TSTP Solution File: SET880+1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET880+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 03:05:56 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 99 ( 55 unt; 10 typ; 0 def)
% Number of atoms : 495 ( 260 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 801 ( 170 ~; 147 |; 8 &; 463 @)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 189 ( 0 ^ 185 !; 4 ?; 189 :)
% 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_SY11,type,
sK2_SY11: $i ).
thf(tp_sK3_A,type,
sK3_A: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_C,type,
sK5_C: $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(1,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(2,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).
thf(4,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(7,conjecture,
! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ ( singleton @ B ) )
= empty_set )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_zfmisc_1) ).
thf(8,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ ( singleton @ B ) )
= empty_set )
=> ( A = B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ ( singleton @ B ) )
= empty_set )
=> ( A = B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(16,plain,
( ( ! [SY11: $i] :
( ( ( set_difference @ ( singleton @ sK1_A ) @ ( singleton @ SY11 ) )
= empty_set )
=> ( sK1_A = SY11 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(17,plain,
( ( ( ( set_difference @ ( singleton @ sK1_A ) @ ( singleton @ sK2_SY11 ) )
= empty_set )
=> ( sK1_A = sK2_SY11 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(18,plain,
( ( ( set_difference @ ( singleton @ sK1_A ) @ ( singleton @ sK2_SY11 ) )
= empty_set )
= $true ),
inference(standard_cnf,[status(thm)],[17]) ).
thf(19,plain,
( ( sK1_A = sK2_SY11 )
= $false ),
inference(standard_cnf,[status(thm)],[17]) ).
thf(20,plain,
( ( ( sK1_A != sK2_SY11 ) )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(21,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(22,plain,
( ( empty @ sK4_A )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
!= empty_set )
| ( in @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK5_C @ B @ A )
!= A )
| ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
& ( ( ( sK5_C @ B @ A )
= A )
| ( in @ ( sK5_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK5_C @ B @ A )
!= A )
| ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
& ( ( ( sK5_C @ B @ A )
= A )
| ( in @ ( sK5_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(28,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(29,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
!= empty_set )
| ( in @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(30,plain,
( ( empty @ sK4_A )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(31,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(32,plain,
( ( ( set_difference @ ( singleton @ sK1_A ) @ ( singleton @ sK2_SY11 ) )
= empty_set )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(33,plain,
( ( ( sK1_A != sK2_SY11 ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(34,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
!= empty_set )
| ( in @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(35,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK5_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK5_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(36,plain,
! [SV1: $i] :
( ( ! [SY12: $i] :
( ~ ( in @ SV1 @ SY12 )
| ~ ( in @ SY12 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(37,plain,
( ( empty @ sK3_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(38,plain,
( ( sK1_A = sK2_SY11 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(39,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
!= empty_set )
| ( in @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(40,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK5_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK5_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV2 )
| ~ ( in @ SV2 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(42,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
!= empty_set )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(43,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(44,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK5_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK5_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(45,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV2 ) )
