TSTP Solution File: SWC182+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWC182+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 12:39:34 EDT 2023
% Result : Theorem 0.16s 0.33s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 76 ( 15 unt; 0 def)
% Number of atoms : 248 ( 52 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 273 ( 101 ~; 97 |; 38 &)
% ( 13 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 72 (; 59 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( memberP(U,V)
<=> ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& app(W,cons(V,X)) = U ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = V
& nil = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( nil != W
| V != X
| U != W
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( app(app(Z,cons(Y,nil)),X1) != U
| ( ~ memberP(Z,Y)
& ~ memberP(X1,Y) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( nil != W
| V != X
| U != W
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( app(app(Z,cons(Y,nil)),X1) != U
| ( ~ memberP(Z,Y)
& ~ memberP(X1,Y) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f106,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssItem(V)
| ( memberP(U,V)
<=> ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& app(W,cons(V,X)) = U ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f107,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssItem(V)
| ( ( ~ memberP(U,V)
| ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& app(W,cons(V,X)) = U ) ) )
& ( memberP(U,V)
| ! [W] :
( ~ ssList(W)
| ! [X] :
( ~ ssList(X)
| app(W,cons(V,X)) != U ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f106]) ).
fof(f108,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssItem(V)
| ( ( ~ memberP(U,V)
| ( ssList(sk0_2(V,U))
& ssList(sk0_3(V,U))
& app(sk0_2(V,U),cons(V,sk0_3(V,U))) = U ) )
& ( memberP(U,V)
| ! [W] :
( ~ ssList(W)
| ! [X] :
( ~ ssList(X)
| app(W,cons(V,X)) != U ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f107]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X0)
| ~ ssItem(X1)
| memberP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ),
inference(cnf_transformation,[status(esa)],[f108]) ).
fof(f221,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssItem(V)
| ssList(cons(V,U)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f222,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f221]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f244,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ssList(app(U,V)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f244]) ).
fof(f278,plain,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(pre_NNF_transformation,[status(esa)],[f38]) ).
fof(f279,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[status(esa)],[f278]) ).
fof(f383,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( nil = app(U,V)
<=> ( nil = V
& nil = U ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f83]) ).
fof(f384,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( ( nil != app(U,V)
| ( nil = V
& nil = U ) )
& ( nil = app(U,V)
| nil != V
| nil != U ) ) ) ),
inference(NNF_transformation,[status(esa)],[f383]) ).
fof(f385,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X1 ),
inference(cnf_transformation,[status(esa)],[f384]) ).
fof(f388,plain,
! [U] :
( ~ ssList(U)
| app(U,nil) = U ),
inference(pre_NNF_transformation,[status(esa)],[f84]) ).
fof(f389,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[status(esa)],[f388]) ).
fof(f415,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& nil = W
& V = X
& U = W
& ? [Y] :
( ssItem(Y)
& ? [Z] :
( ssList(Z)
& ? [X1] :
( ssList(X1)
& app(app(Z,cons(Y,nil)),X1) = U
& ( memberP(Z,Y)
| memberP(X1,Y) ) ) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f97]) ).
fof(f416,plain,
( ssList(sk0_47)
& ssList(sk0_48)
& ssList(sk0_49)
& ssList(sk0_50)
& nil = sk0_49
& sk0_48 = sk0_50
& sk0_47 = sk0_49
& ssItem(sk0_51)
& ssList(sk0_52)
& ssList(sk0_53)
& app(app(sk0_52,cons(sk0_51,nil)),sk0_53) = sk0_47
& ( memberP(sk0_52,sk0_51)
| memberP(sk0_53,sk0_51) ) ),
inference(skolemization,[status(esa)],[f415]) ).
fof(f421,plain,
nil = sk0_49,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f423,plain,
sk0_47 = sk0_49,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f424,plain,
ssItem(sk0_51),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f425,plain,
ssList(sk0_52),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f426,plain,
ssList(sk0_53),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f427,plain,
app(app(sk0_52,cons(sk0_51,nil)),sk0_53) = sk0_47,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f438,plain,
! [X0,X1,X2] :
( ~ ssList(app(X0,cons(X1,X2)))
| ~ ssItem(X1)
| memberP(app(X0,cons(X1,X2)),X1)
| ~ ssList(X0)
| ~ ssList(X2) ),
inference(destructive_equality_resolution,[status(esa)],[f112]) ).
fof(f468,plain,
sk0_47 = nil,
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f470,plain,
app(app(sk0_52,cons(sk0_51,nil)),sk0_53) = nil,
inference(forward_demodulation,[status(thm)],[f468,f427]) ).
fof(f471,plain,
( spl0_2
<=> ssList(app(sk0_52,cons(sk0_51,nil))) ),
introduced(split_symbol_definition) ).
fof(f473,plain,
( ~ ssList(app(sk0_52,cons(sk0_51,nil)))
| spl0_2 ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,plain,
( spl0_3
<=> ssList(sk0_53) ),
introduced(split_symbol_definition) ).
fof(f476,plain,
( ~ ssList(sk0_53)
| spl0_3 ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f477,plain,
( spl0_4
<=> ssList(nil) ),
introduced(split_symbol_definition) ).
