TSTP Solution File: SEU275+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU275+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:09:25 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 24
% Syntax : Number of formulae : 163 ( 99 unt; 13 typ; 0 def)
% Number of atoms : 1067 ( 235 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 1534 ( 454 ~; 399 |; 32 &; 633 @)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 182 ( 0 ^ 180 !; 2 ?; 182 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_connected,type,
connected: $i > $o ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_inclusion_relation,type,
inclusion_relation: $i > $i ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_reflexive,type,
reflexive: $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_A,type,
sK2_A: $i ).
thf(tp_transitive,type,
transitive: $i > $o ).
thf(tp_well_founded_relation,type,
well_founded_relation: $i > $o ).
thf(tp_well_ordering,type,
well_ordering: $i > $o ).
thf(1,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( well_founded_relation @ ( inclusion_relation @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_wellord2) ).
thf(2,axiom,
! [A: $i] : ( antisymmetric @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord2) ).
thf(3,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( connected @ ( inclusion_relation @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_wellord2) ).
thf(4,axiom,
! [A: $i] : ( transitive @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_wellord2) ).
thf(5,axiom,
! [A: $i] : ( reflexive @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_wellord2) ).
thf(6,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(7,axiom,
! [A: $i] : ( relation @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
thf(8,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_ordering @ A )
<=> ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).
thf(9,axiom,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(10,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(11,conjecture,
! [A: $i] :
( ( ordinal @ A )
=> ( well_ordering @ ( inclusion_relation @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_wellord2) ).
thf(12,negated_conjecture,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( well_ordering @ ( inclusion_relation @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[11]) ).
thf(13,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( well_ordering @ ( inclusion_relation @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( well_founded_relation @ ( inclusion_relation @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(15,plain,
( ( ! [A: $i] : ( antisymmetric @ ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(16,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( connected @ ( inclusion_relation @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: $i] : ( transitive @ ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(18,plain,
( ( ! [A: $i] : ( reflexive @ ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(19,plain,
( ( ? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(20,plain,
( ( ! [A: $i] : ( relation @ ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(21,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_ordering @ A )
<=> ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(22,plain,
( ( ! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(23,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(24,plain,
( ( ( ordinal @ sK1_A )
=> ( well_ordering @ ( inclusion_relation @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(25,plain,
( ( ordinal @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[24]) ).
thf(26,plain,
( ( well_ordering @ ( inclusion_relation @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[24]) ).
thf(27,plain,
( ( ~ ( well_ordering @ ( inclusion_relation @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(28,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( well_founded_relation @ ( inclusion_relation @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(29,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( connected @ ( inclusion_relation @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(30,plain,
( ( ( epsilon_connected @ sK2_A )
& ( epsilon_transitive @ sK2_A )
& ( ordinal @ sK2_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(31,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( reflexive @ A )
| ~ ( transitive @ A )
| ~ ( antisymmetric @ A )
| ~ ( connected @ A )
| ~ ( well_founded_relation @ A )
| ( well_ordering @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( reflexive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( antisymmetric @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( connected @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( well_founded_relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(32,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(33,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(34,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(35,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(36,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( reflexive @ A )
| ~ ( transitive @ A )
| ~ ( antisymmetric @ A )
| ~ ( connected @ A )
| ~ ( well_founded_relation @ A )
| ( well_ordering @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( reflexive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( antisymmetric @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( connected @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( well_founded_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(37,plain,
