TSTP Solution File: SWC213+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWC213+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n001.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 12:39:41 EDT 2023
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 10 unt; 0 def)
% Number of atoms : 206 ( 64 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 250 ( 89 ~; 79 |; 61 &)
% ( 7 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 66 (; 42 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
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)
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(Y,W),Z) != X
| ~ equalelemsP(W)
| ? [X1] :
( ssItem(X1)
& ? [X2] :
( ssList(X2)
& app(X2,cons(X1,nil)) = Y
& ? [X3] :
( ssList(X3)
& app(cons(X1,nil),X3) = W ) ) )
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(cons(X4,nil),X5) = Z
& ? [X6] :
( ssList(X6)
& app(X6,cons(X4,nil)) = W ) ) ) ) ) )
| neq(U,nil)
| ( 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)
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(Y,W),Z) != X
| ~ equalelemsP(W)
| ? [X1] :
( ssItem(X1)
& ? [X2] :
( ssList(X2)
& app(X2,cons(X1,nil)) = Y
& ? [X3] :
( ssList(X3)
& app(cons(X1,nil),X3) = W ) ) )
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(cons(X4,nil),X5) = Z
& ? [X6] :
( ssList(X6)
& app(X6,cons(X4,nil)) = W ) ) ) ) ) )
| neq(U,nil)
| ( 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(f415,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& neq(V,nil)
& ? [Y] :
( ssList(Y)
& ? [Z] :
( ssList(Z)
& app(app(Y,W),Z) = X
& equalelemsP(W)
& ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,cons(X1,nil)) != Y
| ! [X3] :
( ~ ssList(X3)
| app(cons(X1,nil),X3) != W ) ) )
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) != Z
| ! [X6] :
( ~ ssList(X6)
| app(X6,cons(X4,nil)) != W ) ) ) ) )
& ~ neq(U,nil)
& ( nil = X
| nil != W ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f97]) ).
fof(f416,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& neq(V,nil)
& ? [Y] :
( ssList(Y)
& ? [Z] :
( ssList(Z)
& app(app(Y,W),Z) = X
& equalelemsP(W)
& ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,cons(X1,nil)) != Y )
| ! [X3] :
( ~ ssList(X3)
| app(cons(X1,nil),X3) != W ) )
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) != Z )
| ! [X6] :
( ~ ssList(X6)
| app(X6,cons(X4,nil)) != W ) ) ) )
& ~ neq(U,nil)
& ( nil = X
| nil != W ) ) ) ) ),
inference(miniscoping,[status(esa)],[f415]) ).
fof(f417,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)
& ssList(sk0_51)
& ssList(sk0_52)
& app(app(sk0_51,sk0_49),sk0_52) = sk0_50
& equalelemsP(sk0_49)
& ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,cons(X1,nil)) != sk0_51 )
| ! [X3] :
( ~ ssList(X3)
| app(cons(X1,nil),X3) != sk0_49 ) )
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) != sk0_52 )
| ! [X6] :
( ~ ssList(X6)
| app(X6,cons(X4,nil)) != sk0_49 ) )
& ~ neq(sk0_47,nil)
& ( nil = sk0_50
| nil != sk0_49 ) ),
inference(skolemization,[status(esa)],[f416]) ).
fof(f418,plain,
ssList(sk0_47),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f422,plain,
sk0_48 = sk0_50,
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f423,plain,
sk0_47 = sk0_49,
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f424,plain,
neq(sk0_48,nil),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f431,plain,
~ neq(sk0_47,nil),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f432,plain,
( nil = sk0_50
| nil != sk0_49 ),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f433,plain,
( spl0_0
<=> nil = sk0_50 ),
introduced(split_symbol_definition) ).
fof(f434,plain,
( nil = sk0_50
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f436,plain,
( spl0_1
<=> nil = sk0_49 ),
introduced(split_symbol_definition) ).
fof(f438,plain,
( nil != sk0_49
| spl0_1 ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f432,f433,f436]) ).
fof(f455,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f219]) ).
fof(f456,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f455]) ).
fof(f479,plain,
( spl0_4
<=> sk0_47 = nil ),
introduced(split_symbol_definition) ).
fof(f480,plain,
( sk0_47 = nil
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f479]) ).
fof(f484,plain,
( nil != sk0_47
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f423,f438]) ).
fof(f489,plain,
( spl0_5
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f491,plain,
( ~ ssList(sk0_47)
| spl0_5 ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f492,plain,
( spl0_6
<=> ssList(nil) ),
introduced(split_symbol_definition) ).
fof(f494,plain,
( ~ ssList(nil)
| spl0_6 ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f495,plain,
( ~ ssList(sk0_47)
| ~ ssList(nil)
| sk0_47 = nil ),
inference(resolution,[status(thm)],[f220,f431]) ).
fof(f496,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_4 ),
inference(split_clause,[status(thm)],[f495,f489,f492,f479]) ).
fof(f497,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f494,f223]) ).
fof(f498,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f497]) ).
fof(f499,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f418]) ).
fof(f500,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f499]) ).
fof(f501,plain,
( $false
| spl0_1
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f484]) ).
fof(f502,plain,
( spl0_1
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f501]) ).
fof(f503,plain,
( nil = sk0_48
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f422,f434]) ).
fof(f506,plain,
( neq(nil,nil)
| ~ spl0_0 ),
inference(backward_demodulation,[status(thm)],[f503,f424]) ).
fof(f515,plain,
( ~ ssList(nil)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f506,f456]) ).
fof(f516,plain,
( ~ spl0_6
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f515,f492,f433]) ).
fof(f518,plain,
$false,
inference(sat_refutation,[status(thm)],[f439,f496,f498,f500,f502,f516]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC213+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 11:53:15 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 0.12/0.36 % Refutation found
% 0.12/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.38 % Elapsed time: 0.031546 seconds
% 0.12/0.38 % CPU time: 0.050595 seconds
% 0.12/0.38 % Memory used: 16.189 MB
%------------------------------------------------------------------------------