TSTP Solution File: PRO009+2 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : PRO009+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 : 300s
% DateTime : Tue Apr 30 20:36:43 EDT 2024
% Result : Theorem 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 3 unt; 0 def)
% Number of atoms : 213 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 264 ( 106 ~; 97 |; 51 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 5 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 94 ( 76 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( min_precedes(X0,X1,X3)
& min_precedes(X1,X2,X3) )
=> min_precedes(X0,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X15,X16,X17] :
( next_subocc(X15,X16,X17)
<=> ( min_precedes(X15,X16,X17)
& ~ ? [X18] :
( min_precedes(X15,X18,X17)
& min_precedes(X18,X16,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X95] :
( occurrence_of(X95,tptp0)
=> ? [X96,X97,X98] :
( occurrence_of(X96,tptp3)
& root_occ(X96,X95)
& occurrence_of(X97,tptp4)
& next_subocc(X96,X97,tptp0)
& ( occurrence_of(X98,tptp2)
| occurrence_of(X98,tptp1) )
& next_subocc(X97,X98,tptp0)
& leaf_occ(X98,X95) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,conjecture,
! [X99] :
( occurrence_of(X99,tptp0)
=> ? [X100,X101] :
( occurrence_of(X100,tptp3)
& root_occ(X100,X99)
& ( occurrence_of(X101,tptp2)
| occurrence_of(X101,tptp1) )
& min_precedes(X100,X101,tptp0)
& leaf_occ(X101,X99) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
~ ! [X99] :
( occurrence_of(X99,tptp0)
=> ? [X100,X101] :
( occurrence_of(X100,tptp3)
& root_occ(X100,X99)
& ( occurrence_of(X101,tptp2)
| occurrence_of(X101,tptp1) )
& min_precedes(X100,X101,tptp0)
& leaf_occ(X101,X99) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ~ min_precedes(X0,X1,X3)
| ~ min_precedes(X1,X2,X3)
| min_precedes(X0,X2,X3) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f49,plain,
! [X0,X2,X3] :
( ! [X1] :
( ~ min_precedes(X0,X1,X3)
| ~ min_precedes(X1,X2,X3) )
| min_precedes(X0,X2,X3) ),
inference(miniscoping,[status(esa)],[f48]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( ~ min_precedes(X0,X1,X2)
| ~ min_precedes(X1,X3,X2)
| min_precedes(X0,X3,X2) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f60,plain,
! [X15,X16,X17] :
( next_subocc(X15,X16,X17)
<=> ( min_precedes(X15,X16,X17)
& ! [X18] :
( ~ min_precedes(X15,X18,X17)
| ~ min_precedes(X18,X16,X17) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f61,plain,
! [X15,X16,X17] :
( ( ~ next_subocc(X15,X16,X17)
| ( min_precedes(X15,X16,X17)
& ! [X18] :
( ~ min_precedes(X15,X18,X17)
| ~ min_precedes(X18,X16,X17) ) ) )
& ( next_subocc(X15,X16,X17)
| ~ min_precedes(X15,X16,X17)
| ? [X18] :
( min_precedes(X15,X18,X17)
& min_precedes(X18,X16,X17) ) ) ),
inference(NNF_transformation,[status(esa)],[f60]) ).
fof(f62,plain,
( ! [X15,X16,X17] :
( ~ next_subocc(X15,X16,X17)
| ( min_precedes(X15,X16,X17)
& ! [X18] :
( ~ min_precedes(X15,X18,X17)
| ~ min_precedes(X18,X16,X17) ) ) )
& ! [X15,X16,X17] :
( next_subocc(X15,X16,X17)
| ~ min_precedes(X15,X16,X17)
| ? [X18] :
( min_precedes(X15,X18,X17)
& min_precedes(X18,X16,X17) ) ) ),
inference(miniscoping,[status(esa)],[f61]) ).
fof(f63,plain,
( ! [X15,X16,X17] :
( ~ next_subocc(X15,X16,X17)
| ( min_precedes(X15,X16,X17)
& ! [X18] :
( ~ min_precedes(X15,X18,X17)
| ~ min_precedes(X18,X16,X17) ) ) )
& ! [X15,X16,X17] :
( next_subocc(X15,X16,X17)
| ~ min_precedes(X15,X16,X17)
| ( min_precedes(X15,sk0_0(X17,X16,X15),X17)
& min_precedes(sk0_0(X17,X16,X15),X16,X17) ) ) ),
inference(skolemization,[status(esa)],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ next_subocc(X0,X1,X2)
| min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f177,plain,
! [X95] :
( ~ occurrence_of(X95,tptp0)
| ? [X96,X97,X98] :
( occurrence_of(X96,tptp3)
& root_occ(X96,X95)
& occurrence_of(X97,tptp4)
& next_subocc(X96,X97,tptp0)
& ( occurrence_of(X98,tptp2)
| occurrence_of(X98,tptp1) )
& next_subocc(X97,X98,tptp0)
& leaf_occ(X98,X95) ) ),
inference(pre_NNF_transformation,[status(esa)],[f33]) ).
