TSTP Solution File: SET984+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET984+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 : n014.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 0.40s 0.58s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of formulae : 135 ( 98 unt; 11 typ; 0 def)
% Number of atoms : 611 ( 394 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 879 ( 128 ~; 175 |; 19 &; 544 @)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 286 ( 0 ^ 282 !; 4 ?; 286 :)
% 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_SY26,type,
sK2_SY26: $i ).
thf(tp_sK3_SY29,type,
sK3_SY29: $i ).
thf(tp_sK4_SY31,type,
sK4_SY31: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(2,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( cartesian_product2 @ A @ B )
= ( cartesian_product2 @ C @ D ) )
=> ( ( A = empty_set )
| ( B = empty_set )
| ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ C @ D ) )
= ( set_intersection2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( cartesian_product2 @ A @ B )
= empty_set )
<=> ( ( A = empty_set )
| ( B = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(6,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(7,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(8,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(10,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(12,conjecture,
! [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/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(13,negated_conjecture,
( ( ! [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 ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,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 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( cartesian_product2 @ A @ B )
= ( cartesian_product2 @ C @ D ) )
=> ( ( A = empty_set )
| ( B = empty_set )
| ( ( A = C )
& ( B = D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ C @ D ) )
= ( set_intersection2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ( ( cartesian_product2 @ A @ B )
= empty_set )
<=> ( ( A = empty_set )
| ( B = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(24,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(26,plain,
( ( ! [SY26: $i,SY27: $i,SY28: $i] :
( ( subset @ ( cartesian_product2 @ sK1_A @ SY26 ) @ ( cartesian_product2 @ SY27 @ SY28 ) )
=> ( ( ( cartesian_product2 @ sK1_A @ SY26 )
= empty_set )
| ( ( subset @ sK1_A @ SY27 )
& ( subset @ SY26 @ SY28 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(27,plain,
( ( ! [SY29: $i,SY30: $i] :
( ( subset @ ( cartesian_product2 @ sK1_A @ sK2_SY26 ) @ ( cartesian_product2 @ SY29 @ SY30 ) )
=> ( ( ( cartesian_product2 @ sK1_A @ sK2_SY26 )
= empty_set )
| ( ( subset @ sK1_A @ SY29 )
& ( subset @ sK2_SY26 @ SY30 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(28,plain,
( ( ! [SY31: $i] :
( ( subset @ ( cartesian_product2 @ sK1_A @ sK2_SY26 ) @ ( cartesian_product2 @ sK3_SY29 @ SY31 ) )
=> ( ( ( cartesian_product2 @ sK1_A @ sK2_SY26 )
= empty_set )
| ( ( subset @ sK1_A @ sK3_SY29 )
& ( subset @ sK2_SY26 @ SY31 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(29,plain,
( ( ( subset @ ( cartesian_product2 @ sK1_A @ sK2_SY26 ) @ ( cartesian_product2 @ sK3_SY29 @ sK4_SY31 ) )
=> ( ( ( cartesian_product2 @ sK1_A @ sK2_SY26 )
= empty_set )
| ( ( subset @ sK1_A @ sK3_SY29 )
& ( subset @ sK2_SY26 @ sK4_SY31 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[28]) ).
thf(30,plain,
( ( subset @ ( cartesian_product2 @ sK1_A @ sK2_SY26 ) @ ( cartesian_product2 @ sK3_SY29 @ sK4_SY31 ) )
= $true ),
inference(standard_cnf,[status(thm)],[29]) ).
thf(31,plain,
( ( ( ( cartesian_product2 @ sK1_A @ sK2_SY26 )
= empty_set )
| ( ( subset @ sK1_A @ sK3_SY29 )
& ( subset @ sK2_SY26 @ sK4_SY31 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[29]) ).
thf(32,plain,
( ( ~ ( ( ( cartesian_product2 @ sK1_A @ sK2_SY26 )
= empty_set )
| ( ( subset @ sK1_A @ sK3_SY29 )
& ( subset @ sK2_SY26 @ sK4_SY31 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[31]) ).
thf(33,plain,
( ( ( ~ ( subset @ sK1_A @ sK3_SY29 )
| ~ ( subset @ sK2_SY26 @ sK4_SY31 ) )
& ( ( cartesian_product2 @ sK1_A @ sK2_SY26 )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ( cartesian_product2 @ A @ B )
!= ( cartesian_product2 @ C @ D ) )
| ( A = C )
| ( A = empty_set )
| ( B = empty_set ) )
& ! [C: $i,D: $i] :
( ( ( cartesian_product2 @ A @ B )
!= ( cartesian_product2 @ C @ D ) )
| ( B = D )
| ( A = empty_set )
| ( B = empty_set ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(36,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)],[19]) ).
