%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LAT092-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:26:57 AM UTC 2026
% Result : Unsatisfiable 126.76s 21.38s
% Output : CNFRefutation 126.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 32 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 664 ( 6 ~; 0 |; 0 &; 658 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_join,type,
join: $i > $i > $i ).
thf(tp_meet,type,
meet: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( join @ ( meet @ ( join @ ( meet @ A @ B ) @ ( meet @ B @ ( join @ A @ B ) ) ) @ C ) @ ( meet @ ( join @ ( meet @ A @ ( join @ ( join @ ( meet @ B @ D ) @ ( meet @ E @ B ) ) @ B ) ) @ ( meet @ ( join @ ( meet @ B @ ( meet @ ( meet @ ( join @ B @ D ) @ ( join @ E @ B ) ) @ B ) ) @ ( meet @ F @ ( join @ B @ ( meet @ ( meet @ ( join @ B @ D ) @ ( join @ E @ B ) ) @ B ) ) ) ) @ ( join @ A @ ( join @ ( join @ ( meet @ B @ D ) @ ( meet @ E @ B ) ) @ B ) ) ) ) @ ( join @ ( join @ ( meet @ A @ B ) @ ( meet @ B @ ( join @ A @ B ) ) ) @ C ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
thf(2,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(3,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,negated_conjecture,
( ( meet @ a @ a )
!= a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wal_axioms_1) ).
thf(5,plain,
$false = $false,
inference(unfold_def,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( join @ ( meet @ ( join @ ( meet @ A @ B ) @ ( meet @ B @ ( join @ A @ B ) ) ) @ C ) @ ( meet @ ( join @ ( meet @ A @ ( join @ ( join @ ( meet @ B @ D ) @ ( meet @ E @ B ) ) @ B ) ) @ ( meet @ ( join @ ( meet @ B @ ( meet @ ( meet @ ( join @ B @ D ) @ ( join @ E @ B ) ) @ B ) ) @ ( meet @ F @ ( join @ B @ ( meet @ ( meet @ ( join @ B @ D ) @ ( join @ E @ B ) ) @ B ) ) ) ) @ ( join @ A @ ( join @ ( join @ ( meet @ B @ D ) @ ( meet @ E @ B ) ) @ B ) ) ) ) @ ( join @ ( join @ ( meet @ A @ B ) @ ( meet @ B @ ( join @ A @ B ) ) ) @ C ) ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ( meet @ a @ a )
!= a )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(9,plain,
( ( ( meet @ a @ a )
!= a )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( join @ ( meet @ ( join @ ( meet @ A @ B ) @ ( meet @ B @ ( join @ A @ B ) ) ) @ C ) @ ( meet @ ( join @ ( meet @ A @ ( join @ ( join @ ( meet @ B @ D ) @ ( meet @ E @ B ) ) @ B ) ) @ ( meet @ ( join @ ( meet @ B @ ( meet @ ( meet @ ( join @ B @ D ) @ ( join @ E @ B ) ) @ B ) ) @ ( meet @ F @ ( join @ B @ ( meet @ ( meet @ ( join @ B @ D ) @ ( join @ E @ B ) ) @ B ) ) ) ) @ ( join @ A @ ( join @ ( join @ ( meet @ B @ D ) @ ( meet @ E @ B ) ) @ B ) ) ) ) @ ( join @ ( join @ ( meet @ A @ B ) @ ( meet @ B @ ( join @ A @ B ) ) ) @ C ) ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ( meet @ a @ a )
!= a )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY6: $i,SY7: $i,SY8: $i,SY9: $i,SY10: $i] :
( ( join @ ( meet @ ( join @ ( meet @ SV1 @ SY6 ) @ ( meet @ SY6 @ ( join @ SV1 @ SY6 ) ) ) @ SY7 ) @ ( meet @ ( join @ ( meet @ SV1 @ ( join @ ( join @ ( meet @ SY6 @ SY8 ) @ ( meet @ SY9 @ SY6 ) ) @ SY6 ) ) @ ( meet @ ( join @ ( meet @ SY6 @ ( meet @ ( meet @ ( join @ SY6 @ SY8 ) @ ( join @ SY9 @ SY6 ) ) @ SY6 ) ) @ ( meet @ SY10 @ ( join @ SY6 @ ( meet @ ( meet @ ( join @ SY6 @ SY8 ) @ ( join @ SY9 @ SY6 ) ) @ SY6 ) ) ) ) @ ( join @ SV1 @ ( join @ ( join @ ( meet @ SY6 @ SY8 ) @ ( meet @ SY9 @ SY6 ) ) @ SY6 ) ) ) ) @ ( join @ ( join @ ( meet @ SV1 @ SY6 ) @ ( meet @ SY6 @ ( join @ SV1 @ SY6 ) ) ) @ SY7 ) ) )
= SY6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(14,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(15,plain,
( ( ( meet @ a @ a )
= a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY11: $i,SY12: $i,SY13: $i,SY14: $i] :
( ( join @ ( meet @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SY11 ) @ ( meet @ ( join @ ( meet @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SY12 ) @ ( meet @ SY13 @ SV2 ) ) @ SV2 ) ) @ ( meet @ ( join @ ( meet @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SY12 ) @ ( join @ SY13 @ SV2 ) ) @ SV2 ) ) @ ( meet @ SY14 @ ( join @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SY12 ) @ ( join @ SY13 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SY12 ) @ ( meet @ SY13 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SY11 ) ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY15: $i,SY16: $i,SY17: $i] :
