TSTP Solution File: LCL953^8 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL953^8 : 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 : n020.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 : Sun Jul 17 12:27:49 EDT 2022
% Result : Theorem 0.40s 0.87s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 52
% Syntax : Number of formulae : 231 ( 83 unt; 34 typ; 10 def)
% Number of atoms : 2576 ( 651 equ; 0 cnn)
% Maximal formula atoms : 13 ( 13 avg)
% Number of connectives : 4610 ( 639 ~; 952 |; 3 &;3012 @)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 11 con; 0-6 aty)
% Number of variables : 881 ( 47 ^ 831 !; 3 ?; 881 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_disjoint,type,
disjoint: $i > $i > mworld > $o ).
thf(tp_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(tp_empty,type,
empty: $i > mworld > $o ).
thf(tp_in,type,
in: $i > $i > mworld > $o ).
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_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_sK10_SY86,type,
sK10_SY86: mworld ).
thf(tp_sK11_SY91,type,
sK11_SY91: mworld > mworld > $i > $i > mworld > mworld ).
thf(tp_sK12_SY94,type,
sK12_SY94: mworld > mworld > $i > $i > mworld > mworld ).
thf(tp_sK13_SY99,type,
sK13_SY99: mworld > mworld ).
thf(tp_sK14_SY96,type,
sK14_SY96: mworld > mworld > $i > $i > mworld > mworld ).
thf(tp_sK15_SY101,type,
sK15_SY101: mworld > mworld > mworld > $i > $i > mworld > mworld ).
thf(tp_sK16_SY102,type,
sK16_SY102: mworld > mworld > mworld > $i > $i > mworld > mworld ).
thf(tp_sK1_X,type,
sK1_X: mworld > $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: mworld ).
thf(tp_sK5_SY23,type,
sK5_SY23: $i ).
thf(tp_sK6_SY41,type,
sK6_SY41: mworld ).
thf(tp_sK7_SY53,type,
sK7_SY53: $i ).
thf(tp_sK8_SY73,type,
sK8_SY73: mworld ).
thf(tp_sK9_SY67,type,
sK9_SY67: mworld > mworld ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(mand,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
& ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv) ).
thf(mexists_di,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
? [X: $i] :
( ( eiw_di @ X @ W )
& ( A @ X @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di) ).
thf(mforall_di,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
! [X: $i] :
( ( eiw_di @ X @ W )
=> ( A @ X @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di) ).
thf(mimplies,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(1,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ A @ B ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ A ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(2,axiom,
( mlocal
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( mnot @ ( mbox @ ( empty @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(3,axiom,
( mlocal
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( empty @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(4,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( in @ A @ B ) ) @ ( mbox @ ( mnot @ ( mbox @ ( in @ B @ A ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(5,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( disjoint @ A @ B ) ) @ ( mbox @ ( disjoint @ B @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(6,axiom,
! [W: mworld] :
? [X: $i] : ( eiw_di @ X @ W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(7,axiom,
! [W: mworld] : ( mrel @ W @ W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(8,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ A @ B ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ A ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(9,negated_conjecture,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ A @ B ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ A ) @ B ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( ~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ A @ B ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ A ) @ B ) ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [W: mworld] : ( eiw_di @ ( sK1_X @ W ) @ W ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(12,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [W: mworld] : ( eiw_di @ ( sK1_X @ W ) @ W ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(14,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( disjoint @ A @ B ) ) @ ( mbox @ ( disjoint @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(15,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( in @ A @ B ) ) @ ( mbox @ ( mnot @ ( mbox @ ( in @ B @ A ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(16,plain,
( ( mlocal
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( empty @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[3]) ).
thf(17,plain,
( ( mlocal
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( mnot @ ( mbox @ ( empty @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(18,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ A @ B ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ A ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(19,plain,
( ( ~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ A @ B ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ A ) @ B ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(20,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ SX0 )
| ! [SX2: mworld] :
( ~ ( mrel @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( in @ SX1 @ SX3 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SX3 @ SX1 @ SX6 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(21,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ SX0 )
| ! [SX2: mworld] :
( ~ ( mrel @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ SX1 @ SX3 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ SX3 @ SX1 @ SX5 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(22,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( eiw_di @ SX0 @ mactual )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ mactual @ SX1 )
| ( empty @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(23,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( eiw_di @ SX0 @ mactual )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ mactual @ SX1 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ( empty @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(24,plain,
( ( ~ ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ SX0 )
| ! [SX2: mworld] :
( ~ ( mrel @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SX1 @ SX3 @ SX6 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ ( singleton @ SX1 ) @ SX3 @ SX5 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(25,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ SX0 )
| ! [SX2: mworld] :
( ~ ( mrel @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SX1 @ SX3 @ SX6 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ ( singleton @ SX1 ) @ SX3 @ SX5 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(26,plain,
! [SV1: mworld] :
( ( mrel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(27,plain,
! [SV2: mworld] :
( ( eiw_di @ ( sK1_X @ SV2 ) @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(28,plain,
! [SV3: mworld] :
( ( ~ ( mrel @ mactual @ SV3 )
| ! [SY0: $i] :
( ~ ( eiw_di @ SY0 @ SV3 )
| ! [SY1: mworld] :
( ~ ( mrel @ SV3 @ SY1 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY1 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY1 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( in @ SY0 @ SX3 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SX3 @ SY0 @ SX6 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(29,plain,
! [SV4: mworld] :
( ( ~ ( mrel @ mactual @ SV4 )
| ! [SY7: $i] :
( ~ ( eiw_di @ SY7 @ SV4 )
| ! [SY8: mworld] :
( ~ ( mrel @ SV4 @ SY8 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY8 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY8 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ SY7 @ SX3 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ SX3 @ SY7 @ SX5 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(30,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( eiw_di @ SX0 @ mactual )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ mactual @ SX1 )
| ( empty @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(31,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( eiw_di @ SX0 @ mactual )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ mactual @ SX1 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ( empty @ SX0 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(32,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ SX0 )
| ! [SX2: mworld] :
( ~ ( mrel @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SX1 @ SX3 @ SX6 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ ( singleton @ SX1 ) @ SX3 @ SX5 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(33,plain,
! [SV5: mworld] :
( ( ~ ( mrel @ mactual @ SV5 )
| ! [SY13: $i] :
( ~ ( eiw_di @ SY13 @ SV5 )
| ! [SY14: mworld] :
( ~ ( mrel @ SV5 @ SY14 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY14 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY14 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SY13 @ SX3 @ SX6 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ ( singleton @ SY13 ) @ SX3 @ SX5 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(34,plain,
! [SV3: mworld] :
( ( ( ~ ( mrel @ mactual @ SV3 ) )
= $true )
| ( ( ! [SY0: $i] :
( ~ ( eiw_di @ SY0 @ SV3 )
| ! [SY1: mworld] :
( ~ ( mrel @ SV3 @ SY1 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY1 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY1 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( in @ SY0 @ SX3 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SX3 @ SY0 @ SX6 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV4: mworld] :
( ( ( ~ ( mrel @ mactual @ SV4 ) )
= $true )
| ( ( ! [SY7: $i] :
( ~ ( eiw_di @ SY7 @ SV4 )
| ! [SY8: mworld] :
( ~ ( mrel @ SV4 @ SY8 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY8 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY8 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ SY7 @ SX3 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ SX3 @ SY7 @ SX5 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(36,plain,
( ( ~ ~ ( ~ ( eiw_di @ sK2_SX0 @ mactual )
| ~ ! [SY20: mworld] :
( ~ ( mrel @ mactual @ SY20 )
| ( empty @ sK2_SX0 @ SY20 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(37,plain,
( ( ~ ~ ( ~ ( eiw_di @ sK3_SX0 @ mactual )
| ~ ! [SY21: mworld] :
( ~ ( mrel @ mactual @ SY21 )
| ~ ! [SY22: mworld] :
( ~ ( mrel @ SY21 @ SY22 )
| ( empty @ sK3_SX0 @ SY22 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(38,plain,
( ( ~ ( mrel @ mactual @ sK4_SX0 )
| ! [SY23: $i] :
( ~ ( eiw_di @ SY23 @ sK4_SX0 )
| ! [SY24: mworld] :
( ~ ( mrel @ sK4_SX0 @ SY24 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY24 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY24 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SY23 @ SX3 @ SX6 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ ( singleton @ SY23 ) @ SX3 @ SX5 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[32]) ).
