TSTP Solution File: SWC207+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWC207+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 12:39:40 EDT 2023
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 11 unt; 0 def)
% Number of atoms : 205 ( 50 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 234 ( 88 ~; 78 |; 45 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 7 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 55 (; 43 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
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(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
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
| ~ neq(V,nil)
| neq(U,nil)
| ( ! [Y] :
( ssItem(Y)
=> ( cons(Y,nil) != W
| ~ memberP(X,Y)
| ? [Z] :
( ssItem(Z)
& Y != Z
& memberP(X,Z)
& leq(Y,Z) ) ) )
& ( nil != X
| nil != W ) ) ) ) ) ) ),
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
| ~ neq(V,nil)
| neq(U,nil)
| ( ! [Y] :
( ssItem(Y)
=> ( cons(Y,nil) != W
| ~ memberP(X,Y)
| ? [Z] :
( ssItem(Z)
& Y != Z
& memberP(X,Z)
& leq(Y,Z) ) ) )
& ( nil != X
| nil != W ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
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(f219,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f218]) ).
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(f224,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssItem(V)
| cons(V,U) != U ) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f225,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) != X0 ),
inference(cnf_transformation,[status(esa)],[f224]) ).
fof(f415,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& neq(V,nil)
& ~ neq(U,nil)
& ( ? [Y] :
( ssItem(Y)
& cons(Y,nil) = W
& memberP(X,Y)
& ! [Z] :
( ~ ssItem(Z)
| Y = Z
| ~ memberP(X,Z)
| ~ leq(Y,Z) ) )
| ( nil = X
& nil = W ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f97]) ).
fof(f416,plain,
! [W,X,Y] :
( pd0_0(Y,X,W)
=> ( ssItem(Y)
& cons(Y,nil) = W
& memberP(X,Y)
& ! [Z] :
( ~ ssItem(Z)
| Y = Z
| ~ memberP(X,Z)
| ~ leq(Y,Z) ) ) ),
introduced(predicate_definition,[f415]) ).
fof(f417,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& neq(V,nil)
& ~ neq(U,nil)
& ( ? [Y] : pd0_0(Y,X,W)
| ( nil = X
& nil = W ) ) ) ) ) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ssList(sk0_47)
& ssList(sk0_48)
& ssList(sk0_49)
& ssList(sk0_50)
& sk0_48 = sk0_50
& sk0_47 = sk0_49
& neq(sk0_48,nil)
& ~ neq(sk0_47,nil)
& ( pd0_0(sk0_51,sk0_50,sk0_49)
| ( nil = sk0_50
& nil = sk0_49 ) ) ),
inference(skolemization,[status(esa)],[f417]) ).
fof(f419,plain,
ssList(sk0_47),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f423,plain,
sk0_48 = sk0_50,
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f424,plain,
sk0_47 = sk0_49,
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f425,plain,
neq(sk0_48,nil),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f426,plain,
~ neq(sk0_47,nil),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f427,plain,
( pd0_0(sk0_51,sk0_50,sk0_49)
| nil = sk0_50 ),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f429,plain,
! [W,X,Y] :
( ~ pd0_0(Y,X,W)
| ( ssItem(Y)
& cons(Y,nil) = W
& memberP(X,Y)
& ! [Z] :
( ~ ssItem(Z)
| Y = Z
| ~ memberP(X,Z)
| ~ leq(Y,Z) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f416]) ).
fof(f430,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1,X2)
| ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f429]) ).
fof(f431,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1,X2)
| cons(X0,nil) = X2 ),
inference(cnf_transformation,[status(esa)],[f429]) ).
fof(f434,plain,
( spl0_0
<=> pd0_0(sk0_51,sk0_50,sk0_49) ),
introduced(split_symbol_definition) ).
fof(f435,plain,
( pd0_0(sk0_51,sk0_50,sk0_49)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,plain,
( spl0_1
<=> nil = sk0_50 ),
introduced(split_symbol_definition) ).
fof(f438,plain,
( nil = sk0_50
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f427,f434,f437]) ).
fof(f460,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f219]) ).
fof(f461,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f460]) ).
fof(f483,plain,
( spl0_5
<=> sk0_47 = nil ),
introduced(split_symbol_definition) ).
fof(f488,plain,
( pd0_0(sk0_51,sk0_48,sk0_49)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f423,f435]) ).
fof(f489,plain,
( pd0_0(sk0_51,sk0_48,sk0_47)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f424,f488]) ).
fof(f491,plain,
( ssItem(sk0_51)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f489,f430]) ).
fof(f492,plain,
( cons(sk0_51,nil) = sk0_47
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f431,f489]) ).
fof(f496,plain,
( spl0_7
<=> ssItem(sk0_51) ),
introduced(split_symbol_definition) ).
fof(f498,plain,
( ~ ssItem(sk0_51)
| spl0_7 ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f499,plain,
( spl0_8
<=> ssList(nil) ),
introduced(split_symbol_definition) ).
fof(f501,plain,
( ~ ssList(nil)
| spl0_8 ),
inference(component_clause,[status(thm)],[f499]) ).
fof(f504,plain,
( ~ ssList(nil)
| ~ ssItem(sk0_51)
| sk0_47 != nil
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f492,f225]) ).
fof(f505,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_5
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f504,f499,f496,f483,f434]) ).
fof(f506,plain,
( nil = sk0_48
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f423,f438]) ).
fof(f508,plain,
( neq(nil,nil)
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f506,f425]) ).
fof(f514,plain,
( ~ ssList(nil)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f508,f461]) ).
fof(f515,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f514,f223]) ).
fof(f516,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f517,plain,
( $false
| spl0_7
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f498]) ).
fof(f518,plain,
( spl0_7
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f517]) ).
fof(f519,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f501,f223]) ).
fof(f520,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f519]) ).
fof(f543,plain,
( spl0_11
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f545,plain,
( ~ ssList(sk0_47)
| spl0_11 ),
inference(component_clause,[status(thm)],[f543]) ).
fof(f546,plain,
( ~ ssList(sk0_47)
| ~ ssList(nil)
| sk0_47 = nil ),
inference(resolution,[status(thm)],[f220,f426]) ).
fof(f547,plain,
( ~ spl0_11
| ~ spl0_8
| spl0_5 ),
inference(split_clause,[status(thm)],[f546,f543,f499,f483]) ).
fof(f548,plain,
( $false
| spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f545,f419]) ).
fof(f549,plain,
spl0_11,
inference(contradiction_clause,[status(thm)],[f548]) ).
fof(f550,plain,
$false,
inference(sat_refutation,[status(thm)],[f440,f505,f516,f518,f520,f547,f549]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC207+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n013.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 : 300
% 0.13/0.34 % DateTime : Tue May 30 11:15:20 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.36 % Drodi V3.5.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.32/0.59 % Elapsed time: 0.031145 seconds
% 0.32/0.59 % CPU time: 0.052837 seconds
% 0.32/0.59 % Memory used: 16.189 MB
%------------------------------------------------------------------------------