TSTP Solution File: SET018-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET018-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : Tue Jul 19 02:58:00 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 59 ( 44 unt; 8 typ; 0 def)
% Number of atoms : 170 ( 85 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 200 ( 19 ~; 25 |; 0 &; 156 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 75 ( 0 ^ 75 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_m1,type,
m1: $i ).
thf(tp_m2,type,
m2: $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_r1,type,
r1: $i ).
thf(tp_r2,type,
r2: $i ).
thf(tp_singleton_set,type,
singleton_set: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( ordered_pair @ X @ Y )
= ( unordered_pair @ ( singleton_set @ X ) @ ( unordered_pair @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( member @ X @ ( unordered_pair @ Y @ Z ) )
| ( X = Y )
| ( X = Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_3) ).
thf(3,axiom,
! [Y: $i,X: $i] : ( member @ Y @ ( unordered_pair @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_2) ).
thf(4,axiom,
! [X: $i,Y: $i] : ( member @ X @ ( unordered_pair @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_1) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ~ ( member @ X @ ( singleton_set @ Y ) )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_2) ).
thf(6,axiom,
! [X: $i] : ( member @ X @ ( singleton_set @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_1) ).
thf(7,axiom,
( ( ordered_pair @ m1 @ r1 )
= ( ordered_pair @ m2 @ r2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_ordered_pairs) ).
thf(8,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(9,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,negated_conjecture,
r1 != r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_second_components_equal) ).
thf(11,plain,
$false = $false,
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i] :
( ( ordered_pair @ X @ Y )
= ( unordered_pair @ ( singleton_set @ X ) @ ( unordered_pair @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( member @ X @ ( unordered_pair @ Y @ Z ) )
| ( X = Y )
| ( X = Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ! [Y: $i,X: $i] : ( member @ Y @ ( unordered_pair @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i] : ( member @ X @ ( unordered_pair @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ X @ ( singleton_set @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ! [X: $i] : ( member @ X @ ( singleton_set @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ( ordered_pair @ m1 @ r1 )
= ( ordered_pair @ m2 @ r2 ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ( r1 != r2 ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(20,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(21,plain,
( ( ( r1 != r2 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(22,plain,
( ( ( r1 != r2 ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(23,plain,
( ( ( ordered_pair @ m1 @ r1 )
= ( ordered_pair @ m2 @ r2 ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(24,plain,
( ( ! [X: $i] : ( member @ X @ ( singleton_set @ X ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ X @ ( singleton_set @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i] : ( member @ X @ ( unordered_pair @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(27,plain,
( ( ! [Y: $i,X: $i] : ( member @ Y @ ( unordered_pair @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( member @ X @ ( unordered_pair @ Y @ Z ) )
| ( X = Y )
| ( X = Z ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ( ordered_pair @ X @ Y )
= ( unordered_pair @ ( singleton_set @ X ) @ ( unordered_pair @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(30,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(31,plain,
( ( r1 = r2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(32,plain,
! [SV1: $i] :
( ( member @ SV1 @ ( singleton_set @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(33,plain,
! [SV2: $i] :
( ( ! [SY12: $i] :
( ~ ( member @ SV2 @ ( singleton_set @ SY12 ) )
| ( SV2 = SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(34,plain,
! [SV3: $i] :
( ( ! [SY13: $i] : ( member @ SV3 @ ( unordered_pair @ SV3 @ SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(35,plain,
! [SV4: $i] :
( ( ! [SY14: $i] : ( member @ SV4 @ ( unordered_pair @ SY14 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(36,plain,
! [SV5: $i] :
( ( ! [SY15: $i,SY16: $i] :
( ~ ( member @ SV5 @ ( unordered_pair @ SY15 @ SY16 ) )
| ( SV5 = SY15 )
| ( SV5 = SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(37,plain,
! [SV6: $i] :
( ( ! [SY17: $i] :
( ( ordered_pair @ SV6 @ SY17 )
= ( unordered_pair @ ( singleton_set @ SV6 ) @ ( unordered_pair @ SV6 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(38,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(39,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( member @ SV2 @ ( singleton_set @ SV7 ) )
| ( SV2 = SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV8: $i,SV3: $i] :
( ( member @ SV3 @ ( unordered_pair @ SV3 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV9: $i,SV4: $i] :
( ( member @ SV4 @ ( unordered_pair @ SV9 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY18: $i] :
( ~ ( member @ SV5 @ ( unordered_pair @ SV10 @ SY18 ) )
| ( SV5 = SV10 )
| ( SV5 = SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV11: $i,SV6: $i] :
( ( ( ordered_pair @ SV6 @ SV11 )
= ( unordered_pair @ ( singleton_set @ SV6 ) @ ( unordered_pair @ SV6 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ ( singleton_set @ SV7 ) ) )
= $true )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ ( unordered_pair @ SV10 @ SV12 ) )
| ( SV5 = SV10 )
| ( SV5 = SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV7: $i,SV2: $i] :
( ( ( member @ SV2 @ ( singleton_set @ SV7 ) )
= $false )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ ( unordered_pair @ SV10 @ SV12 ) ) )
= $true )
| ( ( ( SV5 = SV10 )
| ( SV5 = SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( member @ SV5 @ ( unordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( ( SV5 = SV10 )
| ( SV5 = SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(49,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( SV5 = SV10 )
= $true )
| ( ( SV5 = SV12 )
= $true )
| ( ( member @ SV5 @ ( unordered_pair @ SV10 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(50,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,49,46,43,41,40,38,32,31]) ).
thf(51,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET018-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 08:22:32 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 8
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:8,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:10,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.19/0.41
% 0.19/0.41 ********************************
% 0.19/0.41 * All subproblems solved! *
% 0.19/0.41 ********************************
% 0.19/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:50,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.41
% 0.19/0.41 %**** Beginning of derivation protocol ****
% 0.19/0.41 % SZS output start CNFRefutation
% See solution above
% 0.19/0.41
% 0.19/0.41 %**** End of derivation protocol ****
% 0.19/0.41 %**** no. of clauses in derivation: 51 ****
% 0.19/0.41 %**** clause counter: 50 ****
% 0.19/0.41
% 0.19/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:50,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------