= $true )
| ( ( ~ ( in @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(47,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
!= empty_set )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(48,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(49,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK5_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK5_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(50,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(51,plain,
! [SV2: $i,SV1: $i] :
( ( ( in @ SV1 @ SV2 )
= $false )
| ( ( ~ ( in @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV3: $i] :
( ( ! [SY13: $i] :
( ( ( set_difference @ ( singleton @ SV3 ) @ SY13 )
!= empty_set )
| ( in @ SV3 @ SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV4: $i] :
( ( ! [SY14: $i] :
( ~ ( in @ SV4 @ SY14 )
| ( ( set_difference @ ( singleton @ SV4 ) @ SY14 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV5: $i] :
( ( ! [SY15: $i] :
( ~ ( ~ ( ( ( sK5_C @ SY15 @ SV5 )
!= SV5 )
| ~ ( in @ ( sK5_C @ SY15 @ SV5 ) @ SY15 ) )
| ~ ( ( ( sK5_C @ SY15 @ SV5 )
= SV5 )
| ( in @ ( sK5_C @ SY15 @ SV5 ) @ SY15 ) ) )
| ( SY15
= ( singleton @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV6: $i] :
( ( ! [SY16: $i] :
( ( SY16
!= ( singleton @ SV6 ) )
| ~ ( ~ ! [SY17: $i] :
( ( SY17 != SV6 )
| ( in @ SY17 @ SY16 ) )
| ~ ! [SY18: $i] :
( ~ ( in @ SY18 @ SY16 )
| ( SY18 = SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV1: $i,SV2: $i] :
( ( ( in @ SV2 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV7: $i,SV3: $i] :
( ( ( ( set_difference @ ( singleton @ SV3 ) @ SV7 )
!= empty_set )
| ( in @ SV3 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ SV8 )
| ( ( set_difference @ ( singleton @ SV4 ) @ SV8 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV5: $i,SV9: $i] :
( ( ~ ( ~ ( ( ( sK5_C @ SV9 @ SV5 )
!= SV5 )
| ~ ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) )
| ~ ( ( ( sK5_C @ SV9 @ SV5 )
= SV5 )
| ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) ) )
| ( SV9
= ( singleton @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV6: $i,SV10: $i] :
( ( ( SV10
!= ( singleton @ SV6 ) )
| ~ ( ~ ! [SY19: $i] :
( ( SY19 != SV6 )
| ( in @ SY19 @ SV10 ) )
| ~ ! [SY20: $i] :
( ~ ( in @ SY20 @ SV10 )
| ( SY20 = SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV7: $i,SV3: $i] :
( ( ( ( ( set_difference @ ( singleton @ SV3 ) @ SV7 )
!= empty_set ) )
= $true )
| ( ( in @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV8 ) )
= $true )
| ( ( ( set_difference @ ( singleton @ SV4 ) @ SV8 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV5: $i,SV9: $i] :
( ( ( ~ ( ~ ( ( ( sK5_C @ SV9 @ SV5 )
!= SV5 )
| ~ ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) )
| ~ ( ( ( sK5_C @ SV9 @ SV5 )
= SV5 )
| ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) ) ) )
= $true )
| ( ( SV9
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV6: $i,SV10: $i] :
( ( ( ( SV10
!= ( singleton @ SV6 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY19: $i] :
( ( SY19 != SV6 )
| ( in @ SY19 @ SV10 ) )
| ~ ! [SY20: $i] :
( ~ ( in @ SY20 @ SV10 )
| ( SY20 = SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV7: $i,SV3: $i] :
( ( ( ( set_difference @ ( singleton @ SV3 ) @ SV7 )
= empty_set )
= $false )
| ( ( in @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV8: $i,SV4: $i] :
( ( ( in @ SV4 @ SV8 )
= $false )
| ( ( ( set_difference @ ( singleton @ SV4 ) @ SV8 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV5: $i,SV9: $i] :
( ( ( ~ ( ( ( sK5_C @ SV9 @ SV5 )
!= SV5 )
| ~ ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) )
| ~ ( ( ( sK5_C @ SV9 @ SV5 )
= SV5 )
| ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) ) )
= $false )
| ( ( SV9
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV6: $i,SV10: $i] :
( ( ( SV10
= ( singleton @ SV6 ) )
= $false )
| ( ( ~ ( ~ ! [SY19: $i] :
( ( SY19 != SV6 )
| ( in @ SY19 @ SV10 ) )
| ~ ! [SY20: $i] :
( ~ ( in @ SY20 @ SV10 )
| ( SY20 = SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV5: $i,SV9: $i] :
( ( ( ~ ( ( ( sK5_C @ SV9 @ SV5 )
!= SV5 )
| ~ ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) ) )
= $false )
| ( ( SV9
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(70,plain,
! [SV5: $i,SV9: $i] :
( ( ( ~ ( ( ( sK5_C @ SV9 @ SV5 )
= SV5 )
| ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) ) )
= $false )
| ( ( SV9
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(71,plain,
