TSTP Solution File: SEU144+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU144+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 : n026.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 12:07:04 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 183 ( 96 unt; 7 typ; 0 def)
% Number of atoms : 1090 ( 461 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 1934 ( 424 ~; 346 |; 19 &;1126 @)
% ( 11 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 405 ( 0 ^ 405 !; 0 ?; 405 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY12,type,
sK2_SY12: $i ).
thf(tp_sK3_C,type,
sK3_C: $i > $i > $i ).
thf(tp_sK4_C,type,
sK4_C: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(2,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(6,conjecture,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(7,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
$true = $true,
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [SY12: $i] :
( ( subset @ ( singleton @ sK1_A ) @ SY12 )
<=> ( in @ sK1_A @ SY12 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 )
<=> ( in @ sK1_A @ sK2_SY12 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 )
=> ( in @ sK1_A @ sK2_SY12 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[15]) ).
thf(17,plain,
( ( ( in @ sK1_A @ sK2_SY12 )
=> ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[15]) ).
thf(18,plain,
( ( ~ ( ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 )
=> ( in @ sK1_A @ sK2_SY12 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( ( in @ sK1_A @ sK2_SY12 )
=> ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(20,plain,
( ( ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 )
& ~ ( in @ sK1_A @ sK2_SY12 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(21,plain,
( ( ( in @ sK1_A @ sK2_SY12 )
& ~ ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(22,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK3_C @ B @ A ) @ A )
& ~ ( in @ ( sK3_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK4_C @ B @ A )
!= A )
| ~ ( in @ ( sK4_C @ B @ A ) @ B ) )
& ( ( ( sK4_C @ B @ A )
= A )
| ( in @ ( sK4_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK4_C @ B @ A )
!= A )
| ~ ( in @ ( sK4_C @ B @ A ) @ B ) )
& ( ( ( sK4_C @ B @ A )
= A )
| ( in @ ( sK4_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(28,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK3_C @ B @ A ) @ A )
& ~ ( in @ ( sK3_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(29,plain,
$true = $true,
inference(copy,[status(thm)],[10]) ).
thf(30,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(31,plain,
( ( ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 )
& ~ ( in @ sK1_A @ sK2_SY12 ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(32,plain,
( ( ~ ( ~ ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 )
| ~ ~ ( in @ sK1_A @ sK2_SY12 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(33,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK4_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK4_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(34,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(35,plain,
! [SV1: $i] :
( ( ! [SY13: $i] :
( ~ ( in @ SV1 @ SY13 )
| ~ ( in @ SY13 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(36,plain,
! [SV2: $i] :
( ( subset @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
( ( ~ ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 )
| ~ ~ ( in @ sK1_A @ sK2_SY12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(38,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK4_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK4_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(39,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV3 )
| ~ ( in @ SV3 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(41,plain,
( ( ~ ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(42,plain,
