TSTP Solution File: SWC322+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWC322+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 12:40:03 EDT 2023
% Result : Theorem 0.20s 0.38s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 5 unt; 0 def)
% Number of atoms : 183 ( 79 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 210 ( 74 ~; 69 |; 49 &)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 70 (; 53 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( V != X
| U != W
| ? [Y] :
( ssItem(Y)
& ? [Z] :
( ssList(Z)
& app(cons(Y,nil),Z) != W
& app(Z,cons(Y,nil)) = X ) )
| ( nil != W
& nil = X )
| ( ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,cons(X1,nil)) != V
| app(cons(X1,nil),X2) = U ) ) )
& ( nil != V
| nil = U ) ) ) ) ) ) ),
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
| ? [Y] :
( ssItem(Y)
& ? [Z] :
( ssList(Z)
& app(cons(Y,nil),Z) != W
& app(Z,cons(Y,nil)) = X ) )
| ( nil != W
& nil = X )
| ( ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,cons(X1,nil)) != V
| app(cons(X1,nil),X2) = U ) ) )
& ( nil != V
| nil = U ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f415,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& ! [Y] :
( ~ ssItem(Y)
| ! [Z] :
( ~ ssList(Z)
| app(cons(Y,nil),Z) = W
| app(Z,cons(Y,nil)) != X ) )
& ( nil = W
| nil != X )
& ( ? [X1] :
( ssItem(X1)
& ? [X2] :
( ssList(X2)
& app(X2,cons(X1,nil)) = V
& app(cons(X1,nil),X2) != U ) )
| ( nil = V
& nil != U ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f97]) ).
fof(f416,plain,
! [U,V,X1] :
( pd0_0(X1,V,U)
=> ( ssItem(X1)
& ? [X2] :
( ssList(X2)
& app(X2,cons(X1,nil)) = V
& app(cons(X1,nil),X2) != U ) ) ),
introduced(predicate_definition,[f415]) ).
fof(f417,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& ! [Y] :
( ~ ssItem(Y)
| ! [Z] :
( ~ ssList(Z)
| app(cons(Y,nil),Z) = W
| app(Z,cons(Y,nil)) != X ) )
& ( nil = W
| nil != X )
& ( ? [X1] : pd0_0(X1,V,U)
| ( nil = V
& nil != U ) ) ) ) ) ),
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
& ! [Y] :
( ~ ssItem(Y)
| ! [Z] :
( ~ ssList(Z)
| app(cons(Y,nil),Z) = sk0_49
| app(Z,cons(Y,nil)) != sk0_50 ) )
& ( nil = sk0_49
| nil != sk0_50 )
& ( pd0_0(sk0_51,sk0_48,sk0_47)
| ( nil = sk0_48
& nil != sk0_47 ) ) ),
inference(skolemization,[status(esa)],[f417]) ).
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,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = sk0_49
| app(X1,cons(X0,nil)) != sk0_50 ),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f426,plain,
( nil = sk0_49
| nil != sk0_50 ),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f427,plain,
( pd0_0(sk0_51,sk0_48,sk0_47)
| nil = sk0_48 ),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f428,plain,
( pd0_0(sk0_51,sk0_48,sk0_47)
| nil != sk0_47 ),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f429,plain,
! [U,V,X1] :
( ~ pd0_0(X1,V,U)
| ( ssItem(X1)
& ? [X2] :
( ssList(X2)
& app(X2,cons(X1,nil)) = V
& app(cons(X1,nil),X2) != U ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f416]) ).
fof(f430,plain,
! [U,V,X1] :
( ~ pd0_0(X1,V,U)
| ( ssItem(X1)
& ssList(sk0_52(X1,V,U))
& app(sk0_52(X1,V,U),cons(X1,nil)) = V
& app(cons(X1,nil),sk0_52(X1,V,U)) != U ) ),
inference(skolemization,[status(esa)],[f429]) ).
fof(f431,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1,X2)
| ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f430]) ).
fof(f432,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1,X2)
| ssList(sk0_52(X0,X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f430]) ).
fof(f433,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1,X2)
| app(sk0_52(X0,X1,X2),cons(X0,nil)) = X1 ),
inference(cnf_transformation,[status(esa)],[f430]) ).
