TSTP Solution File: SET579^3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET579^3 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n021.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 03:03:00 EDT 2022
% Result : Theorem 11.34s 11.54s
% Output : CNFRefutation 11.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 47
% Syntax : Number of formulae : 232 ( 106 unt; 22 typ; 10 def)
% Number of atoms : 1399 ( 312 equ; 0 cnn)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 3070 ( 587 ~; 356 |; 2 &;2122 @)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 6 con; 0-3 aty)
% Number of variables : 522 ( 105 ^ 414 !; 3 ?; 522 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_mactual,type,
mactual: mworld ).
thf(tp_mand,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mbox,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(tp_mdia,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(tp_member,type,
member: $i > $i > mworld > $o ).
thf(tp_mequiv,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mexists_di,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(tp_mforall_di,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(tp_mimplies,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mlocal,type,
mlocal: ( mworld > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(tp_mor,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mrel,type,
mrel: mworld > mworld > $o ).
thf(tp_qmltpeq,type,
qmltpeq: $i > $i > mworld > $o ).
thf(tp_sK1_V,type,
sK1_V: mworld > mworld ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY23,type,
sK3_SY23: $i ).
thf(tp_sK4_SY34,type,
sK4_SY34: $i ).
thf(tp_sK5_SY31,type,
sK5_SY31: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > mworld > $o ).
thf(mand,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
& ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv) ).
thf(mexists_di,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
? [X: $i] : ( A @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_di) ).
thf(mforall_di,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
! [X: $i] : ( A @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di) ).
thf(mimplies,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(1,axiom,
( mlocal
@ ( mforall_di
@ ^ [B: $i] : ( subset @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(2,axiom,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mequiv @ ( subset @ B @ C )
@ ( mforall_di
@ ^ [D: $i] : ( mimplies @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(3,axiom,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mequiv @ ( qmltpeq @ B @ C ) @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(4,axiom,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] : ( mequiv @ ( member @ D @ ( difference @ B @ C ) ) @ ( mand @ ( member @ D @ B ) @ ( mnot @ ( member @ D @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
thf(5,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_substitution_2) ).
thf(6,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_substitution_1) ).
thf(7,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_substitution_2) ).
thf(8,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_substitution_1) ).
thf(9,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_substitution_2) ).
thf(10,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_substitution_1) ).
thf(11,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] :
( mforall_di
@ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(12,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(13,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(14,axiom,
! [W: mworld] :
? [V: mworld] : ( mrel @ W @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_serial) ).
thf(15,conjecture,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] :
( mimplies
@ ( mforall_di
@ ^ [E: $i] : ( mequiv @ ( member @ E @ B ) @ ( mand @ ( member @ E @ C ) @ ( mnot @ ( member @ E @ D ) ) ) ) )
@ ( qmltpeq @ B @ ( difference @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th20) ).
thf(16,negated_conjecture,
( ( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] :
( mimplies
@ ( mforall_di
@ ^ [E: $i] : ( mequiv @ ( member @ E @ B ) @ ( mand @ ( member @ E @ C ) @ ( mnot @ ( member @ E @ D ) ) ) ) )
@ ( qmltpeq @ B @ ( difference @ C @ D ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[15]) ).
thf(17,plain,
( ( ~ ( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] :
( mimplies
@ ( mforall_di
@ ^ [E: $i] : ( mequiv @ ( member @ E @ B ) @ ( mand @ ( member @ E @ C ) @ ( mnot @ ( member @ E @ D ) ) ) ) )
@ ( qmltpeq @ B @ ( difference @ C @ D ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [W: mworld] : ( mrel @ W @ ( sK1_V @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(19,plain,
( ( ! [W: mworld] : ( mrel @ W @ ( sK1_V @ W ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(20,plain,
( ( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( qmltpeq @ X @ X ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] :
( mforall_di
@ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(23,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(24,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(25,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(26,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(27,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(28,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(29,plain,
( ( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] : ( mequiv @ ( member @ D @ ( difference @ B @ C ) ) @ ( mand @ ( member @ D @ B ) @ ( mnot @ ( member @ D @ C ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(30,plain,
( ( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mequiv @ ( qmltpeq @ B @ C ) @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[3]) ).