thf(39,plain,
! [SV5: mworld] :
( ( ( ~ ( mrel @ mactual @ SV5 ) )
= $true )
| ( ( ! [SY13: $i] :
( ~ ( eiw_di @ SY13 @ SV5 )
| ! [SY14: mworld] :
( ~ ( mrel @ SV5 @ SY14 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY14 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY14 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SY13 @ SX3 @ SX6 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ ( singleton @ SY13 ) @ SX3 @ SX5 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV3: mworld] :
( ( ( mrel @ mactual @ SV3 )
= $false )
| ( ( ! [SY0: $i] :
( ~ ( eiw_di @ SY0 @ SV3 )
| ! [SY1: mworld] :
( ~ ( mrel @ SV3 @ SY1 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY1 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY1 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( in @ SY0 @ SX3 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SX3 @ SY0 @ SX6 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV4: mworld] :
( ( ( mrel @ mactual @ SV4 )
= $false )
| ( ( ! [SY7: $i] :
( ~ ( eiw_di @ SY7 @ SV4 )
| ! [SY8: mworld] :
( ~ ( mrel @ SV4 @ SY8 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY8 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY8 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ SY7 @ SX3 @ SX5 ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ SX3 @ SY7 @ SX5 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(42,plain,
( ( ~ ( ~ ( eiw_di @ sK2_SX0 @ mactual )
| ~ ! [SY20: mworld] :
( ~ ( mrel @ mactual @ SY20 )
| ( empty @ sK2_SX0 @ SY20 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(43,plain,
( ( ~ ( ~ ( eiw_di @ sK3_SX0 @ mactual )
| ~ ! [SY21: mworld] :
( ~ ( mrel @ mactual @ SY21 )
| ~ ! [SY22: mworld] :
( ~ ( mrel @ SY21 @ SY22 )
| ( empty @ sK3_SX0 @ SY22 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(44,plain,
( ( ~ ( mrel @ mactual @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(45,plain,
( ( ! [SY23: $i] :
( ~ ( eiw_di @ SY23 @ sK4_SX0 )
| ! [SY24: mworld] :
( ~ ( mrel @ sK4_SX0 @ SY24 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY24 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY24 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SY23 @ SX3 @ SX6 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ ( singleton @ SY23 ) @ SX3 @ SX5 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(46,plain,
! [SV5: mworld] :
( ( ( mrel @ mactual @ SV5 )
= $false )
| ( ( ! [SY13: $i] :
( ~ ( eiw_di @ SY13 @ SV5 )
| ! [SY14: mworld] :
( ~ ( mrel @ SV5 @ SY14 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY14 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY14 @ SX4 )
| ~ ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ~ ! [SX6: mworld] :
( ~ ( mrel @ SX5 @ SX6 )
| ( in @ SY13 @ SX3 @ SX6 ) ) )
| ! [SX5: mworld] :
( ~ ( mrel @ SX4 @ SX5 )
| ( disjoint @ ( singleton @ SY13 ) @ SX3 @ SX5 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV3: mworld,SV6: $i] :
( ( ( ~ ( eiw_di @ SV6 @ SV3 )
| ! [SY30: mworld] :
( ~ ( mrel @ SV3 @ SY30 )
| ! [SY31: $i] :
( ~ ( eiw_di @ SY31 @ SY30 )
| ! [SY32: mworld] :
( ~ ( mrel @ SY30 @ SY32 )
| ~ ! [SY33: mworld] :
( ~ ( mrel @ SY32 @ SY33 )
| ( in @ SV6 @ SY31 @ SY33 ) )
| ! [SY34: mworld] :
( ~ ( mrel @ SY32 @ SY34 )
| ~ ! [SY35: mworld] :
( ~ ( mrel @ SY34 @ SY35 )
| ( in @ SY31 @ SV6 @ SY35 ) ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV4: mworld,SV7: $i] :
( ( ( ~ ( eiw_di @ SV7 @ SV4 )
| ! [SY36: mworld] :
( ~ ( mrel @ SV4 @ SY36 )
| ! [SY37: $i] :
( ~ ( eiw_di @ SY37 @ SY36 )
| ! [SY38: mworld] :
( ~ ( mrel @ SY36 @ SY38 )
| ~ ! [SY39: mworld] :
( ~ ( mrel @ SY38 @ SY39 )
| ( disjoint @ SV7 @ SY37 @ SY39 ) )
| ! [SY40: mworld] :
( ~ ( mrel @ SY38 @ SY40 )
| ( disjoint @ SY37 @ SV7 @ SY40 ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(49,plain,
( ( ~ ( eiw_di @ sK2_SX0 @ mactual )
| ~ ! [SY20: mworld] :
( ~ ( mrel @ mactual @ SY20 )
| ( empty @ sK2_SX0 @ SY20 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(50,plain,
( ( ~ ( eiw_di @ sK3_SX0 @ mactual )
| ~ ! [SY21: mworld] :
( ~ ( mrel @ mactual @ SY21 )
| ~ ! [SY22: mworld] :
( ~ ( mrel @ SY21 @ SY22 )
| ( empty @ sK3_SX0 @ SY22 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(51,plain,
( ( mrel @ mactual @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(52,plain,
( ( ~ ( eiw_di @ sK5_SY23 @ sK4_SX0 )
| ! [SY41: mworld] :
( ~ ( mrel @ sK4_SX0 @ SY41 )
| ! [SY42: $i] :
( ~ ( eiw_di @ SY42 @ SY41 )
| ! [SY43: mworld] :
( ~ ( mrel @ SY41 @ SY43 )
| ~ ! [SY44: mworld] :
( ~ ( mrel @ SY43 @ SY44 )
| ~ ! [SY45: mworld] :
( ~ ( mrel @ SY44 @ SY45 )
| ( in @ sK5_SY23 @ SY42 @ SY45 ) ) )
| ! [SY46: mworld] :
( ~ ( mrel @ SY43 @ SY46 )
| ( disjoint @ ( singleton @ sK5_SY23 ) @ SY42 @ SY46 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[45]) ).
thf(53,plain,
! [SV5: mworld,SV8: $i] :
( ( ( ~ ( eiw_di @ SV8 @ SV5 )
| ! [SY47: mworld] :
( ~ ( mrel @ SV5 @ SY47 )
| ! [SY48: $i] :
( ~ ( eiw_di @ SY48 @ SY47 )
| ! [SY49: mworld] :
( ~ ( mrel @ SY47 @ SY49 )
| ~ ! [SY50: mworld] :
( ~ ( mrel @ SY49 @ SY50 )
| ~ ! [SY51: mworld] :
( ~ ( mrel @ SY50 @ SY51 )
| ( in @ SV8 @ SY48 @ SY51 ) ) )
| ! [SY52: mworld] :
( ~ ( mrel @ SY49 @ SY52 )
| ( disjoint @ ( singleton @ SV8 ) @ SY48 @ SY52 ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(54,plain,
! [SV3: mworld,SV6: $i] :
( ( ( ~ ( eiw_di @ SV6 @ SV3 ) )
= $true )
| ( ( ! [SY30: mworld] :
( ~ ( mrel @ SV3 @ SY30 )
| ! [SY31: $i] :
( ~ ( eiw_di @ SY31 @ SY30 )
| ! [SY32: mworld] :
( ~ ( mrel @ SY30 @ SY32 )
| ~ ! [SY33: mworld] :
( ~ ( mrel @ SY32 @ SY33 )
| ( in @ SV6 @ SY31 @ SY33 ) )
| ! [SY34: mworld] :
( ~ ( mrel @ SY32 @ SY34 )
| ~ ! [SY35: mworld] :
( ~ ( mrel @ SY34 @ SY35 )
| ( in @ SY31 @ SV6 @ SY35 ) ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(55,plain,
! [SV4: mworld,SV7: $i] :
( ( ( ~ ( eiw_di @ SV7 @ SV4 ) )
= $true )
| ( ( ! [SY36: mworld] :
( ~ ( mrel @ SV4 @ SY36 )
| ! [SY37: $i] :
( ~ ( eiw_di @ SY37 @ SY36 )
| ! [SY38: mworld] :
( ~ ( mrel @ SY36 @ SY38 )
| ~ ! [SY39: mworld] :
( ~ ( mrel @ SY38 @ SY39 )
| ( disjoint @ SV7 @ SY37 @ SY39 ) )
| ! [SY40: mworld] :
( ~ ( mrel @ SY38 @ SY40 )
| ( disjoint @ SY37 @ SV7 @ SY40 ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(56,plain,
( ( ~ ( eiw_di @ sK2_SX0 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(57,plain,
( ( ~ ! [SY20: mworld] :
( ~ ( mrel @ mactual @ SY20 )
| ( empty @ sK2_SX0 @ SY20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(58,plain,
( ( ~ ( eiw_di @ sK3_SX0 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(59,plain,
( ( ~ ! [SY21: mworld] :
( ~ ( mrel @ mactual @ SY21 )
| ~ ! [SY22: mworld] :
( ~ ( mrel @ SY21 @ SY22 )
| ( empty @ sK3_SX0 @ SY22 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(60,plain,
( ( ~ ( eiw_di @ sK5_SY23 @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(61,plain,
( ( ! [SY41: mworld] :
( ~ ( mrel @ sK4_SX0 @ SY41 )
| ! [SY42: $i] :
( ~ ( eiw_di @ SY42 @ SY41 )
| ! [SY43: mworld] :
( ~ ( mrel @ SY41 @ SY43 )
| ~ ! [SY44: mworld] :
( ~ ( mrel @ SY43 @ SY44 )
| ~ ! [SY45: mworld] :
( ~ ( mrel @ SY44 @ SY45 )
| ( in @ sK5_SY23 @ SY42 @ SY45 ) ) )