( ( ! [A: $i] : ( relation @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(38,plain,
( ( ( epsilon_connected @ sK2_A )
& ( epsilon_transitive @ sK2_A )
& ( ordinal @ sK2_A ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(39,plain,
( ( ! [A: $i] : ( reflexive @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(40,plain,
( ( ! [A: $i] : ( transitive @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(41,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( connected @ ( inclusion_relation @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(42,plain,
( ( ! [A: $i] : ( antisymmetric @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(43,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( well_founded_relation @ ( inclusion_relation @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(44,plain,
( ( ordinal @ sK1_A )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(45,plain,
( ( ~ ( well_ordering @ ( inclusion_relation @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(46,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ~ ( connected @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( well_ordering @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(47,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(48,plain,
( ( ~ ( ~ ~ ( ~ ( epsilon_connected @ sK2_A )
| ~ ( epsilon_transitive @ sK2_A ) )
| ~ ( ordinal @ sK2_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(49,plain,
! [SV1: $i] :
( ( ~ ( epsilon_connected @ SV1 )
| ~ ( epsilon_transitive @ SV1 )
| ( ordinal @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(50,plain,
! [SV2: $i] :
( ( relation @ ( inclusion_relation @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(51,plain,
! [SV3: $i] :
( ( reflexive @ ( inclusion_relation @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(52,plain,
! [SV4: $i] :
( ( transitive @ ( inclusion_relation @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(53,plain,
! [SV5: $i] :
( ( ~ ( ordinal @ SV5 )
| ( connected @ ( inclusion_relation @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(54,plain,
! [SV6: $i] :
( ( antisymmetric @ ( inclusion_relation @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(55,plain,
! [SV7: $i] :
( ( ~ ( ordinal @ SV7 )
| ( well_founded_relation @ ( inclusion_relation @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(56,plain,
( ( well_ordering @ ( inclusion_relation @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(57,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ~ ( connected @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( well_ordering @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(58,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(59,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK2_A )
| ~ ( epsilon_transitive @ sK2_A ) )
| ~ ( ordinal @ sK2_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(60,plain,
! [SV1: $i] :
( ( ( ~ ( epsilon_connected @ SV1 )
| ~ ( epsilon_transitive @ SV1 ) )
= $true )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(61,plain,
! [SV5: $i] :
( ( ( ~ ( ordinal @ SV5 ) )
= $true )
| ( ( connected @ ( inclusion_relation @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(62,plain,
! [SV7: $i] :
( ( ( ~ ( ordinal @ SV7 ) )
= $true )
| ( ( well_founded_relation @ ( inclusion_relation @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(63,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ~ ( connected @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( well_ordering @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(64,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(65,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(66,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(67,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK2_A )
| ~ ( epsilon_transitive @ sK2_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(68,plain,
( ( ~ ( ordinal @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(69,plain,
! [SV1: $i] :
( ( ( ~ ( epsilon_connected @ SV1 ) )
= $true )
| ( ( ~ ( epsilon_transitive @ SV1 ) )
= $true )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(70,plain,
! [SV5: $i] :
( ( ( ordinal @ SV5 )
= $false )
| ( ( connected @ ( inclusion_relation @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(71,plain,
! [SV7: $i] :
( ( ( ordinal @ SV7 )
= $false )
| ( ( well_founded_relation @ ( inclusion_relation @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(72,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ~ ( connected @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( well_ordering @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(73,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(74,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(75,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(76,plain,
( ( ~ ( ~ ( epsilon_connected @ sK2_A )
| ~ ( epsilon_transitive @ sK2_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(77,plain,
( ( ordinal @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(78,plain,
! [SV1: $i] :
( ( ( epsilon_connected @ SV1 )
= $false )
| ( ( ~ ( epsilon_transitive @ SV1 ) )
= $true )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(79,plain,
! [SV8: $i] :
( ( ~ ( relation @ SV8 )
| ~ ( reflexive @ SV8 )
| ~ ( transitive @ SV8 )
| ~ ( antisymmetric @ SV8 )
| ~ ( connected @ SV8 )
| ~ ( well_founded_relation @ SV8 )
| ( well_ordering @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(80,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(81,plain,
! [SV9: $i] :
( ( ~ ( ordinal @ SV9 )
| ( epsilon_connected @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(82,plain,
! [SV10: $i] :
