TSTP Solution File: SET624+3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET624+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n027.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 03:03:40 EDT 2022
% Result : Theorem 21.84s 22.05s
% Output : CNFRefutation 21.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 242 ( 140 unt; 8 typ; 0 def)
% Number of atoms : 1451 ( 426 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 3023 ( 570 ~; 488 |; 29 &;1916 @)
% ( 14 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 626 ( 0 ^ 624 !; 2 ?; 626 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_intersect,type,
intersect: $i > $i > $o ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SY16,type,
sK2_SY16: $i ).
thf(tp_sK3_SY18,type,
sK3_SY18: $i ).
thf(tp_sK4_D,type,
sK4_D: $i > $i > $i ).
thf(tp_sK5_D,type,
sK5_D: $i > $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(1,axiom,
! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
thf(2,axiom,
! [B: $i,C: $i] :
( ( intersect @ B @ C )
=> ( intersect @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).
thf(3,axiom,
! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(4,axiom,
! [B: $i,C: $i] :
( ( intersect @ B @ C )
<=> ? [D: $i] :
( ( member @ D @ B )
& ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
thf(5,axiom,
! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( union @ B @ C ) )
<=> ( ( member @ D @ B )
| ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
thf(6,conjecture,
! [B: $i,C: $i,D: $i] :
( ( intersect @ B @ ( union @ C @ D ) )
<=> ( ( intersect @ B @ C )
| ( intersect @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersect_with_union) ).
thf(7,negated_conjecture,
( ( ! [B: $i,C: $i,D: $i] :
( ( intersect @ B @ ( union @ C @ D ) )
<=> ( ( intersect @ B @ C )
| ( intersect @ B @ D ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( intersect @ B @ ( union @ C @ D ) )
<=> ( ( intersect @ B @ C )
| ( intersect @ B @ D ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [B: $i,C: $i] :
( ( intersect @ B @ C )
=> ( intersect @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [B: $i,C: $i] :
( ( intersect @ B @ C )
<=> ? [D: $i] :
( ( member @ D @ B )
& ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( union @ B @ C ) )
<=> ( ( member @ D @ B )
| ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [SY16: $i,SY17: $i] :
( ( intersect @ sK1_B @ ( union @ SY16 @ SY17 ) )
<=> ( ( intersect @ sK1_B @ SY16 )
| ( intersect @ sK1_B @ SY17 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( ! [SY18: $i] :
( ( intersect @ sK1_B @ ( union @ sK2_SY16 @ SY18 ) )
<=> ( ( intersect @ sK1_B @ sK2_SY16 )
| ( intersect @ sK1_B @ SY18 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) )
<=> ( ( intersect @ sK1_B @ sK2_SY16 )
| ( intersect @ sK1_B @ sK3_SY18 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(17,plain,
( ( ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) )
=> ( ( intersect @ sK1_B @ sK2_SY16 )
| ( intersect @ sK1_B @ sK3_SY18 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[16]) ).
thf(18,plain,
( ( ( ( intersect @ sK1_B @ sK2_SY16 )
| ( intersect @ sK1_B @ sK3_SY18 ) )
=> ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[16]) ).
thf(19,plain,
( ( ~ ( ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) )
=> ( ( intersect @ sK1_B @ sK2_SY16 )
| ( intersect @ sK1_B @ sK3_SY18 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( ( ( intersect @ sK1_B @ sK2_SY16 )
| ( intersect @ sK1_B @ sK3_SY18 ) )
=> ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(21,plain,
( ( ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) )
& ~ ( intersect @ sK1_B @ sK2_SY16 )
& ~ ( intersect @ sK1_B @ sK3_SY18 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(22,plain,
( ( ( ( intersect @ sK1_B @ sK2_SY16 )
| ( intersect @ sK1_B @ sK3_SY18 ) )
& ~ ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(23,plain,
( ( ! [B: $i,C: $i] :
( ( ( ~ ( member @ ( sK4_D @ C @ B ) @ B )
| ~ ( member @ ( sK4_D @ C @ B ) @ C ) )
& ( ( member @ ( sK4_D @ C @ B ) @ B )
| ( member @ ( sK4_D @ C @ B ) @ C ) ) )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) )
& ! [D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(24,plain,
( ( ! [B: $i,C: $i] :
( ~ ( intersect @ B @ C )
| ( intersect @ C @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(25,plain,
( ( ! [B: $i,C: $i] :
( ! [D: $i] :
( ~ ( member @ D @ B )
| ~ ( member @ D @ C ) )
| ( intersect @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( intersect @ B @ C )
| ( ( member @ ( sK5_D @ C @ B ) @ B )
& ( member @ ( sK5_D @ C @ B ) @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(26,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ ( union @ B @ C ) )
| ( member @ D @ B )
| ( member @ D @ C ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ ( union @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ ( union @ B @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(27,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ ( union @ B @ C ) )
| ( member @ D @ B )
| ( member @ D @ C ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ ( union @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ ( union @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(28,plain,
( ( ! [B: $i,C: $i] :
( ! [D: $i] :
( ~ ( member @ D @ B )
| ~ ( member @ D @ C ) )
| ( intersect @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( intersect @ B @ C )
| ( ( member @ ( sK5_D @ C @ B ) @ B )
& ( member @ ( sK5_D @ C @ B ) @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(29,plain,
( ( ! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(30,plain,
( ( ! [B: $i,C: $i] :
( ~ ( intersect @ B @ C )
| ( intersect @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(31,plain,
( ( ! [B: $i,C: $i] :
( ( ( ~ ( member @ ( sK4_D @ C @ B ) @ B )
| ~ ( member @ ( sK4_D @ C @ B ) @ C ) )
& ( ( member @ ( sK4_D @ C @ B ) @ B )
| ( member @ ( sK4_D @ C @ B ) @ C ) ) )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) )