( ( ~ ~ ( in @ sK1_A @ sK2_SY12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(43,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK4_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK4_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(44,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(45,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(46,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(47,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV3 ) )
= $true )
| ( ( ~ ( in @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(48,plain,
( ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(49,plain,
( ( ~ ( in @ sK1_A @ sK2_SY12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(50,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK4_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK4_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(51,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(52,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(53,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(54,plain,
! [SV3: $i,SV1: $i] :
( ( ( in @ SV1 @ SV3 )
= $false )
| ( ( ~ ( in @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(55,plain,
( ( in @ sK1_A @ sK2_SY12 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV4: $i] :
( ( ! [SY14: $i] :
( ~ ( ~ ( ( ( sK4_C @ SY14 @ SV4 )
!= SV4 )
| ~ ( in @ ( sK4_C @ SY14 @ SV4 ) @ SY14 ) )
| ~ ( ( ( sK4_C @ SY14 @ SV4 )
= SV4 )
| ( in @ ( sK4_C @ SY14 @ SV4 ) @ SY14 ) ) )
| ( SY14
= ( singleton @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV5: $i] :
( ( ! [SY15: $i] :
( ( SY15
!= ( singleton @ SV5 ) )
| ~ ( ~ ! [SY16: $i] :
( ( SY16 != SV5 )
| ( in @ SY16 @ SY15 ) )
| ~ ! [SY17: $i] :
( ~ ( in @ SY17 @ SY15 )
| ( SY17 = SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV6: $i] :
( ( ! [SY18: $i] :
( ~ ( ~ ( in @ ( sK3_C @ SY18 @ SV6 ) @ SV6 )
| ~ ~ ( in @ ( sK3_C @ SY18 @ SV6 ) @ SY18 ) )
| ( subset @ SV6 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV7: $i] :
( ( ! [SY19: $i] :
( ~ ( subset @ SV7 @ SY19 )
| ! [SY20: $i] :
( ~ ( in @ SY20 @ SV7 )
| ( in @ SY20 @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(60,plain,
! [SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(61,plain,
! [SV4: $i,SV8: $i] :
( ( ~ ( ~ ( ( ( sK4_C @ SV8 @ SV4 )
!= SV4 )
| ~ ( in @ ( sK4_C @ SV8 @ SV4 ) @ SV8 ) )
| ~ ( ( ( sK4_C @ SV8 @ SV4 )
= SV4 )
| ( in @ ( sK4_C @ SV8 @ SV4 ) @ SV8 ) ) )
| ( SV8
= ( singleton @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV5: $i,SV9: $i] :
( ( ( SV9
!= ( singleton @ SV5 ) )
| ~ ( ~ ! [SY21: $i] :
( ( SY21 != SV5 )
| ( in @ SY21 @ SV9 ) )
| ~ ! [SY22: $i] :
( ~ ( in @ SY22 @ SV9 )
| ( SY22 = SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV6: $i,SV10: $i] :
( ( ~ ( ~ ( in @ ( sK3_C @ SV10 @ SV6 ) @ SV6 )
| ~ ~ ( in @ ( sK3_C @ SV10 @ SV6 ) @ SV10 ) )
| ( subset @ SV6 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(64,plain,
! [SV11: $i,SV7: $i] :
( ( ~ ( subset @ SV7 @ SV11 )
| ! [SY23: $i] :
( ~ ( in @ SY23 @ SV7 )
| ( in @ SY23 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(65,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( ~ ( ( ( sK4_C @ SV8 @ SV4 )
!= SV4 )
| ~ ( in @ ( sK4_C @ SV8 @ SV4 ) @ SV8 ) )
| ~ ( ( ( sK4_C @ SV8 @ SV4 )
= SV4 )
| ( in @ ( sK4_C @ SV8 @ SV4 ) @ SV8 ) ) ) )
= $true )
| ( ( SV8
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV5: $i,SV9: $i] :
( ( ( ( SV9
!= ( singleton @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY21: $i] :
( ( SY21 != SV5 )
| ( in @ SY21 @ SV9 ) )
| ~ ! [SY22: $i] :
( ~ ( in @ SY22 @ SV9 )
| ( SY22 = SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV10 @ SV6 ) @ SV6 )
| ~ ~ ( in @ ( sK3_C @ SV10 @ SV6 ) @ SV10 ) ) )
= $true )
| ( ( subset @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV11: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV11 ) )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( in @ SY23 @ SV7 )
| ( in @ SY23 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( ( ( sK4_C @ SV8 @ SV4 )
