TSTP Solution File: SWC277+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWC277+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n018.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 : Wed May 31 12:39:53 EDT 2023
% Result : Theorem 0.19s 0.54s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 79 ( 18 unt; 0 def)
% Number of atoms : 216 ( 36 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 222 ( 85 ~; 82 |; 26 &)
% ( 16 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 11 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 38 (; 31 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& cons(V,nil) = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( V != X
| U != W
| ~ segmentP(X,W)
| totalorderedP(U)
| ( ~ singletonP(W)
& neq(X,nil) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( V != X
| U != W
| ~ segmentP(X,W)
| totalorderedP(U)
| ( ~ singletonP(W)
& neq(X,nil) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f113,plain,
! [U] :
( ~ ssList(U)
| ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& cons(V,nil) = U ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f114,plain,
! [U] :
( ~ ssList(U)
| ( ( ~ singletonP(U)
| ? [V] :
( ssItem(V)
& cons(V,nil) = U ) )
& ( singletonP(U)
| ! [V] :
( ~ ssItem(V)
| cons(V,nil) != U ) ) ) ),
inference(NNF_transformation,[status(esa)],[f113]) ).
fof(f115,plain,
! [U] :
( ~ ssList(U)
| ( ( ~ singletonP(U)
| ( ssItem(sk0_4(U))
& cons(sk0_4(U),nil) = U ) )
& ( singletonP(U)
| ! [V] :
( ~ ssItem(V)
| cons(V,nil) != U ) ) ) ),
inference(skolemization,[status(esa)],[f114]) ).
fof(f116,plain,
! [X0] :
( ~ ssList(X0)
| ~ singletonP(X0)
| ssItem(sk0_4(X0)) ),
inference(cnf_transformation,[status(esa)],[f115]) ).
fof(f117,plain,
! [X0] :
( ~ ssList(X0)
| ~ singletonP(X0)
| cons(sk0_4(X0),nil) = X0 ),
inference(cnf_transformation,[status(esa)],[f115]) ).
fof(f217,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( neq(U,V)
<=> U != V ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f218,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( ( ~ neq(U,V)
| U != V )
& ( neq(U,V)
| U = V ) ) ) ),
inference(NNF_transformation,[status(esa)],[f217]) ).
fof(f220,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f218]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f324,plain,
! [U] :
( ~ ssList(U)
| ( segmentP(nil,U)
<=> nil = U ) ),
inference(pre_NNF_transformation,[status(esa)],[f58]) ).
fof(f325,plain,
! [U] :
( ~ ssList(U)
| ( ( ~ segmentP(nil,U)
| nil = U )
& ( segmentP(nil,U)
| nil != U ) ) ),
inference(NNF_transformation,[status(esa)],[f324]) ).
fof(f326,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[status(esa)],[f325]) ).
fof(f337,plain,
! [U] :
( ~ ssItem(U)
| totalorderedP(cons(U,nil)) ),
inference(pre_NNF_transformation,[status(esa)],[f65]) ).
fof(f338,plain,
! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
inference(cnf_transformation,[status(esa)],[f337]) ).
fof(f339,plain,
totalorderedP(nil),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f415,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& segmentP(X,W)
& ~ totalorderedP(U)
& ( singletonP(W)
| ~ neq(X,nil) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f97]) ).
fof(f416,plain,
( ssList(sk0_47)
& ssList(sk0_48)
& ssList(sk0_49)
& ssList(sk0_50)
& sk0_48 = sk0_50
& sk0_47 = sk0_49
& segmentP(sk0_50,sk0_49)
& ~ totalorderedP(sk0_47)
& ( singletonP(sk0_49)
| ~ neq(sk0_50,nil) ) ),
inference(skolemization,[status(esa)],[f415]) ).
fof(f417,plain,
ssList(sk0_47),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f418,plain,
ssList(sk0_48),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f421,plain,
sk0_48 = sk0_50,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f422,plain,
sk0_47 = sk0_49,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f423,plain,
segmentP(sk0_50,sk0_49),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f424,plain,
~ totalorderedP(sk0_47),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f425,plain,
( singletonP(sk0_49)
| ~ neq(sk0_50,nil) ),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f426,plain,
( spl0_0
<=> singletonP(sk0_49) ),
introduced(split_symbol_definition) ).
fof(f427,plain,
( singletonP(sk0_49)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f426]) ).
fof(f429,plain,
( spl0_1
<=> neq(sk0_50,nil) ),
introduced(split_symbol_definition) ).
fof(f431,plain,
( ~ neq(sk0_50,nil)
| spl0_1 ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f425,f426,f429]) ).
fof(f465,plain,
segmentP(sk0_48,sk0_49),
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f466,plain,
segmentP(sk0_48,sk0_47),
inference(forward_demodulation,[status(thm)],[f422,f465]) ).
fof(f471,plain,
( ~ neq(sk0_48,nil)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f421,f431]) ).