fof(f178,plain,
! [X95] :
( ~ occurrence_of(X95,tptp0)
| ? [X98] :
( ? [X97] :
( ? [X96] :
( occurrence_of(X96,tptp3)
& root_occ(X96,X95)
& occurrence_of(X97,tptp4)
& next_subocc(X96,X97,tptp0) )
& ( occurrence_of(X98,tptp2)
| occurrence_of(X98,tptp1) )
& next_subocc(X97,X98,tptp0) )
& leaf_occ(X98,X95) ) ),
inference(miniscoping,[status(esa)],[f177]) ).
fof(f179,plain,
! [X95] :
( ~ occurrence_of(X95,tptp0)
| ( occurrence_of(sk0_16(X95),tptp3)
& root_occ(sk0_16(X95),X95)
& occurrence_of(sk0_15(X95),tptp4)
& next_subocc(sk0_16(X95),sk0_15(X95),tptp0)
& ( occurrence_of(sk0_14(X95),tptp2)
| occurrence_of(sk0_14(X95),tptp1) )
& next_subocc(sk0_15(X95),sk0_14(X95),tptp0)
& leaf_occ(sk0_14(X95),X95) ) ),
inference(skolemization,[status(esa)],[f178]) ).
fof(f180,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| occurrence_of(sk0_16(X0),tptp3) ),
inference(cnf_transformation,[status(esa)],[f179]) ).
fof(f181,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| root_occ(sk0_16(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f179]) ).
fof(f183,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| next_subocc(sk0_16(X0),sk0_15(X0),tptp0) ),
inference(cnf_transformation,[status(esa)],[f179]) ).
fof(f184,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| occurrence_of(sk0_14(X0),tptp2)
| occurrence_of(sk0_14(X0),tptp1) ),
inference(cnf_transformation,[status(esa)],[f179]) ).
fof(f185,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| next_subocc(sk0_15(X0),sk0_14(X0),tptp0) ),
inference(cnf_transformation,[status(esa)],[f179]) ).
fof(f186,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| leaf_occ(sk0_14(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f179]) ).
fof(f199,plain,
? [X99] :
( occurrence_of(X99,tptp0)
& ! [X100,X101] :
( ~ occurrence_of(X100,tptp3)
| ~ root_occ(X100,X99)
| ( ~ occurrence_of(X101,tptp2)
& ~ occurrence_of(X101,tptp1) )
| ~ min_precedes(X100,X101,tptp0)
| ~ leaf_occ(X101,X99) ) ),
inference(pre_NNF_transformation,[status(esa)],[f47]) ).
fof(f200,plain,
? [X99] :
( occurrence_of(X99,tptp0)
& ! [X101] :
( ! [X100] :
( ~ occurrence_of(X100,tptp3)
| ~ root_occ(X100,X99)
| ( ~ occurrence_of(X101,tptp2)
& ~ occurrence_of(X101,tptp1) )
| ~ min_precedes(X100,X101,tptp0) )
| ~ leaf_occ(X101,X99) ) ),
inference(miniscoping,[status(esa)],[f199]) ).
fof(f201,plain,
( occurrence_of(sk0_17,tptp0)
& ! [X101] :
( ! [X100] :
( ~ occurrence_of(X100,tptp3)
| ~ root_occ(X100,sk0_17)
| ( ~ occurrence_of(X101,tptp2)
& ~ occurrence_of(X101,tptp1) )
| ~ min_precedes(X100,X101,tptp0) )
| ~ leaf_occ(X101,sk0_17) ) ),
inference(skolemization,[status(esa)],[f200]) ).
fof(f202,plain,
occurrence_of(sk0_17,tptp0),
inference(cnf_transformation,[status(esa)],[f201]) ).
fof(f203,plain,
! [X0,X1] :
( ~ occurrence_of(X0,tptp3)
| ~ root_occ(X0,sk0_17)
| ~ occurrence_of(X1,tptp2)
| ~ min_precedes(X0,X1,tptp0)
| ~ leaf_occ(X1,sk0_17) ),
inference(cnf_transformation,[status(esa)],[f201]) ).
fof(f204,plain,
! [X0,X1] :
( ~ occurrence_of(X0,tptp3)
| ~ root_occ(X0,sk0_17)
| ~ occurrence_of(X1,tptp1)
| ~ min_precedes(X0,X1,tptp0)
| ~ leaf_occ(X1,sk0_17) ),
inference(cnf_transformation,[status(esa)],[f201]) ).
fof(f309,plain,
! [X0] :
( min_precedes(sk0_15(X0),sk0_14(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[status(thm)],[f64,f185]) ).
fof(f310,plain,
! [X0] :
( min_precedes(sk0_16(X0),sk0_15(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[status(thm)],[f64,f183]) ).
