TSTP Solution File: SEU142+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU142+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 : n010.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 12:07:03 EDT 2022
% Result : Theorem 0.59s 0.78s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 146 ( 58 unt; 7 typ; 0 def)
% Number of atoms : 1062 ( 577 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 2158 ( 458 ~; 419 |; 18 &;1249 @)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 421 ( 0 ^ 421 !; 0 ?; 421 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_C,type,
sK2_C: $i > $i > $i ).
thf(tp_sK3_D,type,
sK3_D: $i > $i > $i > $i ).
thf(tp_sK4_C,type,
sK4_C: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(2,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(3,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(8,conjecture,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(9,negated_conjecture,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $false ),
inference(unfold_def,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
$true = $true,
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
$true = $true,
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(18,plain,
( ( ( unordered_pair @ sK1_A @ sK1_A )
= ( singleton @ sK1_A ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(19,plain,
( ( ( ( unordered_pair @ sK1_A @ sK1_A )
!= ( singleton @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK2_C @ B @ A ) @ A )
| ~ ( in @ ( sK2_C @ B @ A ) @ B ) )
& ( ( in @ ( sK2_C @ B @ A ) @ A )
| ( in @ ( sK2_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(21,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK3_D @ C @ B @ A ) @ C )
| ( ( sK3_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK3_D @ C @ B @ A ) @ C )
| ( ( sK3_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK3_D @ C @ B @ A ) @ C )
| ( ( sK3_D @ C @ B @ A )
= A )
| ( ( sK3_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(22,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)],[15]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(26,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)],[22]) ).
thf(27,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK3_D @ C @ B @ A ) @ C )
| ( ( sK3_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK3_D @ C @ B @ A ) @ C )
| ( ( sK3_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK3_D @ C @ B @ A ) @ C )
| ( ( sK3_D @ C @ B @ A )
= A )
| ( ( sK3_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(28,plain,
$true = $true,
inference(copy,[status(thm)],[13]) ).
thf(29,plain,
$true = $true,
inference(copy,[status(thm)],[12]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK2_C @ B @ A ) @ A )
| ~ ( in @ ( sK2_C @ B @ A ) @ B ) )
& ( ( in @ ( sK2_C @ B @ A ) @ A )
| ( in @ ( sK2_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(31,plain,
( ( ( ( unordered_pair @ sK1_A @ sK1_A )
!= ( singleton @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(32,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)],[26]) ).
thf(33,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK3_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK3_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK3_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK3_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK3_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK3_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK3_D @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ( SX3 != SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(34,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK2_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK2_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK2_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK2_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(35,plain,
! [SV1: $i] :
( ( ! [SY15: $i] :
( ~ ( in @ SV1 @ SY15 )
| ~ ( in @ SY15 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(36,plain,
! [SV2: $i] :
( ( ! [SY16: $i] :
( ( unordered_pair @ SV2 @ SY16 )
= ( unordered_pair @ SY16 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(37,plain,
( ( ( unordered_pair @ sK1_A @ sK1_A )
= ( singleton @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
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)],[32]) ).
