
( binunionEcases
= ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).
thf(powersetE,definition,
( powersetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(1,conjecture,
( powersetI
=> ( powersetE
=> ( binunionEcases
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionT_lem) ).
thf(2,negated_conjecture,
( ( powersetI
=> ( powersetE
=> ( binunionEcases
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) )
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binunionEcases,powersetE,powersetI]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ( in @ sK2_SY16 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
& ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK4_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK4_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xx @ B )
| Xphi ) )
& ( ! [Xx: $i] :
~ ( in @ Xx @ ( binunion @ A @ B ) )
| ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xx @ B )
| Xphi ) )
& ( ! [Xx: $i] :
~ ( in @ Xx @ ( binunion @ A @ B ) )
| ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK4_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK4_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ( in @ sK2_SY16 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
& ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(17,plain,
( ( ~ ( ~ ( in @ sK2_SY16 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
| ~ ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,binunionEcases,powersetE,powersetI]) ).
thf(18,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 )
| ! [SX3: $o] : SX3 )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ! [SX3: $o] :
( ~ SX3
| ( in @ SX2 @ SX1 )
| SX3 ) )
| ~ ( ! [SX2: $i] :
~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,binunionEcases,powersetE,powersetI]) ).
thf(19,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,binunionEcases,powersetE,powersetI]) ).
thf(20,plain,
! [SV1: $i] :
( ( ! [SY19: $i] :
( ~ ( in @ SY19 @ ( powerset @ SV1 ) )
| ! [SY20: $i] :
( ~ ( in @ SY20 @ SY19 )
| ( in @ SY20 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(21,plain,
( ( ~ ( in @ sK2_SY16 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
| ~ ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV2: $i] :
( ( ! [SY21: $i] :
~ ( ~ ~ ( ~ ! [SY22: $i] :
( ~ ( in @ SY22 @ ( binunion @ SV2 @ SY21 ) )
| ( in @ SY22 @ SV2 )
| ( in @ SY22 @ SY21 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ ( binunion @ SV2 @ SY21 ) )
| ( in @ SY24 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY26: $i] :
( ~ ( in @ SY26 @ ( binunion @ SV2 @ SY21 ) )
| ! [SX3: $o] :
( ~ SX3
| ( in @ SY26 @ SY21 )
| SX3 ) )
| ~ ( ! [SY28: $i] :
~ ( in @ SY28 @ ( binunion @ SV2 @ SY21 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV3: $i] :
( ( ! [SY30: $i] :
( ~ ( ~ ( in @ ( sK4_Xx @ SY30 @ SV3 ) @ SY30 )
| ~ ~ ( in @ ( sK4_Xx @ SY30 @ SV3 ) @ SV3 ) )
| ( in @ SY30 @ ( powerset @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV1: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ ( powerset @ SV1 ) )
| ! [SY31: $i] :
( ~ ( in @ SY31 @ SV4 )
| ( in @ SY31 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( in @ sK2_SY16 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
| ~ ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(27,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ ( binunion @ SV2 @ SV5 ) )
| ( in @ SY32 @ SV2 )
| ( in @ SY32 @ SV5 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ ( binunion @ SV2 @ SV5 ) )
| ( in @ SY34 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ ( binunion @ SV2 @ SV5 ) )
| ! [SY37: $o] :
( ~ SY37
| ( in @ SY36 @ SV5 )
| SY37 ) )
| ~ ( ! [SY38: $i] :
~ ( in @ SY38 @ ( binunion @ SV2 @ SV5 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 ) )
| ( in @ SV6 @ ( powerset @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( ! [SY31: $i] :
( ~ ( in @ SY31 @ SV4 )
| ( in @ SY31 @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(30,plain,
( ( in @ sK2_SY16 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(31,plain,
( ( ~ ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
| ~ ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(32,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ ( binunion @ SV2 @ SV5 ) )
| ( in @ SY32 @ SV2 )
| ( in @ SY32 @ SV5 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ ( binunion @ SV2 @ SV5 ) )
| ( in @ SY34 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ ( binunion @ SV2 @ SV5 ) )
| ! [SY37: $o] :
( ~ SY37
| ( in @ SY36 @ SV5 )
| SY37 ) )
| ~ ( ! [SY38: $i] :
~ ( in @ SY38 @ ( binunion @ SV2 @ SV5 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 ) ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(34,plain,
! [SV1: $i,SV4: $i] :
( ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false )
| ( ( ! [SY31: $i] :
( ~ ( in @ SY31 @ SV4 )