| ! [SY46: mworld] :
( ~ ( mrel @ SY43 @ SY46 )
| ( disjoint @ ( singleton @ sK5_SY23 ) @ SY42 @ SY46 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(62,plain,
! [SV5: mworld,SV8: $i] :
( ( ( ~ ( eiw_di @ SV8 @ SV5 ) )
= $true )
| ( ( ! [SY47: mworld] :
( ~ ( mrel @ SV5 @ SY47 )
| ! [SY48: $i] :
( ~ ( eiw_di @ SY48 @ SY47 )
| ! [SY49: mworld] :
( ~ ( mrel @ SY47 @ SY49 )
| ~ ! [SY50: mworld] :
( ~ ( mrel @ SY49 @ SY50 )
| ~ ! [SY51: mworld] :
( ~ ( mrel @ SY50 @ SY51 )
| ( in @ SV8 @ SY48 @ SY51 ) ) )
| ! [SY52: mworld] :
( ~ ( mrel @ SY49 @ SY52 )
| ( disjoint @ ( singleton @ SV8 ) @ SY48 @ SY52 ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(63,plain,
! [SV3: mworld,SV6: $i] :
( ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( ! [SY30: mworld] :
( ~ ( mrel @ SV3 @ SY30 )
| ! [SY31: $i] :
( ~ ( eiw_di @ SY31 @ SY30 )
| ! [SY32: mworld] :
( ~ ( mrel @ SY30 @ SY32 )
| ~ ! [SY33: mworld] :
( ~ ( mrel @ SY32 @ SY33 )
| ( in @ SV6 @ SY31 @ SY33 ) )
| ! [SY34: mworld] :
( ~ ( mrel @ SY32 @ SY34 )
| ~ ! [SY35: mworld] :
( ~ ( mrel @ SY34 @ SY35 )
| ( in @ SY31 @ SV6 @ SY35 ) ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(64,plain,
! [SV4: mworld,SV7: $i] :
( ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( ! [SY36: mworld] :
( ~ ( mrel @ SV4 @ SY36 )
| ! [SY37: $i] :
( ~ ( eiw_di @ SY37 @ SY36 )
| ! [SY38: mworld] :
( ~ ( mrel @ SY36 @ SY38 )
| ~ ! [SY39: mworld] :
( ~ ( mrel @ SY38 @ SY39 )
| ( disjoint @ SV7 @ SY37 @ SY39 ) )
| ! [SY40: mworld] :
( ~ ( mrel @ SY38 @ SY40 )
| ( disjoint @ SY37 @ SV7 @ SY40 ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(65,plain,
( ( eiw_di @ sK2_SX0 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(66,plain,
( ( ! [SY20: mworld] :
( ~ ( mrel @ mactual @ SY20 )
| ( empty @ sK2_SX0 @ SY20 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(67,plain,
( ( eiw_di @ sK3_SX0 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(68,plain,
( ( ! [SY21: mworld] :
( ~ ( mrel @ mactual @ SY21 )
| ~ ! [SY22: mworld] :
( ~ ( mrel @ SY21 @ SY22 )
| ( empty @ sK3_SX0 @ SY22 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(69,plain,
( ( eiw_di @ sK5_SY23 @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(70,plain,
( ( ~ ( mrel @ sK4_SX0 @ sK6_SY41 )
| ! [SY53: $i] :
( ~ ( eiw_di @ SY53 @ sK6_SY41 )
| ! [SY54: mworld] :
( ~ ( mrel @ sK6_SY41 @ SY54 )
| ~ ! [SY44: mworld] :
( ~ ( mrel @ SY54 @ SY44 )
| ~ ! [SY45: mworld] :
( ~ ( mrel @ SY44 @ SY45 )
| ( in @ sK5_SY23 @ SY53 @ SY45 ) ) )
| ! [SY46: mworld] :
( ~ ( mrel @ SY54 @ SY46 )
| ( disjoint @ ( singleton @ sK5_SY23 ) @ SY53 @ SY46 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(71,plain,
! [SV5: mworld,SV8: $i] :
( ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( ! [SY47: mworld] :
( ~ ( mrel @ SV5 @ SY47 )
| ! [SY48: $i] :
( ~ ( eiw_di @ SY48 @ SY47 )
| ! [SY49: mworld] :
( ~ ( mrel @ SY47 @ SY49 )
| ~ ! [SY50: mworld] :
( ~ ( mrel @ SY49 @ SY50 )
| ~ ! [SY51: mworld] :
( ~ ( mrel @ SY50 @ SY51 )
| ( in @ SV8 @ SY48 @ SY51 ) ) )
| ! [SY52: mworld] :
( ~ ( mrel @ SY49 @ SY52 )
| ( disjoint @ ( singleton @ SV8 ) @ SY48 @ SY52 ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(72,plain,
! [SV6: $i,SV9: mworld,SV3: mworld] :
( ( ( ~ ( mrel @ SV3 @ SV9 )
| ! [SY58: $i] :
( ~ ( eiw_di @ SY58 @ SV9 )
| ! [SY59: mworld] :
( ~ ( mrel @ SV9 @ SY59 )
| ~ ! [SY33: mworld] :
( ~ ( mrel @ SY59 @ SY33 )
| ( in @ SV6 @ SY58 @ SY33 ) )
| ! [SY34: mworld] :
( ~ ( mrel @ SY59 @ SY34 )
| ~ ! [SY35: mworld] :
( ~ ( mrel @ SY34 @ SY35 )
| ( in @ SY58 @ SV6 @ SY35 ) ) ) ) ) )
= $true )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(73,plain,
! [SV7: $i,SV10: mworld,SV4: mworld] :
( ( ( ~ ( mrel @ SV4 @ SV10 )
| ! [SY63: $i] :
( ~ ( eiw_di @ SY63 @ SV10 )
| ! [SY64: mworld] :
( ~ ( mrel @ SV10 @ SY64 )
| ~ ! [SY39: mworld] :
( ~ ( mrel @ SY64 @ SY39 )
| ( disjoint @ SV7 @ SY63 @ SY39 ) )
| ! [SY40: mworld] :
( ~ ( mrel @ SY64 @ SY40 )
| ( disjoint @ SY63 @ SV7 @ SY40 ) ) ) ) )
= $true )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(74,plain,
! [SV11: mworld] :
( ( ~ ( mrel @ mactual @ SV11 )
| ( empty @ sK2_SX0 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(75,plain,
! [SV12: mworld] :
( ( ~ ( mrel @ mactual @ SV12 )
| ~ ! [SY67: mworld] :
( ~ ( mrel @ SV12 @ SY67 )
| ( empty @ sK3_SX0 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(76,plain,
( ( ~ ( mrel @ sK4_SX0 @ sK6_SY41 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(77,plain,
( ( ! [SY53: $i] :
( ~ ( eiw_di @ SY53 @ sK6_SY41 )
| ! [SY54: mworld] :
( ~ ( mrel @ sK6_SY41 @ SY54 )
| ~ ! [SY44: mworld] :
( ~ ( mrel @ SY54 @ SY44 )
| ~ ! [SY45: mworld] :
( ~ ( mrel @ SY44 @ SY45 )
| ( in @ sK5_SY23 @ SY53 @ SY45 ) ) )
| ! [SY46: mworld] :
( ~ ( mrel @ SY54 @ SY46 )
| ( disjoint @ ( singleton @ sK5_SY23 ) @ SY53 @ SY46 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(78,plain,
! [SV8: $i,SV13: mworld,SV5: mworld] :
( ( ( ~ ( mrel @ SV5 @ SV13 )
| ! [SY68: $i] :
( ~ ( eiw_di @ SY68 @ SV13 )
| ! [SY69: mworld] :
( ~ ( mrel @ SV13 @ SY69 )
| ~ ! [SY50: mworld] :
( ~ ( mrel @ SY69 @ SY50 )
| ~ ! [SY51: mworld] :
( ~ ( mrel @ SY50 @ SY51 )
| ( in @ SV8 @ SY68 @ SY51 ) ) )
| ! [SY52: mworld] :
( ~ ( mrel @ SY69 @ SY52 )
| ( disjoint @ ( singleton @ SV8 ) @ SY68 @ SY52 ) ) ) ) )
= $true )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(79,plain,
! [SV6: $i,SV9: mworld,SV3: mworld] :
( ( ( ~ ( mrel @ SV3 @ SV9 ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( eiw_di @ SY58 @ SV9 )
| ! [SY59: mworld] :
( ~ ( mrel @ SV9 @ SY59 )
| ~ ! [SY33: mworld] :
( ~ ( mrel @ SY59 @ SY33 )
| ( in @ SV6 @ SY58 @ SY33 ) )
| ! [SY34: mworld] :
( ~ ( mrel @ SY59 @ SY34 )
| ~ ! [SY35: mworld] :
( ~ ( mrel @ SY34 @ SY35 )
| ( in @ SY58 @ SV6 @ SY35 ) ) ) ) ) )
= $true )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(80,plain,
! [SV7: $i,SV10: mworld,SV4: mworld] :
( ( ( ~ ( mrel @ SV4 @ SV10 ) )
= $true )
| ( ( ! [SY63: $i] :
( ~ ( eiw_di @ SY63 @ SV10 )
| ! [SY64: mworld] :
( ~ ( mrel @ SV10 @ SY64 )
| ~ ! [SY39: mworld] :
( ~ ( mrel @ SY64 @ SY39 )
| ( disjoint @ SV7 @ SY63 @ SY39 ) )
| ! [SY40: mworld] :
( ~ ( mrel @ SY64 @ SY40 )
| ( disjoint @ SY63 @ SV7 @ SY40 ) ) ) ) )
= $true )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(81,plain,
! [SV11: mworld] :
( ( ( ~ ( mrel @ mactual @ SV11 ) )
= $true )
| ( ( empty @ sK2_SX0 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(82,plain,
! [SV12: mworld] :
( ( ( ~ ( mrel @ mactual @ SV12 ) )
= $true )
| ( ( ~ ! [SY67: mworld] :
( ~ ( mrel @ SV12 @ SY67 )
| ( empty @ sK3_SX0 @ SY67 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(83,plain,
( ( mrel @ sK4_SX0 @ sK6_SY41 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(84,plain,
( ( ~ ( eiw_di @ sK7_SY53 @ sK6_SY41 )
| ! [SY73: mworld] :
( ~ ( mrel @ sK6_SY41 @ SY73 )
| ~ ! [SY74: mworld] :
( ~ ( mrel @ SY73 @ SY74 )
| ~ ! [SY75: mworld] :
( ~ ( mrel @ SY74 @ SY75 )
| ( in @ sK5_SY23 @ sK7_SY53 @ SY75 ) ) )
| ! [SY76: mworld] :
( ~ ( mrel @ SY73 @ SY76 )
| ( disjoint @ ( singleton @ sK5_SY23 ) @ sK7_SY53 @ SY76 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[77]) ).
