TSTP Solution File: SWC256+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWC256+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n010.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 20:45:06 EDT 2024
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 10 unt; 0 def)
% Number of atoms : 204 ( 45 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 225 ( 83 ~; 76 |; 42 &)
% ( 10 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 7 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 54 ( 41 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& cons(V,nil) = U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/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)
| singletonP(U)
| ( ! [Y] :
( ssItem(Y)
=> ( cons(Y,nil) != W
| ~ memberP(X,Y) ) )
& ( nil != X
| nil != W ) ) ) ) ) ) ),
file('/export/starexec/sandbox/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)
| singletonP(U)
| ( ! [Y] :
( ssItem(Y)
=> ( cons(Y,nil) != W
| ~ memberP(X,Y) ) )
& ( nil != X
| nil != W ) ) ) ) ) ) ),
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(f118,plain,
! [X0,X1] :
( ~ ssList(X0)
| singletonP(X0)
| ~ ssItem(X1)
| cons(X1,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(f219,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(f415,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& neq(V,nil)
& ~ singletonP(U)
& ( ? [Y] :
( ssItem(Y)
& cons(Y,nil) = W
& memberP(X,Y) )
| ( 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) ) ),
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)
& ~ singletonP(U)
& ( ? [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)
& ~ singletonP(sk0_47)
& ( 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,
~ singletonP(sk0_47),
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) ) ),
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(f433,plain,
( spl0_0
<=> pd0_0(sk0_51,sk0_50,sk0_49) ),
introduced(split_symbol_definition) ).
fof(f434,plain,
( pd0_0(sk0_51,sk0_50,sk0_49)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f436,plain,
( spl0_1
<=> nil = sk0_50 ),
introduced(split_symbol_definition) ).
fof(f437,plain,
( nil = sk0_50
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f427,f433,f436]) ).
fof(f447,plain,
! [X0] :
( ~ ssList(cons(X0,nil))
| singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(destructive_equality_resolution,[status(esa)],[f118]) ).
fof(f459,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f219]) ).
fof(f460,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f459]) ).
fof(f476,plain,
( pd0_0(sk0_51,sk0_48,sk0_49)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f423,f434]) ).
fof(f477,plain,
( pd0_0(sk0_51,sk0_48,sk0_47)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f424,f476]) ).
fof(f479,plain,
( ssItem(sk0_51)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f477,f430]) ).
fof(f480,plain,
( cons(sk0_51,nil) = sk0_47
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f431,f477]) ).
fof(f484,plain,
( spl0_4
<=> ssItem(sk0_51) ),
introduced(split_symbol_definition) ).
fof(f486,plain,
( ~ ssItem(sk0_51)
| spl0_4 ),
inference(component_clause,[status(thm)],[f484]) ).
fof(f487,plain,
( spl0_5
<=> ssList(nil) ),
introduced(split_symbol_definition) ).
fof(f489,plain,
( ~ ssList(nil)
| spl0_5 ),
inference(component_clause,[status(thm)],[f487]) ).
fof(f497,plain,
( nil = sk0_48
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f423,f437]) ).
fof(f499,plain,
( neq(nil,nil)
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f497,f425]) ).
fof(f504,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f489,f223]) ).
fof(f505,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f504]) ).
fof(f511,plain,
( $false
| ~ spl0_0
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f486,f479]) ).
fof(f512,plain,
( ~ spl0_0
| spl0_4 ),
inference(contradiction_clause,[status(thm)],[f511]) ).
fof(f514,plain,
( ~ ssList(nil)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f499,f460]) ).
fof(f515,plain,
( ~ spl0_5
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f514,f487,f436]) ).
fof(f526,plain,
( spl0_7
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f528,plain,
( ~ ssList(sk0_47)
| spl0_7 ),
inference(component_clause,[status(thm)],[f526]) ).
fof(f529,plain,
( spl0_8
<=> singletonP(cons(sk0_51,nil)) ),
introduced(split_symbol_definition) ).
fof(f530,plain,
( singletonP(cons(sk0_51,nil))
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f529]) ).
fof(f532,plain,
( ~ ssList(sk0_47)
| singletonP(cons(sk0_51,nil))
| ~ ssItem(sk0_51)
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f480,f447]) ).
fof(f533,plain,
( ~ spl0_7
| spl0_8
| ~ spl0_4
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f532,f526,f529,f484,f433]) ).
fof(f534,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f419]) ).
fof(f535,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f536,plain,
( singletonP(sk0_47)
| ~ spl0_0
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f480,f530]) ).
fof(f537,plain,
( $false
| ~ spl0_0
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f426]) ).
fof(f538,plain,
( ~ spl0_0
| ~ spl0_8 ),
inference(contradiction_clause,[status(thm)],[f537]) ).
fof(f539,plain,
$false,
inference(sat_refutation,[status(thm)],[f439,f505,f512,f515,f533,f535,f538]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC256+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 23:57:05 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 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
% 0.13/0.38 % Elapsed time: 0.027503 seconds
% 0.13/0.38 % CPU time: 0.046621 seconds
% 0.13/0.38 % Total memory used: 14.668 MB
% 0.13/0.38 % Net memory used: 14.643 MB
%------------------------------------------------------------------------------