TSTP Solution File: SEU280+1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU280+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 : n029.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 12:09:29 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 19
% Syntax : Number of formulae : 151 ( 63 unt; 13 typ; 0 def)
% Number of atoms : 1007 ( 332 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 1615 ( 470 ~; 329 |; 49 &; 748 @)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 193 ( 0 ^ 182 !; 11 ?; 193 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY16,type,
sK2_SY16: $i > $i ).
thf(tp_sK3_B,type,
sK3_B: $i > $i ).
thf(tp_sK4_D,type,
sK4_D: $i > $i > $i ).
thf(tp_sK5_B,type,
sK5_B: $i ).
thf(tp_sK6_SY21,type,
sK6_SY21: $i ).
thf(tp_sK7_SY23,type,
sK7_SY23: $i ).
thf(tp_sK8_REN,type,
sK8_REN: $o ).
thf(tp_sK9_A,type,
sK9_A: $i ).
thf(1,axiom,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( B = C )
& ( ordinal @ C )
& ( B = D )
& ( ordinal @ D ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ A )
& ( D = C )
& ( ordinal @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_22__wellord2__1) ).
thf(2,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(4,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(5,axiom,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(6,conjecture,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ( ( in @ C @ A )
& ( ordinal @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_22__wellord2) ).
thf(7,negated_conjecture,
( ( ! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ( ( in @ C @ A )
& ( ordinal @ C ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ( ( in @ C @ A )
& ( ordinal @ C ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( B = C )
& ( ordinal @ C )
& ( B = D )
& ( ordinal @ D ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ A )
& ( D = C )
& ( ordinal @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ? [SY15: $i] :
! [SY16: $i] :
( ( in @ SY16 @ SY15 )
<=> ( ( in @ SY16 @ sK1_A )
& ( ordinal @ SY16 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( ~ ? [SY15: $i] :
! [SY16: $i] :
( ( in @ SY16 @ SY15 )
<=> ( ( in @ SY16 @ sK1_A )
& ( ordinal @ SY16 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [SY15: $i] :
( ( ~ ( in @ ( sK2_SY16 @ SY15 ) @ sK1_A )
| ~ ( ordinal @ ( sK2_SY16 @ SY15 ) )
| ~ ( in @ ( sK2_SY16 @ SY15 ) @ SY15 ) )
& ( ( in @ ( sK2_SY16 @ SY15 ) @ sK1_A )
| ( in @ ( sK2_SY16 @ SY15 ) @ SY15 ) )
& ( ( ordinal @ ( sK2_SY16 @ SY15 ) )
| ( in @ ( sK2_SY16 @ SY15 ) @ SY15 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(17,plain,
( ( ( sK8_REN
| ! [A: $i] :
( ! [SY17: $i] :
( ! [D: $i] :
( ( D != SY17 )
| ~ ( in @ D @ A ) )
| ~ ( ordinal @ SY17 )
| ( in @ SY17 @ ( sK3_B @ A ) ) )
& ! [SY19: $i] :
( ~ ( in @ SY19 @ ( sK3_B @ A ) )
| ( ( ( sK4_D @ SY19 @ A )
= SY19 )
& ( in @ ( sK4_D @ SY19 @ A ) @ A )
& ( ordinal @ SY19 ) ) ) ) )
& ( sK8_REN
=> ( ( sK5_B = sK6_SY21 )
& ( ordinal @ sK6_SY21 )
& ( sK5_B = sK7_SY23 )
& ( ordinal @ sK7_SY23 )
& ( sK6_SY21 != sK7_SY23 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(18,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(20,plain,
( ( ( epsilon_connected @ sK9_A )
& ( epsilon_transitive @ sK9_A )
& ( ordinal @ sK9_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(21,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(22,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(23,plain,
( ( ( epsilon_connected @ sK9_A )
& ( epsilon_transitive @ sK9_A )
& ( ordinal @ sK9_A ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(25,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(26,plain,
( ( ( sK8_REN
| ! [A: $i] :
( ! [SY17: $i] :
( ! [D: $i] :
( ( D != SY17 )
| ~ ( in @ D @ A ) )
| ~ ( ordinal @ SY17 )
| ( in @ SY17 @ ( sK3_B @ A ) ) )
& ! [SY19: $i] :
( ~ ( in @ SY19 @ ( sK3_B @ A ) )
| ( ( ( sK4_D @ SY19 @ A )
= SY19 )
& ( in @ ( sK4_D @ SY19 @ A ) @ A )
& ( ordinal @ SY19 ) ) ) ) )
& ( sK8_REN
=> ( ( sK5_B = sK6_SY21 )
& ( ordinal @ sK6_SY21 )
& ( sK5_B = sK7_SY23 )
& ( ordinal @ sK7_SY23 )
& ( sK6_SY21 != sK7_SY23 ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(27,plain,
( ( ! [SY15: $i] :
( ( ~ ( in @ ( sK2_SY16 @ SY15 ) @ sK1_A )
| ~ ( ordinal @ ( sK2_SY16 @ SY15 ) )
| ~ ( in @ ( sK2_SY16 @ SY15 ) @ SY15 ) )
& ( ( in @ ( sK2_SY16 @ SY15 ) @ sK1_A )
| ( in @ ( sK2_SY16 @ SY15 ) @ SY15 ) )
& ( ( ordinal @ ( sK2_SY16 @ SY15 ) )
| ( in @ ( sK2_SY16 @ SY15 ) @ SY15 ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(28,plain,