thf(85,plain,
! [SV8: $i,SV13: mworld,SV5: mworld] :
( ( ( ~ ( mrel @ SV5 @ SV13 ) )
= $true )
| ( ( ! [SY68: $i] :
( ~ ( eiw_di @ SY68 @ SV13 )
| ! [SY69: mworld] :
( ~ ( mrel @ SV13 @ SY69 )
| ~ ! [SY50: mworld] :
( ~ ( mrel @ SY69 @ SY50 )
| ~ ! [SY51: mworld] :
( ~ ( mrel @ SY50 @ SY51 )
| ( in @ SV8 @ SY68 @ SY51 ) ) )
| ! [SY52: mworld] :
( ~ ( mrel @ SY69 @ SY52 )
| ( disjoint @ ( singleton @ SV8 ) @ SY68 @ SY52 ) ) ) ) )
= $true )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV6: $i,SV9: mworld,SV3: mworld] :
( ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( ! [SY58: $i] :
( ~ ( eiw_di @ SY58 @ SV9 )
| ! [SY59: mworld] :
( ~ ( mrel @ SV9 @ SY59 )
| ~ ! [SY33: mworld] :
( ~ ( mrel @ SY59 @ SY33 )
| ( in @ SV6 @ SY58 @ SY33 ) )
| ! [SY34: mworld] :
( ~ ( mrel @ SY59 @ SY34 )
| ~ ! [SY35: mworld] :
( ~ ( mrel @ SY34 @ SY35 )
| ( in @ SY58 @ SV6 @ SY35 ) ) ) ) ) )
= $true )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(87,plain,
! [SV7: $i,SV10: mworld,SV4: mworld] :
( ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( ! [SY63: $i] :
( ~ ( eiw_di @ SY63 @ SV10 )
| ! [SY64: mworld] :
( ~ ( mrel @ SV10 @ SY64 )
| ~ ! [SY39: mworld] :
( ~ ( mrel @ SY64 @ SY39 )
| ( disjoint @ SV7 @ SY63 @ SY39 ) )
| ! [SY40: mworld] :
( ~ ( mrel @ SY64 @ SY40 )
| ( disjoint @ SY63 @ SV7 @ SY40 ) ) ) ) )
= $true )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(88,plain,
! [SV11: mworld] :
( ( ( mrel @ mactual @ SV11 )
= $false )
| ( ( empty @ sK2_SX0 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(89,plain,
! [SV12: mworld] :
( ( ( mrel @ mactual @ SV12 )
= $false )
| ( ( ~ ! [SY67: mworld] :
( ~ ( mrel @ SV12 @ SY67 )
| ( empty @ sK3_SX0 @ SY67 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(90,plain,
( ( ~ ( eiw_di @ sK7_SY53 @ sK6_SY41 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(91,plain,
( ( ! [SY73: mworld] :
( ~ ( mrel @ sK6_SY41 @ SY73 )
| ~ ! [SY74: mworld] :
( ~ ( mrel @ SY73 @ SY74 )
| ~ ! [SY75: mworld] :
( ~ ( mrel @ SY74 @ SY75 )
| ( in @ sK5_SY23 @ sK7_SY53 @ SY75 ) ) )
| ! [SY76: mworld] :
( ~ ( mrel @ SY73 @ SY76 )
| ( disjoint @ ( singleton @ sK5_SY23 ) @ sK7_SY53 @ SY76 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(92,plain,
! [SV8: $i,SV13: mworld,SV5: mworld] :
( ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( ! [SY68: $i] :
( ~ ( eiw_di @ SY68 @ SV13 )
| ! [SY69: mworld] :
( ~ ( mrel @ SV13 @ SY69 )
| ~ ! [SY50: mworld] :
( ~ ( mrel @ SY69 @ SY50 )
| ~ ! [SY51: mworld] :
( ~ ( mrel @ SY50 @ SY51 )
| ( in @ SV8 @ SY68 @ SY51 ) ) )
| ! [SY52: mworld] :
( ~ ( mrel @ SY69 @ SY52 )
| ( disjoint @ ( singleton @ SV8 ) @ SY68 @ SY52 ) ) ) ) )
= $true )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(93,plain,
! [SV3: mworld,SV6: $i,SV9: mworld,SV14: $i] :
( ( ( ~ ( eiw_di @ SV14 @ SV9 )
| ! [SY77: mworld] :
( ~ ( mrel @ SV9 @ SY77 )
| ~ ! [SY78: mworld] :
( ~ ( mrel @ SY77 @ SY78 )
| ( in @ SV6 @ SV14 @ SY78 ) )
| ! [SY79: mworld] :
( ~ ( mrel @ SY77 @ SY79 )
| ~ ! [SY80: mworld] :
( ~ ( mrel @ SY79 @ SY80 )
| ( in @ SV14 @ SV6 @ SY80 ) ) ) ) )
= $true )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(94,plain,
! [SV4: mworld,SV7: $i,SV10: mworld,SV15: $i] :
( ( ( ~ ( eiw_di @ SV15 @ SV10 )
| ! [SY81: mworld] :
( ~ ( mrel @ SV10 @ SY81 )
| ~ ! [SY82: mworld] :
( ~ ( mrel @ SY81 @ SY82 )
| ( disjoint @ SV7 @ SV15 @ SY82 ) )
| ! [SY83: mworld] :
( ~ ( mrel @ SY81 @ SY83 )
| ( disjoint @ SV15 @ SV7 @ SY83 ) ) ) )
= $true )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(95,plain,
! [SV12: mworld] :
( ( ( ! [SY67: mworld] :
( ~ ( mrel @ SV12 @ SY67 )
| ( empty @ sK3_SX0 @ SY67 ) ) )
= $false )
| ( ( mrel @ mactual @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(96,plain,
( ( eiw_di @ sK7_SY53 @ sK6_SY41 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(97,plain,
( ( ~ ( mrel @ sK6_SY41 @ sK8_SY73 )
| ~ ! [SY84: mworld] :
( ~ ( mrel @ sK8_SY73 @ SY84 )
| ~ ! [SY75: mworld] :
( ~ ( mrel @ SY84 @ SY75 )
| ( in @ sK5_SY23 @ sK7_SY53 @ SY75 ) ) )
| ! [SY86: mworld] :
( ~ ( mrel @ sK8_SY73 @ SY86 )
| ( disjoint @ ( singleton @ sK5_SY23 ) @ sK7_SY53 @ SY86 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(98,plain,
! [SV5: mworld,SV8: $i,SV13: mworld,SV16: $i] :
( ( ( ~ ( eiw_di @ SV16 @ SV13 )
| ! [SY87: mworld] :
( ~ ( mrel @ SV13 @ SY87 )
| ~ ! [SY88: mworld] :
( ~ ( mrel @ SY87 @ SY88 )
| ~ ! [SY89: mworld] :
( ~ ( mrel @ SY88 @ SY89 )
| ( in @ SV8 @ SV16 @ SY89 ) ) )
| ! [SY90: mworld] :
( ~ ( mrel @ SY87 @ SY90 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SY90 ) ) ) )
= $true )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(99,plain,
! [SV3: mworld,SV6: $i,SV9: mworld,SV14: $i] :
( ( ( ~ ( eiw_di @ SV14 @ SV9 ) )
= $true )
| ( ( ! [SY77: mworld] :
( ~ ( mrel @ SV9 @ SY77 )
| ~ ! [SY78: mworld] :
( ~ ( mrel @ SY77 @ SY78 )
| ( in @ SV6 @ SV14 @ SY78 ) )
| ! [SY79: mworld] :
( ~ ( mrel @ SY77 @ SY79 )
| ~ ! [SY80: mworld] :
( ~ ( mrel @ SY79 @ SY80 )
| ( in @ SV14 @ SV6 @ SY80 ) ) ) ) )
= $true )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(100,plain,
! [SV4: mworld,SV7: $i,SV10: mworld,SV15: $i] :
( ( ( ~ ( eiw_di @ SV15 @ SV10 ) )
= $true )
| ( ( ! [SY81: mworld] :
( ~ ( mrel @ SV10 @ SY81 )
| ~ ! [SY82: mworld] :
( ~ ( mrel @ SY81 @ SY82 )
| ( disjoint @ SV7 @ SV15 @ SY82 ) )
| ! [SY83: mworld] :
( ~ ( mrel @ SY81 @ SY83 )
| ( disjoint @ SV15 @ SV7 @ SY83 ) ) ) )
= $true )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV12: mworld] :
( ( ( ~ ( mrel @ SV12 @ ( sK9_SY67 @ SV12 ) )
| ( empty @ sK3_SX0 @ ( sK9_SY67 @ SV12 ) ) )
= $false )
| ( ( mrel @ mactual @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[95]) ).
