TSTP Solution File: LAT006-1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LAT006-1 : 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 : 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 : Sun Jul 17 05:43:57 EDT 2022
% Result : Unsatisfiable 0.90s 1.07s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 24 unt; 5 typ; 0 def)
% Number of atoms : 62 ( 35 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 126 ( 6 ~; 0 |; 0 &; 120 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 ^ 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_join,type,
join: $i > $i > $i ).
thf(tp_meet,type,
meet: $i > $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( meet @ X @ ( join @ Y @ Z ) )
= ( join @ ( meet @ Z @ X ) @ ( meet @ Y @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribution) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( meet @ X @ ( join @ X @ Y ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption) ).
thf(3,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(4,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,negated_conjecture,
( meet @ ( meet @ a @ b ) @ c )
!= ( meet @ a @ ( meet @ b @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_meet) ).
thf(6,plain,
$false = $false,
inference(unfold_def,[status(thm)],[4]) ).
thf(7,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( meet @ X @ ( join @ Y @ Z ) )
= ( join @ ( meet @ Z @ X ) @ ( meet @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [X: $i,Y: $i] :
( ( meet @ X @ ( join @ X @ Y ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ( ( meet @ ( meet @ a @ b ) @ c )
!= ( meet @ a @ ( meet @ b @ c ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(10,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(11,plain,
( ( ( ( meet @ ( meet @ a @ b ) @ c )
!= ( meet @ a @ ( meet @ b @ c ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(12,plain,
( ( ( ( meet @ ( meet @ a @ b ) @ c )
!= ( meet @ a @ ( meet @ b @ c ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i] :
( ( meet @ X @ ( join @ X @ Y ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( meet @ X @ ( join @ Y @ Z ) )
= ( join @ ( meet @ Z @ X ) @ ( meet @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(15,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ( meet @ ( meet @ a @ b ) @ c )
= ( meet @ a @ ( meet @ b @ c ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(17,plain,
! [SV1: $i] :
( ( ! [SY5: $i] :
( ( meet @ SV1 @ ( join @ SV1 @ SY5 ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(18,plain,
! [SV2: $i] :
( ( ! [SY6: $i,SY7: $i] :
( ( meet @ SV2 @ ( join @ SY6 @ SY7 ) )
= ( join @ ( meet @ SY7 @ SV2 ) @ ( meet @ SY6 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(19,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV3: $i,SV1: $i] :
( ( ( meet @ SV1 @ ( join @ SV1 @ SV3 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY8: $i] :
( ( meet @ SV2 @ ( join @ SV4 @ SY8 ) )
= ( join @ ( meet @ SY8 @ SV2 ) @ ( meet @ SV4 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ( meet @ SV2 @ ( join @ SV4 @ SV5 ) )
= ( join @ ( meet @ SV5 @ SV2 ) @ ( meet @ SV4 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(23,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,22,20,19]) ).
thf(24,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT006-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % 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 : Thu Jun 30 04:55:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 3
% 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:3,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:5,loop_count:0,foatp_calls:0,translation:fof_full)
% 0.90/1.07 ********************************
% 0.90/1.07 * All subproblems solved! *
% 0.90/1.07 ********************************
% 0.90/1.07 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:23,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.90/1.07
% 0.90/1.07 %**** Beginning of derivation protocol ****
% 0.90/1.07 % SZS output start CNFRefutation
% See solution above
% 0.90/1.07
% 0.90/1.07 %**** End of derivation protocol ****
% 0.90/1.07 %**** no. of clauses in derivation: 24 ****
% 0.90/1.07 %**** clause counter: 23 ****
% 0.90/1.07
% 0.90/1.07 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:23,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------