TSTP Solution File: LAT009-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LAT009-1 : 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 : n020.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 05:43:58 EDT 2022
% Result : Unsatisfiable 4.24s 4.47s
% Output : CNFRefutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 64 ( 59 unt; 5 typ; 0 def)
% Number of atoms : 153 ( 98 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 368 ( 6 ~; 0 |; 0 &; 362 @)
% ( 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 : 102 ( 0 ^ 102 !; 0 ?; 102 :)
% 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] :
( ( join @ ( meet @ ( join @ ( meet @ X @ Y ) @ Z ) @ Y ) @ ( meet @ Z @ X ) )
= ( meet @ ( join @ ( meet @ ( join @ X @ Y ) @ Z ) @ Y ) @ ( join @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_dual) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( join @ ( join @ X @ Y ) @ Z )
= ( join @ X @ ( join @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( meet @ ( meet @ X @ Y ) @ Z )
= ( meet @ X @ ( meet @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ( join @ X @ Y )
= ( join @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( meet @ X @ Y )
= ( meet @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(6,axiom,
! [X: $i,Y: $i] :
( ( join @ X @ ( meet @ X @ Y ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
thf(7,axiom,
! [X: $i,Y: $i] :
( ( meet @ X @ ( join @ X @ Y ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
thf(8,axiom,
! [X: $i] :
( ( join @ X @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(9,axiom,
! [X: $i] :
( ( meet @ X @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(10,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(11,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,negated_conjecture,
( join @ a @ ( meet @ b @ c ) )
!= ( meet @ ( join @ a @ b ) @ ( join @ a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
thf(13,plain,
$false = $false,
inference(unfold_def,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( join @ ( meet @ ( join @ ( meet @ X @ Y ) @ Z ) @ Y ) @ ( meet @ Z @ X ) )
= ( meet @ ( join @ ( meet @ ( join @ X @ Y ) @ Z ) @ Y ) @ ( join @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( join @ ( join @ X @ Y ) @ Z )
= ( join @ X @ ( join @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( meet @ ( meet @ X @ Y ) @ Z )
= ( meet @ X @ ( meet @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i] :
( ( join @ X @ Y )
= ( join @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i] :
( ( meet @ X @ Y )
= ( meet @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i] :
( ( join @ X @ ( meet @ X @ Y ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i] :
( ( meet @ X @ ( join @ X @ Y ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(21,plain,
( ( ! [X: $i] :
( ( join @ X @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(22,plain,
( ( ! [X: $i] :
( ( meet @ X @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(23,plain,
( ( ( ( join @ a @ ( meet @ b @ c ) )
!= ( meet @ ( join @ a @ b ) @ ( join @ a @ c ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(24,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(25,plain,
( ( ( ( join @ a @ ( meet @ b @ c ) )
!= ( meet @ ( join @ a @ b ) @ ( join @ a @ c ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(26,plain,
( ( ( ( join @ a @ ( meet @ b @ c ) )
!= ( meet @ ( join @ a @ b ) @ ( join @ a @ c ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(27,plain,
( ( ! [X: $i] :
( ( meet @ X @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(28,plain,
( ( ! [X: $i] :
( ( join @ X @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ( meet @ X @ ( join @ X @ Y ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i] :
( ( join @ X @ ( meet @ X @ Y ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i] :
( ( meet @ X @ Y )
= ( meet @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ( join @ X @ Y )
= ( join @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( meet @ ( meet @ X @ Y ) @ Z )
= ( meet @ X @ ( meet @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( join @ ( join @ X @ Y ) @ Z )
= ( join @ X @ ( join @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(35,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( join @ ( meet @ ( join @ ( meet @ X @ Y ) @ Z ) @ Y ) @ ( meet @ Z @ X ) )
= ( meet @ ( join @ ( meet @ ( join @ X @ Y ) @ Z ) @ Y ) @ ( join @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(36,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(37,plain,