thf(37,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(38,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(39,plain,
( ( empty @ sK6_A )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(42,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(44,plain,
( ( empty @ sK6_A )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(45,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(46,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(47,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)],[36]) ).
thf(48,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ C @ D ) )
= ( set_intersection2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ( cartesian_product2 @ A @ B )
!= ( cartesian_product2 @ C @ D ) )
| ( A = C )
| ( A = empty_set )
| ( B = empty_set ) )
& ! [C: $i,D: $i] :
( ( ( cartesian_product2 @ A @ B )
!= ( cartesian_product2 @ C @ D ) )
| ( B = D )
| ( A = empty_set )
| ( B = empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(50,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(52,plain,
( ( subset @ ( cartesian_product2 @ sK1_A @ sK2_SY26 ) @ ( cartesian_product2 @ sK3_SY29 @ sK4_SY31 ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(53,plain,
( ( ( ~ ( subset @ sK1_A @ sK3_SY29 )
| ~ ( subset @ sK2_SY26 @ sK4_SY31 ) )
& ( ( cartesian_product2 @ sK1_A @ sK2_SY26 )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(54,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)],[47]) ).
thf(55,plain,
( ( ~ ( ~ ( ~ ( subset @ sK1_A @ sK3_SY29 )
| ~ ( subset @ sK2_SY26 @ sK4_SY31 ) )
| ~ ( ( ( cartesian_product2 @ sK1_A @ sK2_SY26 )
!= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(56,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( cartesian_product2 @ SX0 @ SX1 )
!= ( cartesian_product2 @ SX2 @ SX3 ) )
| ( SX0 = SX2 )
| ( SX0 = empty_set )
| ( SX1 = empty_set ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( cartesian_product2 @ SX0 @ SX1 )
!= ( cartesian_product2 @ SX2 @ SX3 ) )
| ( SX1 = SX3 )
| ( SX0 = empty_set )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(57,plain,
! [SV1: $i] :
( ( ! [SY32: $i] :
( ( set_intersection2 @ SV1 @ SY32 )
= ( set_intersection2 @ SY32 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(58,plain,
! [SV2: $i] :
( ( ( set_intersection2 @ SV2 @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(59,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(60,plain,
! [SV3: $i] :
( ( subset @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(61,plain,
! [SV4: $i] :
( ( ! [SY33: $i,SY34: $i,SY35: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ SV4 @ SY33 ) @ ( set_intersection2 @ SY34 @ SY35 ) )
= ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SY34 ) @ ( cartesian_product2 @ SY33 @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(62,plain,
! [SV5: $i] :
( ( ! [SY36: $i] : ( subset @ ( set_intersection2 @ SV5 @ SY36 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(63,plain,
! [SV6: $i] :
( ( ! [SY37: $i] :
( ~ ( subset @ SV6 @ SY37 )
| ( ( set_intersection2 @ SV6 @ SY37 )
= SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(64,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)],[54]) ).
thf(65,plain,
( ( ~ ( ~ ( subset @ sK1_A @ sK3_SY29 )
| ~ ( subset @ sK2_SY26 @ sK4_SY31 ) )
| ~ ( ( ( cartesian_product2 @ sK1_A @ sK2_SY26 )
!= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(66,plain,
! [SV7: $i] :
( ( ! [SY38: $i] :
~ ( ~ ! [SY39: $i] :
( ! [SY40: $i] :
( ( cartesian_product2 @ SV7 @ SY38 )
!= ( cartesian_product2 @ SY39 @ SY40 ) )
| ( SV7 = SY39 )
| ( SV7 = empty_set )
| ( SY38 = empty_set ) )
| ~ ! [SY41: $i,SY42: $i] :
( ( ( cartesian_product2 @ SV7 @ SY38 )
!= ( cartesian_product2 @ SY41 @ SY42 ) )
| ( SY38 = SY42 )
| ( SV7 = empty_set )
| ( SY38 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(67,plain,
! [SV8: $i,SV1: $i] :
( ( ( set_intersection2 @ SV1 @ SV8 )
= ( set_intersection2 @ SV8 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(68,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ SV4 @ SV9 ) @ ( set_intersection2 @ SY43 @ SY44 ) )
= ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SY43 ) @ ( cartesian_product2 @ SV9 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(69,plain,
! [SV10: $i,SV5: $i] :
( ( subset @ ( set_intersection2 @ SV5 @ SV10 ) @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(70,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ( subset @ SV6 @ SV11 )
| ( ( set_intersection2 @ SV6 @ SV11 )
= SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(71,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( cartesian_product2 @ SX0 @ SX1 )
!= empty_set )
| ( SX0 = empty_set )
| ( SX1 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(72,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)],[64]) ).