| ( in @ SY31 @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(35,plain,
( ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
| ~ ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ ( binunion @ SV2 @ SV5 ) )
| ( in @ SY32 @ SV2 )
| ( in @ SY32 @ SV5 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ ( binunion @ SV2 @ SV5 ) )
| ( in @ SY34 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ~ ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ ( binunion @ SV2 @ SV5 ) )
| ! [SY37: $o] :
( ~ SY37
| ( in @ SY36 @ SV5 )
| SY37 ) )
| ~ ( ! [SY38: $i] :
~ ( in @ SY38 @ ( binunion @ SV2 @ SV5 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(38,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV4 )
| ( in @ SV7 @ SV1 ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(40,plain,
( ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(41,plain,
( ( ~ ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(42,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ ( binunion @ SV2 @ SV5 ) )
| ( in @ SY32 @ SV2 )
| ( in @ SY32 @ SV5 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ ( binunion @ SV2 @ SV5 ) )
| ( in @ SY34 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(43,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ ( binunion @ SV2 @ SV5 ) )
| ! [SY37: $o] :
( ~ SY37
| ( in @ SY36 @ SV5 )
| SY37 ) )
| ~ ( ! [SY38: $i] :
~ ( in @ SY38 @ ( binunion @ SV2 @ SV5 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(44,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV6 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(45,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(46,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV4 ) )
= $true )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(47,plain,
( ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(48,plain,
( ( ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(49,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ ( binunion @ SV2 @ SV5 ) )
| ( in @ SY32 @ SV2 )
| ( in @ SY32 @ SV5 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ ( binunion @ SV2 @ SV5 ) )
| ( in @ SY34 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(50,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ ( binunion @ SV2 @ SV5 ) )
| ! [SY37: $o] :
( ~ SY37
| ( in @ SY36 @ SV5 )
| SY37 ) )
| ~ ( ! [SY38: $i] :
~ ( in @ SY38 @ ( binunion @ SV2 @ SV5 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(51,plain,
! [SV3: $i,SV6: $i] :
( ( ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV6 )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(52,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(53,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( in @ SV7 @ SV4 )
= $false )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(54,plain,
( ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ ( binunion @ SV2 @ SV5 ) )
| ( in @ SY32 @ SV2 )
| ( in @ SY32 @ SV5 )
| ! [SX3: $o] : SX3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(56,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ ( binunion @ SV2 @ SV5 ) )
| ( in @ SY34 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(57,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ ( binunion @ SV2 @ SV5 ) )
| ! [SY37: $o] :
( ~ SY37
| ( in @ SY36 @ SV5 )
| SY37 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(58,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ! [SY38: $i] :
~ ( in @ SY38 @ ( binunion @ SV2 @ SV5 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(59,plain,
! [SV3: $i,SV6: $i] :
( ( ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(60,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY32: $i] :
( ~ ( in @ SY32 @ ( binunion @ SV2 @ SV5 ) )
| ( in @ SY32 @ SV2 )
| ( in @ SY32 @ SV5 )
| ! [SX3: $o] : SX3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(61,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY34: $i] :
( ~ ( in @ SY34 @ ( binunion @ SV2 @ SV5 ) )
| ( in @ SY34 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(62,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY36: $i] :
( ~ ( in @ SY36 @ ( binunion @ SV2 @ SV5 ) )
| ! [SY37: $o] :
( ~ SY37
| ( in @ SY36 @ SV5 )
| SY37 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(63,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY38: $i] :
~ ( in @ SY38 @ ( binunion @ SV2 @ SV5 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(64,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ~ ( in @ SV8 @ ( binunion @ SV2 @ SV5 ) )
| ( in @ SV8 @ SV2 )
| ( in @ SV8 @ SV5 )
| ! [SX3: $o] : SX3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV5: $i,SV2: $i,SV9: $i] :
( ( ~ ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
| ( in @ SV9 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV5: $i,SV2: $i,SV10: $i] :
( ( ~ ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
| ! [SY42: $o] :
( ~ SY42
| ( in @ SV10 @ SV5 )