& ! [D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(32,plain,
( ( ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) )
& ~ ( intersect @ sK1_B @ sK2_SY16 )
& ~ ( intersect @ sK1_B @ sK3_SY18 ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(33,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(34,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( union @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ ( union @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ ( union @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(35,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(36,plain,
( ( ~ ( ~ ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) )
| ~ ~ ( ~ ~ ( intersect @ sK1_B @ sK2_SY16 )
| ~ ~ ( intersect @ sK1_B @ sK3_SY18 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(37,plain,
! [SV1: $i] :
( ( ! [SY19: $i] :
( ( union @ SV1 @ SY19 )
= ( union @ SY19 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(38,plain,
! [SV2: $i] :
( ( ! [SY20: $i] :
( ~ ( intersect @ SV2 @ SY20 )
| ( intersect @ SY20 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(39,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV3: $i] :
( ( ~ ( ~ ! [SY21: $i,SY22: $i] :
( ~ ( member @ SY22 @ ( union @ SV3 @ SY21 ) )
| ( member @ SY22 @ SV3 )
| ( member @ SY22 @ SY21 ) )
| ~ ~ ( ~ ! [SY23: $i,SY24: $i] :
( ~ ( member @ SY24 @ SV3 )
| ( member @ SY24 @ ( union @ SV3 @ SY23 ) ) )
| ~ ! [SY25: $i,SY26: $i] :
( ~ ( member @ SY26 @ SY25 )
| ( member @ SY26 @ ( union @ SV3 @ SY25 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(41,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(42,plain,
( ( ~ ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) )
| ~ ~ ( ~ ~ ( intersect @ sK1_B @ sK2_SY16 )
| ~ ~ ( intersect @ sK1_B @ sK3_SY18 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV4: $i,SV1: $i] :
( ( ( union @ SV1 @ SV4 )
= ( union @ SV4 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( intersect @ SV2 @ SV5 )
| ( intersect @ SV5 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(45,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(46,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(47,plain,
! [SV3: $i] :
( ( ~ ! [SY21: $i,SY22: $i] :
( ~ ( member @ SY22 @ ( union @ SV3 @ SY21 ) )
| ( member @ SY22 @ SV3 )
| ( member @ SY22 @ SY21 ) )
| ~ ~ ( ~ ! [SY23: $i,SY24: $i] :
( ~ ( member @ SY24 @ SV3 )
| ( member @ SY24 @ ( union @ SV3 @ SY23 ) ) )
| ~ ! [SY25: $i,SY26: $i] :
( ~ ( member @ SY26 @ SY25 )
| ( member @ SY26 @ ( union @ SV3 @ SY25 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(48,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(49,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(50,plain,
( ( ~ ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(51,plain,
( ( ~ ~ ( ~ ~ ( intersect @ sK1_B @ sK2_SY16 )
| ~ ~ ( intersect @ sK1_B @ sK3_SY18 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(52,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( intersect @ SV2 @ SV5 ) )
= $true )
| ( ( intersect @ SV5 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(53,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(54,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(55,plain,
! [SV3: $i] :
( ( ~ ! [SY21: $i,SY22: $i] :
( ~ ( member @ SY22 @ ( union @ SV3 @ SY21 ) )
| ( member @ SY22 @ SV3 )
| ( member @ SY22 @ SY21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(56,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ! [SY23: $i,SY24: $i] :
( ~ ( member @ SY24 @ SV3 )
| ( member @ SY24 @ ( union @ SV3 @ SY23 ) ) )
| ~ ! [SY25: $i,SY26: $i] :
( ~ ( member @ SY26 @ SY25 )
| ( member @ SY26 @ ( union @ SV3 @ SY25 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(57,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(58,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(59,plain,
( ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(60,plain,
( ( ~ ( ~ ~ ( intersect @ sK1_B @ sK2_SY16 )
| ~ ~ ( intersect @ sK1_B @ sK3_SY18 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(61,plain,
! [SV5: $i,SV2: $i] :
( ( ( intersect @ SV2 @ SV5 )
= $false )
| ( ( intersect @ SV5 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(62,plain,
! [SV6: $i] :
( ( ! [SY27: $i] :
( ~ ( ~ ( ~ ( member @ ( sK4_D @ SY27 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK4_D @ SY27 @ SV6 ) @ SY27 ) )
| ~ ( ( member @ ( sK4_D @ SY27 @ SV6 ) @ SV6 )
| ( member @ ( sK4_D @ SY27 @ SV6 ) @ SY27 ) ) )
| ( SV6 = SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(63,plain,
! [SV7: $i] :
( ( ! [SY28: $i] :
( ( SV7 != SY28 )
| ~ ( ~ ! [SY29: $i] :
( ~ ( member @ SY29 @ SV7 )
| ( member @ SY29 @ SY28 ) )
| ~ ! [SY30: $i] :
( ~ ( member @ SY30 @ SY28 )
| ( member @ SY30 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(64,plain,
! [SV3: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ~ ( member @ SY22 @ ( union @ SV3 @ SY21 ) )
| ( member @ SY22 @ SV3 )
| ( member @ SY22 @ SY21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(65,plain,
! [SV3: $i] :
( ( ~ ( ~ ! [SY23: $i,SY24: $i] :
( ~ ( member @ SY24 @ SV3 )
| ( member @ SY24 @ ( union @ SV3 @ SY23 ) ) )
| ~ ! [SY25: $i,SY26: $i] :
( ~ ( member @ SY26 @ SY25 )
| ( member @ SY26 @ ( union @ SV3 @ SY25 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(66,plain,
! [SV8: $i] :
( ( ! [SY31: $i] :
( ! [SY32: $i] :
( ~ ( member @ SY32 @ SV8 )
| ~ ( member @ SY32 @ SY31 ) )
| ( intersect @ SV8 @ SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV9: $i] :
( ( ! [SY33: $i] :
( ~ ( intersect @ SV9 @ SY33 )
| ~ ( ~ ( member @ ( sK5_D @ SY33 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK5_D @ SY33 @ SV9 ) @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(68,plain,
( ( ~ ~ ( intersect @ sK1_B @ sK2_SY16 )
| ~ ~ ( intersect @ sK1_B @ sK3_SY18 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(69,plain,
! [SV6: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV10 ) )