thf(31,plain,
( ( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mequiv @ ( subset @ B @ C )
@ ( mforall_di
@ ^ [D: $i] : ( mimplies @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(32,plain,
( ( mlocal
@ ( mforall_di
@ ^ [B: $i] : ( subset @ B @ B ) ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(33,plain,
( ( ~ ( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] :
( mimplies
@ ( mforall_di
@ ^ [E: $i] : ( mequiv @ ( member @ E @ B ) @ ( mand @ ( member @ E @ C ) @ ( mnot @ ( member @ E @ D ) ) ) ) )
@ ( qmltpeq @ B @ ( difference @ C @ D ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(34,plain,
( ( ! [SX0: $i] : ( qmltpeq @ SX0 @ SX0 @ mactual ) )
= $true ),
inference(unfold_def,[status(thm)],[20,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(35,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ ( difference @ SX0 @ SX1 ) @ mactual )
| ~ ( ~ ( member @ SX2 @ SX0 @ mactual )
| ~ ~ ( member @ SX2 @ SX1 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX2 @ SX0 @ mactual )
| ~ ~ ( member @ SX2 @ SX1 @ mactual ) )
| ( member @ SX2 @ ( difference @ SX0 @ SX1 ) @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(36,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( member @ SX2 @ SX0 @ mactual ) )
| ( member @ SX2 @ SX1 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(37,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ SX1 @ SX0 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(38,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( member @ SX3 @ SX0 @ mactual )
| ~ ( ~ ( member @ SX3 @ SX1 @ mactual )
| ~ ~ ( member @ SX3 @ SX2 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX3 @ SX1 @ mactual )
| ~ ~ ( member @ SX3 @ SX2 @ mactual ) )
| ( member @ SX3 @ SX0 @ mactual ) ) )
| ( qmltpeq @ SX0 @ ( difference @ SX1 @ SX2 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(39,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( difference @ SX2 @ SX0 ) @ ( difference @ SX2 @ SX1 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(40,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( difference @ SX0 @ SX2 ) @ ( difference @ SX1 @ SX2 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(41,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX2 @ SX0 @ mactual ) )
| ( subset @ SX2 @ SX1 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(42,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( qmltpeq @ SX1 @ SX2 @ mactual ) )
| ( qmltpeq @ SX0 @ SX2 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(43,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 @ mactual )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual ) )
| ( subset @ SX0 @ SX1 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(44,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX0 @ SX2 @ mactual ) )
| ( subset @ SX1 @ SX2 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(45,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( ~ ( subset @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX1 @ SX0 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX1 @ SX0 @ mactual ) )
| ( qmltpeq @ SX0 @ SX1 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(46,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( member @ SX0 @ SX2 @ mactual ) )
| ( member @ SX1 @ SX2 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(47,plain,
( ( ! [SX0: $i] : ( subset @ SX0 @ SX0 @ mactual ) )
= $true ),
inference(unfold_def,[status(thm)],[32,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(48,plain,
! [SV1: mworld] :
( ( mrel @ SV1 @ ( sK1_V @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(49,plain,
! [SV2: $i] :
( ( qmltpeq @ SV2 @ SV2 @ mactual )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(50,plain,
! [SV3: $i] :
( ( ! [SY0: $i,SY1: $i] :
~ ( ~ ( ~ ( member @ SY1 @ ( difference @ SV3 @ SY0 ) @ mactual )
| ~ ( ~ ( member @ SY1 @ SV3 @ mactual )
| ~ ~ ( member @ SY1 @ SY0 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY1 @ SV3 @ mactual )
| ~ ~ ( member @ SY1 @ SY0 @ mactual ) )
| ( member @ SY1 @ ( difference @ SV3 @ SY0 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(51,plain,
! [SV4: $i] :
( ( ! [SY2: $i,SY3: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV4 @ SY2 @ mactual )
| ~ ( member @ SY3 @ SV4 @ mactual ) )
| ( member @ SY3 @ SY2 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(52,plain,
! [SV5: $i] :
( ( ! [SY4: $i] :
( ~ ( qmltpeq @ SV5 @ SY4 @ mactual )
| ( qmltpeq @ SY4 @ SV5 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(53,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( member @ SX3 @ SX0 @ mactual )
| ~ ( ~ ( member @ SX3 @ SX1 @ mactual )
| ~ ~ ( member @ SX3 @ SX2 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX3 @ SX1 @ mactual )
| ~ ~ ( member @ SX3 @ SX2 @ mactual ) )
| ( member @ SX3 @ SX0 @ mactual ) ) )
| ( qmltpeq @ SX0 @ ( difference @ SX1 @ SX2 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(54,plain,
! [SV6: $i] :
( ( ! [SY5: $i,SY6: $i] :
( ~ ( qmltpeq @ SV6 @ SY5 @ mactual )
| ( qmltpeq @ ( difference @ SY6 @ SV6 ) @ ( difference @ SY6 @ SY5 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(55,plain,
! [SV7: $i] :
( ( ! [SY7: $i,SY8: $i] :
( ~ ( qmltpeq @ SV7 @ SY7 @ mactual )
| ( qmltpeq @ ( difference @ SV7 @ SY8 ) @ ( difference @ SY7 @ SY8 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(56,plain,
! [SV8: $i] :
( ( ! [SY9: $i,SY10: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV8 @ SY9 @ mactual )
| ~ ( subset @ SY10 @ SV8 @ mactual ) )
| ( subset @ SY10 @ SY9 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(57,plain,
! [SV9: $i] :
( ( ! [SY11: $i,SY12: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV9 @ SY11 @ mactual )
| ~ ( qmltpeq @ SY11 @ SY12 @ mactual ) )
| ( qmltpeq @ SV9 @ SY12 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(58,plain,
! [SV10: $i] :
( ( ! [SY13: $i] :
~ ( ~ ( ~ ( subset @ SV10 @ SY13 @ mactual )
| ! [SY14: $i] :
( ~ ( member @ SY14 @ SV10 @ mactual )
| ( member @ SY14 @ SY13 @ mactual ) ) )
| ~ ( ~ ! [SY15: $i] :
( ~ ( member @ SY15 @ SV10 @ mactual )
| ( member @ SY15 @ SY13 @ mactual ) )
| ( subset @ SV10 @ SY13 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(59,plain,
! [SV11: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV11 @ SY16 @ mactual )
| ~ ( subset @ SV11 @ SY17 @ mactual ) )
| ( subset @ SY16 @ SY17 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(60,plain,
! [SV12: $i] :
( ( ! [SY18: $i] :
~ ( ~ ( ~ ( qmltpeq @ SV12 @ SY18 @ mactual )
| ~ ( ~ ( subset @ SV12 @ SY18 @ mactual )
| ~ ( subset @ SY18 @ SV12 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV12 @ SY18 @ mactual )
| ~ ( subset @ SY18 @ SV12 @ mactual ) )
| ( qmltpeq @ SV12 @ SY18 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(61,plain,
! [SV13: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV13 @ SY19 @ mactual )
| ~ ( member @ SV13 @ SY20 @ mactual ) )
| ( member @ SY19 @ SY20 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(62,plain,
! [SV14: $i] :
( ( subset @ SV14 @ SV14 @ mactual )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(63,plain,
! [SV15: $i,SV3: $i] :
( ( ! [SY21: $i] :
~ ( ~ ( ~ ( member @ SY21 @ ( difference @ SV3 @ SV15 ) @ mactual )
| ~ ( ~ ( member @ SY21 @ SV3 @ mactual )
| ~ ~ ( member @ SY21 @ SV15 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY21 @ SV3 @ mactual )
| ~ ~ ( member @ SY21 @ SV15 @ mactual ) )
| ( member @ SY21 @ ( difference @ SV3 @ SV15 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(64,plain,
! [SV16: $i,SV4: $i] :
( ( ! [SY22: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV4 @ SV16 @ mactual )
| ~ ( member @ SY22 @ SV4 @ mactual ) )
| ( member @ SY22 @ SV16 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(65,plain,
! [SV17: $i,SV5: $i] :
( ( ~ ( qmltpeq @ SV5 @ SV17 @ mactual )
| ( qmltpeq @ SV17 @ SV5 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(66,plain,
( ( ! [SY23: $i,SY24: $i] :
( ~ ! [SY25: $i] :
~ ( ~ ( ~ ( member @ SY25 @ sK2_SX0 @ mactual )
| ~ ( ~ ( member @ SY25 @ SY23 @ mactual )
| ~ ~ ( member @ SY25 @ SY24 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY25 @ SY23 @ mactual )
| ~ ~ ( member @ SY25 @ SY24 @ mactual ) )
| ( member @ SY25 @ sK2_SX0 @ mactual ) ) )
| ( qmltpeq @ sK2_SX0 @ ( difference @ SY23 @ SY24 ) @ mactual ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[53]) ).
