TSTP Solution File: SWC254+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWC254+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 12:39:48 EDT 2023
% Result : Theorem 0.09s 0.32s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 4 unt; 0 def)
% Number of atoms : 195 ( 33 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 214 ( 73 ~; 70 |; 49 &)
% ( 8 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 65 (; 48 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& cons(V,nil) = U ) ) ),
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)
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( cons(Y,nil) != W
| app(Z,cons(Y,nil)) != X ) ) )
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) ) ),
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)
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( cons(Y,nil) != W
| app(Z,cons(Y,nil)) != X ) ) )
| singletonP(U) )
& ( ~ neq(V,nil)
| 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(f118,plain,
! [X0,X1] :
( ~ ssList(X0)
| singletonP(X0)
| ~ ssItem(X1)
| cons(X1,nil) != X0 ),
inference(cnf_transformation,[status(esa)],[f115]) ).
fof(f415,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& ( ( neq(V,nil)
& ? [Y] :
( ssItem(Y)
& ? [Z] :
( ssList(Z)
& cons(Y,nil) = W
& app(Z,cons(Y,nil)) = X ) )
& ~ singletonP(U) )
| ( neq(V,nil)
& ~ neq(X,nil) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f97]) ).
fof(f416,plain,
! [U,V,W,X] :
( pd0_0(X,W,V,U)
=> ( neq(V,nil)
& ? [Y] :
( ssItem(Y)
& ? [Z] :
( ssList(Z)
& cons(Y,nil) = W
& app(Z,cons(Y,nil)) = X ) )
& ~ singletonP(U) ) ),
introduced(predicate_definition,[f415]) ).
fof(f417,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& ( pd0_0(X,W,V,U)
| ( neq(V,nil)
& ~ neq(X,nil) ) ) ) ) ) ),
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
& ( pd0_0(sk0_50,sk0_49,sk0_48,sk0_47)
| ( neq(sk0_48,nil)
& ~ neq(sk0_50,nil) ) ) ),
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,
( pd0_0(sk0_50,sk0_49,sk0_48,sk0_47)
| neq(sk0_48,nil) ),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f426,plain,
( pd0_0(sk0_50,sk0_49,sk0_48,sk0_47)
| ~ neq(sk0_50,nil) ),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f427,plain,
! [U,V,W,X] :
( ~ pd0_0(X,W,V,U)
| ( neq(V,nil)
& ? [Y] :
( ssItem(Y)
& ? [Z] :
( ssList(Z)
& cons(Y,nil) = W
& app(Z,cons(Y,nil)) = X ) )
& ~ singletonP(U) ) ),
inference(pre_NNF_transformation,[status(esa)],[f416]) ).
fof(f428,plain,
! [U,V,W,X] :
( ~ pd0_0(X,W,V,U)
| ( neq(V,nil)
& ssItem(sk0_51(X,W,V,U))
& ssList(sk0_52(X,W,V,U))
& cons(sk0_51(X,W,V,U),nil) = W
& app(sk0_52(X,W,V,U),cons(sk0_51(X,W,V,U),nil)) = X
& ~ singletonP(U) ) ),
inference(skolemization,[status(esa)],[f427]) ).
fof(f430,plain,
! [X0,X1,X2,X3] :
( ~ pd0_0(X0,X1,X2,X3)
| ssItem(sk0_51(X0,X1,X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f428]) ).
fof(f432,plain,
! [X0,X1,X2,X3] :
( ~ pd0_0(X0,X1,X2,X3)
| cons(sk0_51(X0,X1,X2,X3),nil) = X1 ),
inference(cnf_transformation,[status(esa)],[f428]) ).
fof(f434,plain,
! [X0,X1,X2,X3] :
( ~ pd0_0(X0,X1,X2,X3)
| ~ singletonP(X3) ),
inference(cnf_transformation,[status(esa)],[f428]) ).
fof(f435,plain,
( spl0_0
<=> pd0_0(sk0_50,sk0_49,sk0_48,sk0_47) ),
introduced(split_symbol_definition) ).
