TSTP Solution File: NUM698^1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM698^1 : 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 : n016.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 11:54:24 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 44 ( 23 unt; 10 typ; 0 def)
% Number of atoms : 148 ( 40 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 212 ( 12 ~; 16 |; 0 &; 180 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 54 ( 14 ^ 40 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_diffprop,type,
diffprop: nat > nat > nat > $o ).
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_pl,type,
pl: nat > nat > nat ).
thf(tp_sK1_E,type,
sK1_E: nat > nat > nat ).
thf(tp_some,type,
some: ( nat > $o ) > $o ).
thf(tp_x,type,
x: nat ).
thf(tp_y,type,
y: nat ).
thf(1,axiom,
! [Xx: nat,Xy: nat] :
( ( some
@ ^ [Xu: nat] : ( diffprop @ Xy @ Xx @ Xu ) )
=> ( moreis @ Xy @ ( pl @ Xx @ n_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz25) ).
thf(2,axiom,
! [Xx: nat,Xy: nat] :
( ( moreis @ Xx @ Xy )
=> ( lessis @ Xy @ Xx ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz13) ).
thf(3,axiom,
( some
@ ^ [Xv: nat] : ( diffprop @ x @ y @ Xv ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(4,conjecture,
lessis @ ( pl @ y @ n_1 ) @ x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz25b) ).
thf(5,negated_conjecture,
( ( lessis @ ( pl @ y @ n_1 ) @ x )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( lessis @ ( pl @ y @ n_1 ) @ x )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( some
@ ^ [Xu: nat] : ( diffprop @ Xy @ Xx @ Xu ) )
=> ( moreis @ Xy @ ( pl @ Xx @ n_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( moreis @ Xx @ Xy )
=> ( lessis @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( some
@ ^ [Xv: nat] : ( diffprop @ x @ y @ Xv ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ~ ( lessis @ ( pl @ y @ n_1 ) @ x ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(11,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( some
@ ^ [Xu: nat] : ( diffprop @ Xy @ Xx @ Xu ) )
| ( moreis @ Xy @ ( pl @ Xx @ n_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(12,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( moreis @ Xx @ Xy )
| ( lessis @ Xy @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(13,plain,
( ( some
@ ^ [Xv: nat] : ( diffprop @ x @ y @ Xv ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(14,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( moreis @ Xx @ Xy )
| ( lessis @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( some
@ ^ [Xu: nat] : ( diffprop @ Xy @ Xx @ Xu ) )
| ( moreis @ Xy @ ( pl @ Xx @ n_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(16,plain,
( ( ~ ( lessis @ ( pl @ y @ n_1 ) @ x ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(17,plain,
! [SV1: nat] :
( ( ! [SY6: nat] :
( ~ ( moreis @ SV1 @ SY6 )
| ( lessis @ SY6 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: nat] :
( ( ! [SY7: nat] :
( ~ ( some
@ ^ [SY8: nat] : ( diffprop @ SY7 @ SV2 @ SY8 ) )
| ( moreis @ SY7 @ ( pl @ SV2 @ n_1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( lessis @ ( pl @ y @ n_1 ) @ x )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV3: nat,SV1: nat] :
( ( ~ ( moreis @ SV1 @ SV3 )
| ( lessis @ SV3 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: nat,SV4: nat] :
( ( ~ ( some
@ ^ [SY9: nat] : ( diffprop @ SV4 @ SV2 @ SY9 ) )
| ( moreis @ SV4 @ ( pl @ SV2 @ n_1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV3: nat,SV1: nat] :
( ( ( ~ ( moreis @ SV1 @ SV3 ) )
= $true )
| ( ( lessis @ SV3 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV2: nat,SV4: nat] :
( ( ( ~ ( some
@ ^ [SY9: nat] : ( diffprop @ SV4 @ SV2 @ SY9 ) ) )
= $true )
| ( ( moreis @ SV4 @ ( pl @ SV2 @ n_1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV3: nat,SV1: nat] :
( ( ( moreis @ SV1 @ SV3 )
= $false )
| ( ( lessis @ SV3 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV2: nat,SV4: nat] :
( ( ( some
@ ^ [SY9: nat] : ( diffprop @ SV4 @ SV2 @ SY9 ) )
= $false )
| ( ( moreis @ SV4 @ ( pl @ SV2 @ n_1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV5: nat,SV6: nat] :
( ( ( moreis @ SV6 @ SV5 )
= $false )
| ( ( lessis @ SV5 @ SV6 )
= $true ) ),
inference(rename,[status(thm)],[24]) ).
thf(30,plain,
! [SV5: nat,SV6: nat] :
( ( ( ( lessis @ SV5 @ SV6 )
= ( lessis @ ( pl @ y @ n_1 ) @ x ) )
= $false )
| ( ( moreis @ SV6 @ SV5 )
= $false ) ),
inference(res,[status(thm)],[27,19]) ).
thf(32,plain,
( ( moreis @ x @ ( pl @ y @ n_1 ) )
= $false ),
inference(extuni,[status(esa)],[30:[bind(SV6,$thf( x )),bind(SV5,$thf( pl @ y @ n_1 ))]]) ).
thf(33,plain,
! [SV7: nat,SV8: nat] :
( ( ( some
@ ^ [SX0: nat] : ( diffprop @ SV8 @ SV7 @ SX0 ) )
= $false )
| ( ( moreis @ SV8 @ ( pl @ SV7 @ n_1 ) )
= $true ) ),
inference(rename,[status(thm)],[25]) ).
thf(39,plain,
! [SV7: nat,SV8: nat] :
( ( ( ( some
@ ^ [SX0: nat] : ( diffprop @ SV8 @ SV7 @ SX0 ) )
= ( some
@ ^ [Xv: nat] : ( diffprop @ x @ y @ Xv ) ) )
= $false )
| ( ( moreis @ SV8 @ ( pl @ SV7 @ n_1 ) )
= $true ) ),
inference(res,[status(thm)],[33,13]) ).
thf(40,plain,
( ( moreis @ x @ ( pl @ y @ n_1 ) )
= $true ),
inference(extuni,[status(esa)],[39:[bind(SV7,$thf( y )),bind(SV8,$thf( x ))]]) ).
thf(50,plain,
( ( ( moreis @ x @ ( pl @ y @ n_1 ) )
= ( moreis @ x @ ( pl @ y @ n_1 ) ) )
= $false ),
inference(res,[status(thm)],[40,32]) ).
thf(54,plain,
$false = $true,
inference(extuni,[status(esa)],[50]) ).
thf(55,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM698^1 : TPTP v8.1.0. Released v3.7.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 16:27:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 3
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.35 (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).
% 0.20/0.43
% 0.20/0.43 ********************************
% 0.20/0.43 * All subproblems solved! *
% 0.20/0.43 ********************************
% 0.20/0.43 % 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:54,loop_count:6,foatp_calls:1,translation:fof_full)
% 0.20/0.44
% 0.20/0.44 %**** Beginning of derivation protocol ****
% 0.20/0.44 % SZS output start CNFRefutation
% See solution above
% 0.20/0.44
% 0.20/0.44 %**** End of derivation protocol ****
% 0.20/0.44 %**** no. of clauses in derivation: 34 ****
% 0.20/0.44 %**** clause counter: 54 ****
% 0.20/0.44
% 0.20/0.44 % 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:54,loop_count:6,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------