TSTP Solution File: NUM699^1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM699^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n028.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 : Mon Jul 18 11:54:25 EDT 2022
% Result : Theorem 0.11s 0.36s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 31 ( 20 unt; 8 typ; 0 def)
% Number of atoms : 71 ( 24 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 99 ( 7 ~; 6 |; 0 &; 84 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 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,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( less @ Xy @ Xx )
| ( lessis @ ( pl @ Xy @ n_1 ) @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(12,plain,
( ( less @ y @ x )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( less @ Xy @ Xx )
| ( lessis @ ( pl @ Xy @ n_1 ) @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [Xx: nat] :
( ( pl @ Xx @ n_1 )
= ( suc @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(15,plain,
( ( ~ ( lessis @ ( suc @ y ) @ x ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
! [SV1: nat] :
( ( ! [SY3: nat] :
( ~ ( less @ SY3 @ SV1 )
| ( lessis @ ( pl @ SY3 @ n_1 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV2: nat] :
( ( ( pl @ SV2 @ n_1 )
= ( suc @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( lessis @ ( suc @ y ) @ x )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV1: nat,SV3: nat] :
( ( ~ ( less @ SV3 @ SV1 )
| ( lessis @ ( pl @ SV3 @ n_1 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV1: nat,SV3: nat] :
( ( ( ~ ( less @ SV3 @ SV1 ) )
= $true )
| ( ( lessis @ ( pl @ SV3 @ n_1 ) @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(21,plain,
! [SV1: nat,SV3: nat] :
( ( ( less @ SV3 @ SV1 )
= $false )
| ( ( lessis @ ( pl @ SV3 @ n_1 ) @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(22,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[12,21,18,17]) ).
thf(23,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM699^1 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.11/0.33 % Computer : n028.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jul 6 06:29:07 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34
% 0.11/0.34 No.of.Axioms: 3
% 0.11/0.34
% 0.11/0.34 Length.of.Defs: 0
% 0.11/0.34
% 0.11/0.34 Contains.Choice.Funs: false
% 0.11/0.34 (rf:0,axioms:3,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:5,loop_count:0,foatp_calls:0,translation:fof_full)
% 0.11/0.36 ********************************
% 0.11/0.36 * All subproblems solved! *
% 0.11/0.36 ********************************
% 0.11/0.36 % 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:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:22,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.36
% 0.11/0.36 %**** Beginning of derivation protocol ****
% 0.11/0.36 % SZS output start CNFRefutation
% See solution above
% 0.11/0.36
% 0.11/0.36 %**** End of derivation protocol ****
% 0.11/0.36 %**** no. of clauses in derivation: 23 ****
% 0.11/0.36 %**** clause counter: 22 ****
% 0.11/0.36
% 0.11/0.36 % 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:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:22,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------