TSTP Solution File: SWC241+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWC241+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 : Tue Apr 30 20:45:03 EDT 2024
% Result : Theorem 0.17s 0.37s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 52 ( 7 unt; 0 def)
% Number of atoms : 262 ( 50 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 329 ( 119 ~; 117 |; 70 &)
% ( 11 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 10 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 69 ( 45 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( lt(U,V)
<=> ( U != V
& leq(U,V) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ~ ssList(X)
| V != X
| U != W
| nil = U
| ? [Y] :
( ssItem(Y)
& ? [Z] :
( ssList(Z)
& ? [X1] :
( ssList(X1)
& app(app(Z,cons(Y,nil)),X1) = U
& ! [X2] :
( ~ ssItem(X2)
| ~ memberP(Z,X2)
| ~ memberP(X1,X2)
| ~ lt(Y,X2)
| leq(Y,X2) ) ) ) )
| ( nil != W
& ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ~ ssList(X5)
| app(app(X4,cons(X3,nil)),X5) != W
| ? [X6] :
( ssItem(X6)
& ~ leq(X6,X3)
& memberP(X4,X6)
& memberP(X5,X6)
& leq(X3,X6) ) ) ) ) ) ) ) ) ),
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
| nil = U
| ? [Y] :
( ssItem(Y)
& ? [Z] :
( ssList(Z)
& ? [X1] :
( ssList(X1)
& app(app(Z,cons(Y,nil)),X1) = U
& ! [X2] :
( ~ ssItem(X2)
| ~ memberP(Z,X2)
| ~ memberP(X1,X2)
| ~ lt(Y,X2)
| leq(Y,X2) ) ) ) )
| ( nil != W
& ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ~ ssList(X5)
| app(app(X4,cons(X3,nil)),X5) != W
| ? [X6] :
( ssItem(X6)
& ~ leq(X6,X3)
& memberP(X4,X6)
& memberP(X5,X6)
& leq(X3,X6) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f406,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ~ ssItem(V)
| ( lt(U,V)
<=> ( U != V
& leq(U,V) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f93]) ).
fof(f407,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ~ ssItem(V)
| ( ( ~ lt(U,V)
| ( U != V
& leq(U,V) ) )
& ( lt(U,V)
| U = V
| ~ leq(U,V) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f406]) ).
fof(f409,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f407]) ).
fof(f415,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& nil != U
& ! [Y] :
( ~ ssItem(Y)
| ! [Z] :
( ~ ssList(Z)
| ! [X1] :
( ~ ssList(X1)
| app(app(Z,cons(Y,nil)),X1) != U
| ? [X2] :
( ssItem(X2)
& memberP(Z,X2)
& memberP(X1,X2)
& lt(Y,X2)
& ~ leq(Y,X2) ) ) ) )
& ( nil = W
| ? [X3] :
( ssItem(X3)
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(app(X4,cons(X3,nil)),X5) = W
& ! [X6] :
( ~ ssItem(X6)
| leq(X6,X3)
| ~ memberP(X4,X6)
| ~ memberP(X5,X6)
| ~ leq(X3,X6) ) ) ) ) ) ) ) ) ),
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
& nil != U
& ! [Y] :
( ~ ssItem(Y)
| ! [Z] :
( ~ ssList(Z)
| ! [X1] :
( ~ ssList(X1)
| app(app(Z,cons(Y,nil)),X1) != U
| ? [X2] :
( ssItem(X2)
& memberP(Z,X2)
& memberP(X1,X2)
& lt(Y,X2)
& ~ leq(Y,X2) ) ) ) )
& ( nil = W
| ? [X3] :
( ssItem(X3)
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(app(X4,cons(X3,nil)),X5) = W
& ! [X6] :
( ~ ssItem(X6)
| leq(X6,X3)
| ~ memberP(X4,X6)
| ~ memberP(X5,X6)
| ~ leq(X3,X6) ) ) ) ) ) ) ) ),
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
& nil != sk0_47
& ! [Y] :
( ~ ssItem(Y)
| ! [Z] :
( ~ ssList(Z)
| ! [X1] :
( ~ ssList(X1)
| app(app(Z,cons(Y,nil)),X1) != sk0_47
| ( ssItem(sk0_51(X1,Z,Y))
& memberP(Z,sk0_51(X1,Z,Y))
& memberP(X1,sk0_51(X1,Z,Y))
& lt(Y,sk0_51(X1,Z,Y))
& ~ leq(Y,sk0_51(X1,Z,Y)) ) ) ) )
& ( nil = sk0_49
| ( ssItem(sk0_52)
& ssList(sk0_53)
& ssList(sk0_54)
& app(app(sk0_53,cons(sk0_52,nil)),sk0_54) = sk0_49
& ! [X6] :
( ~ ssItem(X6)
| leq(X6,sk0_52)
| ~ memberP(sk0_53,X6)
| ~ memberP(sk0_54,X6)
| ~ leq(sk0_52,X6) ) ) ) ),
inference(skolemization,[status(esa)],[f416]) ).
fof(f423,plain,
sk0_47 = sk0_49,
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f424,plain,
nil != sk0_47,
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f425,plain,
! [X0,X1,X2] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk0_47
| ssItem(sk0_51(X2,X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f428,plain,
! [X0,X1,X2] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk0_47
| lt(X0,sk0_51(X2,X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f429,plain,
! [X0,X1,X2] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk0_47
| ~ leq(X0,sk0_51(X2,X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f430,plain,
( nil = sk0_49
| ssItem(sk0_52) ),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f431,plain,
( nil = sk0_49
| ssList(sk0_53) ),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f432,plain,
( nil = sk0_49
| ssList(sk0_54) ),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f433,plain,
( nil = sk0_49
| app(app(sk0_53,cons(sk0_52,nil)),sk0_54) = sk0_49 ),
inference(cnf_transformation,[status(esa)],[f417]) ).
