TSTP Solution File: SET900+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET900+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 : n003.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 03:06:04 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 72 ( 46 unt; 9 typ; 0 def)
% Number of atoms : 295 ( 164 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 394 ( 130 ~; 56 |; 30 &; 176 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 78 ( 0 ^ 74 !; 4 ?; 78 :)
% 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_SY10,type,
sK2_SY10: $i ).
thf(tp_sK3_C,type,
sK3_C: $i > $i > $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( A
!= ( singleton @ B ) )
& ( A != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( C != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_zfmisc_1) ).
thf(2,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(3,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(4,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(6,conjecture,
! [A: $i,B: $i] :
~ ( ( A
!= ( singleton @ B ) )
& ( A != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( C != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(7,negated_conjecture,
( ( ! [A: $i,B: $i] :
~ ( ( A
!= ( singleton @ B ) )
& ( A != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( C != B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [A: $i,B: $i] :
~ ( ( A
!= ( singleton @ B ) )
& ( A != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( C != B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i] :
~ ( ( A
!= ( singleton @ B ) )
& ( A != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( C != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [SY10: $i] :
~ ( ( sK1_A
!= ( singleton @ SY10 ) )
& ( sK1_A != empty_set )
& ! [SY11: $i] :
~ ( ( in @ SY11 @ sK1_A )
& ( SY11 != SY10 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) )
& ( sK1_A != empty_set )
& ! [SY12: $i] :
~ ( ( in @ SY12 @ sK1_A )
& ( SY12 != sK2_SY10 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( ( sK1_A
!= ( singleton @ sK2_SY10 ) )
& ( sK1_A != empty_set )
& ! [SY12: $i] :
~ ( ( in @ SY12 @ sK1_A )
& ( SY12 != sK2_SY10 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [SY12: $i] :
( ( SY12 = sK2_SY10 )
| ~ ( in @ SY12 @ sK1_A ) )
& ( sK1_A
!= ( singleton @ sK2_SY10 ) )
& ( sK1_A != empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( sK3_C @ B @ A )
!= B )
& ( in @ ( sK3_C @ B @ A ) @ A ) )
| ( A
= ( singleton @ B ) )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(19,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(20,plain,
( ( empty @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(22,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(23,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(24,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( sK3_C @ B @ A )
!= B )
& ( in @ ( sK3_C @ B @ A ) @ A ) )
| ( A
= ( singleton @ B ) )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(27,plain,
( ( ! [SY12: $i] :
( ( SY12 = sK2_SY10 )
| ~ ( in @ SY12 @ sK1_A ) )
& ( sK1_A
!= ( singleton @ sK2_SY10 ) )
& ( sK1_A != empty_set ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(28,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK3_C @ SX1 @ SX0 )
!= SX1 ) )
| ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 ) )
| ( SX0
= ( singleton @ SX1 ) )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(29,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = sK2_SY10 )
| ~ ( in @ SX0 @ sK1_A ) )
| ~ ~ ( ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) )
| ~ ( ( sK1_A != empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(30,plain,
! [SV1: $i] :
( ( ! [SY13: $i] :
( ~ ( in @ SV1 @ SY13 )
| ~ ( in @ SY13 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(31,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV2: $i] :
( ( ! [SY14: $i] :
( ~ ( ~ ( ( ( sK3_C @ SY14 @ SV2 )
!= SY14 ) )
| ~ ( in @ ( sK3_C @ SY14 @ SV2 ) @ SV2 ) )
| ( SV2
= ( singleton @ SY14 ) )
| ( SV2 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = sK2_SY10 )
| ~ ( in @ SX0 @ sK1_A ) )
| ~ ~ ( ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) )
| ~ ( ( sK1_A != empty_set ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV3 )
| ~ ( in @ SV3 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV2: $i,SV4: $i] :
( ( ~ ( ~ ( ( ( sK3_C @ SV4 @ SV2 )
!= SV4 ) )
| ~ ( in @ ( sK3_C @ SV4 @ SV2 ) @ SV2 ) )
| ( SV2
= ( singleton @ SV4 ) )
| ( SV2 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(36,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = sK2_SY10 )