fof(f328,plain,
! [X0,X1] :
( ~ occurrence_of(X0,tptp0)
| ~ min_precedes(X1,sk0_15(X0),tptp0)
| min_precedes(X1,sk0_14(X0),tptp0) ),
inference(resolution,[status(thm)],[f309,f50]) ).
fof(f348,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| min_precedes(sk0_16(X0),sk0_14(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[status(thm)],[f328,f310]) ).
fof(f349,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| min_precedes(sk0_16(X0),sk0_14(X0),tptp0) ),
inference(duplicate_literals_removal,[status(esa)],[f348]) ).
fof(f356,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| ~ occurrence_of(sk0_16(X0),tptp3)
| ~ root_occ(sk0_16(X0),sk0_17)
| ~ occurrence_of(sk0_14(X0),tptp1)
| ~ leaf_occ(sk0_14(X0),sk0_17) ),
inference(resolution,[status(thm)],[f349,f204]) ).
fof(f357,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| ~ root_occ(sk0_16(X0),sk0_17)
| ~ occurrence_of(sk0_14(X0),tptp1)
| ~ leaf_occ(sk0_14(X0),sk0_17) ),
inference(forward_subsumption_resolution,[status(thm)],[f356,f180]) ).
fof(f358,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| ~ occurrence_of(sk0_16(X0),tptp3)
| ~ root_occ(sk0_16(X0),sk0_17)
| ~ occurrence_of(sk0_14(X0),tptp2)
| ~ leaf_occ(sk0_14(X0),sk0_17) ),
inference(resolution,[status(thm)],[f349,f203]) ).
fof(f359,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| ~ root_occ(sk0_16(X0),sk0_17)
| ~ occurrence_of(sk0_14(X0),tptp2)
| ~ leaf_occ(sk0_14(X0),sk0_17) ),
inference(forward_subsumption_resolution,[status(thm)],[f358,f180]) ).
fof(f378,plain,
( spl0_6
<=> occurrence_of(sk0_17,tptp0) ),
introduced(split_symbol_definition) ).
fof(f380,plain,
( ~ occurrence_of(sk0_17,tptp0)
| spl0_6 ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f381,plain,
( spl0_7
<=> root_occ(sk0_16(sk0_17),sk0_17) ),
introduced(split_symbol_definition) ).
fof(f383,plain,
( ~ root_occ(sk0_16(sk0_17),sk0_17)
| spl0_7 ),
inference(component_clause,[status(thm)],[f381]) ).
fof(f384,plain,
( spl0_8
<=> occurrence_of(sk0_14(sk0_17),tptp1) ),
introduced(split_symbol_definition) ).
fof(f386,plain,
( ~ occurrence_of(sk0_14(sk0_17),tptp1)
| spl0_8 ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f387,plain,
( ~ occurrence_of(sk0_17,tptp0)
| ~ root_occ(sk0_16(sk0_17),sk0_17)
| ~ occurrence_of(sk0_14(sk0_17),tptp1)
| ~ occurrence_of(sk0_17,tptp0) ),
inference(resolution,[status(thm)],[f357,f186]) ).
fof(f388,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f387,f378,f381,f384]) ).
fof(f389,plain,
( spl0_9
<=> occurrence_of(sk0_14(sk0_17),tptp2) ),
introduced(split_symbol_definition) ).
fof(f392,plain,
( ~ occurrence_of(sk0_17,tptp0)
| ~ root_occ(sk0_16(sk0_17),sk0_17)
| ~ occurrence_of(sk0_14(sk0_17),tptp2)
| ~ occurrence_of(sk0_17,tptp0) ),
inference(resolution,[status(thm)],[f359,f186]) ).
fof(f393,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(split_clause,[status(thm)],[f392,f378,f381,f389]) ).
fof(f569,plain,
( ~ occurrence_of(sk0_17,tptp0)
| occurrence_of(sk0_14(sk0_17),tptp2)
| spl0_8 ),
inference(resolution,[status(thm)],[f386,f184]) ).
fof(f570,plain,
( ~ spl0_6
| spl0_9
| spl0_8 ),
inference(split_clause,[status(thm)],[f569,f378,f389,f384]) ).
fof(f571,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f380,f202]) ).
fof(f572,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f571]) ).
fof(f573,plain,
( ~ occurrence_of(sk0_17,tptp0)
| spl0_7 ),
inference(resolution,[status(thm)],[f383,f181]) ).
fof(f574,plain,
( ~ spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f573,f378,f381]) ).
fof(f575,plain,
$false,
inference(sat_refutation,[status(thm)],[f388,f393,f570,f572,f574]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : PRO009+2 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33 % Computer : n007.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 : 300
% 0.11/0.33 % DateTime : Tue Apr 30 00:06:32 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.34 % Drodi V3.6.0
% 0.17/0.45 % Refutation found
% 0.17/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.46 % Elapsed time: 0.128473 seconds
% 0.17/0.46 % CPU time: 0.918406 seconds
% 0.17/0.46 % Total memory used: 60.917 MB
% 0.17/0.46 % Net memory used: 60.186 MB
%------------------------------------------------------------------------------