TSTP Solution File: NUM531+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM531+2 : TPTP v8.1.0. Released v4.0.0.
% 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 : Mon Jul 18 11:52:11 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 76 ( 46 unt; 7 typ; 0 def)
% Number of atoms : 313 ( 94 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 279 ( 64 ~; 44 |; 14 &; 135 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 0 ^ 63 !; 6 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aElement0,type,
aElement0: $i > $o ).
thf(tp_aElementOf0,type,
aElementOf0: $i > $i > $o ).
thf(tp_aSet0,type,
aSet0: $i > $o ).
thf(tp_isCountable0,type,
isCountable0: $i > $o ).
thf(tp_isFinite0,type,
isFinite0: $i > $o ).
thf(tp_sK1_W0,type,
sK1_W0: $i ).
thf(tp_slcrc0,type,
slcrc0: $i ).
thf(1,axiom,
! [W0: $i] :
( ( ( aSet0 @ W0 )
& ( isCountable0 @ W0 ) )
=> ~ ( isFinite0 @ W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
thf(2,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ( ( isCountable0 @ W0 )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCntRel) ).
thf(3,axiom,
isFinite0 @ slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).
thf(4,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ( ( isFinite0 @ W0 )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFinRel) ).
thf(5,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(6,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(7,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetSort) ).
thf(8,conjecture,
! [W0: $i] :
( ( ( aSet0 @ W0 )
& ( isCountable0 @ W0 ) )
=> ~ ( ~ ? [W1: $i] : ( aElementOf0 @ W1 @ W0 )
& ( W0 = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(9,negated_conjecture,
( ( ! [W0: $i] :
( ( ( aSet0 @ W0 )
& ( isCountable0 @ W0 ) )
=> ~ ( ~ ? [W1: $i] : ( aElementOf0 @ W1 @ W0 )
& ( W0 = slcrc0 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( ! [W0: $i] :
( ( ( aSet0 @ W0 )
& ( isCountable0 @ W0 ) )
=> ~ ( ~ ? [W1: $i] : ( aElementOf0 @ W1 @ W0 )
& ( W0 = slcrc0 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [W0: $i] :
( ( ( aSet0 @ W0 )
& ( isCountable0 @ W0 ) )
=> ~ ( isFinite0 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ( ( isCountable0 @ W0 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( isFinite0 @ slcrc0 )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ( ( isFinite0 @ W0 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(17,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(18,plain,
( ( ( ( aSet0 @ sK1_W0 )
& ( isCountable0 @ sK1_W0 ) )
=> ~ ( ~ ? [SY9: $i] : ( aElementOf0 @ SY9 @ sK1_W0 )
& ( sK1_W0 = slcrc0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(19,plain,
( ( aSet0 @ sK1_W0 )
= $true ),
inference(standard_cnf,[status(thm)],[18]) ).
thf(20,plain,
( ( isCountable0 @ sK1_W0 )
= $true ),
inference(standard_cnf,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ( ~ ? [SY9: $i] : ( aElementOf0 @ SY9 @ sK1_W0 )
& ( sK1_W0 = slcrc0 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ? [SY9: $i] : ( aElementOf0 @ SY9 @ sK1_W0 )
& ( sK1_W0 = slcrc0 ) )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [SY9: $i] :
~ ( aElementOf0 @ SY9 @ sK1_W0 )
& ( sK1_W0 = slcrc0 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(24,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ~ ( isCountable0 @ W0 )
| ~ ( isFinite0 @ W0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(25,plain,
( ( ! [W0: $i] :
~ ( aSet0 @ W0 )
| $true )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(26,plain,
( ( ! [W0: $i] :
~ ( aSet0 @ W0 )
| $true )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(27,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ W0 )
| ( aElement0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(28,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(29,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(30,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(31,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(32,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ W0 )
| ( aElement0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(33,plain,
( ( ! [W0: $i] :
~ ( aSet0 @ W0 )
| $true )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(34,plain,
( ( isFinite0 @ slcrc0 )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(35,plain,
( ( ! [W0: $i] :
~ ( aSet0 @ W0 )
| $true )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(36,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ~ ( isCountable0 @ W0 )
| ~ ( isFinite0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(37,plain,
( ( isCountable0 @ sK1_W0 )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(38,plain,
( ( aSet0 @ sK1_W0 )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(39,plain,
( ( ! [SY9: $i] :
~ ( aElementOf0 @ SY9 @ sK1_W0 )