| ~ ( in @ SX0 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(37,plain,
( ( ~ ~ ( ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) )
| ~ ( ( sK1_A != empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(38,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV3 ) )
= $true )
| ( ( ~ ( in @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( ~ ( ( ( sK3_C @ SV4 @ SV2 )
!= SV4 ) )
| ~ ( in @ ( sK3_C @ SV4 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( ( SV2
= ( singleton @ SV4 ) )
| ( SV2 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(40,plain,
( ( ! [SX0: $i] :
( ( SX0 = sK2_SY10 )
| ~ ( in @ SX0 @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(41,plain,
( ( ~ ( ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) )
| ~ ( ( sK1_A != empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(42,plain,
! [SV3: $i,SV1: $i] :
( ( ( in @ SV1 @ SV3 )
= $false )
| ( ( ~ ( in @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( ( ( sK3_C @ SV4 @ SV2 )
!= SV4 ) )
| ~ ( in @ ( sK3_C @ SV4 @ SV2 ) @ SV2 ) )
= $false )
| ( ( ( SV2
= ( singleton @ SV4 ) )
| ( SV2 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV5: $i] :
( ( ( SV5 = sK2_SY10 )
| ~ ( in @ SV5 @ sK1_A ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(45,plain,
( ( ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) )
| ~ ( ( sK1_A != empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( ( ( sK3_C @ SV4 @ SV2 )
!= SV4 ) ) )
= $false )
| ( ( ( SV2
= ( singleton @ SV4 ) )
| ( SV2 = empty_set ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(48,plain,
! [SV2: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV4 @ SV2 ) @ SV2 ) )
= $false )
| ( ( ( SV2
= ( singleton @ SV4 ) )
| ( SV2 = empty_set ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(49,plain,
! [SV5: $i] :
( ( ( SV5 = sK2_SY10 )
= $true )
| ( ( ~ ( in @ SV5 @ sK1_A ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(50,plain,
( ( ~ ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(51,plain,
( ( ~ ( ( sK1_A != empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(52,plain,
! [SV2: $i,SV4: $i] :
( ( ( ( ( sK3_C @ SV4 @ SV2 )
!= SV4 ) )
= $true )
| ( ( ( SV2
= ( singleton @ SV4 ) )
| ( SV2 = empty_set ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(53,plain,
! [SV2: $i,SV4: $i] :
( ( ( in @ ( sK3_C @ SV4 @ SV2 ) @ SV2 )
= $true )
| ( ( ( SV2
= ( singleton @ SV4 ) )
| ( SV2 = empty_set ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ sK1_A )
= $false )
| ( ( SV5 = sK2_SY10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(55,plain,
( ( ( sK1_A
!= ( singleton @ sK2_SY10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(56,plain,
( ( ( sK1_A != empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(57,plain,
! [SV2: $i,SV4: $i] :
( ( ( ( sK3_C @ SV4 @ SV2 )
= SV4 )
= $false )
| ( ( ( SV2
= ( singleton @ SV4 ) )
| ( SV2 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV4: $i,SV2: $i] :
( ( ( SV2
= ( singleton @ SV4 ) )
= $true )
| ( ( SV2 = empty_set )
= $true )
| ( ( in @ ( sK3_C @ SV4 @ SV2 ) @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(59,plain,
( ( sK1_A
= ( singleton @ sK2_SY10 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(60,plain,
( ( sK1_A = empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV4: $i,SV2: $i] :
( ( ( SV2
= ( singleton @ SV4 ) )
= $true )
| ( ( SV2 = empty_set )
= $true )
| ( ( ( sK3_C @ SV4 @ SV2 )
= SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(62,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,61,60,59,58,54,46,31,24]) ).
thf(63,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET900+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n003.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 : Sun Jul 10 00:53:29 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)..
% 0.13/0.38
% 0.13/0.38 ********************************
% 0.13/0.38 * All subproblems solved! *
% 0.13/0.38 ********************************
% 0.13/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:62,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.38
% 0.13/0.38 %**** Beginning of derivation protocol ****
% 0.13/0.38 % SZS output start CNFRefutation
% See solution above
% 0.13/0.38
% 0.13/0.38 %**** End of derivation protocol ****
% 0.13/0.38 %**** no. of clauses in derivation: 63 ****
% 0.13/0.38 %**** clause counter: 62 ****
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:62,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------