thf(39,plain,
! [SV3: $i] :
( ( ~ ( ~ ! [SY17: $i,SY18: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK3_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK3_D @ SY18 @ SY17 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK3_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK3_D @ SY18 @ SY17 @ SV3 )
!= SY17 ) ) )
| ~ ( ( in @ ( sK3_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK3_D @ SY18 @ SY17 @ SV3 )
= SV3 )
| ( ( sK3_D @ SY18 @ SY17 @ SV3 )
= SY17 ) ) )
| ( SY18
= ( unordered_pair @ SV3 @ SY17 ) ) )
| ~ ! [SY19: $i,SY20: $i] :
( ( SY20
!= ( unordered_pair @ SV3 @ SY19 ) )
| ~ ( ~ ! [SY21: $i] :
( ~ ( in @ SY21 @ SY20 )
| ( SY21 = SV3 )
| ( SY21 = SY19 ) )
| ~ ~ ( ~ ! [SY22: $i] :
( ( SY22 != SV3 )
| ( in @ SY22 @ SY20 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY19 )
| ( in @ SX3 @ SY20 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV4: $i] :
( ( ! [SY24: $i] :
( ~ ( ~ ( ~ ( in @ ( sK2_C @ SY24 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK2_C @ SY24 @ SV4 ) @ SY24 ) )
| ~ ( ( in @ ( sK2_C @ SY24 @ SV4 ) @ SV4 )
| ( in @ ( sK2_C @ SY24 @ SV4 ) @ SY24 ) ) )
| ( SV4 = SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV5: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV5 )
| ~ ( in @ SV5 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV6: $i,SV2: $i] :
( ( ( unordered_pair @ SV2 @ SV6 )
= ( unordered_pair @ SV6 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
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,
! [SV3: $i] :
( ( ~ ! [SY17: $i,SY18: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK3_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK3_D @ SY18 @ SY17 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK3_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK3_D @ SY18 @ SY17 @ SV3 )
!= SY17 ) ) )
| ~ ( ( in @ ( sK3_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK3_D @ SY18 @ SY17 @ SV3 )
= SV3 )
| ( ( sK3_D @ SY18 @ SY17 @ SV3 )
= SY17 ) ) )
| ( SY18
= ( unordered_pair @ SV3 @ SY17 ) ) )
| ~ ! [SY19: $i,SY20: $i] :
( ( SY20
!= ( unordered_pair @ SV3 @ SY19 ) )
| ~ ( ~ ! [SY21: $i] :
( ~ ( in @ SY21 @ SY20 )
| ( SY21 = SV3 )
| ( SY21 = SY19 ) )
| ~ ~ ( ~ ! [SY22: $i] :
( ( SY22 != SV3 )
| ( in @ SY22 @ SY20 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY19 )
| ( in @ SX3 @ SY20 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV4: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV7 ) )
| ~ ( ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV4 )
| ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV7 ) ) )
| ( SV4 = SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV5: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV5 ) )
= $true )
| ( ( ~ ( in @ SV5 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(48,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(49,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(50,plain,
! [SV3: $i] :
( ( ~ ! [SY17: $i,SY18: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK3_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK3_D @ SY18 @ SY17 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK3_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK3_D @ SY18 @ SY17 @ SV3 )
!= SY17 ) ) )
| ~ ( ( in @ ( sK3_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK3_D @ SY18 @ SY17 @ SV3 )
= SV3 )
| ( ( sK3_D @ SY18 @ SY17 @ SV3 )
= SY17 ) ) )
| ( SY18
= ( unordered_pair @ SV3 @ SY17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(51,plain,
! [SV3: $i] :
( ( ~ ! [SY19: $i,SY20: $i] :
( ( SY20
!= ( unordered_pair @ SV3 @ SY19 ) )
| ~ ( ~ ! [SY21: $i] :
( ~ ( in @ SY21 @ SY20 )
| ( SY21 = SV3 )
| ( SY21 = SY19 ) )
| ~ ~ ( ~ ! [SY22: $i] :
( ( SY22 != SV3 )
| ( in @ SY22 @ SY20 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY19 )
| ( in @ SX3 @ SY20 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(52,plain,
! [SV4: $i,SV7: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV7 ) )
| ~ ( ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV4 )
| ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV7 ) ) ) )