!= SV4 )
| ~ ( in @ ( sK4_C @ SV8 @ SV4 ) @ SV8 ) )
| ~ ( ( ( sK4_C @ SV8 @ SV4 )
= SV4 )
| ( in @ ( sK4_C @ SV8 @ SV4 ) @ SV8 ) ) )
= $false )
| ( ( SV8
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV5: $i,SV9: $i] :
( ( ( SV9
= ( singleton @ SV5 ) )
= $false )
| ( ( ~ ( ~ ! [SY21: $i] :
( ( SY21 != SV5 )
| ( in @ SY21 @ SV9 ) )
| ~ ! [SY22: $i] :
( ~ ( in @ SY22 @ SV9 )
| ( SY22 = SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV10 @ SV6 ) @ SV6 )
| ~ ~ ( in @ ( sK3_C @ SV10 @ SV6 ) @ SV10 ) )
= $false )
| ( ( subset @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(72,plain,
! [SV11: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV11 )
= $false )
| ( ( ! [SY23: $i] :
( ~ ( in @ SY23 @ SV7 )
| ( in @ SY23 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(73,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( ( ( sK4_C @ SV8 @ SV4 )
!= SV4 )
| ~ ( in @ ( sK4_C @ SV8 @ SV4 ) @ SV8 ) ) )
= $false )
| ( ( SV8
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(74,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( ( ( sK4_C @ SV8 @ SV4 )
= SV4 )
| ( in @ ( sK4_C @ SV8 @ SV4 ) @ SV8 ) ) )
= $false )
| ( ( SV8
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(75,plain,
! [SV9: $i,SV5: $i] :
( ( ( ~ ! [SY21: $i] :
( ( SY21 != SV5 )
| ( in @ SY21 @ SV9 ) )
| ~ ! [SY22: $i] :
( ~ ( in @ SY22 @ SV9 )
| ( SY22 = SV5 ) ) )
= $false )
| ( ( SV9
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV10 @ SV6 ) @ SV6 ) )
= $false )
| ( ( subset @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(77,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ~ ( in @ ( sK3_C @ SV10 @ SV6 ) @ SV10 ) )
= $false )
| ( ( subset @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(78,plain,
! [SV11: $i,SV7: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV7 )
| ( in @ SV12 @ SV11 ) )
= $true )
| ( ( subset @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(79,plain,
! [SV4: $i,SV8: $i] :
( ( ( ( ( sK4_C @ SV8 @ SV4 )
!= SV4 )
| ~ ( in @ ( sK4_C @ SV8 @ SV4 ) @ SV8 ) )
= $true )
| ( ( SV8
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(80,plain,
! [SV4: $i,SV8: $i] :
( ( ( ( ( sK4_C @ SV8 @ SV4 )
= SV4 )
| ( in @ ( sK4_C @ SV8 @ SV4 ) @ SV8 ) )
= $true )
| ( ( SV8
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(81,plain,
! [SV9: $i,SV5: $i] :
( ( ( ~ ! [SY21: $i] :
( ( SY21 != SV5 )
| ( in @ SY21 @ SV9 ) ) )
= $false )
| ( ( SV9
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(82,plain,
! [SV5: $i,SV9: $i] :
( ( ( ~ ! [SY22: $i] :
( ~ ( in @ SY22 @ SV9 )
| ( SY22 = SV5 ) ) )
= $false )
| ( ( SV9
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(83,plain,
! [SV6: $i,SV10: $i] :
( ( ( in @ ( sK3_C @ SV10 @ SV6 ) @ SV6 )
= $true )
| ( ( subset @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(84,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV10 @ SV6 ) @ SV10 ) )
= $true )
| ( ( subset @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(85,plain,
! [SV11: $i,SV7: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV7 ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( subset @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV4: $i,SV8: $i] :
( ( ( ( ( sK4_C @ SV8 @ SV4 )
!= SV4 ) )
= $true )
| ( ( ~ ( in @ ( sK4_C @ SV8 @ SV4 ) @ SV8 ) )
= $true )
| ( ( SV8
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(87,plain,
! [SV4: $i,SV8: $i] :
( ( ( ( sK4_C @ SV8 @ SV4 )
= SV4 )
= $true )
| ( ( in @ ( sK4_C @ SV8 @ SV4 ) @ SV8 )
= $true )
| ( ( SV8
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(88,plain,
! [SV9: $i,SV5: $i] :
( ( ( ! [SY21: $i] :
( ( SY21 != SV5 )
| ( in @ SY21 @ SV9 ) ) )
= $true )
| ( ( SV9
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(89,plain,
! [SV5: $i,SV9: $i] :
( ( ( ! [SY22: $i] :
( ~ ( in @ SY22 @ SV9 )
| ( SY22 = SV5 ) ) )
= $true )
| ( ( SV9
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(90,plain,
! [SV6: $i,SV10: $i] :