thf(102,plain,
( ( ~ ( mrel @ sK6_SY41 @ sK8_SY73 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(103,plain,
( ( ~ ! [SY84: mworld] :
( ~ ( mrel @ sK8_SY73 @ SY84 )
| ~ ! [SY75: mworld] :
( ~ ( mrel @ SY84 @ SY75 )
| ( in @ sK5_SY23 @ sK7_SY53 @ SY75 ) ) )
| ! [SY86: mworld] :
( ~ ( mrel @ sK8_SY73 @ SY86 )
| ( disjoint @ ( singleton @ sK5_SY23 ) @ sK7_SY53 @ SY86 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(104,plain,
! [SV5: mworld,SV8: $i,SV13: mworld,SV16: $i] :
( ( ( ~ ( eiw_di @ SV16 @ SV13 ) )
= $true )
| ( ( ! [SY87: mworld] :
( ~ ( mrel @ SV13 @ SY87 )
| ~ ! [SY88: mworld] :
( ~ ( mrel @ SY87 @ SY88 )
| ~ ! [SY89: mworld] :
( ~ ( mrel @ SY88 @ SY89 )
| ( in @ SV8 @ SV16 @ SY89 ) ) )
| ! [SY90: mworld] :
( ~ ( mrel @ SY87 @ SY90 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SY90 ) ) ) )
= $true )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(105,plain,
! [SV3: mworld,SV6: $i,SV9: mworld,SV14: $i] :
( ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( ! [SY77: mworld] :
( ~ ( mrel @ SV9 @ SY77 )
| ~ ! [SY78: mworld] :
( ~ ( mrel @ SY77 @ SY78 )
| ( in @ SV6 @ SV14 @ SY78 ) )
| ! [SY79: mworld] :
( ~ ( mrel @ SY77 @ SY79 )
| ~ ! [SY80: mworld] :
( ~ ( mrel @ SY79 @ SY80 )
| ( in @ SV14 @ SV6 @ SY80 ) ) ) ) )
= $true )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(106,plain,
! [SV4: mworld,SV7: $i,SV10: mworld,SV15: $i] :
( ( ( eiw_di @ SV15 @ SV10 )
= $false )
| ( ( ! [SY81: mworld] :
( ~ ( mrel @ SV10 @ SY81 )
| ~ ! [SY82: mworld] :
( ~ ( mrel @ SY81 @ SY82 )
| ( disjoint @ SV7 @ SV15 @ SY82 ) )
| ! [SY83: mworld] :
( ~ ( mrel @ SY81 @ SY83 )
| ( disjoint @ SV15 @ SV7 @ SY83 ) ) ) )
= $true )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(107,plain,
! [SV12: mworld] :
( ( ( ~ ( mrel @ SV12 @ ( sK9_SY67 @ SV12 ) ) )
= $false )
| ( ( mrel @ mactual @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(108,plain,
! [SV12: mworld] :
( ( ( empty @ sK3_SX0 @ ( sK9_SY67 @ SV12 ) )
= $false )
| ( ( mrel @ mactual @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(109,plain,
( ( mrel @ sK6_SY41 @ sK8_SY73 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(110,plain,
( ( ~ ! [SY84: mworld] :
( ~ ( mrel @ sK8_SY73 @ SY84 )
| ~ ! [SY75: mworld] :
( ~ ( mrel @ SY84 @ SY75 )
| ( in @ sK5_SY23 @ sK7_SY53 @ SY75 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(111,plain,
( ( ! [SY86: mworld] :
( ~ ( mrel @ sK8_SY73 @ SY86 )
| ( disjoint @ ( singleton @ sK5_SY23 ) @ sK7_SY53 @ SY86 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(112,plain,
! [SV5: mworld,SV8: $i,SV13: mworld,SV16: $i] :
( ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( ! [SY87: mworld] :
( ~ ( mrel @ SV13 @ SY87 )
| ~ ! [SY88: mworld] :
( ~ ( mrel @ SY87 @ SY88 )
| ~ ! [SY89: mworld] :
( ~ ( mrel @ SY88 @ SY89 )
| ( in @ SV8 @ SV16 @ SY89 ) ) )
| ! [SY90: mworld] :
( ~ ( mrel @ SY87 @ SY90 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SY90 ) ) ) )
= $true )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(113,plain,
! [SV3: mworld,SV14: $i,SV6: $i,SV17: mworld,SV9: mworld] :
( ( ( ~ ( mrel @ SV9 @ SV17 )
| ~ ! [SY91: mworld] :
( ~ ( mrel @ SV17 @ SY91 )
| ( in @ SV6 @ SV14 @ SY91 ) )
| ! [SY92: mworld] :
( ~ ( mrel @ SV17 @ SY92 )
| ~ ! [SY80: mworld] :
( ~ ( mrel @ SY92 @ SY80 )
| ( in @ SV14 @ SV6 @ SY80 ) ) ) )
= $true )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(114,plain,
! [SV4: mworld,SV15: $i,SV7: $i,SV18: mworld,SV10: mworld] :
( ( ( ~ ( mrel @ SV10 @ SV18 )
| ~ ! [SY94: mworld] :
( ~ ( mrel @ SV18 @ SY94 )
| ( disjoint @ SV7 @ SV15 @ SY94 ) )
| ! [SY95: mworld] :
( ~ ( mrel @ SV18 @ SY95 )
| ( disjoint @ SV15 @ SV7 @ SY95 ) ) )
= $true )
| ( ( eiw_di @ SV15 @ SV10 )
= $false )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(115,plain,
! [SV12: mworld] :
( ( ( mrel @ SV12 @ ( sK9_SY67 @ SV12 ) )
= $true )
| ( ( mrel @ mactual @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(116,plain,
( ( ! [SY84: mworld] :
( ~ ( mrel @ sK8_SY73 @ SY84 )
| ~ ! [SY75: mworld] :
( ~ ( mrel @ SY84 @ SY75 )
| ( in @ sK5_SY23 @ sK7_SY53 @ SY75 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(117,plain,
( ( ~ ( mrel @ sK8_SY73 @ sK10_SY86 )
| ( disjoint @ ( singleton @ sK5_SY23 ) @ sK7_SY53 @ sK10_SY86 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[111]) ).
thf(118,plain,
! [SV5: mworld,SV16: $i,SV8: $i,SV19: mworld,SV13: mworld] :
( ( ( ~ ( mrel @ SV13 @ SV19 )
| ~ ! [SY96: mworld] :
( ~ ( mrel @ SV19 @ SY96 )
| ~ ! [SY89: mworld] :
( ~ ( mrel @ SY96 @ SY89 )
| ( in @ SV8 @ SV16 @ SY89 ) ) )
| ! [SY98: mworld] :
( ~ ( mrel @ SV19 @ SY98 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SY98 ) ) )
= $true )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(119,plain,
! [SV3: mworld,SV14: $i,SV6: $i,SV17: mworld,SV9: mworld] :
( ( ( ~ ( mrel @ SV9 @ SV17 ) )
= $true )
| ( ( ~ ! [SY91: mworld] :
( ~ ( mrel @ SV17 @ SY91 )
| ( in @ SV6 @ SV14 @ SY91 ) )
| ! [SY92: mworld] :
( ~ ( mrel @ SV17 @ SY92 )
| ~ ! [SY80: mworld] :
( ~ ( mrel @ SY92 @ SY80 )
| ( in @ SV14 @ SV6 @ SY80 ) ) ) )
= $true )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(120,plain,
! [SV4: mworld,SV15: $i,SV7: $i,SV18: mworld,SV10: mworld] :
( ( ( ~ ( mrel @ SV10 @ SV18 ) )
= $true )
| ( ( ~ ! [SY94: mworld] :
( ~ ( mrel @ SV18 @ SY94 )
| ( disjoint @ SV7 @ SV15 @ SY94 ) )
| ! [SY95: mworld] :
( ~ ( mrel @ SV18 @ SY95 )
| ( disjoint @ SV15 @ SV7 @ SY95 ) ) )
= $true )
| ( ( eiw_di @ SV15 @ SV10 )
= $false )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(121,plain,
! [SV20: mworld] :
( ( ~ ( mrel @ sK8_SY73 @ SV20 )
| ~ ! [SY99: mworld] :
( ~ ( mrel @ SV20 @ SY99 )
| ( in @ sK5_SY23 @ sK7_SY53 @ SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(122,plain,
( ( ~ ( mrel @ sK8_SY73 @ sK10_SY86 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(123,plain,
( ( disjoint @ ( singleton @ sK5_SY23 ) @ sK7_SY53 @ sK10_SY86 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(124,plain,
! [SV5: mworld,SV16: $i,SV8: $i,SV19: mworld,SV13: mworld] :
( ( ( ~ ( mrel @ SV13 @ SV19 ) )
= $true )
| ( ( ~ ! [SY96: mworld] :
( ~ ( mrel @ SV19 @ SY96 )
| ~ ! [SY89: mworld] :
( ~ ( mrel @ SY96 @ SY89 )
| ( in @ SV8 @ SV16 @ SY89 ) ) )
| ! [SY98: mworld] :
( ~ ( mrel @ SV19 @ SY98 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SY98 ) ) )
= $true )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(125,plain,
! [SV3: mworld,SV14: $i,SV6: $i,SV17: mworld,SV9: mworld] :
( ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( ~ ! [SY91: mworld] :
( ~ ( mrel @ SV17 @ SY91 )
| ( in @ SV6 @ SV14 @ SY91 ) )
| ! [SY92: mworld] :
( ~ ( mrel @ SV17 @ SY92 )
| ~ ! [SY80: mworld] :
( ~ ( mrel @ SY92 @ SY80 )
| ( in @ SV14 @ SV6 @ SY80 ) ) ) )
= $true )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(126,plain,
! [SV4: mworld,SV15: $i,SV7: $i,SV18: mworld,SV10: mworld] :
( ( ( mrel @ SV10 @ SV18 )
= $false )
| ( ( ~ ! [SY94: mworld] :
( ~ ( mrel @ SV18 @ SY94 )
| ( disjoint @ SV7 @ SV15 @ SY94 ) )
| ! [SY95: mworld] :
( ~ ( mrel @ SV18 @ SY95 )
| ( disjoint @ SV15 @ SV7 @ SY95 ) ) )
= $true )
| ( ( eiw_di @ SV15 @ SV10 )
= $false )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(127,plain,
! [SV20: mworld] :
( ( ( ~ ( mrel @ sK8_SY73 @ SV20 ) )
= $true )
| ( ( ~ ! [SY99: mworld] :
( ~ ( mrel @ SV20 @ SY99 )
| ( in @ sK5_SY23 @ sK7_SY53 @ SY99 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(128,plain,
( ( mrel @ sK8_SY73 @ sK10_SY86 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(129,plain,
