TSTP Solution File: SWC011+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWC011+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n005.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 20:44:08 EDT 2024
% Result : Theorem 0.16s 0.36s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 4 unt; 0 def)
% Number of atoms : 190 ( 43 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 236 ( 87 ~; 76 |; 55 &)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 129 ( 106 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
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)
& ? [X1] :
( ssList(X1)
& app(app(Z,cons(Y,nil)),X1) = V
& app(Z,X1) = U ) ) )
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( app(app(X3,cons(X2,nil)),X4) != X
| app(X3,X4) != W ) ) ) ) )
& ( ~ neq(V,nil)
| 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
| ( ( ~ neq(V,nil)
| ? [Y] :
( ssItem(Y)
& ? [Z] :
( ssList(Z)
& ? [X1] :
( ssList(X1)
& app(app(Z,cons(Y,nil)),X1) = V
& app(Z,X1) = U ) ) )
| ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( app(app(X3,cons(X2,nil)),X4) != X
| app(X3,X4) != W ) ) ) ) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) ) ),
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
& ( ( neq(V,nil)
& ! [Y] :
( ~ ssItem(Y)
| ! [Z] :
( ~ ssList(Z)
| ! [X1] :
( ~ ssList(X1)
| app(app(Z,cons(Y,nil)),X1) != V
| app(Z,X1) != U ) ) )
& ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,cons(X2,nil)),X4) = X
& app(X3,X4) = W ) ) ) )
| ( 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)
| ! [X1] :
( ~ ssList(X1)
| app(app(Z,cons(Y,nil)),X1) != V
| app(Z,X1) != U ) ) )
& ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,cons(X2,nil)),X4) = X
& app(X3,X4) = W ) ) ) ) ),
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(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)
| ! [X1] :
( ~ ssList(X1)
| app(app(Z,cons(Y,nil)),X1) != V
| app(Z,X1) != U ) ) )
& ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,cons(X2,nil)),X4) = X
& app(X3,X4) = W ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f416]) ).
fof(f428,plain,
! [U,V,W,X] :
( ~ pd0_0(X,W,V,U)
| ( neq(V,nil)
& ! [Y] :
( ~ ssItem(Y)
| ! [Z] :
( ~ ssList(Z)
| ! [X1] :
( ~ ssList(X1)
| app(app(Z,cons(Y,nil)),X1) != V
| app(Z,X1) != U ) ) )
& ssItem(sk0_51(X,W,V,U))
& ssList(sk0_52(X,W,V,U))
& ssList(sk0_53(X,W,V,U))
& app(app(sk0_52(X,W,V,U),cons(sk0_51(X,W,V,U),nil)),sk0_53(X,W,V,U)) = X
& app(sk0_52(X,W,V,U),sk0_53(X,W,V,U)) = W ) ),
inference(skolemization,[status(esa)],[f427]) ).
fof(f430,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ pd0_0(X0,X1,X2,X3)
| ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X2
| app(X5,X6) != X3 ),
inference(cnf_transformation,[status(esa)],[f428]) ).
fof(f431,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)
| ssList(sk0_52(X0,X1,X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f428]) ).
fof(f433,plain,
! [X0,X1,X2,X3] :
( ~ pd0_0(X0,X1,X2,X3)
| ssList(sk0_53(X0,X1,X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f428]) ).
fof(f434,plain,
! [X0,X1,X2,X3] :
( ~ pd0_0(X0,X1,X2,X3)
| app(app(sk0_52(X0,X1,X2,X3),cons(sk0_51(X0,X1,X2,X3),nil)),sk0_53(X0,X1,X2,X3)) = X0 ),
inference(cnf_transformation,[status(esa)],[f428]) ).
fof(f435,plain,
! [X0,X1,X2,X3] :
( ~ pd0_0(X0,X1,X2,X3)
| app(sk0_52(X0,X1,X2,X3),sk0_53(X0,X1,X2,X3)) = X1 ),
inference(cnf_transformation,[status(esa)],[f428]) ).
fof(f436,plain,
( spl0_0
<=> pd0_0(sk0_50,sk0_49,sk0_48,sk0_47) ),
introduced(split_symbol_definition) ).