= $true )
| ( ( SV4 = SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV5: $i,SV1: $i] :
( ( ( in @ SV1 @ SV5 )
= $false )
| ( ( ~ ( in @ SV5 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV8: $i] :
( ( ! [SY25: $i] :
( ~ ( ~ ( ( ( sK4_C @ SY25 @ SV8 )
!= SV8 )
| ~ ( in @ ( sK4_C @ SY25 @ SV8 ) @ SY25 ) )
| ~ ( ( ( sK4_C @ SY25 @ SV8 )
= SV8 )
| ( in @ ( sK4_C @ SY25 @ SV8 ) @ SY25 ) ) )
| ( SY25
= ( singleton @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV9: $i] :
( ( ! [SY26: $i] :
( ( SY26
!= ( singleton @ SV9 ) )
| ~ ( ~ ! [SY27: $i] :
( ( SY27 != SV9 )
| ( in @ SY27 @ SY26 ) )
| ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SY26 )
| ( SY28 = SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV3: $i] :
( ( ! [SY17: $i,SY18: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK3_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK3_D @ SY18 @ SY17 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK3_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK3_D @ SY18 @ SY17 @ SV3 )
!= SY17 ) ) )
| ~ ( ( in @ ( sK3_D @ SY18 @ SY17 @ SV3 ) @ SY18 )
| ( ( sK3_D @ SY18 @ SY17 @ SV3 )
= SV3 )
| ( ( sK3_D @ SY18 @ SY17 @ SV3 )
= SY17 ) ) )
| ( SY18
= ( unordered_pair @ SV3 @ SY17 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(57,plain,
! [SV3: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ( SY20
!= ( unordered_pair @ SV3 @ SY19 ) )
| ~ ( ~ ! [SY21: $i] :
( ~ ( in @ SY21 @ SY20 )
| ( SY21 = SV3 )
| ( SY21 = SY19 ) )
| ~ ~ ( ~ ! [SY22: $i] :
( ( SY22 != SV3 )
| ( in @ SY22 @ SY20 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY19 )
| ( in @ SX3 @ SY20 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(58,plain,
! [SV4: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV7 ) )
| ~ ( ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV4 )
| ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV7 ) ) )
= $false )
| ( ( SV4 = SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV1: $i,SV5: $i] :
( ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(60,plain,
! [SV8: $i,SV10: $i] :
( ( ~ ( ~ ( ( ( sK4_C @ SV10 @ SV8 )
!= SV8 )
| ~ ( in @ ( sK4_C @ SV10 @ SV8 ) @ SV10 ) )
| ~ ( ( ( sK4_C @ SV10 @ SV8 )
= SV8 )
| ( in @ ( sK4_C @ SV10 @ SV8 ) @ SV10 ) ) )
| ( SV10
= ( singleton @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(61,plain,
! [SV9: $i,SV11: $i] :
( ( ( SV11
!= ( singleton @ SV9 ) )
| ~ ( ~ ! [SY29: $i] :
( ( SY29 != SV9 )
| ( in @ SY29 @ SV11 ) )
| ~ ! [SY30: $i] :
( ~ ( in @ SY30 @ SV11 )
| ( SY30 = SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(62,plain,
! [SV3: $i,SV12: $i] :
( ( ! [SY31: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK3_D @ SY31 @ SV12 @ SV3 ) @ SY31 )
| ( ( sK3_D @ SY31 @ SV12 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK3_D @ SY31 @ SV12 @ SV3 ) @ SY31 )
| ( ( sK3_D @ SY31 @ SV12 @ SV3 )
!= SV12 ) ) )
| ~ ( ( in @ ( sK3_D @ SY31 @ SV12 @ SV3 ) @ SY31 )
| ( ( sK3_D @ SY31 @ SV12 @ SV3 )
= SV3 )
| ( ( sK3_D @ SY31 @ SV12 @ SV3 )
= SV12 ) ) )
| ( SY31
= ( unordered_pair @ SV3 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(63,plain,
! [SV13: $i,SV3: $i] :
( ( ! [SY32: $i] :
( ( SY32
!= ( unordered_pair @ SV3 @ SV13 ) )
| ~ ( ~ ! [SY33: $i] :
( ~ ( in @ SY33 @ SY32 )
| ( SY33 = SV3 )
| ( SY33 = SV13 ) )
| ~ ~ ( ~ ! [SY22: $i] :
( ( SY22 != SV3 )
| ( in @ SY22 @ SY32 ) )
| ~ ! [SY35: $i] :
( ( SY35 != SV13 )
| ( in @ SY35 @ SY32 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(64,plain,
! [SV4: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV7 ) ) )
= $false )
| ( ( SV4 = SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(65,plain,
! [SV4: $i,SV7: $i] :
( ( ( ~ ( ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV4 )
| ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV7 ) ) )
= $false )
| ( ( SV4 = SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(66,plain,
! [SV8: $i,SV10: $i] :
( ( ( ~ ( ~ ( ( ( sK4_C @ SV10 @ SV8 )
!= SV8 )
| ~ ( in @ ( sK4_C @ SV10 @ SV8 ) @ SV10 ) )
| ~ ( ( ( sK4_C @ SV10 @ SV8 )
= SV8 )
| ( in @ ( sK4_C @ SV10 @ SV8 ) @ SV10 ) ) ) )
