TSTP Solution File: SET978+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET978+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 : n020.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 03:06:41 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 108 ( 76 unt; 10 typ; 0 def)
% Number of atoms : 416 ( 133 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 883 ( 95 ~; 76 |; 11 &; 688 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 240 ( 0 ^ 236 !; 4 ?; 240 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i ).
thf(tp_sK3_SY17,type,
sK3_SY17: $i ).
thf(tp_sK4_SY19,type,
sK4_SY19: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( disjoint @ ( singleton @ A ) @ ( singleton @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( disjoint @ A @ B )
| ( disjoint @ C @ D ) )
=> ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(4,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(5,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(6,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( disjoint @ ( cartesian_product2 @ ( singleton @ A ) @ C ) @ ( cartesian_product2 @ ( singleton @ B ) @ D ) )
& ( disjoint @ ( cartesian_product2 @ C @ ( singleton @ A ) ) @ ( cartesian_product2 @ D @ ( singleton @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_zfmisc_1) ).
thf(7,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( disjoint @ ( cartesian_product2 @ ( singleton @ A ) @ C ) @ ( cartesian_product2 @ ( singleton @ B ) @ D ) )
& ( disjoint @ ( cartesian_product2 @ C @ ( singleton @ A ) ) @ ( cartesian_product2 @ D @ ( singleton @ B ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( disjoint @ ( cartesian_product2 @ ( singleton @ A ) @ C ) @ ( cartesian_product2 @ ( singleton @ B ) @ D ) )
& ( disjoint @ ( cartesian_product2 @ C @ ( singleton @ A ) ) @ ( cartesian_product2 @ D @ ( singleton @ B ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
=> ( disjoint @ ( singleton @ A ) @ ( singleton @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( disjoint @ A @ B )
| ( disjoint @ C @ D ) )
=> ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [SY14: $i,SY15: $i,SY16: $i] :
( ( sK1_A != SY14 )
=> ( ( disjoint @ ( cartesian_product2 @ ( singleton @ sK1_A ) @ SY15 ) @ ( cartesian_product2 @ ( singleton @ SY14 ) @ SY16 ) )
& ( disjoint @ ( cartesian_product2 @ SY15 @ ( singleton @ sK1_A ) ) @ ( cartesian_product2 @ SY16 @ ( singleton @ SY14 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( ! [SY17: $i,SY18: $i] :
( ( sK1_A != sK2_SY14 )
=> ( ( disjoint @ ( cartesian_product2 @ ( singleton @ sK1_A ) @ SY17 ) @ ( cartesian_product2 @ ( singleton @ sK2_SY14 ) @ SY18 ) )
& ( disjoint @ ( cartesian_product2 @ SY17 @ ( singleton @ sK1_A ) ) @ ( cartesian_product2 @ SY18 @ ( singleton @ sK2_SY14 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( ! [SY19: $i] :
( ( sK1_A != sK2_SY14 )
=> ( ( disjoint @ ( cartesian_product2 @ ( singleton @ sK1_A ) @ sK3_SY17 ) @ ( cartesian_product2 @ ( singleton @ sK2_SY14 ) @ SY19 ) )
& ( disjoint @ ( cartesian_product2 @ sK3_SY17 @ ( singleton @ sK1_A ) ) @ ( cartesian_product2 @ SY19 @ ( singleton @ sK2_SY14 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(17,plain,
( ( ( sK1_A != sK2_SY14 )
=> ( ( disjoint @ ( cartesian_product2 @ ( singleton @ sK1_A ) @ sK3_SY17 ) @ ( cartesian_product2 @ ( singleton @ sK2_SY14 ) @ sK4_SY19 ) )
& ( disjoint @ ( cartesian_product2 @ sK3_SY17 @ ( singleton @ sK1_A ) ) @ ( cartesian_product2 @ sK4_SY19 @ ( singleton @ sK2_SY14 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(18,plain,
( ( ( sK1_A != sK2_SY14 ) )
= $true ),
inference(standard_cnf,[status(thm)],[17]) ).