( ( ( in @ ( sK3_C @ SV10 @ SV6 ) @ SV10 )
= $false )
| ( ( subset @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(91,plain,
! [SV11: $i,SV7: $i,SV12: $i] :
( ( ( in @ SV12 @ SV7 )
= $false )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( subset @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(92,plain,
! [SV4: $i,SV8: $i] :
( ( ( ( sK4_C @ SV8 @ SV4 )
= SV4 )
= $false )
| ( ( ~ ( in @ ( sK4_C @ SV8 @ SV4 ) @ SV8 ) )
= $true )
| ( ( SV8
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV9: $i,SV5: $i,SV13: $i] :
( ( ( ( SV13 != SV5 )
| ( in @ SV13 @ SV9 ) )
= $true )
| ( ( SV9
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(94,plain,
! [SV5: $i,SV9: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV9 )
| ( SV14 = SV5 ) )
= $true )
| ( ( SV9
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(95,plain,
! [SV4: $i,SV8: $i] :
( ( ( in @ ( sK4_C @ SV8 @ SV4 ) @ SV8 )
= $false )
| ( ( ( sK4_C @ SV8 @ SV4 )
= SV4 )
= $false )
| ( ( SV8
= ( singleton @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(96,plain,
! [SV9: $i,SV5: $i,SV13: $i] :
( ( ( ( SV13 != SV5 ) )
= $true )
| ( ( in @ SV13 @ SV9 )
= $true )
| ( ( SV9
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(97,plain,
! [SV5: $i,SV9: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV9 ) )
= $true )
| ( ( SV14 = SV5 )
= $true )
| ( ( SV9
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(98,plain,
! [SV9: $i,SV5: $i,SV13: $i] :
( ( ( SV13 = SV5 )
= $false )
| ( ( in @ SV13 @ SV9 )
= $true )
| ( ( SV9
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(99,plain,
! [SV5: $i,SV9: $i,SV14: $i] :
( ( ( in @ SV14 @ SV9 )
= $false )
| ( ( SV14 = SV5 )
= $true )
| ( ( SV9
= ( singleton @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(100,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[29,99,98,95,91,90,87,83,60,55,48,36]) ).
thf(101,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(102,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK4_C @ B @ A )
!= A )
| ~ ( in @ ( sK4_C @ B @ A ) @ B ) )
& ( ( ( sK4_C @ B @ A )
= A )
| ( in @ ( sK4_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(103,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK3_C @ B @ A ) @ A )
& ~ ( in @ ( sK3_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(104,plain,
$true = $true,
inference(copy,[status(thm)],[10]) ).
thf(105,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(106,plain,
( ( ( in @ sK1_A @ sK2_SY12 )
& ~ ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(107,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK4_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK4_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(108,plain,
( ( ~ ( ~ ( in @ sK1_A @ sK2_SY12 )
| ~ ~ ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(109,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(110,plain,
! [SV15: $i] :
( ( ! [SY24: $i] :
( ~ ( in @ SV15 @ SY24 )
| ~ ( in @ SY24 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(111,plain,
! [SV16: $i] :
( ( subset @ SV16 @ SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(112,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK4_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK4_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(113,plain,
( ( ~ ( in @ sK1_A @ sK2_SY12 )
| ~ ~ ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(114,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(115,plain,
! [SV17: $i,SV15: $i] :
( ( ~ ( in @ SV15 @ SV17 )
| ~ ( in @ SV17 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(116,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK4_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK4_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(117,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(118,plain,
( ( ~ ( in @ sK1_A @ sK2_SY12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(119,plain,