fof(f437,plain,
( pd0_0(sk0_50,sk0_49,sk0_48,sk0_47)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,plain,
( spl0_1
<=> neq(sk0_48,nil) ),
introduced(split_symbol_definition) ).
fof(f440,plain,
( neq(sk0_48,nil)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f425,f436,f439]) ).
fof(f443,plain,
( spl0_2
<=> neq(sk0_50,nil) ),
introduced(split_symbol_definition) ).
fof(f445,plain,
( ~ neq(sk0_50,nil)
| spl0_2 ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,plain,
( spl0_0
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f426,f436,f443]) ).
fof(f461,plain,
( ~ neq(sk0_48,nil)
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f423,f445]) ).
fof(f462,plain,
( pd0_0(sk0_48,sk0_49,sk0_48,sk0_47)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f423,f437]) ).
fof(f463,plain,
( pd0_0(sk0_48,sk0_47,sk0_48,sk0_47)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f424,f462]) ).
fof(f467,plain,
( $false
| spl0_2
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f440,f461]) ).
fof(f468,plain,
( spl0_2
| ~ spl0_1 ),
inference(contradiction_clause,[status(thm)],[f467]) ).
fof(f473,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ pd0_0(X0,X1,X2,X3)
| ~ pd0_0(X4,X5,X0,X6)
| ~ ssItem(sk0_51(X0,X1,X2,X3))
| ~ ssList(sk0_52(X0,X1,X2,X3))
| ~ ssList(sk0_53(X0,X1,X2,X3))
| app(sk0_52(X0,X1,X2,X3),sk0_53(X0,X1,X2,X3)) != X6 ),
inference(resolution,[status(thm)],[f434,f430]) ).
fof(f474,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ pd0_0(X0,X1,X2,X3)
| ~ pd0_0(X4,X5,X0,X6)
| ~ ssList(sk0_52(X0,X1,X2,X3))
| ~ ssList(sk0_53(X0,X1,X2,X3))
| app(sk0_52(X0,X1,X2,X3),sk0_53(X0,X1,X2,X3)) != X6 ),
inference(forward_subsumption_resolution,[status(thm)],[f473,f431]) ).
fof(f483,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ pd0_0(X0,X1,X2,X3)
| ~ pd0_0(X4,X5,X0,X6)
| ~ ssList(sk0_53(X0,X1,X2,X3))
| app(sk0_52(X0,X1,X2,X3),sk0_53(X0,X1,X2,X3)) != X6 ),
inference(forward_subsumption_resolution,[status(thm)],[f474,f432]) ).
fof(f484,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ pd0_0(X0,X1,X2,X3)
| ~ pd0_0(X4,X5,X0,X1)
| ~ ssList(sk0_53(X0,X1,X2,X3))
| ~ pd0_0(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f483,f435]) ).
fof(f485,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ pd0_0(X0,X1,X2,X3)
| ~ pd0_0(X4,X5,X0,X1)
| ~ ssList(sk0_53(X0,X1,X2,X3)) ),
inference(duplicate_literals_removal,[status(esa)],[f484]) ).
fof(f486,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ pd0_0(X0,X1,X2,X3)
| ~ pd0_0(X4,X5,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f485,f433]) ).
fof(f493,plain,
! [X0,X1] :
( ~ pd0_0(sk0_48,sk0_47,X0,X1)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f486,f463]) ).
fof(f494,plain,
( $false
| ~ spl0_0 ),
inference(backward_subsumption_resolution,[status(thm)],[f463,f493]) ).
fof(f495,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f494]) ).
fof(f496,plain,
$false,
inference(sat_refutation,[status(thm)],[f442,f446,f468,f495]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : SWC011+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n005.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Apr 29 23:58:11 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.33 % Drodi V3.6.0
% 0.16/0.36 % Refutation found
% 0.16/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.37 % Elapsed time: 0.051736 seconds
% 0.16/0.37 % CPU time: 0.244551 seconds
% 0.16/0.37 % Total memory used: 62.671 MB
% 0.16/0.37 % Net memory used: 62.551 MB
%------------------------------------------------------------------------------