thf(73,plain,
( ( ~ ( ~ ( subset @ sK1_A @ sK3_SY29 )
| ~ ( subset @ sK2_SY26 @ sK4_SY31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(74,plain,
( ( ~ ( ( ( cartesian_product2 @ sK1_A @ sK2_SY26 )
!= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(75,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ( ~ ! [SY45: $i] :
( ! [SY46: $i] :
( ( cartesian_product2 @ SV7 @ SV12 )
!= ( cartesian_product2 @ SY45 @ SY46 ) )
| ( SV7 = SY45 )
| ( SV7 = empty_set )
| ( SV12 = empty_set ) )
| ~ ! [SY47: $i,SY48: $i] :
( ( ( cartesian_product2 @ SV7 @ SV12 )
!= ( cartesian_product2 @ SY47 @ SY48 ) )
| ( SV12 = SY48 )
| ( SV7 = empty_set )
| ( SV12 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(76,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ! [SY49: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ SV4 @ SV9 ) @ ( set_intersection2 @ SV13 @ SY49 ) )
= ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV13 ) @ ( cartesian_product2 @ SV9 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(77,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV11 ) )
= $true )
| ( ( ( set_intersection2 @ SV6 @ SV11 )
= SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(78,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( cartesian_product2 @ SX0 @ SX1 )
!= empty_set )
| ( SX0 = empty_set )
| ( SX1 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(79,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)],[72]) ).
thf(80,plain,
( ( ~ ( subset @ sK1_A @ sK3_SY29 )
| ~ ( subset @ sK2_SY26 @ sK4_SY31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(81,plain,
( ( ( ( cartesian_product2 @ sK1_A @ sK2_SY26 )
!= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(82,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ! [SY45: $i] :
( ! [SY46: $i] :
( ( cartesian_product2 @ SV7 @ SV12 )
!= ( cartesian_product2 @ SY45 @ SY46 ) )
| ( SV7 = SY45 )
| ( SV7 = empty_set )
| ( SV12 = empty_set ) )
| ~ ! [SY47: $i,SY48: $i] :
( ( ( cartesian_product2 @ SV7 @ SV12 )
!= ( cartesian_product2 @ SY47 @ SY48 ) )
| ( SV12 = SY48 )
| ( SV7 = empty_set )
| ( SV12 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(83,plain,
! [SV14: $i,SV13: $i,SV9: $i,SV4: $i] :
( ( ( cartesian_product2 @ ( set_intersection2 @ SV4 @ SV9 ) @ ( set_intersection2 @ SV13 @ SV14 ) )
= ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV13 ) @ ( cartesian_product2 @ SV9 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(84,plain,
! [SV11: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV11 )
= $false )
| ( ( ( set_intersection2 @ SV6 @ SV11 )
= SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(85,plain,
! [SV15: $i] :
( ( ! [SY50: $i] :
( ( ( cartesian_product2 @ SV15 @ SY50 )
!= empty_set )
| ( SV15 = empty_set )
| ( SY50 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(86,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)],[79]) ).
