%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COL058-2 : TPTP v9.3.1. Released v1.0.0.
% 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 : n014.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 10:11:02 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.21s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 24 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 326 ( 6 ~; 0 |; 0 &; 320 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_lark,type,
lark: $i ).
thf(tp_response,type,
response: $i > $i > $i ).
thf(1,axiom,
! [X1: $i,X2: $i] :
( ( response @ ( response @ lark @ X1 ) @ X2 )
= ( response @ X1 @ ( response @ X2 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lark_exists) ).
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,
( ( response @ ( response @ ( response @ lark @ ( response @ ( response @ lark @ ( response @ lark @ lark ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) @ ( response @ ( response @ lark @ ( response @ ( response @ lark @ ( response @ lark @ lark ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) )
!= ( response @ ( response @ lark @ ( response @ ( response @ lark @ ( response @ lark @ lark ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_the_bird_exists) ).
thf(5,plain,
$false = $false,
inference(unfold_def,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [X1: $i,X2: $i] :
( ( response @ ( response @ lark @ X1 ) @ X2 )
= ( response @ X1 @ ( response @ X2 @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ( response @ ( response @ ( response @ lark @ ( response @ ( response @ lark @ ( response @ lark @ lark ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) @ ( response @ ( response @ lark @ ( response @ ( response @ lark @ ( response @ lark @ lark ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) )
!= ( response @ ( response @ lark @ ( response @ ( response @ lark @ ( response @ lark @ lark ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(9,plain,
( ( ( response @ ( response @ ( response @ lark @ ( response @ ( response @ lark @ ( response @ lark @ lark ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) @ ( response @ ( response @ lark @ ( response @ ( response @ lark @ ( response @ lark @ lark ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) )
!= ( response @ ( response @ lark @ ( response @ ( response @ lark @ ( response @ lark @ lark ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [X1: $i,X2: $i] :
( ( response @ ( response @ lark @ X1 ) @ X2 )
= ( response @ X1 @ ( response @ X2 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ( response @ ( response @ ( response @ lark @ ( response @ ( response @ lark @ ( response @ lark @ lark ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) @ ( response @ ( response @ lark @ ( response @ ( response @ lark @ ( response @ lark @ lark ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) )
!= ( response @ ( response @ lark @ ( response @ ( response @ lark @ ( response @ lark @ lark ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY2: $i] :
( ( response @ ( response @ lark @ SV1 ) @ SY2 )
= ( response @ SV1 @ ( response @ SY2 @ SY2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(14,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(15,plain,
( ( ( response @ ( response @ ( response @ lark @ ( response @ ( response @ lark @ ( response @ lark @ lark ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) @ ( response @ ( response @ lark @ ( response @ ( response @ lark @ ( response @ lark @ lark ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) )
= ( response @ ( response @ lark @ ( response @ ( response @ lark @ ( response @ lark @ lark ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) ) @ ( response @ lark @ ( response @ lark @ lark ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV2: $i,SV1: $i] :
( ( ( response @ ( response @ lark @ SV1 ) @ SV2 )
= ( response @ SV1 @ ( response @ SV2 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,16,15]) ).
thf(18,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL058-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n014.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 18:33:26 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.21
% 0.10/0.21 No.of.Axioms: 2
% 0.10/0.21
% 0.10/0.21 Length.of.Defs: 0
% 0.10/0.21
% 0.10/0.21 Contains.Choice.Funs: false
% 0.10/0.21
% 0.10/0.21 ********************************
% 0.10/0.21 * All subproblems solved! *
% 0.10/0.21 ********************************
% 0.10/0.21 % 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:17,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.21
% 0.10/0.21 %**** Beginning of derivation protocol ****
% 0.10/0.21 % SZS output start CNFRefutation
% See solution above
% 0.10/0.21
% 0.10/0.21 %**** End of derivation protocol ****
% 0.10/0.21 %**** no. of clauses in derivation: 18 ****
% 0.10/0.21 %**** clause counter: 17 ****
% 0.10/0.21
% 0.10/0.21 % 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:17,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------