= $true )
| ( ( SV10
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(67,plain,
! [SV9: $i,SV11: $i] :
( ( ( ( SV11
!= ( singleton @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY29: $i] :
( ( SY29 != SV9 )
| ( in @ SY29 @ SV11 ) )
| ~ ! [SY30: $i] :
( ~ ( in @ SY30 @ SV11 )
| ( SY30 = SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(68,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV12 ) ) )
| ~ ( ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
= SV3 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
= SV12 ) ) )
| ( SV14
= ( unordered_pair @ SV3 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV13: $i,SV3: $i,SV15: $i] :
( ( ( SV15
!= ( unordered_pair @ SV3 @ SV13 ) )
| ~ ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ SV15 )
| ( SY36 = SV3 )
| ( SY36 = SV13 ) )
| ~ ~ ( ~ ! [SY37: $i] :
( ( SY37 != SV3 )
| ( in @ SY37 @ SV15 ) )
| ~ ! [SY38: $i] :
( ( SY38 != SV13 )
| ( in @ SY38 @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV4: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV7 ) )
= $true )
| ( ( SV4 = SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(71,plain,
! [SV4: $i,SV7: $i] :
( ( ( ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV4 )
| ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV7 ) )
= $true )
| ( ( SV4 = SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(72,plain,
! [SV8: $i,SV10: $i] :
( ( ( ~ ( ( ( sK4_C @ SV10 @ SV8 )
!= SV8 )
| ~ ( in @ ( sK4_C @ SV10 @ SV8 ) @ SV10 ) )
| ~ ( ( ( sK4_C @ SV10 @ SV8 )
= SV8 )
| ( in @ ( sK4_C @ SV10 @ SV8 ) @ SV10 ) ) )
= $false )
| ( ( SV10
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(73,plain,
! [SV9: $i,SV11: $i] :
( ( ( SV11
= ( singleton @ SV9 ) )
= $false )
| ( ( ~ ( ~ ! [SY29: $i] :
( ( SY29 != SV9 )
| ( in @ SY29 @ SV11 ) )
| ~ ! [SY30: $i] :
( ~ ( in @ SY30 @ SV11 )
| ( SY30 = SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV12 ) ) )
| ~ ( ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
= SV3 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
= SV12 ) ) ) )
= $true )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV13: $i,SV3: $i,SV15: $i] :
( ( ( ( SV15
!= ( unordered_pair @ SV3 @ SV13 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ SV15 )
| ( SY36 = SV3 )
| ( SY36 = SV13 ) )
| ~ ~ ( ~ ! [SY37: $i] :
( ( SY37 != SV3 )
| ( in @ SY37 @ SV15 ) )
| ~ ! [SY38: $i] :
( ( SY38 != SV13 )
| ( in @ SY38 @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV4: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV4 ) )
= $true )
| ( ( ~ ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV7 ) )
= $true )
| ( ( SV4 = SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV4: $i,SV7: $i] :
( ( ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV7 )
= $true )
| ( ( SV4 = SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV8: $i,SV10: $i] :
( ( ( ~ ( ( ( sK4_C @ SV10 @ SV8 )
!= SV8 )
| ~ ( in @ ( sK4_C @ SV10 @ SV8 ) @ SV10 ) ) )
= $false )
| ( ( SV10
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(79,plain,
! [SV8: $i,SV10: $i] :
( ( ( ~ ( ( ( sK4_C @ SV10 @ SV8 )
= SV8 )
| ( in @ ( sK4_C @ SV10 @ SV8 ) @ SV10 ) ) )
= $false )
| ( ( SV10
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(80,plain,
! [SV11: $i,SV9: $i] :
( ( ( ~ ! [SY29: $i] :
( ( SY29 != SV9 )
| ( in @ SY29 @ SV11 ) )
| ~ ! [SY30: $i] :
( ~ ( in @ SY30 @ SV11 )
| ( SY30 = SV9 ) ) )
= $false )
| ( ( SV11
= ( singleton @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(81,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV12 ) ) )
| ~ ( ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
= SV3 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
= SV12 ) ) )
= $false )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(82,plain,
! [SV13: $i,SV3: $i,SV15: $i] :
( ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false )
| ( ( ~ ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ SV15 )
| ( SY36 = SV3 )
| ( SY36 = SV13 ) )
| ~ ~ ( ~ ! [SY37: $i] :
( ( SY37 != SV3 )
| ( in @ SY37 @ SV15 ) )
| ~ ! [SY38: $i] :
( ( SY38 != SV13 )