thf(19,plain,
( ( ( disjoint @ ( cartesian_product2 @ ( singleton @ sK1_A ) @ sK3_SY17 ) @ ( cartesian_product2 @ ( singleton @ sK2_SY14 ) @ sK4_SY19 ) )
& ( disjoint @ ( cartesian_product2 @ sK3_SY17 @ ( singleton @ sK1_A ) ) @ ( cartesian_product2 @ sK4_SY19 @ ( singleton @ sK2_SY14 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[17]) ).
thf(20,plain,
( ( disjoint @ ( cartesian_product2 @ ( singleton @ sK1_A ) @ sK3_SY17 ) @ ( cartesian_product2 @ ( singleton @ sK2_SY14 ) @ sK4_SY19 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[19]) ).
thf(21,plain,
( ( disjoint @ ( cartesian_product2 @ sK3_SY17 @ ( singleton @ sK1_A ) ) @ ( cartesian_product2 @ sK4_SY19 @ ( singleton @ sK2_SY14 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[19]) ).
thf(22,plain,
( ( ~ ( disjoint @ ( cartesian_product2 @ ( singleton @ sK1_A ) @ sK3_SY17 ) @ ( cartesian_product2 @ ( singleton @ sK2_SY14 ) @ sK4_SY19 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[20]) ).
thf(23,plain,
( ( ~ ( disjoint @ ( cartesian_product2 @ sK3_SY17 @ ( singleton @ sK1_A ) ) @ ( cartesian_product2 @ sK4_SY19 @ ( singleton @ sK2_SY14 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(24,plain,
( ( ( sK1_A != sK2_SY14 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ( disjoint @ ( singleton @ A ) @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( disjoint @ A @ B )
| ! [C: $i,D: $i] : ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) )
& ! [C: $i,D: $i] :
( ~ ( disjoint @ C @ D )
| ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(28,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(29,plain,
( ( empty @ sK6_A )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(30,plain,
( ( empty @ sK6_A )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(31,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(33,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( disjoint @ A @ B )
| ! [C: $i,D: $i] : ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) )
& ! [C: $i,D: $i] :
( ~ ( disjoint @ C @ D )
| ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ( disjoint @ ( singleton @ A ) @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(35,plain,
( ( ( sK1_A != sK2_SY14 ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(36,plain,
( ( ~ ( disjoint @ ( cartesian_product2 @ ( singleton @ sK1_A ) @ sK3_SY17 ) @ ( cartesian_product2 @ ( singleton @ sK2_SY14 ) @ sK4_SY19 ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(37,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( disjoint @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] : ( disjoint @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( disjoint @ SX2 @ SX3 )
| ( disjoint @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(38,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(39,plain,
! [SV1: $i] :
( ( ! [SY20: $i] :
( ~ ( disjoint @ SV1 @ SY20 )
| ( disjoint @ SY20 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(40,plain,
! [SV2: $i] :
( ( ! [SY21: $i] :
( ( SV2 = SY21 )
| ( disjoint @ ( singleton @ SV2 ) @ ( singleton @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(41,plain,
( ( sK1_A = sK2_SY14 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(42,plain,
( ( disjoint @ ( cartesian_product2 @ ( singleton @ sK1_A ) @ sK3_SY17 ) @ ( cartesian_product2 @ ( singleton @ sK2_SY14 ) @ sK4_SY19 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV3: $i] :
( ( ! [SY22: $i] :
~ ( ~ ( ~ ( disjoint @ SV3 @ SY22 )
| ! [SY23: $i,SY24: $i] : ( disjoint @ ( cartesian_product2 @ SV3 @ SY23 ) @ ( cartesian_product2 @ SY22 @ SY24 ) ) )
| ~ ! [SY25: $i,SY26: $i] :
( ~ ( disjoint @ SY25 @ SY26 )
| ( disjoint @ ( cartesian_product2 @ SV3 @ SY25 ) @ ( cartesian_product2 @ SY22 @ SY26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( disjoint @ SV1 @ SV4 )
| ( disjoint @ SV4 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV5: $i,SV2: $i] :
( ( ( SV2 = SV5 )
