TSTP Solution File: SEU134+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU134+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 : n018.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 12:06:57 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 23
% Syntax : Number of formulae : 173 ( 126 unt; 9 typ; 0 def)
% Number of atoms : 677 ( 289 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 751 ( 160 ~; 111 |; 13 &; 452 @)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 217 ( 0 ^ 213 !; 4 ?; 217 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY17,type,
sK2_SY17: $i ).
thf(tp_sK3_A,type,
sK3_A: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(2,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(3,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(4,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(5,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(6,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(7,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(8,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(10,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(11,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(12,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(14,conjecture,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(15,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
$true = $true,
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
$true = $true,
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(27,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(29,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(30,plain,
( ( ! [SY17: $i] :
( ( ( set_difference @ sK1_A @ SY17 )
= empty_set )
<=> ( subset @ sK1_A @ SY17 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(31,plain,
( ( ( ( set_difference @ sK1_A @ sK2_SY17 )
= empty_set )
<=> ( subset @ sK1_A @ sK2_SY17 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(32,plain,
( ( ( ( set_difference @ sK1_A @ sK2_SY17 )
= empty_set )
=> ( subset @ sK1_A @ sK2_SY17 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[31]) ).
thf(33,plain,
( ( ( subset @ sK1_A @ sK2_SY17 )
=> ( ( set_difference @ sK1_A @ sK2_SY17 )
= empty_set ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[31]) ).
thf(34,plain,
( ( ~ ( ( ( set_difference @ sK1_A @ sK2_SY17 )
= empty_set )
=> ( subset @ sK1_A @ sK2_SY17 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(35,plain,
( ( ~ ( ( subset @ sK1_A @ sK2_SY17 )
=> ( ( set_difference @ sK1_A @ sK2_SY17 )
= empty_set ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(36,plain,
( ( ( ( set_difference @ sK1_A @ sK2_SY17 )
= empty_set )
& ~ ( subset @ sK1_A @ sK2_SY17 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(37,plain,
( ( ( subset @ sK1_A @ sK2_SY17 )
& ( ( set_difference @ sK1_A @ sK2_SY17 )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(39,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(40,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(43,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(44,plain,
( ( empty @ sK4_A )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(47,plain,
( ( empty @ sK4_A )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(48,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(50,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(51,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(52,plain,
$true = $true,
inference(copy,[status(thm)],[23]) ).
thf(53,plain,
$true = $true,
inference(copy,[status(thm)],[22]) ).
thf(54,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(57,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(59,plain,
( ( ( ( set_difference @ sK1_A @ sK2_SY17 )
= empty_set )
& ~ ( subset @ sK1_A @ sK2_SY17 ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(60,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(61,plain,
( ( ~ ( ( ( set_difference @ sK1_A @ sK2_SY17 )
!= empty_set )
| ~ ~ ( subset @ sK1_A @ sK2_SY17 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(62,plain,
! [SV1: $i] :
( ( ! [SY18: $i] :
( ~ ( in @ SV1 @ SY18 )
| ~ ( in @ SY18 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(63,plain,
( ( empty @ sK3_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(64,plain,
! [SV2: $i] :
( ( ! [SY19: $i] :
( ~ ( empty @ SY19 )
| ~ ( in @ SV2 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(65,plain,
! [SV3: $i] :
( ( ! [SY20: $i] :
( ( SV3 = SY20 )
| ~ ( empty @ SV3 )
| ~ ( empty @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(66,plain,
! [SV4: $i] :
( ( subset @ SV4 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(67,plain,
! [SV5: $i] :
( ( ( set_difference @ SV5 @ empty_set )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(68,plain,
! [SV6: $i] :
( ( ( set_difference @ empty_set @ SV6 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(69,plain,
! [SV7: $i] :
( ( ~ ( empty @ SV7 )
| ( SV7 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(70,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(71,plain,
( ( ( ( set_difference @ sK1_A @ sK2_SY17 )
!= empty_set )
| ~ ~ ( subset @ sK1_A @ sK2_SY17 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(72,plain,
! [SV8: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV8 )
| ~ ( in @ SV8 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(73,plain,
! [SV2: $i,SV9: $i] :
( ( ~ ( empty @ SV9 )
| ~ ( in @ SV2 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(74,plain,
! [SV10: $i,SV3: $i] :
( ( ( SV3 = SV10 )
| ~ ( empty @ SV3 )
| ~ ( empty @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(75,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ SV7 ) )
= $true )
| ( ( SV7 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(76,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(77,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(78,plain,