| ( in @ SY38 @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(83,plain,
! [SV4: $i,SV7: $i] :
( ( ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV4 )
= $false )
| ( ( ~ ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV7 ) )
= $true )
| ( ( SV4 = SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(84,plain,
! [SV8: $i,SV10: $i] :
( ( ( ( ( sK4_C @ SV10 @ SV8 )
!= SV8 )
| ~ ( in @ ( sK4_C @ SV10 @ SV8 ) @ SV10 ) )
= $true )
| ( ( SV10
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(85,plain,
! [SV8: $i,SV10: $i] :
( ( ( ( ( sK4_C @ SV10 @ SV8 )
= SV8 )
| ( in @ ( sK4_C @ SV10 @ SV8 ) @ SV10 ) )
= $true )
| ( ( SV10
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(86,plain,
! [SV11: $i,SV9: $i] :
( ( ( ~ ! [SY29: $i] :
( ( SY29 != SV9 )
| ( in @ SY29 @ SV11 ) ) )
= $false )
| ( ( SV11
= ( singleton @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(87,plain,
! [SV9: $i,SV11: $i] :
( ( ( ~ ! [SY30: $i] :
( ~ ( in @ SY30 @ SV11 )
| ( SY30 = SV9 ) ) )
= $false )
| ( ( SV11
= ( singleton @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(88,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV12 ) ) ) )
= $false )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(89,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( ~ ( ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
= SV3 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
= SV12 ) ) )
= $false )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(90,plain,
! [SV13: $i,SV3: $i,SV15: $i] :
( ( ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ SV15 )
| ( SY36 = SV3 )
| ( SY36 = SV13 ) )
| ~ ~ ( ~ ! [SY37: $i] :
( ( SY37 != SV3 )
| ( in @ SY37 @ SV15 ) )
| ~ ! [SY38: $i] :
( ( SY38 != SV13 )
| ( in @ SY38 @ SV15 ) ) ) )
= $false )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV4: $i,SV7: $i] :
( ( ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV7 )
= $false )
| ( ( in @ ( sK2_C @ SV7 @ SV4 ) @ SV4 )
= $false )
| ( ( SV4 = SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV8: $i,SV10: $i] :
( ( ( ( ( sK4_C @ SV10 @ SV8 )
!= SV8 ) )
= $true )
| ( ( ~ ( in @ ( sK4_C @ SV10 @ SV8 ) @ SV10 ) )
= $true )
| ( ( SV10
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV8: $i,SV10: $i] :
( ( ( ( sK4_C @ SV10 @ SV8 )
= SV8 )
= $true )
| ( ( in @ ( sK4_C @ SV10 @ SV8 ) @ SV10 )
= $true )
| ( ( SV10
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV11: $i,SV9: $i] :
( ( ( ! [SY29: $i] :
( ( SY29 != SV9 )
| ( in @ SY29 @ SV11 ) ) )
= $true )
| ( ( SV11
= ( singleton @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(95,plain,
! [SV9: $i,SV11: $i] :
( ( ( ! [SY30: $i] :
( ~ ( in @ SY30 @ SV11 )
| ( SY30 = SV9 ) ) )
= $true )
| ( ( SV11
= ( singleton @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(96,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV12 ) ) ) )
= $true )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(97,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
= SV3 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
= SV12 ) )
= $true )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(98,plain,
! [SV13: $i,SV3: $i,SV15: $i] :
( ( ( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ SV15 )
| ( SY36 = SV3 )
| ( SY36 = SV13 ) ) )
= $false )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(99,plain,
! [SV13: $i,SV15: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ! [SY37: $i] :
( ( SY37 != SV3 )
| ( in @ SY37 @ SV15 ) )
| ~ ! [SY38: $i] :
( ( SY38 != SV13 )
| ( in @ SY38 @ SV15 ) ) ) )
= $false )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(100,plain,
! [SV8: $i,SV10: $i] :
( ( ( ( sK4_C @ SV10 @ SV8 )
= SV8 )
= $false )
| ( ( ~ ( in @ ( sK4_C @ SV10 @ SV8 ) @ SV10 ) )
= $true )
| ( ( SV10
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(101,plain,
! [SV11: $i,SV9: $i,SV16: $i] :
( ( ( ( SV16 != SV9 )
| ( in @ SV16 @ SV11 ) )
= $true )
| ( ( SV11
= ( singleton @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(102,plain,
! [SV9: $i,SV11: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV11 )
| ( SV17 = SV9 ) )
= $true )
| ( ( SV11