! [SV10: $i,SV6: $i] :
( ( ( ~ ! [SY19: $i] :
( ( SY19 != SV6 )
| ( in @ SY19 @ SV10 ) )
| ~ ! [SY20: $i] :
( ~ ( in @ SY20 @ SV10 )
| ( SY20 = SV6 ) ) )
= $false )
| ( ( SV10
= ( singleton @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV5: $i,SV9: $i] :
( ( ( ( ( sK5_C @ SV9 @ SV5 )
!= SV5 )
| ~ ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) )
= $true )
| ( ( SV9
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(73,plain,
! [SV5: $i,SV9: $i] :
( ( ( ( ( sK5_C @ SV9 @ SV5 )
= SV5 )
| ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) )
= $true )
| ( ( SV9
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(74,plain,
! [SV10: $i,SV6: $i] :
( ( ( ~ ! [SY19: $i] :
( ( SY19 != SV6 )
| ( in @ SY19 @ SV10 ) ) )
= $false )
| ( ( SV10
= ( singleton @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(75,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ! [SY20: $i] :
( ~ ( in @ SY20 @ SV10 )
| ( SY20 = SV6 ) ) )
= $false )
| ( ( SV10
= ( singleton @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(76,plain,
! [SV5: $i,SV9: $i] :
( ( ( ( ( sK5_C @ SV9 @ SV5 )
!= SV5 ) )
= $true )
| ( ( ~ ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) )
= $true )
| ( ( SV9
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV5: $i,SV9: $i] :
( ( ( ( sK5_C @ SV9 @ SV5 )
= SV5 )
= $true )
| ( ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 )
= $true )
| ( ( SV9
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV10: $i,SV6: $i] :
( ( ( ! [SY19: $i] :
( ( SY19 != SV6 )
| ( in @ SY19 @ SV10 ) ) )
= $true )
| ( ( SV10
= ( singleton @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(79,plain,
! [SV6: $i,SV10: $i] :
( ( ( ! [SY20: $i] :
( ~ ( in @ SY20 @ SV10 )
| ( SY20 = SV6 ) ) )
= $true )
| ( ( SV10
= ( singleton @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(80,plain,
! [SV5: $i,SV9: $i] :
( ( ( ( sK5_C @ SV9 @ SV5 )
= SV5 )
= $false )
| ( ( ~ ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) )
= $true )
| ( ( SV9
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV10: $i,SV6: $i,SV11: $i] :
( ( ( ( SV11 != SV6 )
| ( in @ SV11 @ SV10 ) )
= $true )
| ( ( SV10
= ( singleton @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(82,plain,
! [SV6: $i,SV10: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV10 )
| ( SV12 = SV6 ) )
= $true )
| ( ( SV10
= ( singleton @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV5: $i,SV9: $i] :
( ( ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 )
= $false )
| ( ( ( sK5_C @ SV9 @ SV5 )
= SV5 )
= $false )
| ( ( SV9
= ( singleton @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(84,plain,
! [SV10: $i,SV6: $i,SV11: $i] :
( ( ( ( SV11 != SV6 ) )
= $true )
| ( ( in @ SV11 @ SV10 )
= $true )
| ( ( SV10
= ( singleton @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(85,plain,
! [SV6: $i,SV10: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV10 ) )
= $true )
| ( ( SV12 = SV6 )
= $true )
| ( ( SV10
= ( singleton @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(86,plain,
! [SV10: $i,SV6: $i,SV11: $i] :
( ( ( SV11 = SV6 )
= $false )
| ( ( in @ SV11 @ SV10 )
= $true )
| ( ( SV10
= ( singleton @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(87,plain,
! [SV6: $i,SV10: $i,SV12: $i] :
( ( ( in @ SV12 @ SV10 )
= $false )
| ( ( SV12 = SV6 )
= $true )
| ( ( SV10
= ( singleton @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(88,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,87,86,83,77,66,65,56,38,37,32,30]) ).
thf(89,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET880+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 04:07:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 6
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:8,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.19/0.39
% 0.19/0.39 ********************************
% 0.19/0.39 * All subproblems solved! *
% 0.19/0.39 ********************************
% 0.19/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:88,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.40
% 0.19/0.40 %**** Beginning of derivation protocol ****
% 0.19/0.40 % SZS output start CNFRefutation
% See solution above
% 0.19/0.40
% 0.19/0.40 %**** End of derivation protocol ****
% 0.19/0.40 %**** no. of clauses in derivation: 89 ****
% 0.19/0.40 %**** clause counter: 88 ****
% 0.19/0.40
% 0.19/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:88,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------