thf(67,plain,
! [SV18: $i,SV6: $i] :
( ( ! [SY26: $i] :
( ~ ( qmltpeq @ SV6 @ SV18 @ mactual )
| ( qmltpeq @ ( difference @ SY26 @ SV6 ) @ ( difference @ SY26 @ SV18 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(68,plain,
! [SV19: $i,SV7: $i] :
( ( ! [SY27: $i] :
( ~ ( qmltpeq @ SV7 @ SV19 @ mactual )
| ( qmltpeq @ ( difference @ SV7 @ SY27 ) @ ( difference @ SV19 @ SY27 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(69,plain,
! [SV20: $i,SV8: $i] :
( ( ! [SY28: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV8 @ SV20 @ mactual )
| ~ ( subset @ SY28 @ SV8 @ mactual ) )
| ( subset @ SY28 @ SV20 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(70,plain,
! [SV21: $i,SV9: $i] :
( ( ! [SY29: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV9 @ SV21 @ mactual )
| ~ ( qmltpeq @ SV21 @ SY29 @ mactual ) )
| ( qmltpeq @ SV9 @ SY29 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(71,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV10 @ SV22 @ mactual )
| ! [SY30: $i] :
( ~ ( member @ SY30 @ SV10 @ mactual )
| ( member @ SY30 @ SV22 @ mactual ) ) )
| ~ ( ~ ! [SY31: $i] :
( ~ ( member @ SY31 @ SV10 @ mactual )
| ( member @ SY31 @ SV22 @ mactual ) )
| ( subset @ SV10 @ SV22 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(72,plain,
! [SV23: $i,SV11: $i] :
( ( ! [SY32: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV11 @ SV23 @ mactual )
| ~ ( subset @ SV11 @ SY32 @ mactual ) )
| ( subset @ SV23 @ SY32 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(73,plain,
! [SV24: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( qmltpeq @ SV12 @ SV24 @ mactual )
| ~ ( ~ ( subset @ SV12 @ SV24 @ mactual )
| ~ ( subset @ SV24 @ SV12 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV12 @ SV24 @ mactual )
| ~ ( subset @ SV24 @ SV12 @ mactual ) )
| ( qmltpeq @ SV12 @ SV24 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(74,plain,
! [SV25: $i,SV13: $i] :
( ( ! [SY33: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV13 @ SV25 @ mactual )
| ~ ( member @ SV13 @ SY33 @ mactual ) )
| ( member @ SV25 @ SY33 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(75,plain,
! [SV15: $i,SV3: $i,SV26: $i] :
( ( ~ ( ~ ( ~ ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
| ~ ( ~ ( member @ SV26 @ SV3 @ mactual )
| ~ ~ ( member @ SV26 @ SV15 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV26 @ SV3 @ mactual )
| ~ ~ ( member @ SV26 @ SV15 @ mactual ) )
| ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(76,plain,
! [SV27: $i,SV16: $i,SV4: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV4 @ SV16 @ mactual )
| ~ ( member @ SV27 @ SV4 @ mactual ) )
| ( member @ SV27 @ SV16 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(77,plain,
! [SV17: $i,SV5: $i] :
( ( ( ~ ( qmltpeq @ SV5 @ SV17 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV17 @ SV5 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(78,plain,
( ( ! [SY34: $i] :
( ~ ! [SY35: $i] :
~ ( ~ ( ~ ( member @ SY35 @ sK2_SX0 @ mactual )
| ~ ( ~ ( member @ SY35 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SY35 @ SY34 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY35 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SY35 @ SY34 @ mactual ) )
| ( member @ SY35 @ sK2_SX0 @ mactual ) ) )
| ( qmltpeq @ sK2_SX0 @ ( difference @ sK3_SY23 @ SY34 ) @ mactual ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[66]) ).