| ~ ( ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV6 )
| ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV10 ) ) )
| ( SV6 = SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(70,plain,
! [SV11: $i,SV7: $i] :
( ( ( SV7 != SV11 )
| ~ ( ~ ! [SY34: $i] :
( ~ ( member @ SY34 @ SV7 )
| ( member @ SY34 @ SV11 ) )
| ~ ! [SY35: $i] :
( ~ ( member @ SY35 @ SV11 )
| ( member @ SY35 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(71,plain,
! [SV12: $i,SV3: $i] :
( ( ! [SY36: $i] :
( ~ ( member @ SY36 @ ( union @ SV3 @ SV12 ) )
| ( member @ SY36 @ SV3 )
| ( member @ SY36 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(72,plain,
! [SV3: $i] :
( ( ~ ! [SY23: $i,SY24: $i] :
( ~ ( member @ SY24 @ SV3 )
| ( member @ SY24 @ ( union @ SV3 @ SY23 ) ) )
| ~ ! [SY25: $i,SY26: $i] :
( ~ ( member @ SY26 @ SY25 )
| ( member @ SY26 @ ( union @ SV3 @ SY25 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(73,plain,
! [SV13: $i,SV8: $i] :
( ( ! [SY37: $i] :
( ~ ( member @ SY37 @ SV8 )
| ~ ( member @ SY37 @ SV13 ) )
| ( intersect @ SV8 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(74,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ( intersect @ SV9 @ SV14 )
| ~ ( ~ ( member @ ( sK5_D @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK5_D @ SV14 @ SV9 ) @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(75,plain,
( ( ~ ~ ( intersect @ sK1_B @ sK2_SY16 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(76,plain,
( ( ~ ~ ( intersect @ sK1_B @ sK3_SY18 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(77,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV10 ) )
| ~ ( ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV6 )
| ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV10 ) ) ) )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV11: $i,SV7: $i] :
( ( ( ( SV7 != SV11 ) )
= $true )
| ( ( ~ ( ~ ! [SY34: $i] :
( ~ ( member @ SY34 @ SV7 )
| ( member @ SY34 @ SV11 ) )
| ~ ! [SY35: $i] :
( ~ ( member @ SY35 @ SV11 )
| ( member @ SY35 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV12: $i,SV3: $i,SV15: $i] :
( ( ~ ( member @ SV15 @ ( union @ SV3 @ SV12 ) )
| ( member @ SV15 @ SV3 )
| ( member @ SV15 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(80,plain,
! [SV3: $i] :
( ( ~ ! [SY23: $i,SY24: $i] :
( ~ ( member @ SY24 @ SV3 )
| ( member @ SY24 @ ( union @ SV3 @ SY23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(81,plain,
! [SV3: $i] :
( ( ~ ! [SY25: $i,SY26: $i] :
( ~ ( member @ SY26 @ SY25 )
| ( member @ SY26 @ ( union @ SV3 @ SY25 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(82,plain,
! [SV13: $i,SV8: $i] :
( ( ( ! [SY37: $i] :
( ~ ( member @ SY37 @ SV8 )
| ~ ( member @ SY37 @ SV13 ) ) )
= $true )
| ( ( intersect @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV14: $i,SV9: $i] :
( ( ( ~ ( intersect @ SV9 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( member @ ( sK5_D @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK5_D @ SV14 @ SV9 ) @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(84,plain,
( ( ~ ( intersect @ sK1_B @ sK2_SY16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(85,plain,
( ( ~ ( intersect @ sK1_B @ sK3_SY18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(86,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV10 ) )
| ~ ( ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV6 )
| ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV10 ) ) )
= $false )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV11: $i,SV7: $i] :
( ( ( SV7 = SV11 )
= $false )
| ( ( ~ ( ~ ! [SY34: $i] :
( ~ ( member @ SY34 @ SV7 )
| ( member @ SY34 @ SV11 ) )
| ~ ! [SY35: $i] :
( ~ ( member @ SY35 @ SV11 )
| ( member @ SY35 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV12: $i,SV3: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ ( union @ SV3 @ SV12 ) ) )
= $true )
| ( ( ( member @ SV15 @ SV3 )
| ( member @ SV15 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV3: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ~ ( member @ SY24 @ SV3 )
| ( member @ SY24 @ ( union @ SV3 @ SY23 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(90,plain,
! [SV3: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ~ ( member @ SY26 @ SY25 )
| ( member @ SY26 @ ( union @ SV3 @ SY25 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(91,plain,
! [SV13: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV8 )
| ~ ( member @ SV16 @ SV13 ) )
= $true )
| ( ( intersect @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV14: $i,SV9: $i] :
( ( ( intersect @ SV9 @ SV14 )
= $false )
| ( ( ~ ( ~ ( member @ ( sK5_D @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK5_D @ SV14 @ SV9 ) @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(93,plain,
( ( intersect @ sK1_B @ sK2_SY16 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(94,plain,
( ( intersect @ sK1_B @ sK3_SY18 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV10 ) ) )
= $false )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(96,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV6 )
| ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV10 ) ) )
= $false )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(97,plain,
! [SV11: $i,SV7: $i] :
( ( ( ~ ! [SY34: $i] :
( ~ ( member @ SY34 @ SV7 )
| ( member @ SY34 @ SV11 ) )
| ~ ! [SY35: $i] :
( ~ ( member @ SY35 @ SV11 )
| ( member @ SY35 @ SV7 ) ) )
= $false )
| ( ( SV7 = SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(98,plain,
! [SV12: $i,SV3: $i,SV15: $i] :
( ( ( member @ SV15 @ ( union @ SV3 @ SV12 ) )
= $false )
| ( ( ( member @ SV15 @ SV3 )
| ( member @ SV15 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(99,plain,
! [SV17: $i,SV3: $i] :
( ( ! [SY38: $i] :
( ~ ( member @ SY38 @ SV3 )
| ( member @ SY38 @ ( union @ SV3 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(100,plain,
! [SV3: $i,SV18: $i] :
( ( ! [SY39: $i] :
( ~ ( member @ SY39 @ SV18 )
| ( member @ SY39 @ ( union @ SV3 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(101,plain,