! [SV5: mworld,SV16: $i,SV8: $i,SV19: mworld,SV13: mworld] :
( ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( ~ ! [SY96: mworld] :
( ~ ( mrel @ SV19 @ SY96 )
| ~ ! [SY89: mworld] :
( ~ ( mrel @ SY96 @ SY89 )
| ( in @ SV8 @ SV16 @ SY89 ) ) )
| ! [SY98: mworld] :
( ~ ( mrel @ SV19 @ SY98 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SY98 ) ) )
= $true )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(130,plain,
! [SV3: mworld,SV9: mworld,SV14: $i,SV6: $i,SV17: mworld] :
( ( ( ~ ! [SY91: mworld] :
( ~ ( mrel @ SV17 @ SY91 )
| ( in @ SV6 @ SV14 @ SY91 ) ) )
= $true )
| ( ( ! [SY92: mworld] :
( ~ ( mrel @ SV17 @ SY92 )
| ~ ! [SY80: mworld] :
( ~ ( mrel @ SY92 @ SY80 )
| ( in @ SV14 @ SV6 @ SY80 ) ) ) )
= $true )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(131,plain,
! [SV4: mworld,SV10: mworld,SV15: $i,SV7: $i,SV18: mworld] :
( ( ( ~ ! [SY94: mworld] :
( ~ ( mrel @ SV18 @ SY94 )
| ( disjoint @ SV7 @ SV15 @ SY94 ) ) )
= $true )
| ( ( ! [SY95: mworld] :
( ~ ( mrel @ SV18 @ SY95 )
| ( disjoint @ SV15 @ SV7 @ SY95 ) ) )
= $true )
| ( ( mrel @ SV10 @ SV18 )
= $false )
| ( ( eiw_di @ SV15 @ SV10 )
= $false )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(132,plain,
! [SV20: mworld] :
( ( ( mrel @ sK8_SY73 @ SV20 )
= $false )
| ( ( ~ ! [SY99: mworld] :
( ~ ( mrel @ SV20 @ SY99 )
| ( in @ sK5_SY23 @ sK7_SY53 @ SY99 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(133,plain,
! [SV5: mworld,SV13: mworld,SV16: $i,SV8: $i,SV19: mworld] :
( ( ( ~ ! [SY96: mworld] :
( ~ ( mrel @ SV19 @ SY96 )
| ~ ! [SY89: mworld] :
( ~ ( mrel @ SY96 @ SY89 )
| ( in @ SV8 @ SV16 @ SY89 ) ) ) )
= $true )
| ( ( ! [SY98: mworld] :
( ~ ( mrel @ SV19 @ SY98 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SY98 ) ) )
= $true )
| ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(134,plain,
! [SV3: mworld,SV9: mworld,SV14: $i,SV6: $i,SV17: mworld] :
( ( ( ! [SY91: mworld] :
( ~ ( mrel @ SV17 @ SY91 )
| ( in @ SV6 @ SV14 @ SY91 ) ) )
= $false )
| ( ( ! [SY92: mworld] :
( ~ ( mrel @ SV17 @ SY92 )
| ~ ! [SY80: mworld] :
( ~ ( mrel @ SY92 @ SY80 )
| ( in @ SV14 @ SV6 @ SY80 ) ) ) )
= $true )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(135,plain,
! [SV4: mworld,SV10: mworld,SV15: $i,SV7: $i,SV18: mworld] :
( ( ( ! [SY94: mworld] :
( ~ ( mrel @ SV18 @ SY94 )
| ( disjoint @ SV7 @ SV15 @ SY94 ) ) )
= $false )
| ( ( ! [SY95: mworld] :
( ~ ( mrel @ SV18 @ SY95 )
| ( disjoint @ SV15 @ SV7 @ SY95 ) ) )
= $true )
| ( ( mrel @ SV10 @ SV18 )
= $false )
| ( ( eiw_di @ SV15 @ SV10 )
= $false )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(136,plain,
! [SV20: mworld] :
( ( ( ! [SY99: mworld] :
( ~ ( mrel @ SV20 @ SY99 )
| ( in @ sK5_SY23 @ sK7_SY53 @ SY99 ) ) )
= $false )
| ( ( mrel @ sK8_SY73 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(137,plain,
! [SV5: mworld,SV13: mworld,SV16: $i,SV8: $i,SV19: mworld] :
( ( ( ! [SY96: mworld] :
( ~ ( mrel @ SV19 @ SY96 )
| ~ ! [SY89: mworld] :
( ~ ( mrel @ SY96 @ SY89 )
| ( in @ SV8 @ SV16 @ SY89 ) ) ) )
= $false )
| ( ( ! [SY98: mworld] :
( ~ ( mrel @ SV19 @ SY98 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SY98 ) ) )
= $true )
| ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(138,plain,
! [SV6: $i,SV14: $i,SV9: mworld,SV3: mworld,SV17: mworld] :
( ( ( ~ ( mrel @ SV17 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
| ( in @ SV6 @ SV14 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) ) )
= $false )
| ( ( ! [SY92: mworld] :
( ~ ( mrel @ SV17 @ SY92 )
| ~ ! [SY80: mworld] :
( ~ ( mrel @ SY92 @ SY80 )
| ( in @ SV14 @ SV6 @ SY80 ) ) ) )
= $true )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[134]) ).
thf(139,plain,
! [SV7: $i,SV15: $i,SV10: mworld,SV4: mworld,SV18: mworld] :
( ( ( ~ ( mrel @ SV18 @ ( sK12_SY94 @ SV4 @ SV10 @ SV15 @ SV7 @ SV18 ) )
| ( disjoint @ SV7 @ SV15 @ ( sK12_SY94 @ SV4 @ SV10 @ SV15 @ SV7 @ SV18 ) ) )
= $false )
| ( ( ! [SY95: mworld] :
( ~ ( mrel @ SV18 @ SY95 )
| ( disjoint @ SV15 @ SV7 @ SY95 ) ) )
= $true )
| ( ( mrel @ SV10 @ SV18 )
= $false )
| ( ( eiw_di @ SV15 @ SV10 )
= $false )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[135]) ).
thf(140,plain,
! [SV20: mworld] :
( ( ( ~ ( mrel @ SV20 @ ( sK13_SY99 @ SV20 ) )
| ( in @ sK5_SY23 @ sK7_SY53 @ ( sK13_SY99 @ SV20 ) ) )
= $false )
| ( ( mrel @ sK8_SY73 @ SV20 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[136]) ).
thf(141,plain,
! [SV8: $i,SV16: $i,SV13: mworld,SV5: mworld,SV19: mworld] :
( ( ( ~ ( mrel @ SV19 @ ( sK14_SY96 @ SV5 @ SV13 @ SV16 @ SV8 @ SV19 ) )
| ~ ! [SY100: mworld] :
( ~ ( mrel @ ( sK14_SY96 @ SV5 @ SV13 @ SV16 @ SV8 @ SV19 ) @ SY100 )
| ( in @ SV8 @ SV16 @ SY100 ) ) )
= $false )
| ( ( ! [SY98: mworld] :
( ~ ( mrel @ SV19 @ SY98 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SY98 ) ) )
= $true )
| ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[137]) ).
thf(142,plain,
! [SV6: $i,SV14: $i,SV9: mworld,SV3: mworld,SV17: mworld] :
( ( ( ~ ( mrel @ SV17 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) ) )
= $false )
| ( ( ! [SY92: mworld] :
( ~ ( mrel @ SV17 @ SY92 )
| ~ ! [SY80: mworld] :
( ~ ( mrel @ SY92 @ SY80 )
| ( in @ SV14 @ SV6 @ SY80 ) ) ) )
= $true )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(143,plain,
! [SV17: mworld,SV9: mworld,SV3: mworld,SV14: $i,SV6: $i] :
( ( ( in @ SV6 @ SV14 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $false )
| ( ( ! [SY92: mworld] :
( ~ ( mrel @ SV17 @ SY92 )
| ~ ! [SY80: mworld] :
( ~ ( mrel @ SY92 @ SY80 )
| ( in @ SV14 @ SV6 @ SY80 ) ) ) )
= $true )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(144,plain,
! [SV7: $i,SV15: $i,SV10: mworld,SV4: mworld,SV18: mworld] :
( ( ( ~ ( mrel @ SV18 @ ( sK12_SY94 @ SV4 @ SV10 @ SV15 @ SV7 @ SV18 ) ) )
= $false )
| ( ( ! [SY95: mworld] :
( ~ ( mrel @ SV18 @ SY95 )
| ( disjoint @ SV15 @ SV7 @ SY95 ) ) )
= $true )
| ( ( mrel @ SV10 @ SV18 )
= $false )
| ( ( eiw_di @ SV15 @ SV10 )
= $false )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(145,plain,
! [SV18: mworld,SV10: mworld,SV4: mworld,SV15: $i,SV7: $i] :
( ( ( disjoint @ SV7 @ SV15 @ ( sK12_SY94 @ SV4 @ SV10 @ SV15 @ SV7 @ SV18 ) )
= $false )
| ( ( ! [SY95: mworld] :
( ~ ( mrel @ SV18 @ SY95 )
| ( disjoint @ SV15 @ SV7 @ SY95 ) ) )
= $true )
| ( ( mrel @ SV10 @ SV18 )
= $false )
| ( ( eiw_di @ SV15 @ SV10 )
= $false )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(146,plain,
! [SV20: mworld] :
( ( ( ~ ( mrel @ SV20 @ ( sK13_SY99 @ SV20 ) ) )
= $false )
| ( ( mrel @ sK8_SY73 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(147,plain,
! [SV20: mworld] :
( ( ( in @ sK5_SY23 @ sK7_SY53 @ ( sK13_SY99 @ SV20 ) )
= $false )
| ( ( mrel @ sK8_SY73 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(148,plain,
! [SV8: $i,SV16: $i,SV13: mworld,SV5: mworld,SV19: mworld] :
( ( ( ~ ( mrel @ SV19 @ ( sK14_SY96 @ SV5 @ SV13 @ SV16 @ SV8 @ SV19 ) ) )
= $false )
| ( ( ! [SY98: mworld] :
( ~ ( mrel @ SV19 @ SY98 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SY98 ) ) )
= $true )
| ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(149,plain,
! [SV19: mworld,SV8: $i,SV16: $i,SV13: mworld,SV5: mworld] :
( ( ( ~ ! [SY100: mworld] :
( ~ ( mrel @ ( sK14_SY96 @ SV5 @ SV13 @ SV16 @ SV8 @ SV19 ) @ SY100 )
| ( in @ SV8 @ SV16 @ SY100 ) ) )
= $false )
| ( ( ! [SY98: mworld] :
( ~ ( mrel @ SV19 @ SY98 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SY98 ) ) )
= $true )
| ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(150,plain,