thf(79,plain,
! [SV28: $i,SV18: $i,SV6: $i] :
( ( ~ ( qmltpeq @ SV6 @ SV18 @ mactual )
| ( qmltpeq @ ( difference @ SV28 @ SV6 ) @ ( difference @ SV28 @ SV18 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(80,plain,
! [SV29: $i,SV19: $i,SV7: $i] :
( ( ~ ( qmltpeq @ SV7 @ SV19 @ mactual )
| ( qmltpeq @ ( difference @ SV7 @ SV29 ) @ ( difference @ SV19 @ SV29 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(81,plain,
! [SV30: $i,SV20: $i,SV8: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV8 @ SV20 @ mactual )
| ~ ( subset @ SV30 @ SV8 @ mactual ) )
| ( subset @ SV30 @ SV20 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(82,plain,
! [SV31: $i,SV21: $i,SV9: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV9 @ SV21 @ mactual )
| ~ ( qmltpeq @ SV21 @ SV31 @ mactual ) )
| ( qmltpeq @ SV9 @ SV31 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(83,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( ~ ( subset @ SV10 @ SV22 @ mactual )
| ! [SY30: $i] :
( ~ ( member @ SY30 @ SV10 @ mactual )
| ( member @ SY30 @ SV22 @ mactual ) ) )
| ~ ( ~ ! [SY31: $i] :
( ~ ( member @ SY31 @ SV10 @ mactual )
| ( member @ SY31 @ SV22 @ mactual ) )
| ( subset @ SV10 @ SV22 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(84,plain,
! [SV32: $i,SV23: $i,SV11: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV11 @ SV23 @ mactual )
| ~ ( subset @ SV11 @ SV32 @ mactual ) )
| ( subset @ SV23 @ SV32 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(85,plain,
! [SV24: $i,SV12: $i] :
( ( ~ ( ~ ( qmltpeq @ SV12 @ SV24 @ mactual )
| ~ ( ~ ( subset @ SV12 @ SV24 @ mactual )
| ~ ( subset @ SV24 @ SV12 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV12 @ SV24 @ mactual )
| ~ ( subset @ SV24 @ SV12 @ mactual ) )
| ( qmltpeq @ SV12 @ SV24 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(86,plain,
! [SV33: $i,SV25: $i,SV13: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV13 @ SV25 @ mactual )
| ~ ( member @ SV13 @ SV33 @ mactual ) )
| ( member @ SV25 @ SV33 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(87,plain,
! [SV15: $i,SV3: $i,SV26: $i] :
( ( ~ ( ~ ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
| ~ ( ~ ( member @ SV26 @ SV3 @ mactual )
| ~ ~ ( member @ SV26 @ SV15 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV26 @ SV3 @ mactual )
| ~ ~ ( member @ SV26 @ SV15 @ mactual ) )
| ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(88,plain,
! [SV27: $i,SV16: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV4 @ SV16 @ mactual )
| ~ ( member @ SV27 @ SV4 @ mactual ) ) )
= $true )
| ( ( member @ SV27 @ SV16 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(89,plain,
! [SV17: $i,SV5: $i] :
( ( ( qmltpeq @ SV5 @ SV17 @ mactual )
= $false )
| ( ( qmltpeq @ SV17 @ SV5 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(90,plain,
( ( ~ ! [SY36: $i] :
~ ( ~ ( ~ ( member @ SY36 @ sK2_SX0 @ mactual )
| ~ ( ~ ( member @ SY36 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SY36 @ sK4_SY34 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY36 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SY36 @ sK4_SY34 @ mactual ) )
| ( member @ SY36 @ sK2_SX0 @ mactual ) ) )
| ( qmltpeq @ sK2_SX0 @ ( difference @ sK3_SY23 @ sK4_SY34 ) @ mactual ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[78]) ).
thf(91,plain,
! [SV28: $i,SV18: $i,SV6: $i] :
( ( ( ~ ( qmltpeq @ SV6 @ SV18 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( difference @ SV28 @ SV6 ) @ ( difference @ SV28 @ SV18 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(92,plain,
! [SV29: $i,SV19: $i,SV7: $i] :
( ( ( ~ ( qmltpeq @ SV7 @ SV19 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( difference @ SV7 @ SV29 ) @ ( difference @ SV19 @ SV29 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(93,plain,
! [SV30: $i,SV20: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV8 @ SV20 @ mactual )
| ~ ( subset @ SV30 @ SV8 @ mactual ) ) )
= $true )
| ( ( subset @ SV30 @ SV20 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(94,plain,
! [SV31: $i,SV21: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV9 @ SV21 @ mactual )
| ~ ( qmltpeq @ SV21 @ SV31 @ mactual ) ) )
= $true )
| ( ( qmltpeq @ SV9 @ SV31 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(95,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( ~ ( subset @ SV10 @ SV22 @ mactual )
| ! [SY30: $i] :
( ~ ( member @ SY30 @ SV10 @ mactual )
| ( member @ SY30 @ SV22 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(96,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( ~ ! [SY31: $i] :
( ~ ( member @ SY31 @ SV10 @ mactual )
| ( member @ SY31 @ SV22 @ mactual ) )
| ( subset @ SV10 @ SV22 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(97,plain,
! [SV32: $i,SV23: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV11 @ SV23 @ mactual )
| ~ ( subset @ SV11 @ SV32 @ mactual ) ) )
= $true )
| ( ( subset @ SV23 @ SV32 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(98,plain,
! [SV24: $i,SV12: $i] :
( ( ~ ( ~ ( qmltpeq @ SV12 @ SV24 @ mactual )
| ~ ( ~ ( subset @ SV12 @ SV24 @ mactual )
| ~ ( subset @ SV24 @ SV12 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(99,plain,
! [SV24: $i,SV12: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV12 @ SV24 @ mactual )
| ~ ( subset @ SV24 @ SV12 @ mactual ) )
| ( qmltpeq @ SV12 @ SV24 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(100,plain,
! [SV33: $i,SV25: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV13 @ SV25 @ mactual )
| ~ ( member @ SV13 @ SV33 @ mactual ) ) )
= $true )