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
<=> ssItem(sk0_52) ),
introduced(split_symbol_definition) ).
fof(f441,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f430,f435,f438]) ).
fof(f442,plain,
( spl0_2
<=> ssList(sk0_53) ),
introduced(split_symbol_definition) ).
fof(f445,plain,
( spl0_0
| spl0_2 ),
inference(split_clause,[status(thm)],[f431,f435,f442]) ).
fof(f446,plain,
( spl0_3
<=> ssList(sk0_54) ),
introduced(split_symbol_definition) ).
fof(f449,plain,
( spl0_0
| spl0_3 ),
inference(split_clause,[status(thm)],[f432,f435,f446]) ).
fof(f450,plain,
( spl0_4
<=> app(app(sk0_53,cons(sk0_52,nil)),sk0_54) = sk0_49 ),
introduced(split_symbol_definition) ).
fof(f451,plain,
( app(app(sk0_53,cons(sk0_52,nil)),sk0_54) = sk0_49
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,plain,
( spl0_0
| spl0_4 ),
inference(split_clause,[status(thm)],[f433,f435,f450]) ).
fof(f499,plain,
( nil = sk0_47
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f423,f436]) ).
fof(f500,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f499,f424]) ).
fof(f501,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f500]) ).
fof(f502,plain,
( app(app(sk0_53,cons(sk0_52,nil)),sk0_54) = sk0_47
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f423,f451]) ).
fof(f517,plain,
( spl0_11
<=> ssItem(sk0_51(sk0_54,sk0_53,sk0_52)) ),
introduced(split_symbol_definition) ).
fof(f520,plain,
( ~ ssItem(sk0_52)
| ~ ssList(sk0_53)
| ~ ssList(sk0_54)
| ssItem(sk0_51(sk0_54,sk0_53,sk0_52))
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f425,f502]) ).
fof(f521,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_11
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f520,f438,f442,f446,f517,f450]) ).
fof(f544,plain,
( spl0_16
<=> leq(sk0_52,sk0_51(sk0_54,sk0_53,sk0_52)) ),
introduced(split_symbol_definition) ).
fof(f549,plain,
( spl0_17
<=> lt(sk0_52,sk0_51(sk0_54,sk0_53,sk0_52)) ),
introduced(split_symbol_definition) ).
fof(f550,plain,
( lt(sk0_52,sk0_51(sk0_54,sk0_53,sk0_52))
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f549]) ).
fof(f552,plain,
( ~ ssItem(sk0_52)
| ~ ssList(sk0_53)
| ~ ssList(sk0_54)
| lt(sk0_52,sk0_51(sk0_54,sk0_53,sk0_52))
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f428,f502]) ).
fof(f553,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_17
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f552,f438,f442,f446,f549,f450]) ).
fof(f556,plain,
( ~ ssItem(sk0_52)
| ~ ssList(sk0_53)
| ~ ssList(sk0_54)
| ~ leq(sk0_52,sk0_51(sk0_54,sk0_53,sk0_52))
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f429,f502]) ).
fof(f557,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_16
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f556,f438,f442,f446,f544,f450]) ).
fof(f573,plain,
( spl0_21
<=> ssList(nil) ),
introduced(split_symbol_definition) ).
fof(f575,plain,
( ~ ssList(nil)
| spl0_21 ),
inference(component_clause,[status(thm)],[f573]) ).
fof(f578,plain,
( $false
| spl0_21 ),
inference(forward_subsumption_resolution,[status(thm)],[f575,f223]) ).
fof(f579,plain,
spl0_21,
inference(contradiction_clause,[status(thm)],[f578]) ).
fof(f593,plain,
( ~ ssItem(sk0_52)
| ~ ssItem(sk0_51(sk0_54,sk0_53,sk0_52))
| leq(sk0_52,sk0_51(sk0_54,sk0_53,sk0_52))
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f409,f550]) ).
fof(f594,plain,
( ~ spl0_1
| ~ spl0_11
| spl0_16
| ~ spl0_17 ),
inference(split_clause,[status(thm)],[f593,f438,f517,f544,f549]) ).
fof(f595,plain,
$false,
inference(sat_refutation,[status(thm)],[f441,f445,f449,f453,f501,f521,f553,f557,f579,f594]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SWC241+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.15 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n018.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 Apr 30 00:26:58 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.36 % Drodi V3.6.0
% 0.17/0.37 % Refutation found
% 0.17/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.38 % Elapsed time: 0.027261 seconds
% 0.17/0.38 % CPU time: 0.045486 seconds
% 0.17/0.38 % Total memory used: 14.998 MB
% 0.17/0.38 % Net memory used: 14.968 MB
%------------------------------------------------------------------------------