( ( ~ ~ ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(120,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(121,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(122,plain,
! [SV17: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ SV17 ) )
= $true )
| ( ( ~ ( in @ SV17 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(123,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK4_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK4_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(124,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(125,plain,
( ( in @ sK1_A @ sK2_SY12 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(126,plain,
( ( ~ ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(127,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(128,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(129,plain,
! [SV17: $i,SV15: $i] :
( ( ( in @ SV15 @ SV17 )
= $false )
| ( ( ~ ( in @ SV17 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(130,plain,
! [SV18: $i] :
( ( ! [SY25: $i] :
( ~ ( ~ ( ( ( sK4_C @ SY25 @ SV18 )
!= SV18 )
| ~ ( in @ ( sK4_C @ SY25 @ SV18 ) @ SY25 ) )
| ~ ( ( ( sK4_C @ SY25 @ SV18 )
= SV18 )
| ( in @ ( sK4_C @ SY25 @ SV18 ) @ SY25 ) ) )
| ( SY25
= ( singleton @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(131,plain,
! [SV19: $i] :
( ( ! [SY26: $i] :
( ( SY26
!= ( singleton @ SV19 ) )
| ~ ( ~ ! [SY27: $i] :
( ( SY27 != SV19 )
| ( in @ SY27 @ SY26 ) )
| ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SY26 )
| ( SY28 = SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(132,plain,
( ( subset @ ( singleton @ sK1_A ) @ sK2_SY12 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(133,plain,
! [SV20: $i] :
( ( ! [SY29: $i] :
( ~ ( ~ ( in @ ( sK3_C @ SY29 @ SV20 ) @ SV20 )
| ~ ~ ( in @ ( sK3_C @ SY29 @ SV20 ) @ SY29 ) )
| ( subset @ SV20 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(134,plain,
! [SV21: $i] :
( ( ! [SY30: $i] :
( ~ ( subset @ SV21 @ SY30 )
| ! [SY31: $i] :
( ~ ( in @ SY31 @ SV21 )
| ( in @ SY31 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(135,plain,
! [SV15: $i,SV17: $i] :
( ( ( in @ SV17 @ SV15 )
= $false )
| ( ( in @ SV15 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(136,plain,
! [SV18: $i,SV22: $i] :
( ( ~ ( ~ ( ( ( sK4_C @ SV22 @ SV18 )
!= SV18 )
| ~ ( in @ ( sK4_C @ SV22 @ SV18 ) @ SV22 ) )
| ~ ( ( ( sK4_C @ SV22 @ SV18 )
= SV18 )
| ( in @ ( sK4_C @ SV22 @ SV18 ) @ SV22 ) ) )
| ( SV22
= ( singleton @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(137,plain,
! [SV19: $i,SV23: $i] :
( ( ( SV23
!= ( singleton @ SV19 ) )
| ~ ( ~ ! [SY32: $i] :
( ( SY32 != SV19 )
| ( in @ SY32 @ SV23 ) )
| ~ ! [SY33: $i] :
( ~ ( in @ SY33 @ SV23 )
| ( SY33 = SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(138,plain,
! [SV20: $i,SV24: $i] :
( ( ~ ( ~ ( in @ ( sK3_C @ SV24 @ SV20 ) @ SV20 )
| ~ ~ ( in @ ( sK3_C @ SV24 @ SV20 ) @ SV24 ) )
| ( subset @ SV20 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(139,plain,
! [SV25: $i,SV21: $i] :
( ( ~ ( subset @ SV21 @ SV25 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ SV21 )
| ( in @ SY34 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(140,plain,
! [SV18: $i,SV22: $i] :
( ( ( ~ ( ~ ( ( ( sK4_C @ SV22 @ SV18 )
!= SV18 )
| ~ ( in @ ( sK4_C @ SV22 @ SV18 ) @ SV22 ) )
| ~ ( ( ( sK4_C @ SV22 @ SV18 )
= SV18 )
| ( in @ ( sK4_C @ SV22 @ SV18 ) @ SV22 ) ) ) )
= $true )
| ( ( SV22
= ( singleton @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(141,plain,
! [SV19: $i,SV23: $i] :
( ( ( ( SV23
!= ( singleton @ SV19 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY32: $i] :
( ( SY32 != SV19 )
| ( in @ SY32 @ SV23 ) )
| ~ ! [SY33: $i] :
( ~ ( in @ SY33 @ SV23 )
| ( SY33 = SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(142,plain,
! [SV20: $i,SV24: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV24 @ SV20 ) @ SV20 )
| ~ ~ ( in @ ( sK3_C @ SV24 @ SV20 ) @ SV24 ) ) )
= $true )
| ( ( subset @ SV20 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(143,plain,