( ( ~ ( ~ ( sK8_REN
| ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( SX2 != SX1 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK3_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK3_B @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK4_D @ SX1 @ SX0 )
!= SX1 )
| ~ ( in @ ( sK4_D @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ordinal @ SX1 ) ) ) ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
| ~ ( ordinal @ sK6_SY21 ) )
| ( sK5_B != sK7_SY23 ) )
| ~ ( ordinal @ sK7_SY23 ) )
| ~ ( ( sK6_SY21 != sK7_SY23 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(29,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( in @ ( sK2_SY16 @ SX0 ) @ sK1_A )
| ~ ( ordinal @ ( sK2_SY16 @ SX0 ) )
| ~ ( in @ ( sK2_SY16 @ SX0 ) @ SX0 ) )
| ~ ~ ( ~ ( ( in @ ( sK2_SY16 @ SX0 ) @ sK1_A )
| ( in @ ( sK2_SY16 @ SX0 ) @ SX0 ) )
| ~ ( ( ordinal @ ( sK2_SY16 @ SX0 ) )
| ( in @ ( sK2_SY16 @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(30,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(31,plain,
( ( ~ ( ~ ~ ( ~ ( epsilon_connected @ sK9_A )
| ~ ( epsilon_transitive @ sK9_A ) )
| ~ ( ordinal @ sK9_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(32,plain,
! [SV1: $i] :
( ( ~ ( epsilon_connected @ SV1 )
| ~ ( epsilon_transitive @ SV1 )
| ( ordinal @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(33,plain,
! [SV2: $i] :
( ( ! [SY24: $i] :
( ~ ( in @ SV2 @ SY24 )
| ~ ( in @ SY24 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(34,plain,
( ( ~ ( sK8_REN
| ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( SX2 != SX1 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK3_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK3_B @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK4_D @ SX1 @ SX0 )
!= SX1 )
| ~ ( in @ ( sK4_D @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ordinal @ SX1 ) ) ) ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
| ~ ( ordinal @ sK6_SY21 ) )
| ( sK5_B != sK7_SY23 ) )
| ~ ( ordinal @ sK7_SY23 ) )
| ~ ( ( sK6_SY21 != sK7_SY23 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV3: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
| ~ ( ordinal @ ( sK2_SY16 @ SV3 ) )
| ~ ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
| ~ ~ ( ~ ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
| ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
| ~ ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
| ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(37,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK9_A )
| ~ ( epsilon_transitive @ sK9_A ) )
| ~ ( ordinal @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV1: $i] :
( ( ( ~ ( epsilon_connected @ SV1 )
| ~ ( epsilon_transitive @ SV1 ) )
= $true )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV4: $i,SV2: $i] :
( ( ~ ( in @ SV2 @ SV4 )
| ~ ( in @ SV4 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(40,plain,
( ( ~ ( sK8_REN
| ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( SX2 != SX1 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK3_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK3_B @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK4_D @ SX1 @ SX0 )
!= SX1 )
| ~ ( in @ ( sK4_D @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ordinal @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(41,plain,
( ( ~ ( ~ sK8_REN
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
| ~ ( ordinal @ sK6_SY21 ) )
| ( sK5_B != sK7_SY23 ) )
| ~ ( ordinal @ sK7_SY23 ) )
| ~ ( ( sK6_SY21 != sK7_SY23 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(42,plain,
! [SV3: $i] :
( ( ~ ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
| ~ ( ordinal @ ( sK2_SY16 @ SV3 ) )
| ~ ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
| ~ ~ ( ~ ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
| ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
| ~ ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
| ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(43,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(44,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(45,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK9_A )
| ~ ( epsilon_transitive @ sK9_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(46,plain,
( ( ~ ( ordinal @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(47,plain,
! [SV1: $i] :
( ( ( ~ ( epsilon_connected @ SV1 ) )
= $true )
| ( ( ~ ( epsilon_transitive @ SV1 ) )