fof(f479,plain,
( ~ ssList(nil)
| spl0_4 ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f482,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f476,f426]) ).
fof(f483,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f482]) ).
fof(f484,plain,
( spl0_5
<=> ssList(sk0_52) ),
introduced(split_symbol_definition) ).
fof(f486,plain,
( ~ ssList(sk0_52)
| spl0_5 ),
inference(component_clause,[status(thm)],[f484]) ).
fof(f487,plain,
( spl0_6
<=> ssList(cons(sk0_51,nil)) ),
introduced(split_symbol_definition) ).
fof(f489,plain,
( ~ ssList(cons(sk0_51,nil))
| spl0_6 ),
inference(component_clause,[status(thm)],[f487]) ).
fof(f490,plain,
( ~ ssList(sk0_52)
| ~ ssList(cons(sk0_51,nil))
| spl0_2 ),
inference(resolution,[status(thm)],[f473,f245]) ).
fof(f491,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_2 ),
inference(split_clause,[status(thm)],[f490,f484,f487,f471]) ).
fof(f492,plain,
( spl0_7
<=> ssItem(sk0_51) ),
introduced(split_symbol_definition) ).
fof(f494,plain,
( ~ ssItem(sk0_51)
| spl0_7 ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f495,plain,
( ~ ssList(nil)
| ~ ssItem(sk0_51)
| spl0_6 ),
inference(resolution,[status(thm)],[f489,f222]) ).
fof(f496,plain,
( ~ spl0_4
| ~ spl0_7
| spl0_6 ),
inference(split_clause,[status(thm)],[f495,f477,f492,f487]) ).
fof(f497,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f486,f425]) ).
fof(f498,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f497]) ).
fof(f499,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f494,f424]) ).
fof(f500,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f499]) ).
fof(f501,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f479,f223]) ).
fof(f502,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f501]) ).
fof(f503,plain,
( spl0_8
<=> nil = sk0_53 ),
introduced(split_symbol_definition) ).
fof(f504,plain,
( nil = sk0_53
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,plain,
( ~ ssList(app(sk0_52,cons(sk0_51,nil)))
| ~ ssList(sk0_53)
| nil = sk0_53 ),
inference(resolution,[status(thm)],[f385,f470]) ).
fof(f507,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_8 ),
inference(split_clause,[status(thm)],[f506,f471,f474,f503]) ).
fof(f517,plain,
( app(app(sk0_52,cons(sk0_51,nil)),nil) = nil
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f504,f470]) ).
fof(f521,plain,
( spl0_10
<=> nil = app(sk0_52,cons(sk0_51,nil)) ),
introduced(split_symbol_definition) ).
fof(f522,plain,
( nil = app(sk0_52,cons(sk0_51,nil))
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f521]) ).
fof(f524,plain,
( ~ ssList(app(sk0_52,cons(sk0_51,nil)))
| nil = app(sk0_52,cons(sk0_51,nil))
| ~ spl0_8 ),
inference(paramodulation,[status(thm)],[f517,f389]) ).
fof(f525,plain,
( ~ spl0_2
| spl0_10
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f524,f471,f521,f503]) ).
fof(f537,plain,
( spl0_12
<=> memberP(nil,sk0_51) ),
introduced(split_symbol_definition) ).
fof(f538,plain,
( memberP(nil,sk0_51)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f540,plain,
( ~ ssList(app(sk0_52,cons(sk0_51,nil)))
| ~ ssItem(sk0_51)
| memberP(nil,sk0_51)
| ~ ssList(sk0_52)
| ~ ssList(nil)
| ~ spl0_10 ),
inference(paramodulation,[status(thm)],[f522,f438]) ).
fof(f541,plain,
( ~ spl0_2
| ~ spl0_7
| spl0_12
| ~ spl0_5
| ~ spl0_4
| ~ spl0_10 ),
inference(split_clause,[status(thm)],[f540,f471,f492,f537,f484,f477,f521]) ).
fof(f546,plain,
( ~ ssItem(sk0_51)
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f538,f279]) ).
fof(f547,plain,
( ~ spl0_7
| ~ spl0_12 ),
inference(split_clause,[status(thm)],[f546,f492,f537]) ).
fof(f548,plain,
$false,
inference(sat_refutation,[status(thm)],[f483,f491,f496,f498,f500,f502,f507,f525,f541,f547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SWC182+1 : TPTP v8.1.2. Released v2.4.0.
% 0.09/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.31 % Computer : n018.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.31 % CPULimit : 300
% 0.15/0.31 % WCLimit : 300
% 0.15/0.31 % DateTime : Tue May 30 11:29:10 EDT 2023
% 0.15/0.31 % CPUTime :
% 0.16/0.32 % Drodi V3.5.1
% 0.16/0.33 % Refutation found
% 0.16/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.55 % Elapsed time: 0.023381 seconds
% 0.16/0.55 % CPU time: 0.020204 seconds
% 0.16/0.55 % Memory used: 4.110 MB
%------------------------------------------------------------------------------