| ( ( member @ SV25 @ SV33 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(101,plain,
! [SV15: $i,SV3: $i,SV26: $i] :
( ( ~ ( ~ ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
| ~ ( ~ ( member @ SV26 @ SV3 @ mactual )
| ~ ~ ( member @ SV26 @ SV15 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(102,plain,
! [SV15: $i,SV3: $i,SV26: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV26 @ SV3 @ mactual )
| ~ ~ ( member @ SV26 @ SV15 @ mactual ) )
| ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(103,plain,
! [SV27: $i,SV16: $i,SV4: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV4 @ SV16 @ mactual )
| ~ ( member @ SV27 @ SV4 @ mactual ) ) )
= $false )
| ( ( member @ SV27 @ SV16 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(104,plain,
( ( ~ ! [SY36: $i] :
~ ( ~ ( ~ ( member @ SY36 @ sK2_SX0 @ mactual )
| ~ ( ~ ( member @ SY36 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SY36 @ sK4_SY34 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY36 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SY36 @ sK4_SY34 @ mactual ) )
| ( member @ SY36 @ sK2_SX0 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(105,plain,
( ( qmltpeq @ sK2_SX0 @ ( difference @ sK3_SY23 @ sK4_SY34 ) @ mactual )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(106,plain,
! [SV28: $i,SV18: $i,SV6: $i] :
( ( ( qmltpeq @ SV6 @ SV18 @ mactual )
= $false )
| ( ( qmltpeq @ ( difference @ SV28 @ SV6 ) @ ( difference @ SV28 @ SV18 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(107,plain,
! [SV29: $i,SV19: $i,SV7: $i] :
( ( ( qmltpeq @ SV7 @ SV19 @ mactual )
= $false )
| ( ( qmltpeq @ ( difference @ SV7 @ SV29 ) @ ( difference @ SV19 @ SV29 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(108,plain,
! [SV30: $i,SV20: $i,SV8: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV8 @ SV20 @ mactual )
| ~ ( subset @ SV30 @ SV8 @ mactual ) ) )
= $false )
| ( ( subset @ SV30 @ SV20 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(109,plain,
! [SV31: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV9 @ SV21 @ mactual )
| ~ ( qmltpeq @ SV21 @ SV31 @ mactual ) ) )
= $false )
| ( ( qmltpeq @ SV9 @ SV31 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(110,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( subset @ SV10 @ SV22 @ mactual )
| ! [SY30: $i] :
( ~ ( member @ SY30 @ SV10 @ mactual )
| ( member @ SY30 @ SV22 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(111,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ! [SY31: $i] :
( ~ ( member @ SY31 @ SV10 @ mactual )
| ( member @ SY31 @ SV22 @ mactual ) )
| ( subset @ SV10 @ SV22 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(112,plain,
! [SV32: $i,SV23: $i,SV11: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV11 @ SV23 @ mactual )
| ~ ( subset @ SV11 @ SV32 @ mactual ) ) )
= $false )
| ( ( subset @ SV23 @ SV32 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(113,plain,
! [SV24: $i,SV12: $i] :
( ( ~ ( qmltpeq @ SV12 @ SV24 @ mactual )
| ~ ( ~ ( subset @ SV12 @ SV24 @ mactual )
| ~ ( subset @ SV24 @ SV12 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(114,plain,
! [SV24: $i,SV12: $i] :
( ( ~ ~ ( ~ ( subset @ SV12 @ SV24 @ mactual )
| ~ ( subset @ SV24 @ SV12 @ mactual ) )
| ( qmltpeq @ SV12 @ SV24 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(115,plain,
! [SV33: $i,SV25: $i,SV13: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV13 @ SV25 @ mactual )
| ~ ( member @ SV13 @ SV33 @ mactual ) ) )
= $false )
| ( ( member @ SV25 @ SV33 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(116,plain,
! [SV15: $i,SV3: $i,SV26: $i] :
( ( ~ ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
| ~ ( ~ ( member @ SV26 @ SV3 @ mactual )
| ~ ~ ( member @ SV26 @ SV15 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(117,plain,
! [SV15: $i,SV3: $i,SV26: $i] :
( ( ~ ~ ( ~ ( member @ SV26 @ SV3 @ mactual )
| ~ ~ ( member @ SV26 @ SV15 @ mactual ) )
| ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(118,plain,
! [SV27: $i,SV16: $i,SV4: $i] :
( ( ( ~ ( qmltpeq @ SV4 @ SV16 @ mactual )
| ~ ( member @ SV27 @ SV4 @ mactual ) )
= $true )
| ( ( member @ SV27 @ SV16 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(119,plain,
( ( ! [SY36: $i] :
~ ( ~ ( ~ ( member @ SY36 @ sK2_SX0 @ mactual )
| ~ ( ~ ( member @ SY36 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SY36 @ sK4_SY34 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY36 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SY36 @ sK4_SY34 @ mactual ) )
| ( member @ SY36 @ sK2_SX0 @ mactual ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(120,plain,
! [SV30: $i,SV20: $i,SV8: $i] :
( ( ( ~ ( qmltpeq @ SV8 @ SV20 @ mactual )
| ~ ( subset @ SV30 @ SV8 @ mactual ) )
= $true )
| ( ( subset @ SV30 @ SV20 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(121,plain,
! [SV31: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( qmltpeq @ SV9 @ SV21 @ mactual )
| ~ ( qmltpeq @ SV21 @ SV31 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV9 @ SV31 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(122,plain,
! [SV22: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV22 @ mactual ) )
= $true )
| ( ( ! [SY30: $i] :
( ~ ( member @ SY30 @ SV10 @ mactual )
| ( member @ SY30 @ SV22 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV22: $i,SV10: $i] :
( ( ( ~ ! [SY31: $i] :
( ~ ( member @ SY31 @ SV10 @ mactual )
| ( member @ SY31 @ SV22 @ mactual ) ) )
= $true )
| ( ( subset @ SV10 @ SV22 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(124,plain,
! [SV32: $i,SV23: $i,SV11: $i] :