! [SV25: $i,SV21: $i] :
( ( ( ~ ( subset @ SV21 @ SV25 ) )
= $true )
| ( ( ! [SY34: $i] :
( ~ ( in @ SY34 @ SV21 )
| ( in @ SY34 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(144,plain,
! [SV18: $i,SV22: $i] :
( ( ( ~ ( ( ( sK4_C @ SV22 @ SV18 )
!= SV18 )
| ~ ( in @ ( sK4_C @ SV22 @ SV18 ) @ SV22 ) )
| ~ ( ( ( sK4_C @ SV22 @ SV18 )
= SV18 )
| ( in @ ( sK4_C @ SV22 @ SV18 ) @ SV22 ) ) )
= $false )
| ( ( SV22
= ( singleton @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(145,plain,
! [SV19: $i,SV23: $i] :
( ( ( SV23
= ( singleton @ SV19 ) )
= $false )
| ( ( ~ ( ~ ! [SY32: $i] :
( ( SY32 != SV19 )
| ( in @ SY32 @ SV23 ) )
| ~ ! [SY33: $i] :
( ~ ( in @ SY33 @ SV23 )
| ( SY33 = SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(146,plain,
! [SV20: $i,SV24: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV24 @ SV20 ) @ SV20 )
| ~ ~ ( in @ ( sK3_C @ SV24 @ SV20 ) @ SV24 ) )
= $false )
| ( ( subset @ SV20 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(147,plain,
! [SV25: $i,SV21: $i] :
( ( ( subset @ SV21 @ SV25 )
= $false )
| ( ( ! [SY34: $i] :
( ~ ( in @ SY34 @ SV21 )
| ( in @ SY34 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(148,plain,
! [SV18: $i,SV22: $i] :
( ( ( ~ ( ( ( sK4_C @ SV22 @ SV18 )
!= SV18 )
| ~ ( in @ ( sK4_C @ SV22 @ SV18 ) @ SV22 ) ) )
= $false )
| ( ( SV22
= ( singleton @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(149,plain,
! [SV18: $i,SV22: $i] :
( ( ( ~ ( ( ( sK4_C @ SV22 @ SV18 )
= SV18 )
| ( in @ ( sK4_C @ SV22 @ SV18 ) @ SV22 ) ) )
= $false )
| ( ( SV22
= ( singleton @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(150,plain,
! [SV23: $i,SV19: $i] :
( ( ( ~ ! [SY32: $i] :
( ( SY32 != SV19 )
| ( in @ SY32 @ SV23 ) )
| ~ ! [SY33: $i] :
( ~ ( in @ SY33 @ SV23 )
| ( SY33 = SV19 ) ) )
= $false )
| ( ( SV23
= ( singleton @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(151,plain,
! [SV20: $i,SV24: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV24 @ SV20 ) @ SV20 ) )
= $false )
| ( ( subset @ SV20 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(152,plain,
! [SV20: $i,SV24: $i] :
( ( ( ~ ~ ( in @ ( sK3_C @ SV24 @ SV20 ) @ SV24 ) )
= $false )
| ( ( subset @ SV20 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(153,plain,
! [SV25: $i,SV21: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV21 )
| ( in @ SV26 @ SV25 ) )
= $true )
| ( ( subset @ SV21 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(154,plain,
! [SV18: $i,SV22: $i] :
( ( ( ( ( sK4_C @ SV22 @ SV18 )
!= SV18 )
| ~ ( in @ ( sK4_C @ SV22 @ SV18 ) @ SV22 ) )
= $true )
| ( ( SV22
= ( singleton @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(155,plain,
! [SV18: $i,SV22: $i] :
( ( ( ( ( sK4_C @ SV22 @ SV18 )
= SV18 )
| ( in @ ( sK4_C @ SV22 @ SV18 ) @ SV22 ) )
= $true )
| ( ( SV22
= ( singleton @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(156,plain,
! [SV23: $i,SV19: $i] :
( ( ( ~ ! [SY32: $i] :
( ( SY32 != SV19 )
| ( in @ SY32 @ SV23 ) ) )
= $false )
| ( ( SV23
= ( singleton @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(157,plain,
! [SV19: $i,SV23: $i] :
( ( ( ~ ! [SY33: $i] :
( ~ ( in @ SY33 @ SV23 )
| ( SY33 = SV19 ) ) )
= $false )
| ( ( SV23
= ( singleton @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(158,plain,
! [SV20: $i,SV24: $i] :
( ( ( in @ ( sK3_C @ SV24 @ SV20 ) @ SV20 )
= $true )
| ( ( subset @ SV20 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(159,plain,
! [SV20: $i,SV24: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV24 @ SV20 ) @ SV24 ) )
= $true )
| ( ( subset @ SV20 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(160,plain,
! [SV25: $i,SV21: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV21 ) )
= $true )
| ( ( in @ SV26 @ SV25 )
= $true )
| ( ( subset @ SV21 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(161,plain,
! [SV18: $i,SV22: $i] :
( ( ( ( ( sK4_C @ SV22 @ SV18 )
!= SV18 ) )
= $true )
| ( ( ~ ( in @ ( sK4_C @ SV22 @ SV18 ) @ SV22 ) )