| ( disjoint @ ( singleton @ SV2 ) @ ( singleton @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(46,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( disjoint @ SV3 @ SV6 )
| ! [SY27: $i,SY28: $i] : ( disjoint @ ( cartesian_product2 @ SV3 @ SY27 ) @ ( cartesian_product2 @ SV6 @ SY28 ) ) )
| ~ ! [SY29: $i,SY30: $i] :
( ~ ( disjoint @ SY29 @ SY30 )
| ( disjoint @ ( cartesian_product2 @ SV3 @ SY29 ) @ ( cartesian_product2 @ SV6 @ SY30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( disjoint @ SV1 @ SV4 ) )
= $true )
| ( ( disjoint @ SV4 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV5: $i,SV2: $i] :
( ( ( SV2 = SV5 )
= $true )
| ( ( disjoint @ ( singleton @ SV2 ) @ ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ( disjoint @ SV3 @ SV6 )
| ! [SY27: $i,SY28: $i] : ( disjoint @ ( cartesian_product2 @ SV3 @ SY27 ) @ ( cartesian_product2 @ SV6 @ SY28 ) ) )
| ~ ! [SY29: $i,SY30: $i] :
( ~ ( disjoint @ SY29 @ SY30 )
| ( disjoint @ ( cartesian_product2 @ SV3 @ SY29 ) @ ( cartesian_product2 @ SV6 @ SY30 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(50,plain,
! [SV4: $i,SV1: $i] :
( ( ( disjoint @ SV1 @ SV4 )
= $false )
| ( ( disjoint @ SV4 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ( disjoint @ SV3 @ SV6 )
| ! [SY27: $i,SY28: $i] : ( disjoint @ ( cartesian_product2 @ SV3 @ SY27 ) @ ( cartesian_product2 @ SV6 @ SY28 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(52,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ! [SY29: $i,SY30: $i] :
( ~ ( disjoint @ SY29 @ SY30 )
| ( disjoint @ ( cartesian_product2 @ SV3 @ SY29 ) @ ( cartesian_product2 @ SV6 @ SY30 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(53,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( disjoint @ SV3 @ SV6 )
| ! [SY27: $i,SY28: $i] : ( disjoint @ ( cartesian_product2 @ SV3 @ SY27 ) @ ( cartesian_product2 @ SV6 @ SY28 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(54,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ( disjoint @ SY29 @ SY30 )
| ( disjoint @ ( cartesian_product2 @ SV3 @ SY29 ) @ ( cartesian_product2 @ SV6 @ SY30 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(55,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( disjoint @ SV3 @ SV6 ) )
= $true )
| ( ( ! [SY27: $i,SY28: $i] : ( disjoint @ ( cartesian_product2 @ SV3 @ SY27 ) @ ( cartesian_product2 @ SV6 @ SY28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ! [SY31: $i] :
( ~ ( disjoint @ SV7 @ SY31 )
| ( disjoint @ ( cartesian_product2 @ SV3 @ SV7 ) @ ( cartesian_product2 @ SV6 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV6: $i,SV3: $i] :
( ( ( disjoint @ SV3 @ SV6 )
= $false )
| ( ( ! [SY27: $i,SY28: $i] : ( disjoint @ ( cartesian_product2 @ SV3 @ SY27 ) @ ( cartesian_product2 @ SV6 @ SY28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV6: $i,SV3: $i,SV8: $i,SV7: $i] :
( ( ~ ( disjoint @ SV7 @ SV8 )
| ( disjoint @ ( cartesian_product2 @ SV3 @ SV7 ) @ ( cartesian_product2 @ SV6 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV6: $i,SV9: $i,SV3: $i] :
( ( ( ! [SY32: $i] : ( disjoint @ ( cartesian_product2 @ SV3 @ SV9 ) @ ( cartesian_product2 @ SV6 @ SY32 ) ) )
= $true )
| ( ( disjoint @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV6: $i,SV3: $i,SV8: $i,SV7: $i] :
( ( ( ~ ( disjoint @ SV7 @ SV8 ) )
= $true )
| ( ( disjoint @ ( cartesian_product2 @ SV3 @ SV7 ) @ ( cartesian_product2 @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV10: $i,SV6: $i,SV9: $i,SV3: $i] :
( ( ( disjoint @ ( cartesian_product2 @ SV3 @ SV9 ) @ ( cartesian_product2 @ SV6 @ SV10 ) )
= $true )
| ( ( disjoint @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV6: $i,SV3: $i,SV8: $i,SV7: $i] :
( ( ( disjoint @ SV7 @ SV8 )
= $false )
| ( ( disjoint @ ( cartesian_product2 @ SV3 @ SV7 ) @ ( cartesian_product2 @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(63,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,62,61,50,48,42,41,38]) ).