( ( join @ ( meet @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SV3 ) @ ( meet @ ( join @ ( meet @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SY15 ) @ ( meet @ SY16 @ SV2 ) ) @ SV2 ) ) @ ( meet @ ( join @ ( meet @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SY15 ) @ ( join @ SY16 @ SV2 ) ) @ SV2 ) ) @ ( meet @ SY17 @ ( join @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SY15 ) @ ( join @ SY16 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SY15 ) @ ( meet @ SY16 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SV3 ) ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(18,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ( join @ ( meet @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SV3 ) @ ( meet @ ( join @ ( meet @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SV4 ) @ ( meet @ SY18 @ SV2 ) ) @ SV2 ) ) @ ( meet @ ( join @ ( meet @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SV4 ) @ ( join @ SY18 @ SV2 ) ) @ SV2 ) ) @ ( meet @ SY19 @ ( join @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SV4 ) @ ( join @ SY18 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SV4 ) @ ( meet @ SY18 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SV3 ) ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(19,plain,
! [SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY20: $i] :
( ( join @ ( meet @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SV3 ) @ ( meet @ ( join @ ( meet @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SV4 ) @ ( meet @ SV5 @ SV2 ) ) @ SV2 ) ) @ ( meet @ ( join @ ( meet @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SV4 ) @ ( join @ SV5 @ SV2 ) ) @ SV2 ) ) @ ( meet @ SY20 @ ( join @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SV4 ) @ ( join @ SV5 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SV4 ) @ ( meet @ SV5 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SV3 ) ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(20,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( join @ ( meet @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SV3 ) @ ( meet @ ( join @ ( meet @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SV4 ) @ ( meet @ SV5 @ SV2 ) ) @ SV2 ) ) @ ( meet @ ( join @ ( meet @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SV4 ) @ ( join @ SV5 @ SV2 ) ) @ SV2 ) ) @ ( meet @ SV6 @ ( join @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SV4 ) @ ( join @ SV5 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SV4 ) @ ( meet @ SV5 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SV3 ) ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(21,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,20,15]) ).
thf(22,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LAT092-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.12 % Computer : n012.cluster.edu
% 0.00/0.12 % Model : x86_64 x86_64
% 0.00/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.12 % Memory : 8046.5625MB
% 0.00/0.12 % OS : Linux 6.8.0-71-generic
% 0.00/0.12 % CPULimit : 300
% 0.10/0.12 % WCLimit : 300
% 0.10/0.12 % DateTime : Tue Oct 6 11:46:46 UTC 2026
% 0.10/0.12 % CPUTime :
% 0.10/0.12 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 126.76/21.38
% 126.76/21.38 No.of.Axioms: 2
% 126.76/21.38
% 126.76/21.38 Length.of.Defs: 0
% 126.76/21.38
% 126.76/21.38 Contains.Choice.Funs: false
% 126.76/21.38 .
% 126.76/21.38
% 126.76/21.38 ********************************
% 126.76/21.38 * All subproblems solved! *
% 126.76/21.38 ********************************
% 126.76/21.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:21,loop_count:0,foatp_calls:1,translation:fof_full)
% 126.76/21.38
% 126.76/21.38 %**** Beginning of derivation protocol ****
% 126.76/21.38 % SZS output start CNFRefutation
% See solution above
% 126.76/21.38
% 126.76/21.38 %**** End of derivation protocol ****
% 126.76/21.38 %**** no. of clauses in derivation: 22 ****
% 126.76/21.38 %**** clause counter: 21 ****
% 126.76/21.38
% 126.76/21.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:21,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------