( ( ~ ( ordinal @ SV10 )
| ( epsilon_transitive @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(83,plain,
( ( ~ ( epsilon_connected @ sK2_A )
| ~ ( epsilon_transitive @ sK2_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(84,plain,
! [SV1: $i] :
( ( ( epsilon_transitive @ SV1 )
= $false )
| ( ( epsilon_connected @ SV1 )
= $false )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(85,plain,
! [SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( ~ ( reflexive @ SV8 )
| ~ ( transitive @ SV8 )
| ~ ( antisymmetric @ SV8 )
| ~ ( connected @ SV8 )
| ~ ( well_founded_relation @ SV8 )
| ( well_ordering @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(86,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(87,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(88,plain,
! [SV9: $i] :
( ( ( ~ ( ordinal @ SV9 ) )
= $true )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(89,plain,
! [SV10: $i] :
( ( ( ~ ( ordinal @ SV10 ) )
= $true )
| ( ( epsilon_transitive @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(90,plain,
( ( ~ ( epsilon_connected @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(91,plain,
( ( ~ ( epsilon_transitive @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(92,plain,
! [SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( ~ ( reflexive @ SV8 )
| ~ ( transitive @ SV8 )
| ~ ( antisymmetric @ SV8 )
| ~ ( connected @ SV8 )
| ~ ( well_founded_relation @ SV8 )
| ( well_ordering @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(93,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(94,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(95,plain,
! [SV9: $i] :
( ( ( ordinal @ SV9 )
= $false )
| ( ( epsilon_connected @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(96,plain,
! [SV10: $i] :
( ( ( ordinal @ SV10 )
= $false )
| ( ( epsilon_transitive @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(97,plain,
( ( epsilon_connected @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(98,plain,
( ( epsilon_transitive @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(99,plain,
! [SV8: $i] :
( ( ( ~ ( reflexive @ SV8 )
| ~ ( transitive @ SV8 )
| ~ ( antisymmetric @ SV8 )
| ~ ( connected @ SV8 )
| ~ ( well_founded_relation @ SV8 ) )
= $true )
| ( ( well_ordering @ SV8 )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(100,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(101,plain,
! [SV11: $i] :
( ( ~ ( relation @ SV11 )
| ~ ( well_ordering @ SV11 )
| ( well_founded_relation @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(102,plain,
! [SV8: $i] :
( ( ( ~ ( reflexive @ SV8 )
| ~ ( transitive @ SV8 )
| ~ ( antisymmetric @ SV8 )
| ~ ( connected @ SV8 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV8 ) )
= $true )
| ( ( well_ordering @ SV8 )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(103,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(104,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(105,plain,
! [SV11: $i] :
( ( ( ~ ( relation @ SV11 ) )
= $true )
| ( ( ~ ( well_ordering @ SV11 )
| ( well_founded_relation @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(106,plain,
! [SV8: $i] :
( ( ( ~ ( reflexive @ SV8 )
| ~ ( transitive @ SV8 )
| ~ ( antisymmetric @ SV8 ) )
= $true )
| ( ( ~ ( connected @ SV8 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV8 ) )
= $true )
| ( ( well_ordering @ SV8 )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(107,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(108,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(109,plain,
! [SV11: $i] :
( ( ( relation @ SV11 )
= $false )
| ( ( ~ ( well_ordering @ SV11 )
| ( well_founded_relation @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(110,plain,
! [SV8: $i] :
( ( ( ~ ( reflexive @ SV8 )
| ~ ( transitive @ SV8 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV8 ) )
= $true )
| ( ( ~ ( connected @ SV8 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV8 ) )
= $true )
| ( ( well_ordering @ SV8 )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(111,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV12: $i] :
( ( ~ ( relation @ SV12 )
| ~ ( well_ordering @ SV12 )
| ( connected @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(113,plain,
! [SV11: $i] :
( ( ( ~ ( well_ordering @ SV11 ) )
= $true )
| ( ( well_founded_relation @ SV11 )
= $true )
| ( ( relation @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(114,plain,
! [SV8: $i] :
( ( ( ~ ( reflexive @ SV8 ) )
= $true )
| ( ( ~ ( transitive @ SV8 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV8 ) )
= $true )
| ( ( ~ ( connected @ SV8 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV8 ) )
= $true )
| ( ( well_ordering @ SV8 )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(115,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(116,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(117,plain,
! [SV12: $i] :
( ( ( ~ ( relation @ SV12 ) )
= $true )
| ( ( ~ ( well_ordering @ SV12 )
| ( connected @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(118,plain,
! [SV11: $i] :
( ( ( well_ordering @ SV11 )
= $false )
| ( ( well_founded_relation @ SV11 )
= $true )
| ( ( relation @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(119,plain,
! [SV8: $i] :
( ( ( reflexive @ SV8 )
= $false )
| ( ( ~ ( transitive @ SV8 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV8 ) )
= $true )
| ( ( ~ ( connected @ SV8 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV8 ) )
= $true )
| ( ( well_ordering @ SV8 )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(120,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(121,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(122,plain,
