TSTP Solution File: SET985+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET985+1 : TPTP v8.1.0. Released v3.2.0.
% 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 03:06:46 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 102 ( 73 unt; 10 typ; 0 def)
% Number of atoms : 450 ( 221 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 849 ( 114 ~; 130 |; 10 &; 581 @)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 214 ( 0 ^ 210 !; 4 ?; 214 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY15,type,
sK2_SY15: $i ).
thf(tp_sK3_SY18,type,
sK3_SY18: $i ).
thf(tp_sK4_SY20,type,
sK4_SY20: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
=> ( ( ( cartesian_product2 @ A @ B )
= empty_set )
| ( ( subset @ A @ C )
& ( subset @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( cartesian_product2 @ A @ B )
= empty_set )
<=> ( ( A = empty_set )
| ( B = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(4,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(5,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(6,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(7,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(8,conjecture,
! [A: $i] :
( ~ ( empty @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( subset @ ( cartesian_product2 @ B @ A ) @ ( cartesian_product2 @ D @ C ) ) )
=> ( subset @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(9,negated_conjecture,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( subset @ ( cartesian_product2 @ B @ A ) @ ( cartesian_product2 @ D @ C ) ) )
=> ( subset @ B @ D ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( subset @ ( cartesian_product2 @ B @ A ) @ ( cartesian_product2 @ D @ C ) ) )
=> ( subset @ B @ D ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
=> ( ( ( cartesian_product2 @ A @ B )
= empty_set )
| ( ( subset @ A @ C )
& ( subset @ B @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] :
( ( ( cartesian_product2 @ A @ B )
= empty_set )
<=> ( ( A = empty_set )
| ( B = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(17,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(18,plain,
( ( ~ ( empty @ sK1_A )
=> ! [SY15: $i,SY16: $i,SY17: $i] :
( ( ( subset @ ( cartesian_product2 @ sK1_A @ SY15 ) @ ( cartesian_product2 @ SY16 @ SY17 ) )
| ( subset @ ( cartesian_product2 @ SY15 @ sK1_A ) @ ( cartesian_product2 @ SY17 @ SY16 ) ) )
=> ( subset @ SY15 @ SY17 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(19,plain,
( ( ~ ( empty @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [SY15: $i,SY16: $i,SY17: $i] :
( ( ( subset @ ( cartesian_product2 @ sK1_A @ SY15 ) @ ( cartesian_product2 @ SY16 @ SY17 ) )
| ( subset @ ( cartesian_product2 @ SY15 @ sK1_A ) @ ( cartesian_product2 @ SY17 @ SY16 ) ) )
=> ( subset @ SY15 @ SY17 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ! [SY15: $i,SY16: $i,SY17: $i] :
( ( ( subset @ ( cartesian_product2 @ sK1_A @ SY15 ) @ ( cartesian_product2 @ SY16 @ SY17 ) )
| ( subset @ ( cartesian_product2 @ SY15 @ sK1_A ) @ ( cartesian_product2 @ SY17 @ SY16 ) ) )
=> ( subset @ SY15 @ SY17 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[20]) ).
