TSTP Solution File: SEU518^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU518^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n028.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 12:12:31 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 30 unt; 6 typ; 1 def)
% Number of atoms : 250 ( 59 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 523 ( 87 ~; 62 |; 6 &; 349 @)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 102 ( 0 ^ 102 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetAx,type,
powersetAx: $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY9,type,
sK2_SY9: $i ).
thf(tp_sK3_Xx,type,
sK3_Xx: $i > $i > $i ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(1,conjecture,
( powersetAx
=> ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(2,negated_conjecture,
( ( powersetAx
=> ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,powersetAx]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY11: $i] :
( ~ ( in @ SY11 @ sK2_SY9 )
| ( in @ SY11 @ sK1_A ) )
& ~ ( in @ sK2_SY9 @ ( powerset @ sK1_A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK3_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK3_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK3_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK3_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SY11: $i] :
( ~ ( in @ SY11 @ sK2_SY9 )
| ( in @ SY11 @ sK1_A ) )
& ~ ( in @ sK2_SY9 @ ( powerset @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,powersetAx]) ).
thf(12,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY9 )
| ( in @ SX0 @ sK1_A ) )
| ~ ~ ( in @ sK2_SY9 @ ( powerset @ sK1_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,powersetAx]) ).
thf(13,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY9 )
| ( in @ SX0 @ sK1_A ) )
| ~ ~ ( in @ sK2_SY9 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY9 )
| ( in @ SX0 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ~ ( in @ sK2_SY9 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(19,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(20,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(21,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY9 )
| ( in @ SX0 @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(22,plain,
( ( ~ ( in @ sK2_SY9 @ ( powerset @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(23,plain,
! [SV1: $i] :
( ( ! [SY12: $i] :
( ~ ( ~ ( in @ ( sK3_Xx @ SY12 @ SV1 ) @ SY12 )
| ~ ~ ( in @ ( sK3_Xx @ SY12 @ SV1 ) @ SV1 ) )
| ( in @ SY12 @ ( powerset @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV2: $i] :
( ( ! [SY13: $i] :
( ~ ( in @ SY13 @ ( powerset @ SV2 ) )
| ! [SY14: $i] :
( ~ ( in @ SY14 @ SY13 )
| ( in @ SY14 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV3: $i] :
( ( ~ ( in @ SV3 @ sK2_SY9 )
| ( in @ SV3 @ sK1_A ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
( ( in @ sK2_SY9 @ ( powerset @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV1: $i,SV4: $i] :
( ( ~ ( ~ ( in @ ( sK3_Xx @ SV4 @ SV1 ) @ SV4 )
| ~ ~ ( in @ ( sK3_Xx @ SV4 @ SV1 ) @ SV1 ) )
| ( in @ SV4 @ ( powerset @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV2: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ ( powerset @ SV2 ) )
| ! [SY15: $i] :
( ~ ( in @ SY15 @ SV5 )
| ( in @ SY15 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV3: $i] :
( ( ( ~ ( in @ SV3 @ sK2_SY9 ) )
= $true )
| ( ( in @ SV3 @ sK1_A )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_Xx @ SV4 @ SV1 ) @ SV4 )
| ~ ~ ( in @ ( sK3_Xx @ SV4 @ SV1 ) @ SV1 ) ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ ( powerset @ SV2 ) ) )
= $true )
| ( ( ! [SY15: $i] :
( ~ ( in @ SY15 @ SV5 )
| ( in @ SY15 @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV3: $i] :
( ( ( in @ SV3 @ sK2_SY9 )
= $false )
| ( ( in @ SV3 @ sK1_A )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV4 @ SV1 ) @ SV4 )
| ~ ~ ( in @ ( sK3_Xx @ SV4 @ SV1 ) @ SV1 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV2: $i,SV5: $i] :
( ( ( in @ SV5 @ ( powerset @ SV2 ) )
= $false )
| ( ( ! [SY15: $i] :
( ~ ( in @ SY15 @ SV5 )
| ( in @ SY15 @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV4 @ SV1 ) @ SV4 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(36,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ~ ( in @ ( sK3_Xx @ SV4 @ SV1 ) @ SV1 ) )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV2: $i,SV5: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV5 )
| ( in @ SV6 @ SV2 ) )
= $true )
| ( ( in @ SV5 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV1: $i,SV4: $i] :
( ( ( in @ ( sK3_Xx @ SV4 @ SV1 ) @ SV4 )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(39,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK3_Xx @ SV4 @ SV1 ) @ SV1 ) )
= $true )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(40,plain,
! [SV2: $i,SV5: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV5 ) )
= $true )
| ( ( in @ SV6 @ SV2 )
= $true )
| ( ( in @ SV5 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV1: $i,SV4: $i] :
( ( ( in @ ( sK3_Xx @ SV4 @ SV1 ) @ SV1 )
= $false )
| ( ( in @ SV4 @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV2: $i,SV5: $i,SV6: $i] :
( ( ( in @ SV6 @ SV5 )
= $false )
| ( ( in @ SV6 @ SV2 )
= $true )
| ( ( in @ SV5 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(43,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,42,41,38,32]) ).
thf(44,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU518^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n028.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 : Mon Jun 20 01:52:46 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33
% 0.13/0.33 No.of.Axioms: 0
% 0.13/0.33
% 0.13/0.33 Length.of.Defs: 198
% 0.13/0.33
% 0.13/0.33 Contains.Choice.Funs: false
% 0.13/0.34 (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.13/0.37
% 0.13/0.37 ********************************
% 0.13/0.37 * All subproblems solved! *
% 0.13/0.37 ********************************
% 0.13/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:43,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.37
% 0.13/0.37 %**** Beginning of derivation protocol ****
% 0.13/0.37 % SZS output start CNFRefutation
% See solution above
% 0.13/0.37
% 0.13/0.37 %**** End of derivation protocol ****
% 0.13/0.37 %**** no. of clauses in derivation: 44 ****
% 0.13/0.37 %**** clause counter: 43 ****
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:43,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------