fof(f472,plain,
( spl0_2
<=> ssList(nil) ),
introduced(split_symbol_definition) ).
fof(f474,plain,
( ~ ssList(nil)
| spl0_2 ),
inference(component_clause,[status(thm)],[f472]) ).
fof(f482,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f474,f223]) ).
fof(f483,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f482]) ).
fof(f514,plain,
( spl0_10
<=> ssList(sk0_48) ),
introduced(split_symbol_definition) ).
fof(f516,plain,
( ~ ssList(sk0_48)
| spl0_10 ),
inference(component_clause,[status(thm)],[f514]) ).
fof(f517,plain,
( spl0_11
<=> sk0_48 = nil ),
introduced(split_symbol_definition) ).
fof(f518,plain,
( sk0_48 = nil
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f520,plain,
( ~ ssList(sk0_48)
| ~ ssList(nil)
| sk0_48 = nil
| spl0_1 ),
inference(resolution,[status(thm)],[f220,f471]) ).
fof(f521,plain,
( ~ spl0_10
| ~ spl0_2
| spl0_11
| spl0_1 ),
inference(split_clause,[status(thm)],[f520,f514,f472,f517,f429]) ).
fof(f526,plain,
( $false
| spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f516,f418]) ).
fof(f527,plain,
spl0_10,
inference(contradiction_clause,[status(thm)],[f526]) ).
fof(f528,plain,
( singletonP(sk0_47)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f422,f427]) ).
fof(f529,plain,
( segmentP(nil,sk0_47)
| ~ spl0_11 ),
inference(backward_demodulation,[status(thm)],[f518,f466]) ).
fof(f532,plain,
( spl0_12
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f534,plain,
( ~ ssList(sk0_47)
| spl0_12 ),
inference(component_clause,[status(thm)],[f532]) ).
fof(f535,plain,
( spl0_13
<=> nil = sk0_47 ),
introduced(split_symbol_definition) ).
fof(f536,plain,
( nil = sk0_47
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f535]) ).
fof(f538,plain,
( ~ ssList(sk0_47)
| nil = sk0_47
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f529,f326]) ).
fof(f539,plain,
( ~ spl0_12
| spl0_13
| ~ spl0_11 ),
inference(split_clause,[status(thm)],[f538,f532,f535,f517]) ).
fof(f540,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f534,f417]) ).
fof(f541,plain,
spl0_12,
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f546,plain,
( ~ totalorderedP(nil)
| ~ spl0_13 ),
inference(backward_demodulation,[status(thm)],[f536,f424]) ).
fof(f547,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f546,f339]) ).
fof(f548,plain,
~ spl0_13,
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f812,plain,
( spl0_54
<=> ssItem(sk0_4(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f815,plain,
( ~ ssList(sk0_47)
| ssItem(sk0_4(sk0_47))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f116,f528]) ).
fof(f816,plain,
( ~ spl0_12
| spl0_54
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f815,f532,f812,f426]) ).
fof(f819,plain,
( spl0_55
<=> cons(sk0_4(sk0_47),nil) = sk0_47 ),
introduced(split_symbol_definition) ).
fof(f820,plain,
( cons(sk0_4(sk0_47),nil) = sk0_47
| ~ spl0_55 ),
inference(component_clause,[status(thm)],[f819]) ).
fof(f822,plain,
( ~ ssList(sk0_47)
| cons(sk0_4(sk0_47),nil) = sk0_47
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f117,f528]) ).
fof(f823,plain,
( ~ spl0_12
| spl0_55
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f822,f532,f819,f426]) ).
fof(f901,plain,
( spl0_61
<=> totalorderedP(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f902,plain,
( totalorderedP(sk0_47)
| ~ spl0_61 ),
inference(component_clause,[status(thm)],[f901]) ).
fof(f904,plain,
( ~ ssItem(sk0_4(sk0_47))
| totalorderedP(sk0_47)
| ~ spl0_55 ),
inference(paramodulation,[status(thm)],[f820,f338]) ).
fof(f905,plain,
( ~ spl0_54
| spl0_61
| ~ spl0_55 ),
inference(split_clause,[status(thm)],[f904,f812,f901,f819]) ).
fof(f937,plain,
( $false
| ~ spl0_61 ),
inference(forward_subsumption_resolution,[status(thm)],[f902,f424]) ).
fof(f938,plain,
~ spl0_61,
inference(contradiction_clause,[status(thm)],[f937]) ).
fof(f939,plain,
$false,
inference(sat_refutation,[status(thm)],[f432,f483,f521,f527,f539,f541,f548,f816,f823,f905,f938]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC277+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 11:31:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 0.19/0.54 % Refutation found
% 0.19/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.01/0.56 % Elapsed time: 0.219227 seconds
% 1.01/0.56 % CPU time: 0.963908 seconds
% 1.01/0.56 % Memory used: 66.066 MB
%------------------------------------------------------------------------------