thf(22,plain,
( ( ( ( subset @ ( cartesian_product2 @ sK1_A @ sK2_SY15 ) @ ( cartesian_product2 @ sK3_SY18 @ sK4_SY20 ) )
| ( subset @ ( cartesian_product2 @ sK2_SY15 @ sK1_A ) @ ( cartesian_product2 @ sK4_SY20 @ sK3_SY18 ) ) )
& ~ ( subset @ sK2_SY15 @ sK4_SY20 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
~ ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( subset @ A @ C )
| ( ( cartesian_product2 @ A @ B )
= empty_set ) )
& ! [C: $i,D: $i] :
( ~ ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( subset @ B @ D )
| ( ( cartesian_product2 @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ( ( cartesian_product2 @ A @ B )
!= empty_set )
| ( A = empty_set )
| ( B = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( cartesian_product2 @ A @ B )
= empty_set ) )
& ! [A: $i,B: $i] :
( ( B != empty_set )
| ( ( cartesian_product2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(25,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(26,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(27,plain,
( ( empty @ sK6_A )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(28,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(29,plain,
( ( empty @ sK6_A )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(30,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(31,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
( ( ( cartesian_product2 @ A @ B )
!= empty_set )
| ( A = empty_set )
| ( B = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( cartesian_product2 @ A @ B )
= empty_set ) )
& ! [A: $i,B: $i] :
( ( B != empty_set )
| ( ( cartesian_product2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(33,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
~ ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( subset @ A @ C )
| ( ( cartesian_product2 @ A @ B )
= empty_set ) )
& ! [C: $i,D: $i] :
( ~ ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( subset @ B @ D )
| ( ( cartesian_product2 @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(34,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(35,plain,
( ( ~ ( empty @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(36,plain,
( ( ( ( subset @ ( cartesian_product2 @ sK1_A @ sK2_SY15 ) @ ( cartesian_product2 @ sK3_SY18 @ sK4_SY20 ) )
| ( subset @ ( cartesian_product2 @ sK2_SY15 @ sK1_A ) @ ( cartesian_product2 @ sK4_SY20 @ sK3_SY18 ) ) )
& ~ ( subset @ sK2_SY15 @ sK4_SY20 ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(37,plain,
( ( ~ ( ~ ( ( subset @ ( cartesian_product2 @ sK1_A @ sK2_SY15 ) @ ( cartesian_product2 @ sK3_SY18 @ sK4_SY20 ) )
| ( subset @ ( cartesian_product2 @ sK2_SY15 @ sK1_A ) @ ( cartesian_product2 @ sK4_SY20 @ sK3_SY18 ) ) )
| ~ ~ ( subset @ sK2_SY15 @ sK4_SY20 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(38,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( subset @ ( cartesian_product2 @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( subset @ SX0 @ SX2 )
| ( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( subset @ ( cartesian_product2 @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( subset @ SX1 @ SX3 )
| ( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(39,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( cartesian_product2 @ SX0 @ SX1 )
!= empty_set )
| ( SX0 = empty_set )
| ( SX1 = empty_set ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != empty_set )
| ( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(40,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(41,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(42,plain,
! [SV2: $i] :
( ( subset @ empty_set @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(43,plain,
( ( empty @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(44,plain,
( ( ~ ( ( subset @ ( cartesian_product2 @ sK1_A @ sK2_SY15 ) @ ( cartesian_product2 @ sK3_SY18 @ sK4_SY20 ) )
| ( subset @ ( cartesian_product2 @ sK2_SY15 @ sK1_A ) @ ( cartesian_product2 @ sK4_SY20 @ sK3_SY18 ) ) )
| ~ ~ ( subset @ sK2_SY15 @ sK4_SY20 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV3: $i] :
( ( ! [SY21: $i] :
~ ( ~ ! [SY22: $i] :
( ! [SY23: $i] :
~ ( subset @ ( cartesian_product2 @ SV3 @ SY21 ) @ ( cartesian_product2 @ SY22 @ SY23 ) )
| ( subset @ SV3 @ SY22 )
| ( ( cartesian_product2 @ SV3 @ SY21 )
= empty_set ) )
| ~ ! [SY24: $i,SY25: $i] :
( ~ ( subset @ ( cartesian_product2 @ SV3 @ SY21 ) @ ( cartesian_product2 @ SY24 @ SY25 ) )
| ( subset @ SY21 @ SY25 )
| ( ( cartesian_product2 @ SV3 @ SY21 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( cartesian_product2 @ SX0 @ SX1 )
!= empty_set )
| ( SX0 = empty_set )
| ( SX1 = empty_set ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != empty_set )
| ( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(47,plain,
( ( ~ ( ( subset @ ( cartesian_product2 @ sK1_A @ sK2_SY15 ) @ ( cartesian_product2 @ sK3_SY18 @ sK4_SY20 ) )
| ( subset @ ( cartesian_product2 @ sK2_SY15 @ sK1_A ) @ ( cartesian_product2 @ sK4_SY20 @ sK3_SY18 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(48,plain,
( ( ~ ~ ( subset @ sK2_SY15 @ sK4_SY20 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(49,plain,
! [SV4: $i,SV3: $i] :
( ( ~ ( ~ ! [SY26: $i] :
( ! [SY27: $i] :
~ ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SY26 @ SY27 ) )
| ( subset @ SV3 @ SY26 )
| ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set ) )
| ~ ! [SY28: $i,SY29: $i] :
( ~ ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SY28 @ SY29 ) )
| ( subset @ SV4 @ SY29 )
| ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(50,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( cartesian_product2 @ SX0 @ SX1 )
!= empty_set )
| ( SX0 = empty_set )
| ( SX1 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(51,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != empty_set )
| ( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(52,plain,
( ( ( subset @ ( cartesian_product2 @ sK1_A @ sK2_SY15 ) @ ( cartesian_product2 @ sK3_SY18 @ sK4_SY20 ) )
| ( subset @ ( cartesian_product2 @ sK2_SY15 @ sK1_A ) @ ( cartesian_product2 @ sK4_SY20 @ sK3_SY18 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(53,plain,
( ( ~ ( subset @ sK2_SY15 @ sK4_SY20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV4: $i,SV3: $i] :
( ( ~ ! [SY26: $i] :
( ! [SY27: $i] :
~ ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SY26 @ SY27 ) )
| ( subset @ SV3 @ SY26 )
| ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set ) )
| ~ ! [SY28: $i,SY29: $i] :
( ~ ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SY28 @ SY29 ) )
| ( subset @ SV4 @ SY29 )
| ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(55,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( cartesian_product2 @ SX0 @ SX1 )
!= empty_set )
| ( SX0 = empty_set )
| ( SX1 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(56,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != empty_set )
| ( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(57,plain,
( ( ( subset @ ( cartesian_product2 @ sK1_A @ sK2_SY15 ) @ ( cartesian_product2 @ sK3_SY18 @ sK4_SY20 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ sK2_SY15 @ sK1_A ) @ ( cartesian_product2 @ sK4_SY20 @ sK3_SY18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(58,plain,
( ( subset @ sK2_SY15 @ sK4_SY20 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV4: $i,SV3: $i] :
( ( ~ ! [SY26: $i] :
( ! [SY27: $i] :
~ ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SY26 @ SY27 ) )
| ( subset @ SV3 @ SY26 )
| ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(60,plain,
! [SV4: $i,SV3: $i] :
( ( ~ ! [SY28: $i,SY29: $i] :
( ~ ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SY28 @ SY29 ) )
| ( subset @ SV4 @ SY29 )
| ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(61,plain,
! [SV5: $i] :
( ( ! [SY30: $i] :
( ( ( cartesian_product2 @ SV5 @ SY30 )
!= empty_set )
| ( SV5 = empty_set )
| ( SY30 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(62,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != empty_set )
| ( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(63,plain,
! [SV4: $i,SV3: $i] :
( ( ! [SY26: $i] :
( ! [SY27: $i] :
~ ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SY26 @ SY27 ) )
| ( subset @ SV3 @ SY26 )
| ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(64,plain,
! [SV4: $i,SV3: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ~ ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SY28 @ SY29 ) )
| ( subset @ SV4 @ SY29 )
| ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(65,plain,
! [SV6: $i,SV5: $i] :
( ( ( ( cartesian_product2 @ SV5 @ SV6 )
!= empty_set )
| ( SV5 = empty_set )
| ( SV6 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(66,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(67,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != empty_set )
| ( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(68,plain,
! [SV7: $i,SV4: $i,SV3: $i] :
( ( ! [SY31: $i] :
~ ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SV7 @ SY31 ) )
| ( subset @ SV3 @ SV7 )
| ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(69,plain,
! [SV8: $i,SV4: $i,SV3: $i] :
( ( ! [SY32: $i] :
( ~ ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SV8 @ SY32 ) )
| ( subset @ SV4 @ SY32 )
| ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(70,plain,
! [SV6: $i,SV5: $i] :
( ( ( ( ( cartesian_product2 @ SV5 @ SV6 )
!= empty_set ) )
= $true )