fof(f434,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1,X2)
| app(cons(X0,nil),sk0_52(X0,X1,X2)) != X2 ),
inference(cnf_transformation,[status(esa)],[f430]) ).
fof(f435,plain,
( spl0_0
<=> nil = sk0_49 ),
introduced(split_symbol_definition) ).
fof(f436,plain,
( nil = sk0_49
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,plain,
( spl0_1
<=> nil = sk0_50 ),
introduced(split_symbol_definition) ).
fof(f440,plain,
( nil != sk0_50
| spl0_1 ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f426,f435,f438]) ).
fof(f442,plain,
( spl0_2
<=> pd0_0(sk0_51,sk0_48,sk0_47) ),
introduced(split_symbol_definition) ).
fof(f443,plain,
( pd0_0(sk0_51,sk0_48,sk0_47)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( spl0_3
<=> nil = sk0_48 ),
introduced(split_symbol_definition) ).
fof(f446,plain,
( nil = sk0_48
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f448,plain,
( spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f427,f442,f445]) ).
fof(f449,plain,
( spl0_4
<=> nil = sk0_47 ),
introduced(split_symbol_definition) ).
fof(f451,plain,
( nil != sk0_47
| spl0_4 ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( spl0_2
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f428,f442,f449]) ).
fof(f502,plain,
( nil != sk0_48
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f423,f440]) ).
fof(f507,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = sk0_47
| app(X1,cons(X0,nil)) != sk0_50 ),
inference(forward_demodulation,[status(thm)],[f424,f425]) ).
fof(f508,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = sk0_47
| app(X1,cons(X0,nil)) != sk0_48 ),
inference(forward_demodulation,[status(thm)],[f423,f507]) ).
fof(f509,plain,
! [X0,X1] :
( ~ pd0_0(X0,sk0_48,X1)
| ~ ssItem(X0)
| ~ ssList(sk0_52(X0,sk0_48,X1))
| app(cons(X0,nil),sk0_52(X0,sk0_48,X1)) = sk0_47 ),
inference(resolution,[status(thm)],[f433,f508]) ).
fof(f510,plain,
! [X0,X1] :
( ~ pd0_0(X0,sk0_48,X1)
| ~ ssList(sk0_52(X0,sk0_48,X1))
| app(cons(X0,nil),sk0_52(X0,sk0_48,X1)) = sk0_47 ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f431]) ).
fof(f511,plain,
! [X0,X1] :
( ~ pd0_0(X0,sk0_48,X1)
| app(cons(X0,nil),sk0_52(X0,sk0_48,X1)) = sk0_47 ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f432]) ).
fof(f512,plain,
! [X0] :
( ~ pd0_0(X0,sk0_48,sk0_47)
| ~ pd0_0(X0,sk0_48,sk0_47) ),
inference(resolution,[status(thm)],[f511,f434]) ).
fof(f513,plain,
! [X0] : ~ pd0_0(X0,sk0_48,sk0_47),
inference(duplicate_literals_removal,[status(esa)],[f512]) ).
fof(f514,plain,
( $false
| ~ spl0_2 ),
inference(backward_subsumption_resolution,[status(thm)],[f443,f513]) ).
fof(f515,plain,
~ spl0_2,
inference(contradiction_clause,[status(thm)],[f514]) ).
fof(f516,plain,
( $false
| spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f446,f502]) ).
fof(f517,plain,
( spl0_1
| ~ spl0_3 ),
inference(contradiction_clause,[status(thm)],[f516]) ).
fof(f518,plain,
( nil = sk0_47
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f424,f436]) ).
fof(f519,plain,
( $false
| spl0_4
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f451]) ).
fof(f520,plain,
( spl0_4
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f519]) ).
fof(f521,plain,
$false,
inference(sat_refutation,[status(thm)],[f441,f448,f452,f515,f517,f520]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC322+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n018.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 11:30:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.36 % Drodi V3.5.1
% 0.20/0.38 % Refutation found
% 0.20/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.64 % Elapsed time: 0.073715 seconds
% 0.22/0.64 % CPU time: 0.036828 seconds
% 0.22/0.64 % Memory used: 4.091 MB
%------------------------------------------------------------------------------