TSTP Solution File: SET902+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET902+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 : n021.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 03:06:05 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 22
% Syntax : Number of formulae : 128 ( 91 unt; 10 typ; 0 def)
% Number of atoms : 554 ( 330 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 819 ( 220 ~; 120 |; 52 &; 421 @)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 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 : 166 ( 0 ^ 162 !; 4 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
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_SY20,type,
sK2_SY20: $i ).
thf(tp_sK3_SY22,type,
sK3_SY22: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(2,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(3,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(4,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(6,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_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_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(12,conjecture,
! [A: $i,B: $i,C: $i] :
~ ( ( ( singleton @ A )
= ( set_union2 @ B @ C ) )
& ~ ( ( B
= ( singleton @ A ) )
& ( C
= ( singleton @ A ) ) )
& ~ ( ( B = empty_set )
& ( C
= ( singleton @ A ) ) )
& ~ ( ( B
= ( singleton @ A ) )
& ( C = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_zfmisc_1) ).
thf(13,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( ( singleton @ A )
= ( set_union2 @ B @ C ) )
& ~ ( ( B
= ( singleton @ A ) )
& ( C
= ( singleton @ A ) ) )
& ~ ( ( B = empty_set )
& ( C
= ( singleton @ A ) ) )
& ~ ( ( B
= ( singleton @ A ) )
& ( C = empty_set ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( ( singleton @ A )
= ( set_union2 @ B @ C ) )
& ~ ( ( B
= ( singleton @ A ) )
& ( C
= ( singleton @ A ) ) )
& ~ ( ( B = empty_set )
& ( C
= ( singleton @ A ) ) )
& ~ ( ( B
= ( singleton @ A ) )
& ( C = empty_set ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $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_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(26,plain,
( ( ! [SY20: $i,SY21: $i] :
~ ( ( ( singleton @ sK1_A )
= ( set_union2 @ SY20 @ SY21 ) )
& ~ ( ( SY20
= ( singleton @ sK1_A ) )
& ( SY21
= ( singleton @ sK1_A ) ) )
& ~ ( ( SY20 = empty_set )
& ( SY21
= ( singleton @ sK1_A ) ) )
& ~ ( ( SY20
= ( singleton @ sK1_A ) )
& ( SY21 = empty_set ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(27,plain,
( ( ! [SY22: $i] :
~ ( ( ( singleton @ sK1_A )
= ( set_union2 @ sK2_SY20 @ SY22 ) )
& ~ ( ( sK2_SY20
= ( singleton @ sK1_A ) )
& ( SY22
= ( singleton @ sK1_A ) ) )
& ~ ( ( sK2_SY20 = empty_set )
& ( SY22
= ( singleton @ sK1_A ) ) )
& ~ ( ( sK2_SY20
= ( singleton @ sK1_A ) )
& ( SY22 = empty_set ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(28,plain,
( ( ~ ( ( ( singleton @ sK1_A )
= ( set_union2 @ sK2_SY20 @ sK3_SY22 ) )
& ~ ( ( sK2_SY20
= ( singleton @ sK1_A ) )
& ( sK3_SY22
= ( singleton @ sK1_A ) ) )
& ~ ( ( sK2_SY20 = empty_set )
& ( sK3_SY22
= ( singleton @ sK1_A ) ) )
& ~ ( ( sK2_SY20
= ( singleton @ sK1_A ) )
& ( sK3_SY22 = empty_set ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(29,plain,
( ( ( ( singleton @ sK1_A )
= ( set_union2 @ sK2_SY20 @ sK3_SY22 ) )
& ~ ( ( sK2_SY20
= ( singleton @ sK1_A ) )
& ( sK3_SY22
= ( singleton @ sK1_A ) ) )
& ~ ( ( sK2_SY20 = empty_set )
& ( sK3_SY22
= ( singleton @ sK1_A ) ) )
& ~ ( ( sK2_SY20
= ( singleton @ sK1_A ) )
& ( sK3_SY22 = empty_set ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[28]) ).
