%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM699^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 10:34:58 AM UTC 2026
% Result : Theorem 0.11s 0.23s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 24 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 98 ( 6 ~; 5 |; 0 &; 84 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_less,type,
less: nat > nat > $o ).
thf(tp_lessis,type,
lessis: nat > nat > $o ).
thf(tp_n_1,type,
n_1: nat ).
thf(tp_pl,type,
pl: nat > nat > nat ).
thf(tp_suc,type,
suc: nat > nat ).
thf(tp_x,type,
x: nat ).
thf(tp_y,type,
y: nat ).
thf(1,axiom,
! [Xx: nat] :
( ( pl @ Xx @ n_1 )
= ( suc @ Xx ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz4a) ).
thf(2,axiom,
! [Xx: nat,Xy: nat] :
( ( less @ Xy @ Xx )
=> ( lessis @ ( pl @ Xy @ n_1 ) @ Xx ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz25b) ).
thf(3,axiom,
less @ y @ x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(4,conjecture,
lessis @ ( suc @ y ) @ x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz25c) ).
thf(5,negated_conjecture,
( ( lessis @ ( suc @ y ) @ x )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( lessis @ ( suc @ y ) @ x )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [Xx: nat] :
( ( pl @ Xx @ n_1 )
= ( suc @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( less @ Xy @ Xx )
=> ( lessis @ ( pl @ Xy @ n_1 ) @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( less @ y @ x )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ~ ( lessis @ ( suc @ y ) @ x ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(11,plain,
( ( less @ y @ x )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( less @ Xy @ Xx )
=> ( lessis @ ( pl @ Xy @ n_1 ) @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ! [Xx: nat] :
( ( pl @ Xx @ n_1 )
= ( suc @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ ( lessis @ ( suc @ y ) @ x ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( less @ SX1 @ SX0 )
| ( lessis @ ( pl @ SX1 @ n_1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(16,plain,
! [SV1: nat] :
( ( ( pl @ SV1 @ n_1 )
= ( suc @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,plain,
( ( lessis @ ( suc @ y ) @ x )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: nat] :
( ( ! [SY3: nat] :
( ~ ( less @ SY3 @ SV2 )
| ( lessis @ ( pl @ SY3 @ n_1 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: nat,SV3: nat] :
( ( ~ ( less @ SV3 @ SV2 )
| ( lessis @ ( pl @ SV3 @ n_1 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(20,plain,
! [SV2: nat,SV3: nat] :
( ( ( ~ ( less @ SV3 @ SV2 ) )
= $true )
| ( ( lessis @ ( pl @ SV3 @ n_1 ) @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(21,plain,
! [SV2: nat,SV3: nat] :
( ( ( less @ SV3 @ SV2 )
= $false )
| ( ( lessis @ ( pl @ SV3 @ n_1 ) @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(22,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[11,21,17,16]) ).
thf(23,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM699^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.18 % Computer : n013.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 13:34:36 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.23
% 0.11/0.23 No.of.Axioms: 3
% 0.11/0.23
% 0.11/0.23 Length.of.Defs: 0
% 0.11/0.23
% 0.11/0.23 Contains.Choice.Funs: false
% 0.11/0.23
% 0.11/0.23 ********************************
% 0.11/0.23 * All subproblems solved! *
% 0.11/0.23 ********************************
% 0.11/0.23 % SZS status Theorem for /export/starexec/sandbox/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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:22,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.23
% 0.11/0.23 %**** Beginning of derivation protocol ****
% 0.11/0.23 % SZS output start CNFRefutation
% See solution above
% 0.11/0.23
% 0.11/0.23 %**** End of derivation protocol ****
% 0.11/0.23 %**** no. of clauses in derivation: 23 ****
% 0.11/0.23 %**** clause counter: 22 ****
% 0.11/0.23
% 0.11/0.23 % SZS status Theorem for /export/starexec/sandbox/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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:22,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------