thf(64,plain,
( ( empty @ sK6_A )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(65,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( disjoint @ A @ B )
| ! [C: $i,D: $i] : ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) )
& ! [C: $i,D: $i] :
( ~ ( disjoint @ C @ D )
| ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ( disjoint @ ( singleton @ A ) @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(69,plain,
( ( ( sK1_A != sK2_SY14 ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(70,plain,
( ( ~ ( disjoint @ ( cartesian_product2 @ sK3_SY17 @ ( singleton @ sK1_A ) ) @ ( cartesian_product2 @ sK4_SY19 @ ( singleton @ sK2_SY14 ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(71,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( disjoint @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] : ( disjoint @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( disjoint @ SX2 @ SX3 )
| ( disjoint @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(72,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(73,plain,
! [SV11: $i] :
( ( ! [SY33: $i] :
( ~ ( disjoint @ SV11 @ SY33 )
| ( disjoint @ SY33 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(74,plain,
! [SV12: $i] :
( ( ! [SY34: $i] :
( ( SV12 = SY34 )
| ( disjoint @ ( singleton @ SV12 ) @ ( singleton @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(75,plain,
( ( sK1_A = sK2_SY14 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(76,plain,
( ( disjoint @ ( cartesian_product2 @ sK3_SY17 @ ( singleton @ sK1_A ) ) @ ( cartesian_product2 @ sK4_SY19 @ ( singleton @ sK2_SY14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV13: $i] :
( ( ! [SY35: $i] :
~ ( ~ ( ~ ( disjoint @ SV13 @ SY35 )
| ! [SY36: $i,SY37: $i] : ( disjoint @ ( cartesian_product2 @ SV13 @ SY36 ) @ ( cartesian_product2 @ SY35 @ SY37 ) ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ( disjoint @ SY38 @ SY39 )
| ( disjoint @ ( cartesian_product2 @ SV13 @ SY38 ) @ ( cartesian_product2 @ SY35 @ SY39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV14: $i,SV11: $i] :
( ( ~ ( disjoint @ SV11 @ SV14 )
| ( disjoint @ SV14 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(79,plain,
! [SV15: $i,SV12: $i] :
( ( ( SV12 = SV15 )
| ( disjoint @ ( singleton @ SV12 ) @ ( singleton @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV16: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( disjoint @ SV13 @ SV16 )
| ! [SY40: $i,SY41: $i] : ( disjoint @ ( cartesian_product2 @ SV13 @ SY40 ) @ ( cartesian_product2 @ SV16 @ SY41 ) ) )
| ~ ! [SY42: $i,SY43: $i] :
( ~ ( disjoint @ SY42 @ SY43 )
| ( disjoint @ ( cartesian_product2 @ SV13 @ SY42 ) @ ( cartesian_product2 @ SV16 @ SY43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(81,plain,
! [SV14: $i,SV11: $i] :
( ( ( ~ ( disjoint @ SV11 @ SV14 ) )
= $true )
| ( ( disjoint @ SV14 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(82,plain,
! [SV15: $i,SV12: $i] :
( ( ( SV12 = SV15 )
= $true )
| ( ( disjoint @ ( singleton @ SV12 ) @ ( singleton @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV16: $i,SV13: $i] :
( ( ~ ( ~ ( disjoint @ SV13 @ SV16 )
| ! [SY40: $i,SY41: $i] : ( disjoint @ ( cartesian_product2 @ SV13 @ SY40 ) @ ( cartesian_product2 @ SV16 @ SY41 ) ) )
| ~ ! [SY42: $i,SY43: $i] :
( ~ ( disjoint @ SY42 @ SY43 )
| ( disjoint @ ( cartesian_product2 @ SV13 @ SY42 ) @ ( cartesian_product2 @ SV16 @ SY43 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(84,plain,
! [SV14: $i,SV11: $i] :
( ( ( disjoint @ SV11 @ SV14 )
= $false )
| ( ( disjoint @ SV14 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(85,plain,
! [SV16: $i,SV13: $i] :
( ( ~ ( ~ ( disjoint @ SV13 @ SV16 )
| ! [SY40: $i,SY41: $i] : ( disjoint @ ( cartesian_product2 @ SV13 @ SY40 ) @ ( cartesian_product2 @ SV16 @ SY41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(86,plain,
