%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM694^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n001.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 10:34:57 AM UTC 2026
% Result : Theorem 0.11s 0.18s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 18 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 66 ( 6 ~; 5 |; 0 &; 52 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_lessis,type,
lessis: nat > nat > $o ).
thf(tp_moreis,type,
moreis: nat > nat > $o ).
thf(tp_n_1,type,
n_1: nat ).
thf(tp_x,type,
x: nat ).
thf(1,axiom,
! [Xx: nat] : ( moreis @ Xx @ n_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz24) ).
thf(2,axiom,
! [Xx: nat,Xy: nat] :
( ( moreis @ Xx @ Xy )
=> ( lessis @ Xy @ Xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz13) ).
thf(3,conjecture,
lessis @ n_1 @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz24a) ).
thf(4,negated_conjecture,
( ( lessis @ n_1 @ x )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( lessis @ n_1 @ x )
= $false ),
inference(unfold_def,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [Xx: nat] : ( moreis @ Xx @ n_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( moreis @ Xx @ Xy )
=> ( lessis @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(8,plain,
( ( ~ ( lessis @ n_1 @ x ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( moreis @ Xx @ Xy )
=> ( lessis @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [Xx: nat] : ( moreis @ Xx @ n_1 ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
( ( ~ ( lessis @ n_1 @ x ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( moreis @ SX0 @ SX1 )
| ( lessis @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(13,plain,
! [SV1: nat] :
( ( moreis @ SV1 @ n_1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(14,plain,
( ( lessis @ n_1 @ x )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(15,plain,
! [SV2: nat] :
( ( ! [SY3: nat] :
( ~ ( moreis @ SV2 @ SY3 )
| ( lessis @ SY3 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV3: nat,SV2: nat] :
( ( ~ ( moreis @ SV2 @ SV3 )
| ( lessis @ SV3 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(17,plain,
! [SV3: nat,SV2: nat] :
( ( ( ~ ( moreis @ SV2 @ SV3 ) )
= $true )
| ( ( lessis @ SV3 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(18,plain,
! [SV3: nat,SV2: nat] :
( ( ( moreis @ SV2 @ SV3 )
= $false )
| ( ( lessis @ SV3 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(19,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[13,18,14]) ).
thf(20,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM694^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.11/0.16 % Computer : n001.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Oct 6 13:41:24 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.18
% 0.11/0.18 No.of.Axioms: 2
% 0.11/0.18
% 0.11/0.18 Length.of.Defs: 0
% 0.11/0.18
% 0.11/0.18 Contains.Choice.Funs: false
% 0.11/0.18
% 0.11/0.18 ********************************
% 0.11/0.18 * All subproblems solved! *
% 0.11/0.18 ********************************
% 0.11/0.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,ps:0,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:19,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.18
% 0.11/0.18 %**** Beginning of derivation protocol ****
% 0.11/0.18 % SZS output start CNFRefutation
% See solution above
% 0.11/0.18
% 0.11/0.18 %**** End of derivation protocol ****
% 0.11/0.18 %**** no. of clauses in derivation: 20 ****
% 0.11/0.18 %**** clause counter: 19 ****
% 0.11/0.18
% 0.11/0.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,ps:0,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:19,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------