! [SV12: $i] :
( ( ( relation @ SV12 )
= $false )
| ( ( ~ ( well_ordering @ SV12 )
| ( connected @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(123,plain,
! [SV8: $i] :
( ( ( transitive @ SV8 )
= $false )
| ( ( reflexive @ SV8 )
= $false )
| ( ( ~ ( antisymmetric @ SV8 ) )
= $true )
| ( ( ~ ( connected @ SV8 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV8 ) )
= $true )
| ( ( well_ordering @ SV8 )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(124,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(125,plain,
! [SV13: $i] :
( ( ~ ( relation @ SV13 )
| ~ ( well_ordering @ SV13 )
| ( antisymmetric @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(126,plain,
! [SV12: $i] :
( ( ( ~ ( well_ordering @ SV12 ) )
= $true )
| ( ( connected @ SV12 )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(127,plain,
! [SV8: $i] :
( ( ( antisymmetric @ SV8 )
= $false )
| ( ( reflexive @ SV8 )
= $false )
| ( ( transitive @ SV8 )
= $false )
| ( ( ~ ( connected @ SV8 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV8 ) )
= $true )
| ( ( well_ordering @ SV8 )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(128,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(129,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(130,plain,
! [SV13: $i] :
( ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( ~ ( well_ordering @ SV13 )
| ( antisymmetric @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(131,plain,
! [SV12: $i] :
( ( ( well_ordering @ SV12 )
= $false )
| ( ( connected @ SV12 )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(132,plain,
! [SV8: $i] :
( ( ( connected @ SV8 )
= $false )
| ( ( transitive @ SV8 )
= $false )
| ( ( reflexive @ SV8 )
= $false )
| ( ( antisymmetric @ SV8 )
= $false )
| ( ( ~ ( well_founded_relation @ SV8 ) )
= $true )
| ( ( well_ordering @ SV8 )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(133,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(134,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(135,plain,
! [SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( ~ ( well_ordering @ SV13 )
| ( antisymmetric @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(136,plain,
! [SV8: $i] :
( ( ( well_founded_relation @ SV8 )
= $false )
| ( ( antisymmetric @ SV8 )
= $false )
| ( ( reflexive @ SV8 )
= $false )
| ( ( transitive @ SV8 )
= $false )
| ( ( connected @ SV8 )
= $false )
| ( ( well_ordering @ SV8 )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(137,plain,
! [SV14: $i] :
( ( ~ ( relation @ SV14 )
| ~ ( well_ordering @ SV14 )
| ( reflexive @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(138,plain,
! [SV15: $i] :
( ( ~ ( relation @ SV15 )
| ~ ( well_ordering @ SV15 )
| ( transitive @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(139,plain,
! [SV13: $i] :
( ( ( ~ ( well_ordering @ SV13 ) )
= $true )
| ( ( antisymmetric @ SV13 )
= $true )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(140,plain,
! [SV14: $i] :
( ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( ~ ( well_ordering @ SV14 )
| ( reflexive @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(141,plain,
! [SV15: $i] :
( ( ( ~ ( relation @ SV15 ) )
= $true )
| ( ( ~ ( well_ordering @ SV15 )
| ( transitive @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(142,plain,
! [SV13: $i] :
( ( ( well_ordering @ SV13 )
= $false )
| ( ( antisymmetric @ SV13 )
= $true )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(143,plain,
! [SV14: $i] :
( ( ( relation @ SV14 )
= $false )
| ( ( ~ ( well_ordering @ SV14 )
| ( reflexive @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(144,plain,
! [SV15: $i] :
( ( ( relation @ SV15 )
= $false )
| ( ( ~ ( well_ordering @ SV15 )
| ( transitive @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(145,plain,
! [SV14: $i] :
( ( ( ~ ( well_ordering @ SV14 ) )
= $true )
| ( ( reflexive @ SV14 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(146,plain,
! [SV15: $i] :
( ( ( ~ ( well_ordering @ SV15 ) )
= $true )
| ( ( transitive @ SV15 )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(147,plain,
! [SV14: $i] :
( ( ( well_ordering @ SV14 )
= $false )
| ( ( reflexive @ SV14 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(148,plain,
! [SV15: $i] :
( ( ( well_ordering @ SV15 )
= $false )
| ( ( transitive @ SV15 )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(149,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[44,148,147,142,136,131,118,98,97,96,95,84,77,71,70,56,54,52,51,50]) ).
thf(150,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU275+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 03:14:22 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 10
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:10,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:12,loop_count:0,foatp_calls:0,translation:fof_full).......
% 0.20/0.41
% 0.20/0.41 ********************************
% 0.20/0.41 * All subproblems solved! *
% 0.20/0.41 ********************************
% 0.20/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:11,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:149,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.41
% 0.20/0.41 %**** Beginning of derivation protocol ****
% 0.20/0.41 % SZS output start CNFRefutation
% See solution above
% 0.20/0.41
% 0.20/0.41 %**** End of derivation protocol ****
% 0.20/0.41 %**** no. of clauses in derivation: 150 ****
% 0.20/0.41 %**** clause counter: 149 ****
% 0.20/0.41
% 0.20/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:11,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:149,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------