thf(30,plain,
( ( ( ( singleton @ sK1_A )
= ( set_union2 @ sK2_SY20 @ sK3_SY22 ) )
& ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) )
& ( ( sK2_SY20 != empty_set )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) )
& ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22 != empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(31,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(32,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(33,plain,
( ( empty @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(35,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(38,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(40,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(41,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(42,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(44,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(46,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(47,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(48,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(50,plain,
( ( ( ( singleton @ sK1_A )
= ( set_union2 @ sK2_SY20 @ sK3_SY22 ) )
& ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) )
& ( ( sK2_SY20 != empty_set )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) )
& ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22 != empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(51,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(52,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY20 @ sK3_SY22 ) )
| ~ ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) ) )
| ~ ( ( sK2_SY20 != empty_set )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) ) )
| ~ ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22 != empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(53,plain,
! [SV1: $i] :
( ( ! [SY23: $i] :
( ( set_union2 @ SV1 @ SY23 )
= ( set_union2 @ SY23 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(54,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
| ! [SY24: $i] :
~ ( empty @ ( set_union2 @ SV2 @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(55,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
| ! [SY25: $i] :
~ ( empty @ ( set_union2 @ SY25 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(56,plain,
! [SV4: $i] :
( ( ( set_union2 @ SV4 @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(57,plain,
! [SV5: $i] :
( ( ( ( singleton @ SV5 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(58,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(59,plain,
! [SV6: $i] :
( ( subset @ SV6 @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(60,plain,
! [SV7: $i] :
( ( ! [SY26: $i] : ( subset @ SV7 @ ( set_union2 @ SV7 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(61,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(62,plain,
( ( ~ ~ ( ~ ~ ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY20 @ sK3_SY22 ) )
| ~ ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) ) )
| ~ ( ( sK2_SY20 != empty_set )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) ) )
| ~ ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22 != empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(63,plain,
! [SV8: $i,SV1: $i] :
( ( ( set_union2 @ SV1 @ SV8 )
= ( set_union2 @ SV8 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(64,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $true )
| ( ( ! [SY24: $i] :
~ ( empty @ ( set_union2 @ SV2 @ SY24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(65,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
= $true )
| ( ( ! [SY25: $i] :
~ ( empty @ ( set_union2 @ SY25 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(66,plain,
! [SV5: $i] :
( ( ( singleton @ SV5 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV9: $i,SV7: $i] :
( ( subset @ SV7 @ ( set_union2 @ SV7 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(68,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(69,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(70,plain,
( ( ~ ~ ( ~ ~ ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY20 @ sK3_SY22 ) )
| ~ ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) ) )
| ~ ( ( sK2_SY20 != empty_set )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(71,plain,
( ( ~ ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22 != empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(72,plain,
! [SV10: $i,SV2: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV2 @ SV10 ) ) )
= $true )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV3: $i,SV11: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV11 @ SV3 ) ) )
= $true )
| ( ( empty @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(75,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(76,plain,
( ( ~ ( ~ ~ ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY20 @ sK3_SY22 ) )
| ~ ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) ) )
| ~ ( ( sK2_SY20 != empty_set )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(77,plain,
( ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22 != empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(78,plain,
! [SV10: $i,SV2: $i] :
( ( ( empty @ ( set_union2 @ SV2 @ SV10 ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(79,plain,
! [SV3: $i,SV11: $i] :
( ( ( empty @ ( set_union2 @ SV11 @ SV3 ) )
= $false )
| ( ( empty @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(80,plain,
! [SV12: $i] :
( ( ! [SY27: $i] :
( ~ ( subset @ SV12 @ ( singleton @ SY27 ) )
| ( SV12 = empty_set )
| ( SV12
= ( singleton @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(81,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(82,plain,
( ( ~ ~ ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY20 @ sK3_SY22 ) )
| ~ ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) ) )
| ~ ( ( sK2_SY20 != empty_set )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(83,plain,