! [SV13: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV8 ) )
= $true )
| ( ( ~ ( member @ SV16 @ SV13 ) )
= $true )
| ( ( intersect @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(102,plain,
! [SV9: $i,SV14: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK5_D @ SV14 @ SV9 ) @ SV14 ) )
= $false )
| ( ( intersect @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(103,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV10 ) )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(104,plain,
! [SV6: $i,SV10: $i] :
( ( ( ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV6 )
| ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV10 ) )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(105,plain,
! [SV11: $i,SV7: $i] :
( ( ( ~ ! [SY34: $i] :
( ~ ( member @ SY34 @ SV7 )
| ( member @ SY34 @ SV11 ) ) )
= $false )
| ( ( SV7 = SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(106,plain,
! [SV7: $i,SV11: $i] :
( ( ( ~ ! [SY35: $i] :
( ~ ( member @ SY35 @ SV11 )
| ( member @ SY35 @ SV7 ) ) )
= $false )
| ( ( SV7 = SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(107,plain,
! [SV12: $i,SV3: $i,SV15: $i] :
( ( ( member @ SV15 @ SV3 )
= $true )
| ( ( member @ SV15 @ SV12 )
= $true )
| ( ( member @ SV15 @ ( union @ SV3 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(108,plain,
! [SV17: $i,SV3: $i,SV19: $i] :
( ( ~ ( member @ SV19 @ SV3 )
| ( member @ SV19 @ ( union @ SV3 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(109,plain,
! [SV3: $i,SV18: $i,SV20: $i] :
( ( ~ ( member @ SV20 @ SV18 )
| ( member @ SV20 @ ( union @ SV3 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(110,plain,
! [SV13: $i,SV8: $i,SV16: $i] :
( ( ( member @ SV16 @ SV8 )
= $false )
| ( ( ~ ( member @ SV16 @ SV13 ) )
= $true )
| ( ( intersect @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(111,plain,
! [SV9: $i,SV14: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV14 @ SV9 ) @ SV9 ) )
= $false )
| ( ( intersect @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(112,plain,
! [SV9: $i,SV14: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV14 @ SV9 ) @ SV14 ) )
= $false )
| ( ( intersect @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(113,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV6 ) )
= $true )
| ( ( ~ ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV10 ) )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(114,plain,
! [SV6: $i,SV10: $i] :
( ( ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV6 )
= $true )
| ( ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV10 )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(115,plain,
! [SV11: $i,SV7: $i] :
( ( ( ! [SY34: $i] :
( ~ ( member @ SY34 @ SV7 )
| ( member @ SY34 @ SV11 ) ) )
= $true )
| ( ( SV7 = SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(116,plain,
! [SV7: $i,SV11: $i] :
( ( ( ! [SY35: $i] :
( ~ ( member @ SY35 @ SV11 )
| ( member @ SY35 @ SV7 ) ) )
= $true )
| ( ( SV7 = SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(117,plain,
! [SV17: $i,SV3: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ SV3 ) )
= $true )
| ( ( member @ SV19 @ ( union @ SV3 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(118,plain,
! [SV3: $i,SV18: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ SV18 ) )
= $true )
| ( ( member @ SV20 @ ( union @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(119,plain,
! [SV8: $i,SV13: $i,SV16: $i] :
( ( ( member @ SV16 @ SV13 )
= $false )
| ( ( member @ SV16 @ SV8 )
= $false )
| ( ( intersect @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(120,plain,
! [SV9: $i,SV14: $i] :
( ( ( member @ ( sK5_D @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( intersect @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(121,plain,
! [SV9: $i,SV14: $i] :
( ( ( member @ ( sK5_D @ SV14 @ SV9 ) @ SV14 )
= $true )
| ( ( intersect @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(122,plain,
! [SV6: $i,SV10: $i] :
( ( ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV6 )
= $false )
| ( ( ~ ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV10 ) )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(123,plain,
! [SV11: $i,SV7: $i,SV21: $i] :
( ( ( ~ ( member @ SV21 @ SV7 )
| ( member @ SV21 @ SV11 ) )
= $true )
| ( ( SV7 = SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(124,plain,
! [SV7: $i,SV11: $i,SV22: $i] :
( ( ( ~ ( member @ SV22 @ SV11 )
| ( member @ SV22 @ SV7 ) )
= $true )
| ( ( SV7 = SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(125,plain,
! [SV17: $i,SV3: $i,SV19: $i] :
( ( ( member @ SV19 @ SV3 )
= $false )
| ( ( member @ SV19 @ ( union @ SV3 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(126,plain,
! [SV3: $i,SV18: $i,SV20: $i] :
( ( ( member @ SV20 @ SV18 )
= $false )
| ( ( member @ SV20 @ ( union @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(127,plain,
! [SV6: $i,SV10: $i] :
( ( ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV10 )
= $false )
| ( ( member @ ( sK4_D @ SV10 @ SV6 ) @ SV6 )
= $false )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(128,plain,
! [SV11: $i,SV7: $i,SV21: $i] :
( ( ( ~ ( member @ SV21 @ SV7 ) )
= $true )
| ( ( member @ SV21 @ SV11 )
= $true )
| ( ( SV7 = SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(129,plain,
! [SV7: $i,SV11: $i,SV22: $i] :
( ( ( ~ ( member @ SV22 @ SV11 ) )
= $true )
| ( ( member @ SV22 @ SV7 )
= $true )
| ( ( SV7 = SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(130,plain,
! [SV11: $i,SV7: $i,SV21: $i] :
( ( ( member @ SV21 @ SV7 )
= $false )
| ( ( member @ SV21 @ SV11 )
= $true )
| ( ( SV7 = SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(131,plain,
! [SV7: $i,SV11: $i,SV22: $i] :
( ( ( member @ SV22 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV7 )
= $true )
| ( ( SV7 = SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(132,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[43,131,130,127,126,125,121,120,119,114,107,94,93,61,59]) ).