! [SV6: $i,SV14: $i,SV9: mworld,SV3: mworld,SV17: mworld] :
( ( ( mrel @ SV17 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $true )
| ( ( ! [SY92: mworld] :
( ~ ( mrel @ SV17 @ SY92 )
| ~ ! [SY80: mworld] :
( ~ ( mrel @ SY92 @ SY80 )
| ( in @ SV14 @ SV6 @ SY80 ) ) ) )
= $true )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(151,plain,
! [SV9: mworld,SV3: mworld,SV6: $i,SV14: $i,SV21: mworld,SV17: mworld] :
( ( ( ~ ( mrel @ SV17 @ SV21 )
| ~ ! [SY101: mworld] :
( ~ ( mrel @ SV21 @ SY101 )
| ( in @ SV14 @ SV6 @ SY101 ) ) )
= $true )
| ( ( in @ SV6 @ SV14 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $false )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(152,plain,
! [SV7: $i,SV15: $i,SV10: mworld,SV4: mworld,SV18: mworld] :
( ( ( mrel @ SV18 @ ( sK12_SY94 @ SV4 @ SV10 @ SV15 @ SV7 @ SV18 ) )
= $true )
| ( ( ! [SY95: mworld] :
( ~ ( mrel @ SV18 @ SY95 )
| ( disjoint @ SV15 @ SV7 @ SY95 ) ) )
= $true )
| ( ( mrel @ SV10 @ SV18 )
= $false )
| ( ( eiw_di @ SV15 @ SV10 )
= $false )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(153,plain,
! [SV10: mworld,SV4: mworld,SV7: $i,SV15: $i,SV22: mworld,SV18: mworld] :
( ( ( ~ ( mrel @ SV18 @ SV22 )
| ( disjoint @ SV15 @ SV7 @ SV22 ) )
= $true )
| ( ( disjoint @ SV7 @ SV15 @ ( sK12_SY94 @ SV4 @ SV10 @ SV15 @ SV7 @ SV18 ) )
= $false )
| ( ( mrel @ SV10 @ SV18 )
= $false )
| ( ( eiw_di @ SV15 @ SV10 )
= $false )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(154,plain,
! [SV20: mworld] :
( ( ( mrel @ SV20 @ ( sK13_SY99 @ SV20 ) )
= $true )
| ( ( mrel @ sK8_SY73 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(155,plain,
! [SV8: $i,SV16: $i,SV13: mworld,SV5: mworld,SV19: mworld] :
( ( ( mrel @ SV19 @ ( sK14_SY96 @ SV5 @ SV13 @ SV16 @ SV8 @ SV19 ) )
= $true )
| ( ( ! [SY98: mworld] :
( ~ ( mrel @ SV19 @ SY98 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SY98 ) ) )
= $true )
| ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(156,plain,
! [SV19: mworld,SV8: $i,SV16: $i,SV13: mworld,SV5: mworld] :
( ( ( ! [SY100: mworld] :
( ~ ( mrel @ ( sK14_SY96 @ SV5 @ SV13 @ SV16 @ SV8 @ SV19 ) @ SY100 )
| ( in @ SV8 @ SV16 @ SY100 ) ) )
= $true )
| ( ( ! [SY98: mworld] :
( ~ ( mrel @ SV19 @ SY98 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SY98 ) ) )
= $true )
| ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(157,plain,
! [SV9: mworld,SV3: mworld,SV6: $i,SV14: $i,SV23: mworld,SV17: mworld] :
( ( ( ~ ( mrel @ SV17 @ SV23 )
| ~ ! [SY102: mworld] :
( ~ ( mrel @ SV23 @ SY102 )
| ( in @ SV14 @ SV6 @ SY102 ) ) )
= $true )
| ( ( mrel @ SV17 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $true )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(158,plain,
! [SV9: mworld,SV3: mworld,SV6: $i,SV14: $i,SV21: mworld,SV17: mworld] :
( ( ( ~ ( mrel @ SV17 @ SV21 ) )
= $true )
| ( ( ~ ! [SY101: mworld] :
( ~ ( mrel @ SV21 @ SY101 )
| ( in @ SV14 @ SV6 @ SY101 ) ) )
= $true )
| ( ( in @ SV6 @ SV14 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $false )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(159,plain,
! [SV10: mworld,SV4: mworld,SV7: $i,SV15: $i,SV24: mworld,SV18: mworld] :
( ( ( ~ ( mrel @ SV18 @ SV24 )
| ( disjoint @ SV15 @ SV7 @ SV24 ) )
= $true )
| ( ( mrel @ SV18 @ ( sK12_SY94 @ SV4 @ SV10 @ SV15 @ SV7 @ SV18 ) )
= $true )
| ( ( mrel @ SV10 @ SV18 )
= $false )
| ( ( eiw_di @ SV15 @ SV10 )
= $false )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(160,plain,
! [SV10: mworld,SV4: mworld,SV7: $i,SV15: $i,SV22: mworld,SV18: mworld] :
( ( ( ~ ( mrel @ SV18 @ SV22 ) )
= $true )
| ( ( disjoint @ SV15 @ SV7 @ SV22 )
= $true )
| ( ( disjoint @ SV7 @ SV15 @ ( sK12_SY94 @ SV4 @ SV10 @ SV15 @ SV7 @ SV18 ) )
= $false )
| ( ( mrel @ SV10 @ SV18 )
= $false )
| ( ( eiw_di @ SV15 @ SV10 )
= $false )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(161,plain,
! [SV13: mworld,SV5: mworld,SV16: $i,SV8: $i,SV25: mworld,SV19: mworld] :
( ( ( ~ ( mrel @ SV19 @ SV25 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SV25 ) )
= $true )
| ( ( mrel @ SV19 @ ( sK14_SY96 @ SV5 @ SV13 @ SV16 @ SV8 @ SV19 ) )
= $true )
| ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(162,plain,
! [SV26: mworld,SV19: mworld,SV8: $i,SV16: $i,SV13: mworld,SV5: mworld] :
( ( ( ~ ( mrel @ ( sK14_SY96 @ SV5 @ SV13 @ SV16 @ SV8 @ SV19 ) @ SV26 )
| ( in @ SV8 @ SV16 @ SV26 ) )
= $true )
| ( ( ! [SY98: mworld] :
( ~ ( mrel @ SV19 @ SY98 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SY98 ) ) )
= $true )
| ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(163,plain,
! [SV9: mworld,SV3: mworld,SV6: $i,SV14: $i,SV23: mworld,SV17: mworld] :
( ( ( ~ ( mrel @ SV17 @ SV23 ) )
= $true )
| ( ( ~ ! [SY102: mworld] :
( ~ ( mrel @ SV23 @ SY102 )
| ( in @ SV14 @ SV6 @ SY102 ) ) )
= $true )
| ( ( mrel @ SV17 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $true )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(164,plain,
! [SV9: mworld,SV3: mworld,SV6: $i,SV14: $i,SV21: mworld,SV17: mworld] :
( ( ( mrel @ SV17 @ SV21 )
= $false )
| ( ( ~ ! [SY101: mworld] :
( ~ ( mrel @ SV21 @ SY101 )
| ( in @ SV14 @ SV6 @ SY101 ) ) )
= $true )
| ( ( in @ SV6 @ SV14 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $false )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(165,plain,
! [SV10: mworld,SV4: mworld,SV7: $i,SV15: $i,SV24: mworld,SV18: mworld] :
( ( ( ~ ( mrel @ SV18 @ SV24 ) )
= $true )
| ( ( disjoint @ SV15 @ SV7 @ SV24 )
= $true )
| ( ( mrel @ SV18 @ ( sK12_SY94 @ SV4 @ SV10 @ SV15 @ SV7 @ SV18 ) )
= $true )
| ( ( mrel @ SV10 @ SV18 )
= $false )
| ( ( eiw_di @ SV15 @ SV10 )
= $false )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(166,plain,
! [SV10: mworld,SV4: mworld,SV7: $i,SV15: $i,SV22: mworld,SV18: mworld] :
( ( ( mrel @ SV18 @ SV22 )
= $false )
| ( ( disjoint @ SV15 @ SV7 @ SV22 )
= $true )
| ( ( disjoint @ SV7 @ SV15 @ ( sK12_SY94 @ SV4 @ SV10 @ SV15 @ SV7 @ SV18 ) )
= $false )
| ( ( mrel @ SV10 @ SV18 )
= $false )
| ( ( eiw_di @ SV15 @ SV10 )
= $false )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(167,plain,
! [SV13: mworld,SV5: mworld,SV16: $i,SV8: $i,SV25: mworld,SV19: mworld] :
( ( ( ~ ( mrel @ SV19 @ SV25 ) )
= $true )
| ( ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SV25 )
= $true )
| ( ( mrel @ SV19 @ ( sK14_SY96 @ SV5 @ SV13 @ SV16 @ SV8 @ SV19 ) )
= $true )
| ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(168,plain,
! [SV26: mworld,SV19: mworld,SV8: $i,SV16: $i,SV13: mworld,SV5: mworld] :
( ( ( ~ ( mrel @ ( sK14_SY96 @ SV5 @ SV13 @ SV16 @ SV8 @ SV19 ) @ SV26 ) )
= $true )
| ( ( in @ SV8 @ SV16 @ SV26 )
= $true )
| ( ( ! [SY98: mworld] :
( ~ ( mrel @ SV19 @ SY98 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SY98 ) ) )
= $true )
| ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(169,plain,
! [SV9: mworld,SV3: mworld,SV6: $i,SV14: $i,SV23: mworld,SV17: mworld] :
( ( ( mrel @ SV17 @ SV23 )
= $false )
| ( ( ~ ! [SY102: mworld] :
( ~ ( mrel @ SV23 @ SY102 )
| ( in @ SV14 @ SV6 @ SY102 ) ) )
= $true )
| ( ( mrel @ SV17 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $true )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(170,plain,
! [SV9: mworld,SV3: mworld,SV17: mworld,SV6: $i,SV14: $i,SV21: mworld] :
( ( ( ! [SY101: mworld] :
( ~ ( mrel @ SV21 @ SY101 )
| ( in @ SV14 @ SV6 @ SY101 ) ) )
= $false )
| ( ( mrel @ SV17 @ SV21 )
= $false )
| ( ( in @ SV6 @ SV14 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $false )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(171,plain,
