TSTP Solution File: SET574+3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET574+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n025.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 03:02:57 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 33 unt; 6 typ; 0 def)
% Number of atoms : 256 ( 63 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 462 ( 74 ~; 58 |; 12 &; 308 @)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 103 ( 0 ^ 101 !; 2 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_intersect,type,
intersect: $i > $i > $o ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SY8,type,
sK2_SY8: $i ).
thf(tp_sK3_SY10,type,
sK3_SY10: $i ).
thf(tp_sK4_D,type,
sK4_D: $i > $i > $i ).
thf(1,axiom,
! [B: $i,C: $i] :
( ( intersect @ B @ C )
=> ( intersect @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).
thf(2,axiom,
! [B: $i,C: $i] :
( ( intersect @ B @ C )
<=> ? [D: $i] :
( ( member @ D @ B )
& ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
thf(3,conjecture,
! [B: $i,C: $i,D: $i] :
( ( ( member @ B @ C )
& ( member @ B @ D ) )
=> ( intersect @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th13) ).
thf(4,negated_conjecture,
( ( ! [B: $i,C: $i,D: $i] :
( ( ( member @ B @ C )
& ( member @ B @ D ) )
=> ( intersect @ C @ D ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( ( member @ B @ C )
& ( member @ B @ D ) )
=> ( intersect @ C @ D ) ) )
= $false ),
inference(unfold_def,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [B: $i,C: $i] :
( ( intersect @ B @ C )
=> ( intersect @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ! [B: $i,C: $i] :
( ( intersect @ B @ C )
<=> ? [D: $i] :
( ( member @ D @ B )
& ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(8,plain,
( ( ! [SY8: $i,SY9: $i] :
( ( ( member @ sK1_B @ SY8 )
& ( member @ sK1_B @ SY9 ) )
=> ( intersect @ SY8 @ SY9 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(9,plain,
( ( ! [SY10: $i] :
( ( ( member @ sK1_B @ sK2_SY8 )
& ( member @ sK1_B @ SY10 ) )
=> ( intersect @ sK2_SY8 @ SY10 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(10,plain,
( ( ( ( member @ sK1_B @ sK2_SY8 )
& ( member @ sK1_B @ sK3_SY10 ) )
=> ( intersect @ sK2_SY8 @ sK3_SY10 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(11,plain,
( ( member @ sK1_B @ sK2_SY8 )
= $true ),
inference(standard_cnf,[status(thm)],[10]) ).
thf(12,plain,
( ( member @ sK1_B @ sK3_SY10 )
= $true ),
inference(standard_cnf,[status(thm)],[10]) ).
thf(13,plain,
( ( intersect @ sK2_SY8 @ sK3_SY10 )
= $false ),
inference(standard_cnf,[status(thm)],[10]) ).
thf(14,plain,
( ( ~ ( intersect @ sK2_SY8 @ sK3_SY10 ) )
= $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [B: $i,C: $i] :
( ~ ( intersect @ B @ C )
| ( intersect @ C @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(16,plain,
( ( ! [B: $i,C: $i] :
( ! [D: $i] :
( ~ ( member @ D @ B )
| ~ ( member @ D @ C ) )
| ( intersect @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( intersect @ B @ C )
| ( ( member @ ( sK4_D @ C @ B ) @ B )
& ( member @ ( sK4_D @ C @ B ) @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(17,plain,
( ( ! [B: $i,C: $i] :
( ! [D: $i] :
( ~ ( member @ D @ B )
| ~ ( member @ D @ C ) )
| ( intersect @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( intersect @ B @ C )
| ( ( member @ ( sK4_D @ C @ B ) @ B )
& ( member @ ( sK4_D @ C @ B ) @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [B: $i,C: $i] :
( ~ ( intersect @ B @ C )
| ( intersect @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(19,plain,
( ( member @ sK1_B @ sK3_SY10 )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(20,plain,
( ( member @ sK1_B @ sK2_SY8 )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(21,plain,
( ( ~ ( intersect @ sK2_SY8 @ sK3_SY10 ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(22,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(23,plain,
! [SV1: $i] :
( ( ! [SY11: $i] :
( ~ ( intersect @ SV1 @ SY11 )
| ( intersect @ SY11 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(24,plain,
( ( intersect @ sK2_SY8 @ sK3_SY10 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( intersect @ SV1 @ SV2 )
| ( intersect @ SV2 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(28,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( intersect @ SV1 @ SV2 ) )
= $true )