= $true )
| ( ( SV22
= ( singleton @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(162,plain,
! [SV18: $i,SV22: $i] :
( ( ( ( sK4_C @ SV22 @ SV18 )
= SV18 )
= $true )
| ( ( in @ ( sK4_C @ SV22 @ SV18 ) @ SV22 )
= $true )
| ( ( SV22
= ( singleton @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(163,plain,
! [SV23: $i,SV19: $i] :
( ( ( ! [SY32: $i] :
( ( SY32 != SV19 )
| ( in @ SY32 @ SV23 ) ) )
= $true )
| ( ( SV23
= ( singleton @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(164,plain,
! [SV19: $i,SV23: $i] :
( ( ( ! [SY33: $i] :
( ~ ( in @ SY33 @ SV23 )
| ( SY33 = SV19 ) ) )
= $true )
| ( ( SV23
= ( singleton @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(165,plain,
! [SV20: $i,SV24: $i] :
( ( ( in @ ( sK3_C @ SV24 @ SV20 ) @ SV24 )
= $false )
| ( ( subset @ SV20 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(166,plain,
! [SV25: $i,SV21: $i,SV26: $i] :
( ( ( in @ SV26 @ SV21 )
= $false )
| ( ( in @ SV26 @ SV25 )
= $true )
| ( ( subset @ SV21 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(167,plain,
! [SV18: $i,SV22: $i] :
( ( ( ( sK4_C @ SV22 @ SV18 )
= SV18 )
= $false )
| ( ( ~ ( in @ ( sK4_C @ SV22 @ SV18 ) @ SV22 ) )
= $true )
| ( ( SV22
= ( singleton @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(168,plain,
! [SV23: $i,SV19: $i,SV27: $i] :
( ( ( ( SV27 != SV19 )
| ( in @ SV27 @ SV23 ) )
= $true )
| ( ( SV23
= ( singleton @ SV19 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(169,plain,
! [SV19: $i,SV23: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV23 )
| ( SV28 = SV19 ) )
= $true )
| ( ( SV23
= ( singleton @ SV19 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(170,plain,
! [SV18: $i,SV22: $i] :
( ( ( in @ ( sK4_C @ SV22 @ SV18 ) @ SV22 )
= $false )
| ( ( ( sK4_C @ SV22 @ SV18 )
= SV18 )
= $false )
| ( ( SV22
= ( singleton @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(171,plain,
! [SV23: $i,SV19: $i,SV27: $i] :
( ( ( ( SV27 != SV19 ) )
= $true )
| ( ( in @ SV27 @ SV23 )
= $true )
| ( ( SV23
= ( singleton @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(172,plain,
! [SV19: $i,SV23: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV23 ) )
= $true )
| ( ( SV28 = SV19 )
= $true )
| ( ( SV23
= ( singleton @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(173,plain,
! [SV23: $i,SV19: $i,SV27: $i] :
( ( ( SV27 = SV19 )
= $false )
| ( ( in @ SV27 @ SV23 )
= $true )
| ( ( SV23
= ( singleton @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(174,plain,
! [SV19: $i,SV23: $i,SV28: $i] :
( ( ( in @ SV28 @ SV23 )
= $false )
| ( ( SV28 = SV19 )
= $true )
| ( ( SV23
= ( singleton @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(175,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[104,174,173,170,166,165,162,158,135,132,125,111]) ).
thf(176,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[175,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU144+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 06:22:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 5
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (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).........
% 0.19/0.44
% 0.19/0.44 ********************************
% 0.19/0.44 * All subproblems solved! *
% 0.19/0.44 ********************************
% 0.19/0.44 % 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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:175,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.46
% 0.19/0.46 %**** Beginning of derivation protocol ****
% 0.19/0.46 % SZS output start CNFRefutation
% See solution above
% 0.19/0.46
% 0.19/0.46 %**** End of derivation protocol ****
% 0.19/0.46 %**** no. of clauses in derivation: 176 ****
% 0.19/0.46 %**** clause counter: 175 ****
% 0.19/0.46
% 0.19/0.46 % 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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:175,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------