fof(f436,plain,
( pd0_0(sk0_50,sk0_49,sk0_48,sk0_47)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,plain,
( spl0_1
<=> neq(sk0_48,nil) ),
introduced(split_symbol_definition) ).
fof(f439,plain,
( neq(sk0_48,nil)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f425,f435,f438]) ).
fof(f442,plain,
( spl0_2
<=> neq(sk0_50,nil) ),
introduced(split_symbol_definition) ).
fof(f444,plain,
( ~ neq(sk0_50,nil)
| spl0_2 ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( spl0_0
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f426,f435,f442]) ).
fof(f449,plain,
! [X0] :
( ~ ssList(cons(X0,nil))
| singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(destructive_equality_resolution,[status(esa)],[f118]) ).
fof(f488,plain,
( ~ neq(sk0_48,nil)
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f423,f444]) ).
fof(f489,plain,
( pd0_0(sk0_48,sk0_49,sk0_48,sk0_47)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f423,f436]) ).
fof(f490,plain,
( pd0_0(sk0_48,sk0_47,sk0_48,sk0_47)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f424,f489]) ).
fof(f495,plain,
( $false
| spl0_2
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f439,f488]) ).
fof(f496,plain,
( spl0_2
| ~ spl0_1 ),
inference(contradiction_clause,[status(thm)],[f495]) ).
fof(f498,plain,
( ssItem(sk0_51(sk0_48,sk0_47,sk0_48,sk0_47))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f430,f490]) ).
fof(f501,plain,
( spl0_3
<=> ssItem(sk0_51(sk0_48,sk0_47,sk0_48,sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f503,plain,
( ~ ssItem(sk0_51(sk0_48,sk0_47,sk0_48,sk0_47))
| spl0_3 ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f514,plain,
( $false
| ~ spl0_0
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f503,f498]) ).
fof(f515,plain,
( ~ spl0_0
| spl0_3 ),
inference(contradiction_clause,[status(thm)],[f514]) ).
fof(f519,plain,
( cons(sk0_51(sk0_48,sk0_47,sk0_48,sk0_47),nil) = sk0_47
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f432,f490]) ).
fof(f520,plain,
( spl0_6
<=> ssList(cons(sk0_51(sk0_48,sk0_47,sk0_48,sk0_47),nil)) ),
introduced(split_symbol_definition) ).
fof(f522,plain,
( ~ ssList(cons(sk0_51(sk0_48,sk0_47,sk0_48,sk0_47),nil))
| spl0_6 ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f523,plain,
( spl0_7
<=> singletonP(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f524,plain,
( singletonP(sk0_47)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f526,plain,
( ~ ssList(cons(sk0_51(sk0_48,sk0_47,sk0_48,sk0_47),nil))
| singletonP(sk0_47)
| ~ ssItem(sk0_51(sk0_48,sk0_47,sk0_48,sk0_47))
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f519,f449]) ).
fof(f527,plain,
( ~ spl0_6
| spl0_7
| ~ spl0_3
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f526,f520,f523,f501,f435]) ).
fof(f528,plain,
( ~ ssList(sk0_47)
| ~ spl0_0
| spl0_6 ),
inference(forward_demodulation,[status(thm)],[f519,f522]) ).
fof(f529,plain,
( $false
| ~ spl0_0
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f419]) ).
fof(f530,plain,
( ~ spl0_0
| spl0_6 ),
inference(contradiction_clause,[status(thm)],[f529]) ).
fof(f532,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1,X2,sk0_47)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f524,f434]) ).
fof(f533,plain,
( $false
| ~ spl0_7
| ~ spl0_0 ),
inference(backward_subsumption_resolution,[status(thm)],[f490,f532]) ).
fof(f534,plain,
( ~ spl0_7
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f533]) ).
fof(f535,plain,
$false,
inference(sat_refutation,[status(thm)],[f441,f445,f496,f515,f527,f530,f534]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWC254+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n029.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 11:36:51 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 0.09/0.32 % Refutation found
% 0.09/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.55 % Elapsed time: 0.027027 seconds
% 0.15/0.55 % CPU time: 0.023220 seconds
% 0.15/0.55 % Memory used: 8.140 MB
%------------------------------------------------------------------------------