& ( sK1_W0 = slcrc0 ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(40,plain,
( ( ~ ( ~ ! [SX0: $i] :
~ ( aElementOf0 @ SX0 @ sK1_W0 )
| ( sK1_W0 != slcrc0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(41,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(42,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(43,plain,
! [SV3: $i] :
( ( ~ ( aSet0 @ SV3 )
| ! [SY10: $i] :
( ~ ( aElementOf0 @ SY10 @ SV3 )
| ( aElement0 @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(44,plain,
( ( ( ! [W0: $i] :
~ ( aSet0 @ W0 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(45,plain,
( ( ( ! [W0: $i] :
~ ( aSet0 @ W0 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(46,plain,
! [SV4: $i] :
( ( ~ ( aSet0 @ SV4 )
| ~ ( isCountable0 @ SV4 )
| ~ ( isFinite0 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(47,plain,
( ( ~ ! [SX0: $i] :
~ ( aElementOf0 @ SX0 @ sK1_W0 )
| ( sK1_W0 != slcrc0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV3: $i] :
( ( ( ~ ( aSet0 @ SV3 ) )
= $true )
| ( ( ! [SY10: $i] :
( ~ ( aElementOf0 @ SY10 @ SV3 )
| ( aElement0 @ SY10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV5: $i] :
( ( ( ~ ( aSet0 @ SV5 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV6: $i] :
( ( ( ~ ( aSet0 @ SV6 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV4: $i] :
( ( ( ~ ( aSet0 @ SV4 )
| ~ ( isCountable0 @ SV4 ) )
= $true )
| ( ( ~ ( isFinite0 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(52,plain,
( ( ~ ! [SX0: $i] :
~ ( aElementOf0 @ SX0 @ sK1_W0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(53,plain,
( ( ( sK1_W0 != slcrc0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(54,plain,
! [SV3: $i] :
( ( ( aSet0 @ SV3 )
= $false )
| ( ( ! [SY10: $i] :
( ~ ( aElementOf0 @ SY10 @ SV3 )
| ( aElement0 @ SY10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV5: $i] :
( ( ( aSet0 @ SV5 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV6: $i] :
( ( ( aSet0 @ SV6 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV4: $i] :
( ( ( ~ ( aSet0 @ SV4 ) )
= $true )
| ( ( ~ ( isCountable0 @ SV4 ) )
= $true )
| ( ( ~ ( isFinite0 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(58,plain,
( ( ! [SX0: $i] :
~ ( aElementOf0 @ SX0 @ sK1_W0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(59,plain,
( ( sK1_W0 = slcrc0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(60,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( aElementOf0 @ SV7 @ SV3 )
| ( aElement0 @ SV7 ) )
= $true )
| ( ( aSet0 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(61,plain,
! [SV4: $i] :
( ( ( aSet0 @ SV4 )
= $false )
| ( ( ~ ( isCountable0 @ SV4 ) )
= $true )
| ( ( ~ ( isFinite0 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV8: $i] :
( ( ~ ( aElementOf0 @ SV8 @ sK1_W0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( aElementOf0 @ SV7 @ SV3 ) )
= $true )
| ( ( aElement0 @ SV7 )
= $true )
| ( ( aSet0 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV4: $i] :
( ( ( isCountable0 @ SV4 )
= $false )
| ( ( aSet0 @ SV4 )
= $false )
| ( ( ~ ( isFinite0 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV8: $i] :
( ( aElementOf0 @ SV8 @ sK1_W0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV3: $i,SV7: $i] :
( ( ( aElementOf0 @ SV7 @ SV3 )
= $false )
| ( ( aElement0 @ SV7 )
= $true )
| ( ( aSet0 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(67,plain,
! [SV4: $i] :
( ( ( isFinite0 @ SV4 )
= $false )
| ( ( aSet0 @ SV4 )
= $false )
| ( ( isCountable0 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(68,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[34,67,66,65,59,56,55,42,41,38,37]) ).
thf(69,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM531+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % 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 : Thu Jul 7 04:23:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 7
% 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: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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:9,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.12/0.37
% 0.12/0.37 ********************************
% 0.12/0.37 * All subproblems solved! *
% 0.12/0.37 ********************************
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,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:68,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.37
% 0.12/0.37 %**** Beginning of derivation protocol ****
% 0.12/0.37 % SZS output start CNFRefutation
% See solution above
% 0.12/0.37
% 0.12/0.37 %**** End of derivation protocol ****
% 0.12/0.37 %**** no. of clauses in derivation: 69 ****
% 0.12/0.37 %**** clause counter: 68 ****
% 0.12/0.37
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,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:68,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------