| SY42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV5: $i,SV2: $i] :
( ( ( ! [SY38: $i] :
~ ( in @ SY38 @ ( binunion @ SV2 @ SV5 ) ) )
= $true )
| ( ( ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( binunion @ SV2 @ SV5 ) ) )
= $true )
| ( ( ( in @ SV8 @ SV2 )
| ( in @ SV8 @ SV5 )
| ! [SX3: $o] : SX3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV5: $i,SV2: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) ) )
= $true )
| ( ( ( in @ SV9 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV5: $i,SV2: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) ) )
= $true )
| ( ( ! [SY42: $o] :
( ~ SY42
| ( in @ SV10 @ SV5 )
| SY42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV5: $i,SV2: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) ) )
= $true )
| ( ( ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(72,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( in @ SV8 @ ( binunion @ SV2 @ SV5 ) )
= $false )
| ( ( ( in @ SV8 @ SV2 )
| ( in @ SV8 @ SV5 )
| ! [SX3: $o] : SX3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(73,plain,
! [SV5: $i,SV2: $i,SV9: $i] :
( ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
= $false )
| ( ( ( in @ SV9 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(74,plain,
! [SV5: $i,SV2: $i,SV10: $i] :
( ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
= $false )
| ( ( ! [SY42: $o] :
( ~ SY42
| ( in @ SV10 @ SV5 )
| SY42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV5: $i,SV2: $i,SV11: $i] :
( ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
= $false )
| ( ( ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( in @ SV8 @ SV2 )
= $true )
| ( ( ( in @ SV8 @ SV5 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV8 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV5: $i,SV2: $i,SV9: $i] :
( ( ( in @ SV9 @ SV2 )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV2: $i,SV5: $i,SV10: $i,SV12: $o] :
( ( ( ~ SV12
| ( in @ SV10 @ SV5 )
| SV12 )
= $true )
| ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV2: $i,SV5: $i,SV10: $i] :
( ( ( ~ $true
| ( in @ SV10 @ SV5 )
| $true )
= $true )
| ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV2: $i,SV5: $i,SV10: $i] :
( ( ( ~ $false
| ( in @ SV10 @ SV5 )
| $false )
= $true )
| ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[74]) ).
thf(81,plain,
! [SV5: $i,SV2: $i,SV11: $i,SV13: $o] :
( ( ( ~ SV13
| ~ SV13
| SV13 )
= $true )
| ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[75]) ).
thf(82,plain,
! [SV5: $i,SV2: $i,SV11: $i] :
( ( ( ~ $true
| ~ $true
| $true )
= $true )
| ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[75]) ).
thf(83,plain,
! [SV5: $i,SV2: $i,SV11: $i] :
( ( ( ~ $false
| ~ $false
| $false )
= $true )
| ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[75]) ).
thf(84,plain,
! [SV2: $i,SV5: $i,SV8: $i] :
( ( ( in @ SV8 @ SV5 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV8 @ SV2 )
= $true )
| ( ( in @ SV8 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(85,plain,
! [SV5: $i,SV2: $i,SV9: $i,SV14: $o] :
( ( ( ~ SV14
| SV14 )
= $true )
| ( ( in @ SV9 @ SV2 )
= $true )
| ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[77]) ).
thf(86,plain,
! [SV5: $i,SV2: $i,SV9: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV9 @ SV2 )
= $true )
| ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV5: $i,SV2: $i,SV9: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV9 @ SV2 )
= $true )
| ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[77]) ).
thf(88,plain,
! [SV2: $i,SV5: $i,SV10: $i,SV12: $o] :
( ( ( ~ SV12 )
= $true )
| ( ( ( in @ SV10 @ SV5 )
| SV12 )
= $true )
| ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(89,plain,
! [SV2: $i,SV5: $i,SV10: $i] :
( ( ( ~ $true )
= $true )
| ( ( ( in @ SV10 @ SV5 )
| $true )
= $true )
| ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(90,plain,
! [SV2: $i,SV5: $i,SV10: $i] :
( ( ( ~ $false )
= $true )
| ( ( ( in @ SV10 @ SV5 )
| $false )
= $true )
| ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(91,plain,
! [SV5: $i,SV2: $i,SV11: $i,SV13: $o] :
( ( ( ~ SV13 )
= $true )
| ( ( ~ SV13
| SV13 )
= $true )
| ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(92,plain,
! [SV5: $i,SV2: $i,SV11: $i] :
( ( ( ~ $true )
= $true )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(93,plain,
! [SV5: $i,SV2: $i,SV11: $i] :
( ( ( ~ $false )
= $true )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(94,plain,
! [SV2: $i,SV5: $i,SV8: $i,SV15: $o] :
( ( SV15 = $true )
| ( ( in @ SV8 @ SV5 )
= $true )
| ( ( in @ SV8 @ SV2 )
= $true )
| ( ( in @ SV8 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[84]) ).
thf(95,plain,
! [SV2: $i,SV5: $i,SV8: $i] :
( ( $true = $true )
| ( ( in @ SV8 @ SV5 )
= $true )
| ( ( in @ SV8 @ SV2 )
= $true )
| ( ( in @ SV8 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[84]) ).