( ( ( ( sK2_SY20
!= ( singleton @ sK1_A ) ) )
= $true )
| ( ( ( sK3_SY22 != empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(84,plain,
! [SV13: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ ( singleton @ SV13 ) )
| ( SV12 = empty_set )
| ( SV12
= ( singleton @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(85,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(86,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(87,plain,
( ( ~ ~ ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY20 @ sK3_SY22 ) )
| ~ ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(88,plain,
( ( ~ ( ( sK2_SY20 != empty_set )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(89,plain,
( ( ( sK2_SY20
= ( singleton @ sK1_A ) )
= $false )
| ( ( ( sK3_SY22 != empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(90,plain,
! [SV13: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ ( singleton @ SV13 ) ) )
= $true )
| ( ( ( SV12 = empty_set )
| ( SV12
= ( singleton @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(91,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(92,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(93,plain,
( ( ~ ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY20 @ sK3_SY22 ) )
| ~ ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(94,plain,
( ( ( sK2_SY20 != empty_set )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(95,plain,
( ( ( sK3_SY22 = empty_set )
= $false )
| ( ( sK2_SY20
= ( singleton @ sK1_A ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV13: $i,SV12: $i] :
( ( ( subset @ SV12 @ ( singleton @ SV13 ) )
= $false )
| ( ( ( SV12 = empty_set )
| ( SV12
= ( singleton @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(97,plain,
! [SV14: $i] :
( ( ( SV14 != empty_set )
| ! [SY28: $i] : ( subset @ SV14 @ ( singleton @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(98,plain,
! [SV15: $i] :
( ( ! [SY29: $i] :
( ( SV15
!= ( singleton @ SY29 ) )
| ( subset @ SV15 @ ( singleton @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(99,plain,
( ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY20 @ sK3_SY22 ) )
| ~ ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(100,plain,
( ( ( ( sK2_SY20 != empty_set ) )
= $true )
| ( ( ( sK3_SY22
!= ( singleton @ sK1_A ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV13: $i,SV12: $i] :
( ( ( SV12 = empty_set )
= $true )
| ( ( SV12
= ( singleton @ SV13 ) )
= $true )
| ( ( subset @ SV12 @ ( singleton @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(102,plain,
! [SV14: $i] :
( ( ( ( SV14 != empty_set ) )
= $true )
| ( ( ! [SY28: $i] : ( subset @ SV14 @ ( singleton @ SY28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV16: $i,SV15: $i] :
( ( ( SV15
!= ( singleton @ SV16 ) )
| ( subset @ SV15 @ ( singleton @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(104,plain,
( ( ( ( singleton @ sK1_A )
!= ( set_union2 @ sK2_SY20 @ sK3_SY22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(105,plain,
( ( ~ ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(106,plain,
( ( ( sK2_SY20 = empty_set )
= $false )
| ( ( ( sK3_SY22
!= ( singleton @ sK1_A ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(107,plain,
! [SV14: $i] :
( ( ( SV14 = empty_set )
= $false )
| ( ( ! [SY28: $i] : ( subset @ SV14 @ ( singleton @ SY28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(108,plain,
! [SV16: $i,SV15: $i] :
( ( ( ( SV15
!= ( singleton @ SV16 ) ) )
= $true )
| ( ( subset @ SV15 @ ( singleton @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(109,plain,
( ( ( singleton @ sK1_A )
= ( set_union2 @ sK2_SY20 @ sK3_SY22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(110,plain,
( ( ( sK2_SY20
!= ( singleton @ sK1_A ) )
| ( sK3_SY22
!= ( singleton @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(111,plain,
( ( ( sK3_SY22
= ( singleton @ sK1_A ) )
= $false )
| ( ( sK2_SY20 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(112,plain,
! [SV17: $i,SV14: $i] :
( ( ( subset @ SV14 @ ( singleton @ SV17 ) )
= $true )
| ( ( SV14 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(113,plain,
! [SV16: $i,SV15: $i] :
( ( ( SV15
= ( singleton @ SV16 ) )
= $false )
| ( ( subset @ SV15 @ ( singleton @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(114,plain,
( ( ( ( sK2_SY20
!= ( singleton @ sK1_A ) ) )
= $true )
| ( ( ( sK3_SY22
!= ( singleton @ sK1_A ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(115,plain,
( ( ( sK2_SY20
= ( singleton @ sK1_A ) )
= $false )
| ( ( ( sK3_SY22
!= ( singleton @ sK1_A ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(116,plain,
( ( ( sK3_SY22
= ( singleton @ sK1_A ) )
= $false )
| ( ( sK2_SY20
= ( singleton @ sK1_A ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(117,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[40,116,113,112,111,109,101,95,79,78,67,66,63,59,58,56,46]) ).
thf(118,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET902+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 : n021.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 02:14:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 11
% 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: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).....
% 0.20/0.42
% 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/sandbox/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:117,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.43
% 0.20/0.43 %**** Beginning of derivation protocol ****
% 0.20/0.43 % SZS output start CNFRefutation
% See solution above
% 0.20/0.43
% 0.20/0.43 %**** End of derivation protocol ****
% 0.20/0.43 %**** no. of clauses in derivation: 118 ****
% 0.20/0.43 %**** clause counter: 117 ****
% 0.20/0.43
% 0.20/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:117,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------