thf(133,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ ( union @ B @ C ) )
| ( member @ D @ B )
| ( member @ D @ C ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ ( union @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ ( union @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(134,plain,
( ( ! [B: $i,C: $i] :
( ! [D: $i] :
( ~ ( member @ D @ B )
| ~ ( member @ D @ C ) )
| ( intersect @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( intersect @ B @ C )
| ( ( member @ ( sK5_D @ C @ B ) @ B )
& ( member @ ( sK5_D @ C @ B ) @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(135,plain,
( ( ! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(136,plain,
( ( ! [B: $i,C: $i] :
( ~ ( intersect @ B @ C )
| ( intersect @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(137,plain,
( ( ! [B: $i,C: $i] :
( ( ( ~ ( member @ ( sK4_D @ C @ B ) @ B )
| ~ ( member @ ( sK4_D @ C @ B ) @ C ) )
& ( ( member @ ( sK4_D @ C @ B ) @ B )
| ( member @ ( sK4_D @ C @ B ) @ C ) ) )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) )
& ! [D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(138,plain,
( ( ( ( intersect @ sK1_B @ sK2_SY16 )
| ( intersect @ sK1_B @ sK3_SY18 ) )
& ~ ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(139,plain,
( ( ~ ( ~ ( ( intersect @ sK1_B @ sK2_SY16 )
| ( intersect @ sK1_B @ sK3_SY18 ) )
| ~ ~ ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(140,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(141,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( union @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ ( union @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ ( union @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(142,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(143,plain,
! [SV23: $i] :
( ( ! [SY40: $i] :
( ( union @ SV23 @ SY40 )
= ( union @ SY40 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(144,plain,
! [SV24: $i] :
( ( ! [SY41: $i] :
( ~ ( intersect @ SV24 @ SY41 )
| ( intersect @ SY41 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(145,plain,
( ( ~ ( ( intersect @ sK1_B @ sK2_SY16 )
| ( intersect @ sK1_B @ sK3_SY18 ) )
| ~ ~ ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(146,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(147,plain,
! [SV25: $i] :
( ( ~ ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( member @ SY43 @ ( union @ SV25 @ SY42 ) )
| ( member @ SY43 @ SV25 )
| ( member @ SY43 @ SY42 ) )
| ~ ~ ( ~ ! [SY44: $i,SY45: $i] :
( ~ ( member @ SY45 @ SV25 )
| ( member @ SY45 @ ( union @ SV25 @ SY44 ) ) )
| ~ ! [SY46: $i,SY47: $i] :
( ~ ( member @ SY47 @ SY46 )
| ( member @ SY47 @ ( union @ SV25 @ SY46 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(148,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(149,plain,
! [SV26: $i,SV23: $i] :
( ( ( union @ SV23 @ SV26 )
= ( union @ SV26 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(150,plain,
! [SV27: $i,SV24: $i] :
( ( ~ ( intersect @ SV24 @ SV27 )
| ( intersect @ SV27 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(151,plain,
( ( ~ ( ( intersect @ sK1_B @ sK2_SY16 )
| ( intersect @ sK1_B @ sK3_SY18 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(152,plain,
( ( ~ ~ ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(153,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(154,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(155,plain,
! [SV25: $i] :
( ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( member @ SY43 @ ( union @ SV25 @ SY42 ) )
| ( member @ SY43 @ SV25 )
| ( member @ SY43 @ SY42 ) )
| ~ ~ ( ~ ! [SY44: $i,SY45: $i] :
( ~ ( member @ SY45 @ SV25 )
| ( member @ SY45 @ ( union @ SV25 @ SY44 ) ) )
| ~ ! [SY46: $i,SY47: $i] :
( ~ ( member @ SY47 @ SY46 )
| ( member @ SY47 @ ( union @ SV25 @ SY46 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(156,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(157,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(158,plain,
! [SV27: $i,SV24: $i] :
( ( ( ~ ( intersect @ SV24 @ SV27 ) )
= $true )
| ( ( intersect @ SV27 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(159,plain,
( ( ( intersect @ sK1_B @ sK2_SY16 )
| ( intersect @ sK1_B @ sK3_SY18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(160,plain,
( ( ~ ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(161,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(162,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(163,plain,
! [SV25: $i] :
( ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( member @ SY43 @ ( union @ SV25 @ SY42 ) )
| ( member @ SY43 @ SV25 )
| ( member @ SY43 @ SY42 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(164,plain,
! [SV25: $i] :
( ( ~ ~ ( ~ ! [SY44: $i,SY45: $i] :
( ~ ( member @ SY45 @ SV25 )
| ( member @ SY45 @ ( union @ SV25 @ SY44 ) ) )
| ~ ! [SY46: $i,SY47: $i] :
( ~ ( member @ SY47 @ SY46 )
| ( member @ SY47 @ ( union @ SV25 @ SY46 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(165,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(166,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(167,plain,
! [SV27: $i,SV24: $i] :
( ( ( intersect @ SV24 @ SV27 )
= $false )