thf(87,plain,
( ( ( ~ ( subset @ sK1_A @ sK3_SY29 ) )
= $true )
| ( ( ~ ( subset @ sK2_SY26 @ sK4_SY31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(88,plain,
( ( ( cartesian_product2 @ sK1_A @ sK2_SY26 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(89,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ! [SY45: $i] :
( ! [SY46: $i] :
( ( cartesian_product2 @ SV7 @ SV12 )
!= ( cartesian_product2 @ SY45 @ SY46 ) )
| ( SV7 = SY45 )
| ( SV7 = empty_set )
| ( SV12 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(90,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ! [SY47: $i,SY48: $i] :
( ( ( cartesian_product2 @ SV7 @ SV12 )
!= ( cartesian_product2 @ SY47 @ SY48 ) )
| ( SV12 = SY48 )
| ( SV7 = empty_set )
| ( SV12 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(91,plain,
! [SV16: $i,SV15: $i] :
( ( ( ( cartesian_product2 @ SV15 @ SV16 )
!= empty_set )
| ( SV15 = empty_set )
| ( SV16 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(92,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(93,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != empty_set )
| ( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(94,plain,
( ( ( subset @ sK1_A @ sK3_SY29 )
= $false )
| ( ( ~ ( subset @ sK2_SY26 @ sK4_SY31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(95,plain,
! [SV12: $i,SV7: $i] :
( ( ! [SY45: $i] :
( ! [SY46: $i] :
( ( cartesian_product2 @ SV7 @ SV12 )
!= ( cartesian_product2 @ SY45 @ SY46 ) )
| ( SV7 = SY45 )
| ( SV7 = empty_set )
| ( SV12 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(96,plain,
! [SV12: $i,SV7: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ( ( cartesian_product2 @ SV7 @ SV12 )
!= ( cartesian_product2 @ SY47 @ SY48 ) )
| ( SV12 = SY48 )
| ( SV7 = empty_set )
| ( SV12 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(97,plain,
! [SV16: $i,SV15: $i] :
( ( ( ( ( cartesian_product2 @ SV15 @ SV16 )
!= empty_set ) )
= $true )
| ( ( ( SV15 = empty_set )
| ( SV16 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(98,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(99,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != empty_set )
| ( ( cartesian_product2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(100,plain,
( ( ( subset @ sK2_SY26 @ sK4_SY31 )
= $false )
| ( ( subset @ sK1_A @ sK3_SY29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV17: $i,SV12: $i,SV7: $i] :
( ( ! [SY51: $i] :
( ( cartesian_product2 @ SV7 @ SV12 )
!= ( cartesian_product2 @ SV17 @ SY51 ) )
| ( SV7 = SV17 )
| ( SV7 = empty_set )
| ( SV12 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(102,plain,
! [SV18: $i,SV12: $i,SV7: $i] :
( ( ! [SY52: $i] :
( ( ( cartesian_product2 @ SV7 @ SV12 )
!= ( cartesian_product2 @ SV18 @ SY52 ) )
| ( SV12 = SY52 )
| ( SV7 = empty_set )
| ( SV12 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(103,plain,
! [SV16: $i,SV15: $i] :
( ( ( ( cartesian_product2 @ SV15 @ SV16 )
= empty_set )
= $false )
| ( ( ( SV15 = empty_set )
| ( SV16 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(104,plain,
! [SV19: $i] :
( ( ( SV19 != empty_set )
| ! [SY53: $i] :
( ( cartesian_product2 @ SV19 @ SY53 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(105,plain,
! [SV20: $i] :
( ( ! [SY54: $i] :
( ( SY54 != empty_set )
| ( ( cartesian_product2 @ SV20 @ SY54 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(106,plain,
! [SV17: $i,SV12: $i,SV7: $i] :
( ( ( ! [SY51: $i] :
( ( cartesian_product2 @ SV7 @ SV12 )
!= ( cartesian_product2 @ SV17 @ SY51 ) ) )
= $true )
| ( ( ( SV7 = SV17 )
| ( SV7 = empty_set )
| ( SV12 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(107,plain,
! [SV21: $i,SV18: $i,SV12: $i,SV7: $i] :
( ( ( ( cartesian_product2 @ SV7 @ SV12 )
!= ( cartesian_product2 @ SV18 @ SV21 ) )
| ( SV12 = SV21 )
| ( SV7 = empty_set )
| ( SV12 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(108,plain,
! [SV16: $i,SV15: $i] :
( ( ( SV15 = empty_set )
= $true )
| ( ( SV16 = empty_set )
= $true )
| ( ( ( cartesian_product2 @ SV15 @ SV16 )
= empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(109,plain,
! [SV19: $i] :
( ( ( ( SV19 != empty_set ) )
= $true )
| ( ( ! [SY53: $i] :
( ( cartesian_product2 @ SV19 @ SY53 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(110,plain,