= ( singleton @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(103,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV3 ) )
| ~ ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV12 ) ) )
= $false )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(104,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
= $true )
| ( ( ( ( sK3_D @ SV14 @ SV12 @ SV3 )
= SV3 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
= SV12 ) )
= $true )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(105,plain,
! [SV13: $i,SV3: $i,SV15: $i] :
( ( ( ! [SY36: $i] :
( ~ ( in @ SY36 @ SV15 )
| ( SY36 = SV3 )
| ( SY36 = SV13 ) ) )
= $true )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(106,plain,
! [SV13: $i,SV15: $i,SV3: $i] :
( ( ( ~ ( ~ ! [SY37: $i] :
( ( SY37 != SV3 )
| ( in @ SY37 @ SV15 ) )
| ~ ! [SY38: $i] :
( ( SY38 != SV13 )
| ( in @ SY38 @ SV15 ) ) ) )
= $true )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(107,plain,
! [SV8: $i,SV10: $i] :
( ( ( in @ ( sK4_C @ SV10 @ SV8 ) @ SV10 )
= $false )
| ( ( ( sK4_C @ SV10 @ SV8 )
= SV8 )
= $false )
| ( ( SV10
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(108,plain,
! [SV11: $i,SV9: $i,SV16: $i] :
( ( ( ( SV16 != SV9 ) )
= $true )
| ( ( in @ SV16 @ SV11 )
= $true )
| ( ( SV11
= ( singleton @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(109,plain,
! [SV9: $i,SV11: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV11 ) )
= $true )
| ( ( SV17 = SV9 )
= $true )
| ( ( SV11
= ( singleton @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(110,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV3 ) ) )
= $false )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(111,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV12 ) ) )
= $false )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(112,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( ( sK3_D @ SV14 @ SV12 @ SV3 )
= SV3 )
= $true )
| ( ( ( sK3_D @ SV14 @ SV12 @ SV3 )
= SV12 )
= $true )
| ( ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
= $true )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(113,plain,
! [SV13: $i,SV3: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV15 )
| ( SV18 = SV3 )
| ( SV18 = SV13 ) )
= $true )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(114,plain,
! [SV13: $i,SV15: $i,SV3: $i] :
( ( ( ~ ! [SY37: $i] :
( ( SY37 != SV3 )
| ( in @ SY37 @ SV15 ) )
| ~ ! [SY38: $i] :
( ( SY38 != SV13 )
| ( in @ SY38 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(115,plain,
! [SV11: $i,SV9: $i,SV16: $i] :
( ( ( SV16 = SV9 )
= $false )
| ( ( in @ SV16 @ SV11 )
= $true )
| ( ( SV11
= ( singleton @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(116,plain,
! [SV9: $i,SV11: $i,SV17: $i] :
( ( ( in @ SV17 @ SV11 )
= $false )
| ( ( SV17 = SV9 )
= $true )
| ( ( SV11
= ( singleton @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(117,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV3 ) )
= $true )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(118,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
| ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV12 ) )
= $true )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(119,plain,
! [SV13: $i,SV3: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV15 ) )
= $true )
| ( ( ( SV18 = SV3 )
| ( SV18 = SV13 ) )
= $true )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(120,plain,
! [SV13: $i,SV15: $i,SV3: $i] :
( ( ( ~ ! [SY37: $i] :
( ( SY37 != SV3 )
| ( in @ SY37 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(121,plain,
! [SV3: $i,SV15: $i,SV13: $i] :
( ( ( ~ ! [SY38: $i] :
( ( SY38 != SV13 )
| ( in @ SY38 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(122,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 ) )
= $true )
| ( ( ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV3 ) )
= $true )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(123,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 ) )
= $true )
| ( ( ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV12 ) )
= $true )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(124,plain,