= $true )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(48,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV4 ) )
= $true )
| ( ( ~ ( in @ SV4 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(49,plain,
( ( sK8_REN
| ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( SX2 != SX1 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK3_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK3_B @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK4_D @ SX1 @ SX0 )
!= SX1 )
| ~ ( in @ ( sK4_D @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ordinal @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(50,plain,
( ( ~ sK8_REN
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
| ~ ( ordinal @ sK6_SY21 ) )
| ( sK5_B != sK7_SY23 ) )
| ~ ( ordinal @ sK7_SY23 ) )
| ~ ( ( sK6_SY21 != sK7_SY23 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(51,plain,
! [SV3: $i] :
( ( ~ ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
| ~ ( ordinal @ ( sK2_SY16 @ SV3 ) )
| ~ ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(52,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
| ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
| ~ ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
| ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(53,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(54,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(55,plain,
( ( ~ ( ~ ( epsilon_connected @ sK9_A )
| ~ ( epsilon_transitive @ sK9_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(56,plain,
( ( ordinal @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(57,plain,
! [SV1: $i] :
( ( ( epsilon_connected @ SV1 )
= $false )
| ( ( ~ ( epsilon_transitive @ SV1 ) )
= $true )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(58,plain,
! [SV4: $i,SV2: $i] :
( ( ( in @ SV2 @ SV4 )
= $false )
| ( ( ~ ( in @ SV4 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(59,plain,
( ( sK8_REN = $true )
| ( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( SX2 != SX1 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK3_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK3_B @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK4_D @ SX1 @ SX0 )
!= SX1 )
| ~ ( in @ ( sK4_D @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ordinal @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(60,plain,
( ( ( ~ sK8_REN )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
| ~ ( ordinal @ sK6_SY21 ) )
| ( sK5_B != sK7_SY23 ) )
| ~ ( ordinal @ sK7_SY23 ) )
| ~ ( ( sK6_SY21 != sK7_SY23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(61,plain,
! [SV3: $i] :
( ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
| ~ ( ordinal @ ( sK2_SY16 @ SV3 ) )
| ~ ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(62,plain,
! [SV3: $i] :
( ( ~ ( ~ ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
| ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
| ~ ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
| ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(63,plain,
! [SV5: $i] :
( ( ~ ( ordinal @ SV5 )
| ( epsilon_connected @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(64,plain,
! [SV6: $i] :
( ( ~ ( ordinal @ SV6 )
| ( epsilon_transitive @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(65,plain,
( ( ~ ( epsilon_connected @ sK9_A )
| ~ ( epsilon_transitive @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(66,plain,
! [SV1: $i] :
( ( ( epsilon_transitive @ SV1 )
= $false )
| ( ( epsilon_connected @ SV1 )
= $false )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV2: $i,SV4: $i] :
( ( ( in @ SV4 @ SV2 )
= $false )
| ( ( in @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(68,plain,
! [SV7: $i] :
( ( ( ~ ( ~ ! [SY25: $i] :
( ! [SY26: $i] :
( ( SY26 != SY25 )
| ~ ( in @ SY26 @ SV7 ) )
| ~ ( ordinal @ SY25 )
| ( in @ SY25 @ ( sK3_B @ SV7 ) ) )
| ~ ! [SY27: $i] :
( ~ ( in @ SY27 @ ( sK3_B @ SV7 ) )
| ~ ( ~ ~ ( ( ( sK4_D @ SY27 @ SV7 )
!= SY27 )
| ~ ( in @ ( sK4_D @ SY27 @ SV7 ) @ SV7 ) )
| ~ ( ordinal @ SY27 ) ) ) ) )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(69,plain,
( ( sK8_REN = $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
| ~ ( ordinal @ sK6_SY21 ) )
| ( sK5_B != sK7_SY23 ) )
| ~ ( ordinal @ sK7_SY23 ) )
| ~ ( ( sK6_SY21 != sK7_SY23 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(70,plain,
! [SV3: $i] :
( ( ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
| ~ ( ordinal @ ( sK2_SY16 @ SV3 ) ) )
= $true )
| ( ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(71,plain,