| ( ( intersect @ SV27 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(168,plain,
( ( ( intersect @ sK1_B @ sK2_SY16 )
= $true )
| ( ( intersect @ sK1_B @ sK3_SY18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(169,plain,
( ( intersect @ sK1_B @ ( union @ sK2_SY16 @ sK3_SY18 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(170,plain,
! [SV28: $i] :
( ( ! [SY48: $i] :
( ! [SY49: $i] :
( ~ ( member @ SY49 @ SV28 )
| ~ ( member @ SY49 @ SY48 ) )
| ( intersect @ SV28 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(171,plain,
! [SV29: $i] :
( ( ! [SY50: $i] :
( ~ ( intersect @ SV29 @ SY50 )
| ~ ( ~ ( member @ ( sK5_D @ SY50 @ SV29 ) @ SV29 )
| ~ ( member @ ( sK5_D @ SY50 @ SV29 ) @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(172,plain,
! [SV25: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ~ ( member @ SY43 @ ( union @ SV25 @ SY42 ) )
| ( member @ SY43 @ SV25 )
| ( member @ SY43 @ SY42 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(173,plain,
! [SV25: $i] :
( ( ~ ( ~ ! [SY44: $i,SY45: $i] :
( ~ ( member @ SY45 @ SV25 )
| ( member @ SY45 @ ( union @ SV25 @ SY44 ) ) )
| ~ ! [SY46: $i,SY47: $i] :
( ~ ( member @ SY47 @ SY46 )
| ( member @ SY47 @ ( union @ SV25 @ SY46 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(174,plain,
! [SV30: $i] :
( ( ! [SY51: $i] :
( ~ ( ~ ( ~ ( member @ ( sK4_D @ SY51 @ SV30 ) @ SV30 )
| ~ ( member @ ( sK4_D @ SY51 @ SV30 ) @ SY51 ) )
| ~ ( ( member @ ( sK4_D @ SY51 @ SV30 ) @ SV30 )
| ( member @ ( sK4_D @ SY51 @ SV30 ) @ SY51 ) ) )
| ( SV30 = SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(175,plain,
! [SV31: $i] :
( ( ! [SY52: $i] :
( ( SV31 != SY52 )
| ~ ( ~ ! [SY53: $i] :
( ~ ( member @ SY53 @ SV31 )
| ( member @ SY53 @ SY52 ) )
| ~ ! [SY54: $i] :
( ~ ( member @ SY54 @ SY52 )
| ( member @ SY54 @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(176,plain,
! [SV32: $i,SV28: $i] :
( ( ! [SY55: $i] :
( ~ ( member @ SY55 @ SV28 )
| ~ ( member @ SY55 @ SV32 ) )
| ( intersect @ SV28 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(177,plain,
! [SV33: $i,SV29: $i] :
( ( ~ ( intersect @ SV29 @ SV33 )
| ~ ( ~ ( member @ ( sK5_D @ SV33 @ SV29 ) @ SV29 )
| ~ ( member @ ( sK5_D @ SV33 @ SV29 ) @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(178,plain,
! [SV34: $i,SV25: $i] :
( ( ! [SY56: $i] :
( ~ ( member @ SY56 @ ( union @ SV25 @ SV34 ) )
| ( member @ SY56 @ SV25 )
| ( member @ SY56 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(179,plain,
! [SV25: $i] :
( ( ~ ! [SY44: $i,SY45: $i] :
( ~ ( member @ SY45 @ SV25 )
| ( member @ SY45 @ ( union @ SV25 @ SY44 ) ) )
| ~ ! [SY46: $i,SY47: $i] :
( ~ ( member @ SY47 @ SY46 )
| ( member @ SY47 @ ( union @ SV25 @ SY46 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(180,plain,
! [SV30: $i,SV35: $i] :
( ( ~ ( ~ ( ~ ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV30 )
| ~ ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV35 ) )
| ~ ( ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV30 )
| ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV35 ) ) )
| ( SV30 = SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(181,plain,
! [SV36: $i,SV31: $i] :
( ( ( SV31 != SV36 )
| ~ ( ~ ! [SY57: $i] :
( ~ ( member @ SY57 @ SV31 )
| ( member @ SY57 @ SV36 ) )
| ~ ! [SY58: $i] :
( ~ ( member @ SY58 @ SV36 )
| ( member @ SY58 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(182,plain,
! [SV32: $i,SV28: $i] :
( ( ( ! [SY55: $i] :
( ~ ( member @ SY55 @ SV28 )
| ~ ( member @ SY55 @ SV32 ) ) )
= $true )
| ( ( intersect @ SV28 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(183,plain,
! [SV33: $i,SV29: $i] :
( ( ( ~ ( intersect @ SV29 @ SV33 ) )
= $true )
| ( ( ~ ( ~ ( member @ ( sK5_D @ SV33 @ SV29 ) @ SV29 )
| ~ ( member @ ( sK5_D @ SV33 @ SV29 ) @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(184,plain,
! [SV34: $i,SV25: $i,SV37: $i] :
( ( ~ ( member @ SV37 @ ( union @ SV25 @ SV34 ) )
| ( member @ SV37 @ SV25 )
| ( member @ SV37 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(185,plain,
! [SV25: $i] :
( ( ~ ! [SY44: $i,SY45: $i] :
( ~ ( member @ SY45 @ SV25 )
| ( member @ SY45 @ ( union @ SV25 @ SY44 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(186,plain,
! [SV25: $i] :
( ( ~ ! [SY46: $i,SY47: $i] :
( ~ ( member @ SY47 @ SY46 )
| ( member @ SY47 @ ( union @ SV25 @ SY46 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(187,plain,
! [SV30: $i,SV35: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV30 )
| ~ ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV35 ) )
| ~ ( ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV30 )
| ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV35 ) ) ) )
= $true )
| ( ( SV30 = SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(188,plain,
! [SV36: $i,SV31: $i] :
( ( ( ( SV31 != SV36 ) )
= $true )
| ( ( ~ ( ~ ! [SY57: $i] :
( ~ ( member @ SY57 @ SV31 )
| ( member @ SY57 @ SV36 ) )
| ~ ! [SY58: $i] :
( ~ ( member @ SY58 @ SV36 )
| ( member @ SY58 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(189,plain,
! [SV32: $i,SV28: $i,SV38: $i] :
( ( ( ~ ( member @ SV38 @ SV28 )
| ~ ( member @ SV38 @ SV32 ) )
= $true )
| ( ( intersect @ SV28 @ SV32 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(190,plain,