! [SV16: $i,SV13: $i] :
( ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( disjoint @ SY42 @ SY43 )
| ( disjoint @ ( cartesian_product2 @ SV13 @ SY42 ) @ ( cartesian_product2 @ SV16 @ SY43 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(87,plain,
! [SV16: $i,SV13: $i] :
( ( ~ ( disjoint @ SV13 @ SV16 )
| ! [SY40: $i,SY41: $i] : ( disjoint @ ( cartesian_product2 @ SV13 @ SY40 ) @ ( cartesian_product2 @ SV16 @ SY41 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(88,plain,
! [SV16: $i,SV13: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ~ ( disjoint @ SY42 @ SY43 )
| ( disjoint @ ( cartesian_product2 @ SV13 @ SY42 ) @ ( cartesian_product2 @ SV16 @ SY43 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(89,plain,
! [SV16: $i,SV13: $i] :
( ( ( ~ ( disjoint @ SV13 @ SV16 ) )
= $true )
| ( ( ! [SY40: $i,SY41: $i] : ( disjoint @ ( cartesian_product2 @ SV13 @ SY40 ) @ ( cartesian_product2 @ SV16 @ SY41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(90,plain,
! [SV16: $i,SV13: $i,SV17: $i] :
( ( ! [SY44: $i] :
( ~ ( disjoint @ SV17 @ SY44 )
| ( disjoint @ ( cartesian_product2 @ SV13 @ SV17 ) @ ( cartesian_product2 @ SV16 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(91,plain,
! [SV16: $i,SV13: $i] :
( ( ( disjoint @ SV13 @ SV16 )
= $false )
| ( ( ! [SY40: $i,SY41: $i] : ( disjoint @ ( cartesian_product2 @ SV13 @ SY40 ) @ ( cartesian_product2 @ SV16 @ SY41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(92,plain,
! [SV16: $i,SV13: $i,SV18: $i,SV17: $i] :
( ( ~ ( disjoint @ SV17 @ SV18 )
| ( disjoint @ ( cartesian_product2 @ SV13 @ SV17 ) @ ( cartesian_product2 @ SV16 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(93,plain,
! [SV16: $i,SV19: $i,SV13: $i] :
( ( ( ! [SY45: $i] : ( disjoint @ ( cartesian_product2 @ SV13 @ SV19 ) @ ( cartesian_product2 @ SV16 @ SY45 ) ) )
= $true )
| ( ( disjoint @ SV13 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(94,plain,
! [SV16: $i,SV13: $i,SV18: $i,SV17: $i] :
( ( ( ~ ( disjoint @ SV17 @ SV18 ) )
= $true )
| ( ( disjoint @ ( cartesian_product2 @ SV13 @ SV17 ) @ ( cartesian_product2 @ SV16 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(95,plain,
! [SV20: $i,SV16: $i,SV19: $i,SV13: $i] :
( ( ( disjoint @ ( cartesian_product2 @ SV13 @ SV19 ) @ ( cartesian_product2 @ SV16 @ SV20 ) )
= $true )
| ( ( disjoint @ SV13 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(96,plain,
! [SV16: $i,SV13: $i,SV18: $i,SV17: $i] :
( ( ( disjoint @ SV17 @ SV18 )
= $false )
| ( ( disjoint @ ( cartesian_product2 @ SV13 @ SV17 ) @ ( cartesian_product2 @ SV16 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(97,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[64,96,95,84,82,76,75,72]) ).
thf(98,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[97,63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET978+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 16:03:13 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 5
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.34 (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:7,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.19/0.41
% 0.19/0.41 ********************************
% 0.19/0.41 * All subproblems solved! *
% 0.19/0.41 ********************************
% 0.19/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:97,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.42
% 0.19/0.42 %**** Beginning of derivation protocol ****
% 0.19/0.42 % SZS output start CNFRefutation
% See solution above
% 0.19/0.42
% 0.19/0.42 %**** End of derivation protocol ****
% 0.19/0.42 %**** no. of clauses in derivation: 98 ****
% 0.19/0.42 %**** clause counter: 97 ****
% 0.19/0.42
% 0.19/0.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:97,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------