| ( ( ( SV5 = empty_set )
| ( SV6 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(71,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != empty_set )
| ( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(73,plain,
! [SV7: $i,SV4: $i,SV3: $i] :
( ( ( ! [SY31: $i] :
~ ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SV7 @ SY31 ) ) )
= $true )
| ( ( ( subset @ SV3 @ SV7 )
| ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(74,plain,
! [SV9: $i,SV8: $i,SV4: $i,SV3: $i] :
( ( ~ ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SV8 @ SV9 ) )
| ( subset @ SV4 @ SV9 )
| ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(75,plain,
! [SV6: $i,SV5: $i] :
( ( ( ( cartesian_product2 @ SV5 @ SV6 )
= empty_set )
= $false )
| ( ( ( SV5 = empty_set )
| ( SV6 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV10: $i] :
( ( ( SV10 != empty_set )
| ! [SY33: $i] :
( ( cartesian_product2 @ SV10 @ SY33 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV11: $i] :
( ( ! [SY34: $i] :
( ( SY34 != empty_set )
| ( ( cartesian_product2 @ SV11 @ SY34 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV12: $i,SV7: $i,SV4: $i,SV3: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SV7 @ SV12 ) ) )
= $true )
| ( ( ( subset @ SV3 @ SV7 )
| ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(79,plain,
! [SV9: $i,SV8: $i,SV4: $i,SV3: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
= $true )
| ( ( ( subset @ SV4 @ SV9 )
| ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV6: $i,SV5: $i] :
( ( ( SV5 = empty_set )
= $true )
| ( ( SV6 = empty_set )
= $true )
| ( ( ( cartesian_product2 @ SV5 @ SV6 )
= empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV10: $i] :
( ( ( ( SV10 != empty_set ) )
= $true )
| ( ( ! [SY33: $i] :
( ( cartesian_product2 @ SV10 @ SY33 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV11: $i,SV13: $i] :
( ( ( SV13 != empty_set )
| ( ( cartesian_product2 @ SV11 @ SV13 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(83,plain,
! [SV12: $i,SV7: $i,SV4: $i,SV3: $i] :
( ( ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SV7 @ SV12 ) )
= $false )
| ( ( ( subset @ SV3 @ SV7 )
| ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(84,plain,
! [SV9: $i,SV8: $i,SV4: $i,SV3: $i] :
( ( ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SV8 @ SV9 ) )
= $false )
| ( ( ( subset @ SV4 @ SV9 )
| ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(85,plain,
! [SV10: $i] :
( ( ( SV10 = empty_set )
= $false )
| ( ( ! [SY33: $i] :
( ( cartesian_product2 @ SV10 @ SY33 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV11: $i,SV13: $i] :
( ( ( ( SV13 != empty_set ) )
= $true )
| ( ( ( cartesian_product2 @ SV11 @ SV13 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV12: $i,SV4: $i,SV7: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV7 )
= $true )
| ( ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SV7 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV8: $i,SV3: $i,SV9: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV9 )
= $true )
| ( ( ( cartesian_product2 @ SV3 @ SV4 )
= empty_set )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV3 @ SV4 ) @ ( cartesian_product2 @ SV8 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(89,plain,
! [SV14: $i,SV10: $i] :
( ( ( ( cartesian_product2 @ SV10 @ SV14 )
= empty_set )
= $true )
| ( ( SV10 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(90,plain,
! [SV11: $i,SV13: $i] :
( ( ( SV13 = empty_set )
= $false )
| ( ( ( cartesian_product2 @ SV11 @ SV13 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(91,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,90,89,88,87,80,58,57,43,42,41,40,29]) ).
thf(92,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET985+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % 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 Jul 11 06:33:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 7
% 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: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)......
% 0.20/0.42
% 0.20/0.42 ********************************
% 0.20/0.42 * All subproblems solved! *
% 0.20/0.42 ********************************
% 0.20/0.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:91,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.42
% 0.20/0.42 %**** Beginning of derivation protocol ****
% 0.20/0.42 % SZS output start CNFRefutation
% See solution above
% 0.20/0.42
% 0.20/0.42 %**** End of derivation protocol ****
% 0.20/0.42 %**** no. of clauses in derivation: 92 ****
% 0.20/0.42 %**** clause counter: 91 ****
% 0.20/0.42
% 0.20/0.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:91,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------