! [SV3: $i] :
( ( ~ ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
| ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
| ~ ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
| ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(72,plain,
! [SV5: $i] :
( ( ( ~ ( ordinal @ SV5 ) )
= $true )
| ( ( epsilon_connected @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(73,plain,
! [SV6: $i] :
( ( ( ~ ( ordinal @ SV6 ) )
= $true )
| ( ( epsilon_transitive @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(74,plain,
( ( ~ ( epsilon_connected @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(75,plain,
( ( ~ ( epsilon_transitive @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(76,plain,
! [SV7: $i] :
( ( ( ~ ! [SY25: $i] :
( ! [SY26: $i] :
( ( SY26 != SY25 )
| ~ ( in @ SY26 @ SV7 ) )
| ~ ( ordinal @ SY25 )
| ( in @ SY25 @ ( sK3_B @ SV7 ) ) )
| ~ ! [SY27: $i] :
( ~ ( in @ SY27 @ ( sK3_B @ SV7 ) )
| ~ ( ~ ~ ( ( ( sK4_D @ SY27 @ SV7 )
!= SY27 )
| ~ ( in @ ( sK4_D @ SY27 @ SV7 ) @ SV7 ) )
| ~ ( ordinal @ SY27 ) ) ) )
= $false )
| ( sK8_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(77,plain,
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
| ~ ( ordinal @ sK6_SY21 ) )
| ( sK5_B != sK7_SY23 ) )
| ~ ( ordinal @ sK7_SY23 ) )
| ~ ( ( sK6_SY21 != sK7_SY23 ) ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV3: $i] :
( ( ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A ) )
= $true )
| ( ( ~ ( ordinal @ ( sK2_SY16 @ SV3 ) ) )
= $true )
| ( ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV3: $i] :
( ( ~ ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
| ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(80,plain,
! [SV3: $i] :
( ( ~ ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
| ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(81,plain,
! [SV5: $i] :
( ( ( ordinal @ SV5 )
= $false )
| ( ( epsilon_connected @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV6: $i] :
( ( ( ordinal @ SV6 )
= $false )
| ( ( epsilon_transitive @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(83,plain,
( ( epsilon_connected @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(84,plain,
( ( epsilon_transitive @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(85,plain,
! [SV7: $i] :
( ( ( ~ ! [SY25: $i] :
( ! [SY26: $i] :
( ( SY26 != SY25 )
| ~ ( in @ SY26 @ SV7 ) )
| ~ ( ordinal @ SY25 )
| ( in @ SY25 @ ( sK3_B @ SV7 ) ) ) )
= $false )
| ( sK8_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(86,plain,
! [SV7: $i] :
( ( ( ~ ! [SY27: $i] :
( ~ ( in @ SY27 @ ( sK3_B @ SV7 ) )
| ~ ( ~ ~ ( ( ( sK4_D @ SY27 @ SV7 )
!= SY27 )
| ~ ( in @ ( sK4_D @ SY27 @ SV7 ) @ SV7 ) )
| ~ ( ordinal @ SY27 ) ) ) )
= $false )
| ( sK8_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(87,plain,
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
| ~ ( ordinal @ sK6_SY21 ) )
| ( sK5_B != sK7_SY23 ) )
| ~ ( ordinal @ sK7_SY23 ) ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(88,plain,
( ( ( ~ ( ( sK6_SY21 != sK7_SY23 ) ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(89,plain,
! [SV3: $i] :
( ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
= $false )
| ( ( ~ ( ordinal @ ( sK2_SY16 @ SV3 ) ) )
= $true )
| ( ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(90,plain,
! [SV3: $i] :
( ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
| ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(91,plain,
! [SV3: $i] :
( ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
| ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(92,plain,
! [SV7: $i] :
( ( ( ! [SY25: $i] :
( ! [SY26: $i] :
( ( SY26 != SY25 )
| ~ ( in @ SY26 @ SV7 ) )
| ~ ( ordinal @ SY25 )
| ( in @ SY25 @ ( sK3_B @ SV7 ) ) ) )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(93,plain,
! [SV7: $i] :
( ( ( ! [SY27: $i] :
( ~ ( in @ SY27 @ ( sK3_B @ SV7 ) )
| ~ ( ~ ~ ( ( ( sK4_D @ SY27 @ SV7 )
!= SY27 )
| ~ ( in @ ( sK4_D @ SY27 @ SV7 ) @ SV7 ) )
| ~ ( ordinal @ SY27 ) ) ) )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(94,plain,
( ( ( ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
| ~ ( ordinal @ sK6_SY21 ) )
| ( sK5_B != sK7_SY23 ) )
| ~ ( ordinal @ sK7_SY23 ) ) )
= $true )
| ( sK8_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(95,plain,
( ( ( ( sK6_SY21 != sK7_SY23 ) )
= $true )
| ( sK8_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(96,plain,
! [SV3: $i] :
( ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
= $false )
| ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
= $false )
| ( ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(97,plain,
! [SV3: $i] :
( ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
= $true )
| ( ( in @ ( sK2_SY16 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(98,plain,
! [SV3: $i] :
( ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
= $true )
| ( ( in @ ( sK2_SY16 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(99,plain,
! [SV7: $i,SV8: $i] :
( ( ( ! [SY28: $i] :
( ( SY28 != SV8 )
| ~ ( in @ SY28 @ SV7 ) )
| ~ ( ordinal @ SV8 )
| ( in @ SV8 @ ( sK3_B @ SV7 ) ) )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(100,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( sK3_B @ SV7 ) )
| ~ ( ~ ~ ( ( ( sK4_D @ SV9 @ SV7 )
!= SV9 )
| ~ ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 ) )
| ~ ( ordinal @ SV9 ) ) )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(101,plain,
( ( ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
| ~ ( ordinal @ sK6_SY21 ) )
| ( sK5_B != sK7_SY23 ) )
| ~ ( ordinal @ sK7_SY23 ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(102,plain,
( ( ( sK6_SY21 = sK7_SY23 )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(103,plain,
! [SV3: $i] :
( ( ( in @ ( sK2_SY16 @ SV3 ) @ SV3 )
= $false )
| ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
= $false )
| ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(104,plain,
! [SV7: $i,SV8: $i] :
( ( ( ! [SY28: $i] :
( ( SY28 != SV8 )
| ~ ( in @ SY28 @ SV7 ) )
| ~ ( ordinal @ SV8 ) )
= $true )
| ( ( in @ SV8 @ ( sK3_B @ SV7 ) )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(105,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( sK3_B @ SV7 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK4_D @ SV9 @ SV7 )
!= SV9 )
| ~ ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 ) )
| ~ ( ordinal @ SV9 ) ) )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(106,plain,
( ( ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
| ~ ( ordinal @ sK6_SY21 ) )
| ( sK5_B != sK7_SY23 ) ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(107,plain,
( ( ( ~ ( ordinal @ sK7_SY23 ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(108,plain,
! [SV7: $i,SV8: $i] :
( ( ( ! [SY28: $i] :
( ( SY28 != SV8 )
| ~ ( in @ SY28 @ SV7 ) ) )
= $true )
| ( ( ~ ( ordinal @ SV8 ) )
= $true )
| ( ( in @ SV8 @ ( sK3_B @ SV7 ) )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(109,plain,
! [SV7: $i,SV9: $i] :
( ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK4_D @ SV9 @ SV7 )
!= SV9 )
| ~ ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 ) )
| ~ ( ordinal @ SV9 ) ) )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(110,plain,
( ( ( ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
| ~ ( ordinal @ sK6_SY21 ) )
| ( sK5_B != sK7_SY23 ) ) )
= $true )
| ( sK8_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(111,plain,
( ( ( ordinal @ sK7_SY23 )
= $true )
| ( sK8_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(112,plain,
! [SV7: $i,SV8: $i,SV10: $i] :
( ( ( ( SV10 != SV8 )
| ~ ( in @ SV10 @ SV7 ) )
= $true )
| ( ( ~ ( ordinal @ SV8 ) )
= $true )
| ( ( in @ SV8 @ ( sK3_B @ SV7 ) )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(113,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ~ ( ( ( sK4_D @ SV9 @ SV7 )
!= SV9 )
| ~ ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 ) )
| ~ ( ordinal @ SV9 ) )
= $false )
| ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
= $false )
| ( sK8_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(114,plain,
( ( ( ~ ~ ( ( sK5_B != sK6_SY21 )
| ~ ( ordinal @ sK6_SY21 ) )
| ( sK5_B != sK7_SY23 ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(115,plain,
! [SV7: $i,SV8: $i,SV10: $i] :
( ( ( ( SV10 != SV8 ) )
= $true )
| ( ( ~ ( in @ SV10 @ SV7 ) )
= $true )
| ( ( ~ ( ordinal @ SV8 ) )
= $true )
| ( ( in @ SV8 @ ( sK3_B @ SV7 ) )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(116,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ~ ( ( ( sK4_D @ SV9 @ SV7 )
!= SV9 )
| ~ ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 ) ) )
= $false )
| ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
= $false )
| ( sK8_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(117,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( ordinal @ SV9 ) )
= $false )
| ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
= $false )
| ( sK8_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(118,plain,
( ( ( ~ ~ ( ( sK5_B != sK6_SY21 )