! [SV33: $i,SV29: $i] :
( ( ( intersect @ SV29 @ SV33 )
= $false )
| ( ( ~ ( ~ ( member @ ( sK5_D @ SV33 @ SV29 ) @ SV29 )
| ~ ( member @ ( sK5_D @ SV33 @ SV29 ) @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(191,plain,
! [SV34: $i,SV25: $i,SV37: $i] :
( ( ( ~ ( member @ SV37 @ ( union @ SV25 @ SV34 ) ) )
= $true )
| ( ( ( member @ SV37 @ SV25 )
| ( member @ SV37 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(192,plain,
! [SV25: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ( member @ SY45 @ SV25 )
| ( member @ SY45 @ ( union @ SV25 @ SY44 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(193,plain,
! [SV25: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ~ ( member @ SY47 @ SY46 )
| ( member @ SY47 @ ( union @ SV25 @ SY46 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(194,plain,
! [SV30: $i,SV35: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV30 )
| ~ ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV35 ) )
| ~ ( ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV30 )
| ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV35 ) ) )
= $false )
| ( ( SV30 = SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(195,plain,
! [SV36: $i,SV31: $i] :
( ( ( SV31 = SV36 )
= $false )
| ( ( ~ ( ~ ! [SY57: $i] :
( ~ ( member @ SY57 @ SV31 )
| ( member @ SY57 @ SV36 ) )
| ~ ! [SY58: $i] :
( ~ ( member @ SY58 @ SV36 )
| ( member @ SY58 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(196,plain,
! [SV32: $i,SV28: $i,SV38: $i] :
( ( ( ~ ( member @ SV38 @ SV28 ) )
= $true )
| ( ( ~ ( member @ SV38 @ SV32 ) )
= $true )
| ( ( intersect @ SV28 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(197,plain,
! [SV29: $i,SV33: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV33 @ SV29 ) @ SV29 )
| ~ ( member @ ( sK5_D @ SV33 @ SV29 ) @ SV33 ) )
= $false )
| ( ( intersect @ SV29 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(198,plain,
! [SV34: $i,SV25: $i,SV37: $i] :
( ( ( member @ SV37 @ ( union @ SV25 @ SV34 ) )
= $false )
| ( ( ( member @ SV37 @ SV25 )
| ( member @ SV37 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(199,plain,
! [SV39: $i,SV25: $i] :
( ( ! [SY59: $i] :
( ~ ( member @ SY59 @ SV25 )
| ( member @ SY59 @ ( union @ SV25 @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(200,plain,
! [SV25: $i,SV40: $i] :
( ( ! [SY60: $i] :
( ~ ( member @ SY60 @ SV40 )
| ( member @ SY60 @ ( union @ SV25 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(201,plain,
! [SV30: $i,SV35: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV30 )
| ~ ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV35 ) ) )
= $false )
| ( ( SV30 = SV35 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(202,plain,
! [SV30: $i,SV35: $i] :
( ( ( ~ ( ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV30 )
| ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV35 ) ) )
= $false )
| ( ( SV30 = SV35 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(203,plain,
! [SV36: $i,SV31: $i] :
( ( ( ~ ! [SY57: $i] :
( ~ ( member @ SY57 @ SV31 )
| ( member @ SY57 @ SV36 ) )
| ~ ! [SY58: $i] :
( ~ ( member @ SY58 @ SV36 )
| ( member @ SY58 @ SV31 ) ) )
= $false )
| ( ( SV31 = SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(204,plain,
! [SV32: $i,SV28: $i,SV38: $i] :
( ( ( member @ SV38 @ SV28 )
= $false )
| ( ( ~ ( member @ SV38 @ SV32 ) )
= $true )
| ( ( intersect @ SV28 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(205,plain,
! [SV29: $i,SV33: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV33 @ SV29 ) @ SV29 ) )
= $false )
| ( ( intersect @ SV29 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(206,plain,
! [SV29: $i,SV33: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV33 @ SV29 ) @ SV33 ) )
= $false )
| ( ( intersect @ SV29 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(207,plain,
! [SV34: $i,SV25: $i,SV37: $i] :
( ( ( member @ SV37 @ SV25 )
= $true )
| ( ( member @ SV37 @ SV34 )
= $true )
| ( ( member @ SV37 @ ( union @ SV25 @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(208,plain,
! [SV39: $i,SV25: $i,SV41: $i] :
( ( ~ ( member @ SV41 @ SV25 )
| ( member @ SV41 @ ( union @ SV25 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(209,plain,
! [SV25: $i,SV40: $i,SV42: $i] :
( ( ~ ( member @ SV42 @ SV40 )
| ( member @ SV42 @ ( union @ SV25 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(210,plain,
! [SV30: $i,SV35: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV30 )
| ~ ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV35 ) )
= $true )
| ( ( SV30 = SV35 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(211,plain,
! [SV30: $i,SV35: $i] :
( ( ( ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV30 )
| ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV35 ) )
= $true )
| ( ( SV30 = SV35 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(212,plain,
! [SV36: $i,SV31: $i] :
( ( ( ~ ! [SY57: $i] :
( ~ ( member @ SY57 @ SV31 )
| ( member @ SY57 @ SV36 ) ) )
= $false )
| ( ( SV31 = SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(213,plain,
! [SV31: $i,SV36: $i] :
( ( ( ~ ! [SY58: $i] :
( ~ ( member @ SY58 @ SV36 )
| ( member @ SY58 @ SV31 ) ) )
= $false )
| ( ( SV31 = SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(214,plain,