( ( ( ( set_difference @ sK1_A @ sK2_SY17 )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(79,plain,
( ( ~ ~ ( subset @ sK1_A @ sK2_SY17 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(80,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV8 ) )
= $true )
| ( ( ~ ( in @ SV8 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(81,plain,
! [SV2: $i,SV9: $i] :
( ( ( ~ ( empty @ SV9 ) )
= $true )
| ( ( ~ ( in @ SV2 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(82,plain,
! [SV10: $i,SV3: $i] :
( ( ( ( SV3 = SV10 )
| ~ ( empty @ SV3 ) )
= $true )
| ( ( ~ ( empty @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(83,plain,
! [SV7: $i] :
( ( ( empty @ SV7 )
= $false )
| ( ( SV7 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(84,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(85,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(86,plain,
( ( ( set_difference @ sK1_A @ sK2_SY17 )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(87,plain,
( ( ~ ( subset @ sK1_A @ sK2_SY17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(88,plain,
! [SV8: $i,SV1: $i] :
( ( ( in @ SV1 @ SV8 )
= $false )
| ( ( ~ ( in @ SV8 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV2: $i,SV9: $i] :
( ( ( empty @ SV9 )
= $false )
| ( ( ~ ( in @ SV2 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV10: $i,SV3: $i] :
( ( ( SV3 = SV10 )
= $true )
| ( ( ~ ( empty @ SV3 ) )
= $true )
| ( ( ~ ( empty @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV11: $i] :
( ( ! [SY21: $i] :
( ( ( set_difference @ SV11 @ SY21 )
!= empty_set )
| ( subset @ SV11 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(92,plain,
! [SV12: $i] :
( ( ! [SY22: $i] :
( ~ ( subset @ SV12 @ SY22 )
| ( ( set_difference @ SV12 @ SY22 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(93,plain,
( ( subset @ sK1_A @ sK2_SY17 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV1: $i,SV8: $i] :
( ( ( in @ SV8 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV9: $i,SV2: $i] :
( ( ( in @ SV2 @ SV9 )
= $false )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV10: $i,SV3: $i] :
( ( ( empty @ SV3 )
= $false )
| ( ( SV3 = SV10 )
= $true )
| ( ( ~ ( empty @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(97,plain,
! [SV13: $i,SV11: $i] :
( ( ( ( set_difference @ SV11 @ SV13 )
!= empty_set )
| ( subset @ SV11 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(98,plain,
! [SV14: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV14 )
| ( ( set_difference @ SV12 @ SV14 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(99,plain,
! [SV3: $i,SV10: $i] :
( ( ( empty @ SV10 )
= $false )
| ( ( SV3 = SV10 )
= $true )
| ( ( empty @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(100,plain,
! [SV13: $i,SV11: $i] :
( ( ( ( ( set_difference @ SV11 @ SV13 )
!= empty_set ) )
= $true )
| ( ( subset @ SV11 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(101,plain,
! [SV14: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV14 ) )
= $true )
| ( ( ( set_difference @ SV12 @ SV14 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(102,plain,
! [SV13: $i,SV11: $i] :
( ( ( ( set_difference @ SV11 @ SV13 )
= empty_set )
= $false )
| ( ( subset @ SV11 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(103,plain,
! [SV14: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV14 )
= $false )
| ( ( ( set_difference @ SV12 @ SV14 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(104,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[47,103,102,99,95,94,93,86,83,68,67,66,63,54,53,52]) ).
thf(105,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(106,plain,
( ( empty @ sK4_A )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(107,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(109,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(110,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(111,plain,
$true = $true,
inference(copy,[status(thm)],[23]) ).
thf(112,plain,
$true = $true,
inference(copy,[status(thm)],[22]) ).
thf(113,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(114,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(115,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(116,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(117,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(118,plain,
( ( ( subset @ sK1_A @ sK2_SY17 )
& ( ( set_difference @ sK1_A @ sK2_SY17 )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(119,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(120,plain,
( ( ~ ( ~ ( subset @ sK1_A @ sK2_SY17 )
| ~ ( ( ( set_difference @ sK1_A @ sK2_SY17 )
!= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(121,plain,
! [SV15: $i] :
( ( ! [SY23: $i] :
( ~ ( in @ SV15 @ SY23 )
| ~ ( in @ SY23 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(122,plain,
( ( empty @ sK3_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(123,plain,
! [SV16: $i] :
( ( ! [SY24: $i] :
( ~ ( empty @ SY24 )
| ~ ( in @ SV16 @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(124,plain,
! [SV17: $i] :
( ( ! [SY25: $i] :
( ( SV17 = SY25 )
| ~ ( empty @ SV17 )
| ~ ( empty @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(125,plain,
! [SV18: $i] :
( ( subset @ SV18 @ SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(126,plain,
! [SV19: $i] :
( ( ( set_difference @ SV19 @ empty_set )
= SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(127,plain,
! [SV20: $i] :
( ( ( set_difference @ empty_set @ SV20 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV21: $i] :
( ( ~ ( empty @ SV21 )
| ( SV21 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(129,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(130,plain,