| ~ ( ordinal @ sK6_SY21 ) ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(119,plain,
( ( ( ( sK5_B != sK7_SY23 ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(120,plain,
! [SV7: $i,SV8: $i,SV10: $i] :
( ( ( SV10 = SV8 )
= $false )
| ( ( ~ ( in @ SV10 @ SV7 ) )
= $true )
| ( ( ~ ( ordinal @ SV8 ) )
= $true )
| ( ( in @ SV8 @ ( sK3_B @ SV7 ) )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(121,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( ( ( sK4_D @ SV9 @ SV7 )
!= SV9 )
| ~ ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
= $false )
| ( sK8_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(122,plain,
! [SV7: $i,SV9: $i] :
( ( ( ordinal @ SV9 )
= $true )
| ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
= $false )
| ( sK8_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(123,plain,
( ( ( ~ ( ( sK5_B != sK6_SY21 )
| ~ ( ordinal @ sK6_SY21 ) ) )
= $true )
| ( sK8_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(124,plain,
( ( ( sK5_B = sK7_SY23 )
= $true )
| ( sK8_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(125,plain,
! [SV8: $i,SV7: $i,SV10: $i] :
( ( ( in @ SV10 @ SV7 )
= $false )
| ( ( SV10 = SV8 )
= $false )
| ( ( ~ ( ordinal @ SV8 ) )
= $true )
| ( ( in @ SV8 @ ( sK3_B @ SV7 ) )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(126,plain,
! [SV7: $i,SV9: $i] :
( ( ( ( ( sK4_D @ SV9 @ SV7 )
!= SV9 )
| ~ ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 ) )
= $false )
| ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
= $false )
| ( sK8_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(127,plain,
( ( ( ( sK5_B != sK6_SY21 )
| ~ ( ordinal @ sK6_SY21 ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(128,plain,
! [SV7: $i,SV10: $i,SV8: $i] :
( ( ( ordinal @ SV8 )
= $false )
| ( ( SV10 = SV8 )
= $false )
| ( ( in @ SV10 @ SV7 )
= $false )
| ( ( in @ SV8 @ ( sK3_B @ SV7 ) )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(129,plain,
! [SV7: $i,SV9: $i] :
( ( ( ( ( sK4_D @ SV9 @ SV7 )
!= SV9 ) )
= $false )
| ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
= $false )
| ( sK8_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(130,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 ) )
= $false )
| ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
= $false )
| ( sK8_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(131,plain,
( ( ( ( sK5_B != sK6_SY21 ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(132,plain,
( ( ( ~ ( ordinal @ sK6_SY21 ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(133,plain,
! [SV7: $i,SV9: $i] :
( ( ( ( sK4_D @ SV9 @ SV7 )
= SV9 )
= $true )
| ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
= $false )
| ( sK8_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(134,plain,
! [SV7: $i,SV9: $i] :
( ( ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 )
= $true )
| ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
= $false )
| ( sK8_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(135,plain,
( ( ( sK5_B = sK6_SY21 )
= $true )
| ( sK8_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(136,plain,
( ( ( ordinal @ sK6_SY21 )
= $true )
| ( sK8_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(137,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[56,136,135,134,133,128,124,122,111,103,102,98,97,84,83,82,81,67,66]) ).
thf(138,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU280+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 01:35:00 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
% 0.13/0.36 (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)......
% 0.20/0.52
% 0.20/0.52 ********************************
% 0.20/0.52 * All subproblems solved! *
% 0.20/0.52 ********************************
% 0.20/0.52 % SZS status Theorem for /export/starexec/sandbox2/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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:137,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.53
% 0.20/0.53 %**** Beginning of derivation protocol ****
% 0.20/0.53 % SZS output start CNFRefutation
% See solution above
% 0.20/0.53
% 0.20/0.53 %**** End of derivation protocol ****
% 0.20/0.53 %**** no. of clauses in derivation: 138 ****
% 0.20/0.53 %**** clause counter: 137 ****
% 0.20/0.53
% 0.20/0.53 % SZS status Theorem for /export/starexec/sandbox2/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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:137,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------