( ( ( ~ ( qmltpeq @ SV11 @ SV23 @ mactual )
| ~ ( subset @ SV11 @ SV32 @ mactual ) )
= $true )
| ( ( subset @ SV23 @ SV32 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(125,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ( qmltpeq @ SV12 @ SV24 @ mactual ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV12 @ SV24 @ mactual )
| ~ ( subset @ SV24 @ SV12 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(126,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV12 @ SV24 @ mactual )
| ~ ( subset @ SV24 @ SV12 @ mactual ) ) )
= $true )
| ( ( qmltpeq @ SV12 @ SV24 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(127,plain,
! [SV33: $i,SV25: $i,SV13: $i] :
( ( ( ~ ( qmltpeq @ SV13 @ SV25 @ mactual )
| ~ ( member @ SV13 @ SV33 @ mactual ) )
= $true )
| ( ( member @ SV25 @ SV33 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(128,plain,
! [SV15: $i,SV3: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual ) )
= $true )
| ( ( ~ ( ~ ( member @ SV26 @ SV3 @ mactual )
| ~ ~ ( member @ SV26 @ SV15 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(129,plain,
! [SV15: $i,SV3: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( member @ SV26 @ SV3 @ mactual )
| ~ ~ ( member @ SV26 @ SV15 @ mactual ) ) )
= $true )
| ( ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV27: $i,SV16: $i,SV4: $i] :
( ( ( ~ ( qmltpeq @ SV4 @ SV16 @ mactual ) )
= $true )
| ( ( ~ ( member @ SV27 @ SV4 @ mactual ) )
= $true )
| ( ( member @ SV27 @ SV16 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(131,plain,
! [SV34: $i] :
( ( ~ ( ~ ( ~ ( member @ SV34 @ sK2_SX0 @ mactual )
| ~ ( ~ ( member @ SV34 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV34 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) )
| ( member @ SV34 @ sK2_SX0 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(132,plain,
! [SV30: $i,SV20: $i,SV8: $i] :
( ( ( ~ ( qmltpeq @ SV8 @ SV20 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV30 @ SV8 @ mactual ) )
= $true )
| ( ( subset @ SV30 @ SV20 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(133,plain,
! [SV31: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( qmltpeq @ SV9 @ SV21 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV21 @ SV31 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV9 @ SV31 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(134,plain,
! [SV22: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV22 @ mactual )
= $false )
| ( ( ! [SY30: $i] :
( ~ ( member @ SY30 @ SV10 @ mactual )
| ( member @ SY30 @ SV22 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(135,plain,
! [SV22: $i,SV10: $i] :
( ( ( ! [SY31: $i] :
( ~ ( member @ SY31 @ SV10 @ mactual )
| ( member @ SY31 @ SV22 @ mactual ) ) )
= $false )
| ( ( subset @ SV10 @ SV22 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(136,plain,
! [SV32: $i,SV23: $i,SV11: $i] :
( ( ( ~ ( qmltpeq @ SV11 @ SV23 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV11 @ SV32 @ mactual ) )
= $true )
| ( ( subset @ SV23 @ SV32 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV24: $i,SV12: $i] :
( ( ( qmltpeq @ SV12 @ SV24 @ mactual )
= $false )
| ( ( ~ ( ~ ( subset @ SV12 @ SV24 @ mactual )
| ~ ( subset @ SV24 @ SV12 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ( ~ ( subset @ SV12 @ SV24 @ mactual )
| ~ ( subset @ SV24 @ SV12 @ mactual ) ) )
= $false )
| ( ( qmltpeq @ SV12 @ SV24 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(139,plain,
! [SV33: $i,SV25: $i,SV13: $i] :
( ( ( ~ ( qmltpeq @ SV13 @ SV25 @ mactual ) )
= $true )
| ( ( ~ ( member @ SV13 @ SV33 @ mactual ) )
= $true )
| ( ( member @ SV25 @ SV33 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(140,plain,
! [SV15: $i,SV3: $i,SV26: $i] :
( ( ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
= $false )
| ( ( ~ ( ~ ( member @ SV26 @ SV3 @ mactual )
| ~ ~ ( member @ SV26 @ SV15 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(141,plain,
! [SV15: $i,SV3: $i,SV26: $i] :
( ( ( ~ ( ~ ( member @ SV26 @ SV3 @ mactual )
| ~ ~ ( member @ SV26 @ SV15 @ mactual ) ) )
= $false )
| ( ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(142,plain,
! [SV27: $i,SV16: $i,SV4: $i] :
( ( ( qmltpeq @ SV4 @ SV16 @ mactual )
= $false )
| ( ( ~ ( member @ SV27 @ SV4 @ mactual ) )
= $true )
| ( ( member @ SV27 @ SV16 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(143,plain,
! [SV34: $i] :
( ( ~ ( ~ ( member @ SV34 @ sK2_SX0 @ mactual )
| ~ ( ~ ( member @ SV34 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV34 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) )
| ( member @ SV34 @ sK2_SX0 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV30: $i,SV20: $i,SV8: $i] :
( ( ( qmltpeq @ SV8 @ SV20 @ mactual )
= $false )
| ( ( ~ ( subset @ SV30 @ SV8 @ mactual ) )
= $true )
| ( ( subset @ SV30 @ SV20 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(145,plain,
! [SV31: $i,SV21: $i,SV9: $i] :
( ( ( qmltpeq @ SV9 @ SV21 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV21 @ SV31 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV9 @ SV31 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(146,plain,
! [SV22: $i,SV10: $i,SV35: $i] :
( ( ( ~ ( member @ SV35 @ SV10 @ mactual )
| ( member @ SV35 @ SV22 @ mactual ) )
= $true )
| ( ( subset @ SV10 @ SV22 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(147,plain,
! [SV10: $i,SV22: $i] :
( ( ( ~ ( member @ ( sK5_SY31 @ SV22 @ SV10 ) @ SV10 @ mactual )
| ( member @ ( sK5_SY31 @ SV22 @ SV10 ) @ SV22 @ mactual ) )
= $false )
| ( ( subset @ SV10 @ SV22 @ mactual )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[135]) ).