! [SV20: $i,SV22: $i] :
( ( ( SV22 != empty_set )
| ( ( cartesian_product2 @ SV20 @ SV22 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(111,plain,
! [SV23: $i,SV17: $i,SV12: $i,SV7: $i] :
( ( ( ( ( cartesian_product2 @ SV7 @ SV12 )
!= ( cartesian_product2 @ SV17 @ SV23 ) ) )
= $true )
| ( ( ( SV7 = SV17 )
| ( SV7 = empty_set )
| ( SV12 = empty_set ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(112,plain,
! [SV21: $i,SV18: $i,SV12: $i,SV7: $i] :
( ( ( ( ( cartesian_product2 @ SV7 @ SV12 )
!= ( cartesian_product2 @ SV18 @ SV21 ) ) )
= $true )
| ( ( ( SV12 = SV21 )
| ( SV7 = empty_set )
| ( SV12 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(113,plain,
! [SV19: $i] :
( ( ( SV19 = empty_set )
= $false )
| ( ( ! [SY53: $i] :
( ( cartesian_product2 @ SV19 @ SY53 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(114,plain,
! [SV20: $i,SV22: $i] :
( ( ( ( SV22 != empty_set ) )
= $true )
| ( ( ( cartesian_product2 @ SV20 @ SV22 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(115,plain,
! [SV23: $i,SV17: $i,SV12: $i,SV7: $i] :
( ( ( ( cartesian_product2 @ SV7 @ SV12 )
= ( cartesian_product2 @ SV17 @ SV23 ) )
= $false )
| ( ( ( SV7 = SV17 )
| ( SV7 = empty_set )
| ( SV12 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(116,plain,
! [SV21: $i,SV18: $i,SV12: $i,SV7: $i] :
( ( ( ( cartesian_product2 @ SV7 @ SV12 )
= ( cartesian_product2 @ SV18 @ SV21 ) )
= $false )
| ( ( ( SV12 = SV21 )
| ( SV7 = empty_set )
| ( SV12 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(117,plain,
! [SV24: $i,SV19: $i] :
( ( ( ( cartesian_product2 @ SV19 @ SV24 )
= empty_set )
= $true )
| ( ( SV19 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(118,plain,
! [SV20: $i,SV22: $i] :
( ( ( SV22 = empty_set )
= $false )
| ( ( ( cartesian_product2 @ SV20 @ SV22 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(119,plain,
! [SV23: $i,SV12: $i,SV17: $i,SV7: $i] :
( ( ( SV7 = SV17 )
= $true )
| ( ( ( SV7 = empty_set )
| ( SV12 = empty_set ) )
= $true )
| ( ( ( cartesian_product2 @ SV7 @ SV12 )
= ( cartesian_product2 @ SV17 @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(120,plain,
! [SV18: $i,SV7: $i,SV21: $i,SV12: $i] :
( ( ( SV12 = SV21 )
= $true )
| ( ( ( SV7 = empty_set )
| ( SV12 = empty_set ) )
= $true )
| ( ( ( cartesian_product2 @ SV7 @ SV12 )
= ( cartesian_product2 @ SV18 @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(121,plain,
! [SV23: $i,SV17: $i,SV12: $i,SV7: $i] :
( ( ( SV7 = empty_set )
= $true )
| ( ( SV12 = empty_set )
= $true )
| ( ( SV7 = SV17 )
= $true )
| ( ( ( cartesian_product2 @ SV7 @ SV12 )
= ( cartesian_product2 @ SV17 @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(122,plain,
! [SV18: $i,SV21: $i,SV12: $i,SV7: $i] :
( ( ( SV7 = empty_set )
= $true )
| ( ( SV12 = empty_set )
= $true )
| ( ( SV12 = SV21 )
= $true )
| ( ( ( cartesian_product2 @ SV7 @ SV12 )
= ( cartesian_product2 @ SV18 @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(123,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[42,122,121,118,117,108,100,88,84,83,69,67,60,59,58,52,44]) ).
thf(124,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET984+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 06:37:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 11
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.19/0.35 (rf:0,axioms:11,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:13,loop_count:0,foatp_calls:0,translation:fof_full).......
% 0.40/0.58
% 0.40/0.58 ********************************
% 0.40/0.58 * All subproblems solved! *
% 0.40/0.58 ********************************
% 0.40/0.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,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:123,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.40/0.58
% 0.40/0.58 %**** Beginning of derivation protocol ****
% 0.40/0.58 % SZS output start CNFRefutation
% See solution above
% 0.40/0.59
% 0.40/0.59 %**** End of derivation protocol ****
% 0.40/0.59 %**** no. of clauses in derivation: 124 ****
% 0.40/0.59 %**** clause counter: 123 ****
% 0.40/0.59
% 0.40/0.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,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:123,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------