( ( ( join @ a @ ( meet @ b @ c ) )
= ( meet @ ( join @ a @ b ) @ ( join @ a @ c ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(38,plain,
! [SV1: $i] :
( ( ( meet @ SV1 @ SV1 )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(39,plain,
! [SV2: $i] :
( ( ( join @ SV2 @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(40,plain,
! [SV3: $i] :
( ( ! [SY19: $i] :
( ( meet @ SV3 @ ( join @ SV3 @ SY19 ) )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(41,plain,
! [SV4: $i] :
( ( ! [SY20: $i] :
( ( join @ SV4 @ ( meet @ SV4 @ SY20 ) )
= SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(42,plain,
! [SV5: $i] :
( ( ! [SY21: $i] :
( ( meet @ SV5 @ SY21 )
= ( meet @ SY21 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(43,plain,
! [SV6: $i] :
( ( ! [SY22: $i] :
( ( join @ SV6 @ SY22 )
= ( join @ SY22 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(44,plain,
! [SV7: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ( meet @ ( meet @ SV7 @ SY23 ) @ SY24 )
= ( meet @ SV7 @ ( meet @ SY23 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(45,plain,
! [SV8: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ( join @ ( join @ SV8 @ SY25 ) @ SY26 )
= ( join @ SV8 @ ( join @ SY25 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(46,plain,
! [SV9: $i] :
( ( ! [SY27: $i,SY28: $i] :
( ( join @ ( meet @ ( join @ ( meet @ SV9 @ SY27 ) @ SY28 ) @ SY27 ) @ ( meet @ SY28 @ SV9 ) )
= ( meet @ ( join @ ( meet @ ( join @ SV9 @ SY27 ) @ SY28 ) @ SY27 ) @ ( join @ SY28 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(47,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(48,plain,
! [SV10: $i,SV3: $i] :
( ( ( meet @ SV3 @ ( join @ SV3 @ SV10 ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(49,plain,
! [SV11: $i,SV4: $i] :
( ( ( join @ SV4 @ ( meet @ SV4 @ SV11 ) )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV12: $i,SV5: $i] :
( ( ( meet @ SV5 @ SV12 )
= ( meet @ SV12 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV13: $i,SV6: $i] :
( ( ( join @ SV6 @ SV13 )
= ( join @ SV13 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV14: $i,SV7: $i] :
( ( ! [SY29: $i] :
( ( meet @ ( meet @ SV7 @ SV14 ) @ SY29 )
= ( meet @ SV7 @ ( meet @ SV14 @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(53,plain,
! [SV15: $i,SV8: $i] :
( ( ! [SY30: $i] :
( ( join @ ( join @ SV8 @ SV15 ) @ SY30 )
= ( join @ SV8 @ ( join @ SV15 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(54,plain,
! [SV16: $i,SV9: $i] :
( ( ! [SY31: $i] :
( ( join @ ( meet @ ( join @ ( meet @ SV9 @ SV16 ) @ SY31 ) @ SV16 ) @ ( meet @ SY31 @ SV9 ) )
= ( meet @ ( join @ ( meet @ ( join @ SV9 @ SV16 ) @ SY31 ) @ SV16 ) @ ( join @ SY31 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(55,plain,
! [SV17: $i,SV14: $i,SV7: $i] :
( ( ( meet @ ( meet @ SV7 @ SV14 ) @ SV17 )
= ( meet @ SV7 @ ( meet @ SV14 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV18: $i,SV15: $i,SV8: $i] :
( ( ( join @ ( join @ SV8 @ SV15 ) @ SV18 )
= ( join @ SV8 @ ( join @ SV15 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV19: $i,SV16: $i,SV9: $i] :
( ( ( join @ ( meet @ ( join @ ( meet @ SV9 @ SV16 ) @ SV19 ) @ SV16 ) @ ( meet @ SV19 @ SV9 ) )
= ( meet @ ( join @ ( meet @ ( join @ SV9 @ SV16 ) @ SV19 ) @ SV16 ) @ ( join @ SV19 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(58,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[37,57,56,55,51,50,49,48,47,39,38]) ).
thf(59,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT009-1 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 29 22:21:46 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 10
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:10,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:12,loop_count:0,foatp_calls:0,translation:fof_full)...
% 4.24/4.47
% 4.24/4.47 ********************************
% 4.24/4.47 * All subproblems solved! *
% 4.24/4.47 ********************************
% 4.24/4.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,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:58,loop_count:0,foatp_calls:1,translation:fof_full)
% 4.24/4.47
% 4.24/4.47 %**** Beginning of derivation protocol ****
% 4.24/4.47 % SZS output start CNFRefutation
% See solution above
% 4.24/4.47
% 4.24/4.47 %**** End of derivation protocol ****
% 4.24/4.47 %**** no. of clauses in derivation: 59 ****
% 4.24/4.47 %**** clause counter: 58 ****
% 4.24/4.47
% 4.24/4.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,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:58,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------