thf(148,plain,
! [SV32: $i,SV23: $i,SV11: $i] :
( ( ( qmltpeq @ SV11 @ SV23 @ mactual )
= $false )
| ( ( ~ ( subset @ SV11 @ SV32 @ mactual ) )
= $true )
| ( ( subset @ SV23 @ SV32 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(149,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV24 @ mactual )
| ~ ( subset @ SV24 @ SV12 @ mactual ) )
= $false )
| ( ( qmltpeq @ SV12 @ SV24 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(150,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV24 @ mactual )
| ~ ( subset @ SV24 @ SV12 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV12 @ SV24 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(151,plain,
! [SV33: $i,SV25: $i,SV13: $i] :
( ( ( qmltpeq @ SV13 @ SV25 @ mactual )
= $false )
| ( ( ~ ( member @ SV13 @ SV33 @ mactual ) )
= $true )
| ( ( member @ SV25 @ SV33 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(152,plain,
! [SV15: $i,SV3: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ SV3 @ mactual )
| ~ ~ ( member @ SV26 @ SV15 @ mactual ) )
= $false )
| ( ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(153,plain,
! [SV15: $i,SV3: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ SV3 @ mactual )
| ~ ~ ( member @ SV26 @ SV15 @ mactual ) )
= $true )
| ( ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(154,plain,
! [SV16: $i,SV4: $i,SV27: $i] :
( ( ( member @ SV27 @ SV4 @ mactual )
= $false )
| ( ( qmltpeq @ SV4 @ SV16 @ mactual )
= $false )
| ( ( member @ SV27 @ SV16 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(155,plain,
! [SV34: $i] :
( ( ~ ( ~ ( member @ SV34 @ sK2_SX0 @ mactual )
| ~ ( ~ ( member @ SV34 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(156,plain,
! [SV34: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV34 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) )
| ( member @ SV34 @ sK2_SX0 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(157,plain,
! [SV20: $i,SV8: $i,SV30: $i] :
( ( ( subset @ SV30 @ SV8 @ mactual )
= $false )
| ( ( qmltpeq @ SV8 @ SV20 @ mactual )
= $false )
| ( ( subset @ SV30 @ SV20 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(158,plain,
! [SV9: $i,SV31: $i,SV21: $i] :
( ( ( qmltpeq @ SV21 @ SV31 @ mactual )
= $false )
| ( ( qmltpeq @ SV9 @ SV21 @ mactual )
= $false )
| ( ( qmltpeq @ SV9 @ SV31 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(159,plain,
! [SV22: $i,SV10: $i,SV35: $i] :
( ( ( ~ ( member @ SV35 @ SV10 @ mactual ) )
= $true )
| ( ( member @ SV35 @ SV22 @ mactual )
= $true )
| ( ( subset @ SV10 @ SV22 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(160,plain,
! [SV10: $i,SV22: $i] :
( ( ( ~ ( member @ ( sK5_SY31 @ SV22 @ SV10 ) @ SV10 @ mactual ) )
= $false )
| ( ( subset @ SV10 @ SV22 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(161,plain,
! [SV10: $i,SV22: $i] :
( ( ( member @ ( sK5_SY31 @ SV22 @ SV10 ) @ SV22 @ mactual )
= $false )
| ( ( subset @ SV10 @ SV22 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(162,plain,
! [SV23: $i,SV32: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV32 @ mactual )
= $false )
| ( ( qmltpeq @ SV11 @ SV23 @ mactual )
= $false )
| ( ( subset @ SV23 @ SV32 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(163,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV24 @ mactual ) )
= $false )
| ( ( qmltpeq @ SV12 @ SV24 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(164,plain,
! [SV12: $i,SV24: $i] :
( ( ( ~ ( subset @ SV24 @ SV12 @ mactual ) )
= $false )
| ( ( qmltpeq @ SV12 @ SV24 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(165,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV24 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV24 @ SV12 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV12 @ SV24 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(166,plain,
! [SV25: $i,SV33: $i,SV13: $i] :
( ( ( member @ SV13 @ SV33 @ mactual )
= $false )
| ( ( qmltpeq @ SV13 @ SV25 @ mactual )
= $false )
| ( ( member @ SV25 @ SV33 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(167,plain,
! [SV15: $i,SV3: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ SV3 @ mactual ) )
= $false )
| ( ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(168,plain,
! [SV3: $i,SV15: $i,SV26: $i] :
( ( ( ~ ~ ( member @ SV26 @ SV15 @ mactual ) )
= $false )
| ( ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(169,plain,
! [SV15: $i,SV3: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ SV3 @ mactual ) )
= $true )
| ( ( ~ ~ ( member @ SV26 @ SV15 @ mactual ) )
= $true )
| ( ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(170,plain,
! [SV34: $i] :
( ( ~ ( member @ SV34 @ sK2_SX0 @ mactual )
| ~ ( ~ ( member @ SV34 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(171,plain,
! [SV34: $i] :
( ( ~ ~ ( ~ ( member @ SV34 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) )
| ( member @ SV34 @ sK2_SX0 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(172,plain,
! [SV22: $i,SV10: $i,SV35: $i] :
( ( ( member @ SV35 @ SV10 @ mactual )
= $false )
| ( ( member @ SV35 @ SV22 @ mactual )
= $true )
| ( ( subset @ SV10 @ SV22 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(173,plain,
! [SV10: $i,SV22: $i] :
( ( ( member @ ( sK5_SY31 @ SV22 @ SV10 ) @ SV10 @ mactual )
= $true )
| ( ( subset @ SV10 @ SV22 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(174,plain,
! [SV24: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV24 @ mactual )
= $true )
| ( ( qmltpeq @ SV12 @ SV24 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(175,plain,
! [SV12: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV12 @ mactual )
= $true )
| ( ( qmltpeq @ SV12 @ SV24 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(176,plain,
! [SV24: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV24 @ mactual )
= $false )