| ( ( intersect @ SV2 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(31,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV2: $i,SV1: $i] :
( ( ( intersect @ SV1 @ SV2 )
= $false )
| ( ( intersect @ SV2 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV3: $i] :
( ( ! [SY12: $i] :
( ! [SY13: $i] :
( ~ ( member @ SY13 @ SV3 )
| ~ ( member @ SY13 @ SY12 ) )
| ( intersect @ SV3 @ SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV4: $i] :
( ( ! [SY14: $i] :
( ~ ( intersect @ SV4 @ SY14 )
| ~ ( ~ ( member @ ( sK4_D @ SY14 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK4_D @ SY14 @ SV4 ) @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV5: $i,SV3: $i] :
( ( ! [SY15: $i] :
( ~ ( member @ SY15 @ SV3 )
| ~ ( member @ SY15 @ SV5 ) )
| ( intersect @ SV3 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV6: $i,SV4: $i] :
( ( ~ ( intersect @ SV4 @ SV6 )
| ~ ( ~ ( member @ ( sK4_D @ SV6 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK4_D @ SV6 @ SV4 ) @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV5: $i,SV3: $i] :
( ( ( ! [SY15: $i] :
( ~ ( member @ SY15 @ SV3 )
| ~ ( member @ SY15 @ SV5 ) ) )
= $true )
| ( ( intersect @ SV3 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV6: $i,SV4: $i] :
( ( ( ~ ( intersect @ SV4 @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( member @ ( sK4_D @ SV6 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK4_D @ SV6 @ SV4 ) @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV5: $i,SV3: $i,SV7: $i] :
( ( ( ~ ( member @ SV7 @ SV3 )
| ~ ( member @ SV7 @ SV5 ) )
= $true )
| ( ( intersect @ SV3 @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV6: $i,SV4: $i] :
( ( ( intersect @ SV4 @ SV6 )
= $false )
| ( ( ~ ( ~ ( member @ ( sK4_D @ SV6 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK4_D @ SV6 @ SV4 ) @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV5: $i,SV3: $i,SV7: $i] :
( ( ( ~ ( member @ SV7 @ SV3 ) )
= $true )
| ( ( ~ ( member @ SV7 @ SV5 ) )
= $true )
| ( ( intersect @ SV3 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV4: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV6 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK4_D @ SV6 @ SV4 ) @ SV6 ) )
= $false )
| ( ( intersect @ SV4 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV5: $i,SV3: $i,SV7: $i] :
( ( ( member @ SV7 @ SV3 )
= $false )
| ( ( ~ ( member @ SV7 @ SV5 ) )
= $true )
| ( ( intersect @ SV3 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV4: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV6 @ SV4 ) @ SV4 ) )
= $false )
| ( ( intersect @ SV4 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(45,plain,
! [SV4: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV6 @ SV4 ) @ SV6 ) )
= $false )
| ( ( intersect @ SV4 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV3: $i,SV5: $i,SV7: $i] :
( ( ( member @ SV7 @ SV5 )
= $false )
| ( ( member @ SV7 @ SV3 )
= $false )
| ( ( intersect @ SV3 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV4: $i,SV6: $i] :
( ( ( member @ ( sK4_D @ SV6 @ SV4 ) @ SV4 )
= $true )
| ( ( intersect @ SV4 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(48,plain,
! [SV4: $i,SV6: $i] :
( ( ( member @ ( sK4_D @ SV6 @ SV4 ) @ SV6 )
= $true )
| ( ( intersect @ SV4 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(49,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,48,47,46,32,24,20]) ).
thf(50,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET574+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 : Sat Jul 9 23:28:46 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 2
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:2,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:4,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.13/0.39
% 0.13/0.39 ********************************
% 0.13/0.39 * All subproblems solved! *
% 0.13/0.39 ********************************
% 0.13/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:49,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.39
% 0.13/0.39 %**** Beginning of derivation protocol ****
% 0.13/0.39 % SZS output start CNFRefutation
% See solution above
% 0.13/0.39
% 0.13/0.39 %**** End of derivation protocol ****
% 0.13/0.39 %**** no. of clauses in derivation: 50 ****
% 0.13/0.39 %**** clause counter: 49 ****
% 0.13/0.39
% 0.13/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:49,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------