( ( ~ ( subset @ sK1_A @ sK2_SY17 )
| ~ ( ( ( set_difference @ sK1_A @ sK2_SY17 )
!= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(131,plain,
! [SV22: $i,SV15: $i] :
( ( ~ ( in @ SV15 @ SV22 )
| ~ ( in @ SV22 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(132,plain,
! [SV16: $i,SV23: $i] :
( ( ~ ( empty @ SV23 )
| ~ ( in @ SV16 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(133,plain,
! [SV24: $i,SV17: $i] :
( ( ( SV17 = SV24 )
| ~ ( empty @ SV17 )
| ~ ( empty @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(134,plain,
! [SV21: $i] :
( ( ( ~ ( empty @ SV21 ) )
= $true )
| ( ( SV21 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(135,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(136,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(137,plain,
( ( ~ ( subset @ sK1_A @ sK2_SY17 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(138,plain,
( ( ~ ( ( ( set_difference @ sK1_A @ sK2_SY17 )
!= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(139,plain,
! [SV22: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ SV22 ) )
= $true )
| ( ( ~ ( in @ SV22 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(140,plain,
! [SV16: $i,SV23: $i] :
( ( ( ~ ( empty @ SV23 ) )
= $true )
| ( ( ~ ( in @ SV16 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(141,plain,
! [SV24: $i,SV17: $i] :
( ( ( ( SV17 = SV24 )
| ~ ( empty @ SV17 ) )
= $true )
| ( ( ~ ( empty @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(142,plain,
! [SV21: $i] :
( ( ( empty @ SV21 )
= $false )
| ( ( SV21 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(143,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(144,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(145,plain,
( ( subset @ sK1_A @ sK2_SY17 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(146,plain,
( ( ( ( set_difference @ sK1_A @ sK2_SY17 )
!= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(147,plain,
! [SV22: $i,SV15: $i] :
( ( ( in @ SV15 @ SV22 )
= $false )
| ( ( ~ ( in @ SV22 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(148,plain,
! [SV16: $i,SV23: $i] :
( ( ( empty @ SV23 )
= $false )
| ( ( ~ ( in @ SV16 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(149,plain,
! [SV24: $i,SV17: $i] :
( ( ( SV17 = SV24 )
= $true )
| ( ( ~ ( empty @ SV17 ) )
= $true )
| ( ( ~ ( empty @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(150,plain,
! [SV25: $i] :
( ( ! [SY26: $i] :
( ( ( set_difference @ SV25 @ SY26 )
!= empty_set )
| ( subset @ SV25 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(151,plain,
! [SV26: $i] :
( ( ! [SY27: $i] :
( ~ ( subset @ SV26 @ SY27 )
| ( ( set_difference @ SV26 @ SY27 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(152,plain,
( ( ( set_difference @ sK1_A @ sK2_SY17 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(153,plain,
! [SV15: $i,SV22: $i] :
( ( ( in @ SV22 @ SV15 )
= $false )
| ( ( in @ SV15 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(154,plain,
! [SV23: $i,SV16: $i] :
( ( ( in @ SV16 @ SV23 )
= $false )
| ( ( empty @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(155,plain,
! [SV24: $i,SV17: $i] :
( ( ( empty @ SV17 )
= $false )
| ( ( SV17 = SV24 )
= $true )
| ( ( ~ ( empty @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(156,plain,
! [SV27: $i,SV25: $i] :
( ( ( ( set_difference @ SV25 @ SV27 )
!= empty_set )
| ( subset @ SV25 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(157,plain,
! [SV28: $i,SV26: $i] :
( ( ~ ( subset @ SV26 @ SV28 )
| ( ( set_difference @ SV26 @ SV28 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(158,plain,
! [SV17: $i,SV24: $i] :
( ( ( empty @ SV24 )
= $false )
| ( ( SV17 = SV24 )
= $true )
| ( ( empty @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(159,plain,
! [SV27: $i,SV25: $i] :
( ( ( ( ( set_difference @ SV25 @ SV27 )
!= empty_set ) )
= $true )
| ( ( subset @ SV25 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(160,plain,
! [SV28: $i,SV26: $i] :
( ( ( ~ ( subset @ SV26 @ SV28 ) )
= $true )
| ( ( ( set_difference @ SV26 @ SV28 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(161,plain,
! [SV27: $i,SV25: $i] :
( ( ( ( set_difference @ SV25 @ SV27 )
= empty_set )
= $false )
| ( ( subset @ SV25 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(162,plain,
! [SV28: $i,SV26: $i] :
( ( ( subset @ SV26 @ SV28 )
= $false )
| ( ( ( set_difference @ SV26 @ SV28 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(163,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[106,162,161,158,154,153,152,145,142,127,126,125,122,113,112,111]) ).
thf(164,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[163,104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU134+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 20 12:10:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 13
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:13,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:15,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.20/0.43
% 0.20/0.43 ********************************
% 0.20/0.43 * All subproblems solved! *
% 0.20/0.43 ********************************
% 0.20/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,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:163,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.44
% 0.20/0.44 %**** Beginning of derivation protocol ****
% 0.20/0.44 % SZS output start CNFRefutation
% See solution above
% 0.20/0.44
% 0.20/0.44 %**** End of derivation protocol ****
% 0.20/0.44 %**** no. of clauses in derivation: 164 ****
% 0.20/0.44 %**** clause counter: 163 ****
% 0.20/0.44
% 0.20/0.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,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:163,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------