thf(96,plain,
! [SV2: $i,SV5: $i,SV8: $i] :
( ( $false = $true )
| ( ( in @ SV8 @ SV5 )
= $true )
| ( ( in @ SV8 @ SV2 )
= $true )
| ( ( in @ SV8 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[84]) ).
thf(97,plain,
! [SV5: $i,SV2: $i,SV9: $i,SV14: $o] :
( ( ( ~ SV14 )
= $true )
| ( SV14 = $true )
| ( ( in @ SV9 @ SV2 )
= $true )
| ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(98,plain,
! [SV5: $i,SV2: $i,SV9: $i] :
( ( ( ~ $true )
= $true )
| ( $true = $true )
| ( ( in @ SV9 @ SV2 )
= $true )
| ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(99,plain,
! [SV5: $i,SV2: $i,SV9: $i] :
( ( ( ~ $false )
= $true )
| ( $false = $true )
| ( ( in @ SV9 @ SV2 )
= $true )
| ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(100,plain,
! [SV2: $i,SV5: $i,SV10: $i,SV12: $o] :
( ( SV12 = $false )
| ( ( ( in @ SV10 @ SV5 )
| SV12 )
= $true )
| ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(101,plain,
! [SV2: $i,SV5: $i,SV10: $i] :
( ( $true = $false )
| ( ( ( in @ SV10 @ SV5 )
| $true )
= $true )
| ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(102,plain,
! [SV2: $i,SV5: $i,SV10: $i] :
( ( $false = $false )
| ( ( ( in @ SV10 @ SV5 )
| $false )
= $true )
| ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(103,plain,
! [SV5: $i,SV2: $i,SV11: $i,SV13: $o] :
( ( SV13 = $false )
| ( ( ~ SV13
| SV13 )
= $true )
| ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(104,plain,
! [SV5: $i,SV2: $i,SV11: $i] :
( ( $true = $false )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(105,plain,
! [SV5: $i,SV2: $i,SV11: $i] :
( ( $false = $false )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(106,plain,
! [SV5: $i,SV2: $i,SV9: $i,SV14: $o] :
( ( SV14 = $false )
| ( SV14 = $true )
| ( ( in @ SV9 @ SV2 )
= $true )
| ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(107,plain,
! [SV5: $i,SV2: $i,SV9: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV9 @ SV2 )
= $true )
| ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(108,plain,
! [SV5: $i,SV2: $i,SV9: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV9 @ SV2 )
= $true )
| ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(109,plain,
! [SV2: $i,SV12: $o,SV5: $i,SV10: $i] :
( ( ( in @ SV10 @ SV5 )
= $true )
| ( SV12 = $true )
| ( SV12 = $false )
| ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(110,plain,
! [SV2: $i,SV5: $i,SV10: $i] :
( ( ( in @ SV10 @ SV5 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(111,plain,
! [SV2: $i,SV5: $i,SV10: $i] :
( ( ( in @ SV10 @ SV5 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(112,plain,
! [SV5: $i,SV2: $i,SV11: $i,SV13: $o] :
( ( ( ~ SV13 )
= $true )
| ( SV13 = $true )
| ( SV13 = $false )
| ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(113,plain,
! [SV5: $i,SV2: $i,SV11: $i] :
( ( ( ~ $true )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(114,plain,
! [SV5: $i,SV2: $i,SV11: $i] :
( ( ( ~ $false )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(115,plain,
! [SV5: $i,SV2: $i,SV11: $i,SV13: $o] :
( ( SV13 = $false )
| ( SV13 = $true )
| ( SV13 = $false )
| ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(116,plain,
! [SV5: $i,SV2: $i,SV11: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(117,plain,
! [SV5: $i,SV2: $i,SV11: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(118,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,117,116,115,111,110,109,108,107,106,96,95,94,59,54,53,51,47]) ).
thf(119,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU711^2 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 20:59:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 0
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 631
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)........
% 0.19/0.53
% 0.19/0.53 ********************************
% 0.19/0.53 * All subproblems solved! *
% 0.19/0.53 ********************************
% 0.19/0.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:118,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.54
% 0.19/0.54 %**** Beginning of derivation protocol ****
% 0.19/0.54 % SZS output start CNFRefutation
% See solution above
% 0.19/0.54
% 0.19/0.54 %**** End of derivation protocol ****
% 0.19/0.54 %**** no. of clauses in derivation: 119 ****
% 0.19/0.54 %**** clause counter: 118 ****
% 0.19/0.54
% 0.19/0.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:118,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------