| ( ( ~ ( subset @ SV24 @ SV12 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV12 @ SV24 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(177,plain,
! [SV15: $i,SV3: $i,SV26: $i] :
( ( ( member @ SV26 @ SV3 @ mactual )
= $true )
| ( ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(178,plain,
! [SV3: $i,SV15: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ SV15 @ mactual ) )
= $true )
| ( ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(179,plain,
! [SV15: $i,SV3: $i,SV26: $i] :
( ( ( member @ SV26 @ SV3 @ mactual )
= $false )
| ( ( ~ ~ ( member @ SV26 @ SV15 @ mactual ) )
= $true )
| ( ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(180,plain,
! [SV34: $i] :
( ( ( ~ ( member @ SV34 @ sK2_SX0 @ mactual ) )
= $true )
| ( ( ~ ( ~ ( member @ SV34 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(181,plain,
! [SV34: $i] :
( ( ( ~ ~ ( ~ ( member @ SV34 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) ) )
= $true )
| ( ( member @ SV34 @ sK2_SX0 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(182,plain,
! [SV12: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV12 @ mactual )
= $false )
| ( ( subset @ SV12 @ SV24 @ mactual )
= $false )
| ( ( qmltpeq @ SV12 @ SV24 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(183,plain,
! [SV3: $i,SV15: $i,SV26: $i] :
( ( ( member @ SV26 @ SV15 @ mactual )
= $false )
| ( ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(184,plain,
! [SV3: $i,SV15: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ SV15 @ mactual ) )
= $false )
| ( ( member @ SV26 @ SV3 @ mactual )
= $false )
| ( ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(185,plain,
! [SV34: $i] :
( ( ( member @ SV34 @ sK2_SX0 @ mactual )
= $false )
| ( ( ~ ( ~ ( member @ SV34 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(186,plain,
! [SV34: $i] :
( ( ( ~ ( ~ ( member @ SV34 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) ) )
= $false )
| ( ( member @ SV34 @ sK2_SX0 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(187,plain,
! [SV3: $i,SV15: $i,SV26: $i] :
( ( ( member @ SV26 @ SV15 @ mactual )
= $true )
| ( ( member @ SV26 @ SV3 @ mactual )
= $false )
| ( ( member @ SV26 @ ( difference @ SV3 @ SV15 ) @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(188,plain,
! [SV34: $i] :
( ( ( ~ ( member @ SV34 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) )
= $false )
| ( ( member @ SV34 @ sK2_SX0 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(189,plain,
! [SV34: $i] :
( ( ( ~ ( member @ SV34 @ sK3_SY23 @ mactual )
| ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) )
= $true )
| ( ( member @ SV34 @ sK2_SX0 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(190,plain,
! [SV34: $i] :
( ( ( ~ ( member @ SV34 @ sK3_SY23 @ mactual ) )
= $false )
| ( ( member @ SV34 @ sK2_SX0 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(191,plain,
! [SV34: $i] :
( ( ( ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) )
= $false )
| ( ( member @ SV34 @ sK2_SX0 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(192,plain,
! [SV34: $i] :
( ( ( ~ ( member @ SV34 @ sK3_SY23 @ mactual ) )
= $true )
| ( ( ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) )
= $true )
| ( ( member @ SV34 @ sK2_SX0 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(193,plain,
! [SV34: $i] :
( ( ( member @ SV34 @ sK3_SY23 @ mactual )
= $true )
| ( ( member @ SV34 @ sK2_SX0 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(194,plain,
! [SV34: $i] :
( ( ( ~ ( member @ SV34 @ sK4_SY34 @ mactual ) )
= $true )
| ( ( member @ SV34 @ sK2_SX0 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(195,plain,
! [SV34: $i] :
( ( ( member @ SV34 @ sK3_SY23 @ mactual )
= $false )
| ( ( ~ ~ ( member @ SV34 @ sK4_SY34 @ mactual ) )
= $true )
| ( ( member @ SV34 @ sK2_SX0 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(196,plain,
! [SV34: $i] :
( ( ( member @ SV34 @ sK4_SY34 @ mactual )
= $false )
| ( ( member @ SV34 @ sK2_SX0 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(197,plain,
! [SV34: $i] :
( ( ( ~ ( member @ SV34 @ sK4_SY34 @ mactual ) )
= $false )
| ( ( member @ SV34 @ sK3_SY23 @ mactual )
= $false )
| ( ( member @ SV34 @ sK2_SX0 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(198,plain,
! [SV34: $i] :
( ( ( member @ SV34 @ sK4_SY34 @ mactual )
= $true )
| ( ( member @ SV34 @ sK3_SY23 @ mactual )
= $false )
| ( ( member @ SV34 @ sK2_SX0 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(199,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[48,198,196,193,187,183,182,177,175,174,173,172,166,162,161,158,157,154,107,106,105,89,62,49]) ).
thf(200,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET579^3 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jul 11 07:33:53 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.37
% 0.15/0.37 No.of.Axioms: 14
% 0.15/0.37
% 0.15/0.37 Length.of.Defs: 1574
% 0.15/0.37
% 0.15/0.37 Contains.Choice.Funs: false
% 0.15/0.39 (rf:0,axioms:14,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:16,loop_count:0,foatp_calls:0,translation:fof_full).........
% 11.34/11.54
% 11.34/11.54 ********************************
% 11.34/11.54 * All subproblems solved! *
% 11.34/11.54 ********************************
% 11.34/11.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:14,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:199,loop_count:0,foatp_calls:1,translation:fof_full)
% 11.34/11.55
% 11.34/11.55 %**** Beginning of derivation protocol ****
% 11.34/11.55 % SZS output start CNFRefutation
% See solution above
% 11.34/11.55
% 11.34/11.55 %**** End of derivation protocol ****
% 11.34/11.55 %**** no. of clauses in derivation: 200 ****
% 11.34/11.55 %**** clause counter: 199 ****
% 11.34/11.55
% 11.34/11.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:14,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:199,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------