! [SV13: $i,SV3: $i,SV15: $i,SV18: $i] :
( ( ( in @ SV18 @ SV15 )
= $false )
| ( ( ( SV18 = SV3 )
| ( SV18 = SV13 ) )
= $true )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(125,plain,
! [SV13: $i,SV15: $i,SV3: $i] :
( ( ( ! [SY37: $i] :
( ( SY37 != SV3 )
| ( in @ SY37 @ SV15 ) ) )
= $true )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(126,plain,
! [SV3: $i,SV15: $i,SV13: $i] :
( ( ( ! [SY38: $i] :
( ( SY38 != SV13 )
| ( in @ SY38 @ SV15 ) ) )
= $true )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(127,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
= $false )
| ( ( ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV3 ) )
= $true )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(128,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
= $false )
| ( ( ( ( sK3_D @ SV14 @ SV12 @ SV3 )
!= SV12 ) )
= $true )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(129,plain,
! [SV15: $i,SV13: $i,SV3: $i,SV18: $i] :
( ( ( SV18 = SV3 )
= $true )
| ( ( SV18 = SV13 )
= $true )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(130,plain,
! [SV13: $i,SV15: $i,SV3: $i,SV19: $i] :
( ( ( ( SV19 != SV3 )
| ( in @ SV19 @ SV15 ) )
= $true )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(131,plain,
! [SV3: $i,SV15: $i,SV13: $i,SV20: $i] :
( ( ( ( SV20 != SV13 )
| ( in @ SV20 @ SV15 ) )
= $true )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(132,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( ( sK3_D @ SV14 @ SV12 @ SV3 )
= SV3 )
= $false )
| ( ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
= $false )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(133,plain,
! [SV3: $i,SV12: $i,SV14: $i] :
( ( ( ( sK3_D @ SV14 @ SV12 @ SV3 )
= SV12 )
= $false )
| ( ( in @ ( sK3_D @ SV14 @ SV12 @ SV3 ) @ SV14 )
= $false )
| ( ( SV14
= ( unordered_pair @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(134,plain,
! [SV13: $i,SV15: $i,SV3: $i,SV19: $i] :
( ( ( ( SV19 != SV3 ) )
= $true )
| ( ( in @ SV19 @ SV15 )
= $true )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(135,plain,
! [SV3: $i,SV15: $i,SV13: $i,SV20: $i] :
( ( ( ( SV20 != SV13 ) )
= $true )
| ( ( in @ SV20 @ SV15 )
= $true )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(136,plain,
! [SV13: $i,SV15: $i,SV3: $i,SV19: $i] :
( ( ( SV19 = SV3 )
= $false )
| ( ( in @ SV19 @ SV15 )
= $true )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(137,plain,
! [SV3: $i,SV15: $i,SV13: $i,SV20: $i] :
( ( ( SV20 = SV13 )
= $false )
| ( ( in @ SV20 @ SV15 )
= $true )
| ( ( SV15
= ( unordered_pair @ SV3 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(138,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,137,136,133,132,129,116,115,112,107,93,91,77,59,42,37,29]) ).
thf(139,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SEU142+1 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.15 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 20 09:34:22 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37
% 0.14/0.37 No.of.Axioms: 7
% 0.14/0.37
% 0.14/0.37 Length.of.Defs: 0
% 0.14/0.37
% 0.14/0.37 Contains.Choice.Funs: false
% 0.14/0.37 (rf:0,axioms:7,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:9,loop_count:0,foatp_calls:0,translation:fof_full)..........
% 0.59/0.78
% 0.59/0.78 ********************************
% 0.59/0.78 * All subproblems solved! *
% 0.59/0.78 ********************************
% 0.59/0.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,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:138,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.59/0.79
% 0.59/0.79 %**** Beginning of derivation protocol ****
% 0.59/0.79 % SZS output start CNFRefutation
% See solution above
% 0.59/0.79
% 0.59/0.79 %**** End of derivation protocol ****
% 0.59/0.79 %**** no. of clauses in derivation: 139 ****
% 0.59/0.79 %**** clause counter: 138 ****
% 0.59/0.79
% 0.59/0.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,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:138,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------