! [SV10: mworld,SV4: mworld,SV7: $i,SV15: $i,SV24: mworld,SV18: mworld] :
( ( ( mrel @ SV18 @ SV24 )
= $false )
| ( ( disjoint @ SV15 @ SV7 @ SV24 )
= $true )
| ( ( mrel @ SV18 @ ( sK12_SY94 @ SV4 @ SV10 @ SV15 @ SV7 @ SV18 ) )
= $true )
| ( ( mrel @ SV10 @ SV18 )
= $false )
| ( ( eiw_di @ SV15 @ SV10 )
= $false )
| ( ( mrel @ SV4 @ SV10 )
= $false )
| ( ( eiw_di @ SV7 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(172,plain,
! [SV13: mworld,SV5: mworld,SV16: $i,SV8: $i,SV25: mworld,SV19: mworld] :
( ( ( mrel @ SV19 @ SV25 )
= $false )
| ( ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SV25 )
= $true )
| ( ( mrel @ SV19 @ ( sK14_SY96 @ SV5 @ SV13 @ SV16 @ SV8 @ SV19 ) )
= $true )
| ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(173,plain,
! [SV26: mworld,SV19: mworld,SV8: $i,SV16: $i,SV13: mworld,SV5: mworld] :
( ( ( mrel @ ( sK14_SY96 @ SV5 @ SV13 @ SV16 @ SV8 @ SV19 ) @ SV26 )
= $false )
| ( ( in @ SV8 @ SV16 @ SV26 )
= $true )
| ( ( ! [SY98: mworld] :
( ~ ( mrel @ SV19 @ SY98 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SY98 ) ) )
= $true )
| ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(174,plain,
! [SV9: mworld,SV3: mworld,SV17: mworld,SV6: $i,SV14: $i,SV23: mworld] :
( ( ( ! [SY102: mworld] :
( ~ ( mrel @ SV23 @ SY102 )
| ( in @ SV14 @ SV6 @ SY102 ) ) )
= $false )
| ( ( mrel @ SV17 @ SV23 )
= $false )
| ( ( mrel @ SV17 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $true )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(175,plain,
! [SV14: $i,SV6: $i,SV17: mworld,SV3: mworld,SV9: mworld,SV21: mworld] :
( ( ( ~ ( mrel @ SV21 @ ( sK15_SY101 @ SV9 @ SV3 @ SV17 @ SV6 @ SV14 @ SV21 ) )
| ( in @ SV14 @ SV6 @ ( sK15_SY101 @ SV9 @ SV3 @ SV17 @ SV6 @ SV14 @ SV21 ) ) )
= $false )
| ( ( mrel @ SV17 @ SV21 )
= $false )
| ( ( in @ SV6 @ SV14 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $false )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[170]) ).
thf(176,plain,
! [SV13: mworld,SV5: mworld,SV26: mworld,SV16: $i,SV8: $i,SV27: mworld,SV19: mworld] :
( ( ( ~ ( mrel @ SV19 @ SV27 )
| ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SV27 ) )
= $true )
| ( ( in @ SV8 @ SV16 @ SV26 )
= $true )
| ( ( mrel @ ( sK14_SY96 @ SV5 @ SV13 @ SV16 @ SV8 @ SV19 ) @ SV26 )
= $false )
| ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(177,plain,
! [SV14: $i,SV6: $i,SV17: mworld,SV3: mworld,SV9: mworld,SV23: mworld] :
( ( ( ~ ( mrel @ SV23 @ ( sK16_SY102 @ SV9 @ SV3 @ SV17 @ SV6 @ SV14 @ SV23 ) )
| ( in @ SV14 @ SV6 @ ( sK16_SY102 @ SV9 @ SV3 @ SV17 @ SV6 @ SV14 @ SV23 ) ) )
= $false )
| ( ( mrel @ SV17 @ SV23 )
= $false )
| ( ( mrel @ SV17 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $true )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[174]) ).
thf(178,plain,
! [SV14: $i,SV6: $i,SV17: mworld,SV3: mworld,SV9: mworld,SV21: mworld] :
( ( ( ~ ( mrel @ SV21 @ ( sK15_SY101 @ SV9 @ SV3 @ SV17 @ SV6 @ SV14 @ SV21 ) ) )
= $false )
| ( ( mrel @ SV17 @ SV21 )
= $false )
| ( ( in @ SV6 @ SV14 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $false )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(179,plain,
! [SV21: mworld,SV17: mworld,SV3: mworld,SV9: mworld,SV6: $i,SV14: $i] :
( ( ( in @ SV14 @ SV6 @ ( sK15_SY101 @ SV9 @ SV3 @ SV17 @ SV6 @ SV14 @ SV21 ) )
= $false )
| ( ( mrel @ SV17 @ SV21 )
= $false )
| ( ( in @ SV6 @ SV14 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $false )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(180,plain,
! [SV13: mworld,SV5: mworld,SV26: mworld,SV16: $i,SV8: $i,SV27: mworld,SV19: mworld] :
( ( ( ~ ( mrel @ SV19 @ SV27 ) )
= $true )
| ( ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SV27 )
= $true )
| ( ( in @ SV8 @ SV16 @ SV26 )
= $true )
| ( ( mrel @ ( sK14_SY96 @ SV5 @ SV13 @ SV16 @ SV8 @ SV19 ) @ SV26 )
= $false )
| ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(181,plain,
! [SV14: $i,SV6: $i,SV17: mworld,SV3: mworld,SV9: mworld,SV23: mworld] :
( ( ( ~ ( mrel @ SV23 @ ( sK16_SY102 @ SV9 @ SV3 @ SV17 @ SV6 @ SV14 @ SV23 ) ) )
= $false )
| ( ( mrel @ SV17 @ SV23 )
= $false )
| ( ( mrel @ SV17 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $true )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(182,plain,
! [SV23: mworld,SV17: mworld,SV3: mworld,SV9: mworld,SV6: $i,SV14: $i] :
( ( ( in @ SV14 @ SV6 @ ( sK16_SY102 @ SV9 @ SV3 @ SV17 @ SV6 @ SV14 @ SV23 ) )
= $false )
| ( ( mrel @ SV17 @ SV23 )
= $false )
| ( ( mrel @ SV17 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $true )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(183,plain,
! [SV14: $i,SV6: $i,SV17: mworld,SV3: mworld,SV9: mworld,SV21: mworld] :
( ( ( mrel @ SV21 @ ( sK15_SY101 @ SV9 @ SV3 @ SV17 @ SV6 @ SV14 @ SV21 ) )
= $true )
| ( ( mrel @ SV17 @ SV21 )
= $false )
| ( ( in @ SV6 @ SV14 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $false )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(184,plain,
! [SV13: mworld,SV5: mworld,SV26: mworld,SV16: $i,SV8: $i,SV27: mworld,SV19: mworld] :
( ( ( mrel @ SV19 @ SV27 )
= $false )
| ( ( disjoint @ ( singleton @ SV8 ) @ SV16 @ SV27 )
= $true )
| ( ( in @ SV8 @ SV16 @ SV26 )
= $true )
| ( ( mrel @ ( sK14_SY96 @ SV5 @ SV13 @ SV16 @ SV8 @ SV19 ) @ SV26 )
= $false )
| ( ( mrel @ SV13 @ SV19 )
= $false )
| ( ( eiw_di @ SV16 @ SV13 )
= $false )
| ( ( mrel @ SV5 @ SV13 )
= $false )
| ( ( eiw_di @ SV8 @ SV5 )
= $false )
| ( ( mrel @ mactual @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(185,plain,
! [SV14: $i,SV6: $i,SV17: mworld,SV3: mworld,SV9: mworld,SV23: mworld] :
( ( ( mrel @ SV23 @ ( sK16_SY102 @ SV9 @ SV3 @ SV17 @ SV6 @ SV14 @ SV23 ) )
= $true )
| ( ( mrel @ SV17 @ SV23 )
= $false )
| ( ( mrel @ SV17 @ ( sK11_SY91 @ SV3 @ SV9 @ SV14 @ SV6 @ SV17 ) )
= $true )
| ( ( mrel @ SV9 @ SV17 )
= $false )
| ( ( eiw_di @ SV14 @ SV9 )
= $false )
| ( ( mrel @ SV3 @ SV9 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( mrel @ mactual @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(186,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,185,184,183,182,179,172,171,166,154,147,128,123,115,109,108,96,88,83,69,67,65,51,27]) ).
thf(187,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL953^8 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n020.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 : Mon Jul 4 04:00:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.37
% 0.20/0.37 No.of.Axioms: 7
% 0.20/0.37
% 0.20/0.37 Length.of.Defs: 1623
% 0.20/0.37
% 0.20/0.37 Contains.Choice.Funs: false
% 0.20/0.40 (rf:0,axioms:7,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:9,loop_count:0,foatp_calls:0,translation:fof_full).................
% 0.40/0.87
% 0.40/0.87 ********************************
% 0.40/0.87 * All subproblems solved! *
% 0.40/0.87 ********************************
% 0.40/0.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,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:186,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.40/0.89
% 0.40/0.89 %**** Beginning of derivation protocol ****
% 0.40/0.89 % SZS output start CNFRefutation
% See solution above
% 0.40/0.90
% 0.40/0.90 %**** End of derivation protocol ****
% 0.40/0.90 %**** no. of clauses in derivation: 187 ****
% 0.40/0.90 %**** clause counter: 186 ****
% 0.40/0.90
% 0.40/0.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,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:186,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------