! [SV28: $i,SV32: $i,SV38: $i] :
( ( ( member @ SV38 @ SV32 )
= $false )
| ( ( member @ SV38 @ SV28 )
= $false )
| ( ( intersect @ SV28 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(215,plain,
! [SV29: $i,SV33: $i] :
( ( ( member @ ( sK5_D @ SV33 @ SV29 ) @ SV29 )
= $true )
| ( ( intersect @ SV29 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(216,plain,
! [SV29: $i,SV33: $i] :
( ( ( member @ ( sK5_D @ SV33 @ SV29 ) @ SV33 )
= $true )
| ( ( intersect @ SV29 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(217,plain,
! [SV39: $i,SV25: $i,SV41: $i] :
( ( ( ~ ( member @ SV41 @ SV25 ) )
= $true )
| ( ( member @ SV41 @ ( union @ SV25 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(218,plain,
! [SV25: $i,SV40: $i,SV42: $i] :
( ( ( ~ ( member @ SV42 @ SV40 ) )
= $true )
| ( ( member @ SV42 @ ( union @ SV25 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(219,plain,
! [SV30: $i,SV35: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV30 ) )
= $true )
| ( ( ~ ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV35 ) )
= $true )
| ( ( SV30 = SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(220,plain,
! [SV30: $i,SV35: $i] :
( ( ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV30 )
= $true )
| ( ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV35 )
= $true )
| ( ( SV30 = SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(221,plain,
! [SV36: $i,SV31: $i] :
( ( ( ! [SY57: $i] :
( ~ ( member @ SY57 @ SV31 )
| ( member @ SY57 @ SV36 ) ) )
= $true )
| ( ( SV31 = SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(222,plain,
! [SV31: $i,SV36: $i] :
( ( ( ! [SY58: $i] :
( ~ ( member @ SY58 @ SV36 )
| ( member @ SY58 @ SV31 ) ) )
= $true )
| ( ( SV31 = SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(223,plain,
! [SV39: $i,SV25: $i,SV41: $i] :
( ( ( member @ SV41 @ SV25 )
= $false )
| ( ( member @ SV41 @ ( union @ SV25 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(224,plain,
! [SV25: $i,SV40: $i,SV42: $i] :
( ( ( member @ SV42 @ SV40 )
= $false )
| ( ( member @ SV42 @ ( union @ SV25 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(225,plain,
! [SV30: $i,SV35: $i] :
( ( ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV30 )
= $false )
| ( ( ~ ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV35 ) )
= $true )
| ( ( SV30 = SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(226,plain,
! [SV36: $i,SV31: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ SV31 )
| ( member @ SV43 @ SV36 ) )
= $true )
| ( ( SV31 = SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(227,plain,
! [SV31: $i,SV36: $i,SV44: $i] :
( ( ( ~ ( member @ SV44 @ SV36 )
| ( member @ SV44 @ SV31 ) )
= $true )
| ( ( SV31 = SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(228,plain,
! [SV30: $i,SV35: $i] :
( ( ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV35 )
= $false )
| ( ( member @ ( sK4_D @ SV35 @ SV30 ) @ SV30 )
= $false )
| ( ( SV30 = SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(229,plain,
! [SV36: $i,SV31: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ SV31 ) )
= $true )
| ( ( member @ SV43 @ SV36 )
= $true )
| ( ( SV31 = SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(230,plain,
! [SV31: $i,SV36: $i,SV44: $i] :
( ( ( ~ ( member @ SV44 @ SV36 ) )
= $true )
| ( ( member @ SV44 @ SV31 )
= $true )
| ( ( SV31 = SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(231,plain,
! [SV36: $i,SV31: $i,SV43: $i] :
( ( ( member @ SV43 @ SV31 )
= $false )
| ( ( member @ SV43 @ SV36 )
= $true )
| ( ( SV31 = SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(232,plain,
! [SV31: $i,SV36: $i,SV44: $i] :
( ( ( member @ SV44 @ SV36 )
= $false )
| ( ( member @ SV44 @ SV31 )
= $true )
| ( ( SV31 = SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(233,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[149,232,231,228,224,223,220,216,215,214,207,169,168,167]) ).
thf(234,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[233,132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET624+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n027.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 : Sun Jul 10 21:28:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 5
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:7,loop_count:0,foatp_calls:0,translation:fof_full).............
% 21.84/22.05
% 21.84/22.05 ********************************
% 21.84/22.05 * All subproblems solved! *
% 21.84/22.05 ********************************
% 21.84/22.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:53,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:233,loop_count:0,foatp_calls:1,translation:fof_full)
% 21.84/22.07
% 21.84/22.07 %**** Beginning of derivation protocol ****
% 21.84/22.07 % SZS output start CNFRefutation
% See solution above
% 21.84/22.07
% 21.84/22.07 %**** End of derivation protocol ****
% 21.84/22.07 %**** no. of clauses in derivation: 234 ****
% 21.84/22.07 %**** clause counter: 233 ****
% 21.84/22.07
% 21.84/22.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:53,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:233,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------