TSTP Solution File: SWC086+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWC086+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 : Wed May 31 12:39:11 EDT 2023
% Result : Theorem 0.15s 0.32s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 62 ( 9 unt; 0 def)
% Number of atoms : 198 ( 29 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 217 ( 81 ~; 76 |; 39 &)
% ( 9 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 41 (; 31 !; 10 ?)
% 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(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
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)
& neq(Y,nil)
& segmentP(V,Y)
& segmentP(U,Y) )
| ( ( nil != X
| nil != W )
& ( ~ neq(W,nil)
| ~ segmentP(X,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)
& neq(Y,nil)
& segmentP(V,Y)
& segmentP(U,Y) )
| ( ( nil != X
| nil != W )
& ( ~ neq(W,nil)
| ~ segmentP(X,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(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f318,plain,
! [U] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(pre_NNF_transformation,[status(esa)],[f55]) ).
fof(f319,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f318]) ).
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)
| ~ neq(Y,nil)
| ~ segmentP(V,Y)
| ~ segmentP(U,Y) )
& ( ( nil = X
& nil = W )
| ( neq(W,nil)
& segmentP(X,W) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f97]) ).
fof(f416,plain,
! [W,X] :
( pd0_0(X,W)
=> ( nil = X
& nil = W ) ),
introduced(predicate_definition,[f415]) ).
fof(f417,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& neq(V,nil)
& ! [Y] :
( ~ ssList(Y)
| ~ neq(Y,nil)
| ~ segmentP(V,Y)
| ~ segmentP(U,Y) )
& ( pd0_0(X,W)
| ( neq(W,nil)
& segmentP(X,W) ) ) ) ) ) ),
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
& neq(sk0_48,nil)
& ! [Y] :
( ~ ssList(Y)
| ~ neq(Y,nil)
| ~ segmentP(sk0_48,Y)
| ~ segmentP(sk0_47,Y) )
& ( pd0_0(sk0_50,sk0_49)
| ( neq(sk0_49,nil)
& segmentP(sk0_50,sk0_49) ) ) ),
inference(skolemization,[status(esa)],[f417]) ).
fof(f419,plain,
ssList(sk0_47),
inference(cnf_transformation,[status(esa)],[f418]) ).
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,
neq(sk0_48,nil),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f426,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk0_48,X0)
| ~ segmentP(sk0_47,X0) ),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f427,plain,
( pd0_0(sk0_50,sk0_49)
| neq(sk0_49,nil) ),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f428,plain,
( pd0_0(sk0_50,sk0_49)
| segmentP(sk0_50,sk0_49) ),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f429,plain,
! [W,X] :
( ~ pd0_0(X,W)
| ( nil = X
& nil = W ) ),
inference(pre_NNF_transformation,[status(esa)],[f416]) ).
fof(f430,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| nil = X0 ),
inference(cnf_transformation,[status(esa)],[f429]) ).
fof(f432,plain,
( spl0_0
<=> pd0_0(sk0_50,sk0_49) ),
introduced(split_symbol_definition) ).
fof(f433,plain,
( pd0_0(sk0_50,sk0_49)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f435,plain,
( spl0_1
<=> neq(sk0_49,nil) ),
introduced(split_symbol_definition) ).
fof(f436,plain,
( neq(sk0_49,nil)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f427,f432,f435]) ).
fof(f439,plain,
( spl0_2
<=> segmentP(sk0_50,sk0_49) ),
introduced(split_symbol_definition) ).
fof(f440,plain,
( segmentP(sk0_50,sk0_49)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,plain,
( spl0_0
| spl0_2 ),
inference(split_clause,[status(thm)],[f428,f432,f439]) ).
fof(f458,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f219]) ).
fof(f459,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f458]) ).
fof(f475,plain,
( spl0_3
<=> ssList(nil) ),
introduced(split_symbol_definition) ).
fof(f477,plain,
( ~ ssList(nil)
| spl0_3 ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f485,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f477,f223]) ).
fof(f486,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f485]) ).
fof(f491,plain,
( pd0_0(sk0_48,sk0_49)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f423,f433]) ).
fof(f492,plain,
( pd0_0(sk0_48,sk0_47)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f424,f491]) ).
fof(f494,plain,
( nil = sk0_48
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f492,f430]) ).
fof(f498,plain,
( neq(nil,nil)
| ~ spl0_0 ),
inference(backward_demodulation,[status(thm)],[f494,f425]) ).
fof(f502,plain,
( ~ ssList(nil)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f498,f459]) ).
fof(f503,plain,
( ~ spl0_3
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f502,f475,f432]) ).
fof(f505,plain,
( segmentP(sk0_48,sk0_49)
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f423,f440]) ).
fof(f506,plain,
( segmentP(sk0_48,sk0_47)
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f424,f505]) ).
fof(f508,plain,
( neq(sk0_47,nil)
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f424,f436]) ).
fof(f515,plain,
( spl0_7
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f517,plain,
( ~ ssList(sk0_47)
| spl0_7 ),
inference(component_clause,[status(thm)],[f515]) ).
fof(f520,plain,
( spl0_8
<=> neq(sk0_47,nil) ),
introduced(split_symbol_definition) ).
fof(f522,plain,
( ~ neq(sk0_47,nil)
| spl0_8 ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f523,plain,
( spl0_9
<=> segmentP(sk0_48,sk0_47) ),
introduced(split_symbol_definition) ).
fof(f525,plain,
( ~ segmentP(sk0_48,sk0_47)
| spl0_9 ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f526,plain,
( ~ ssList(sk0_47)
| ~ neq(sk0_47,nil)
| ~ segmentP(sk0_48,sk0_47)
| ~ ssList(sk0_47) ),
inference(resolution,[status(thm)],[f426,f319]) ).
fof(f527,plain,
( ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(split_clause,[status(thm)],[f526,f515,f520,f523]) ).
fof(f528,plain,
( $false
| ~ spl0_2
| spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f525,f506]) ).
fof(f529,plain,
( ~ spl0_2
| spl0_9 ),
inference(contradiction_clause,[status(thm)],[f528]) ).
fof(f530,plain,
( $false
| ~ spl0_1
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f522,f508]) ).
fof(f531,plain,
( ~ spl0_1
| spl0_8 ),
inference(contradiction_clause,[status(thm)],[f530]) ).
fof(f532,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f517,f419]) ).
fof(f533,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f532]) ).
fof(f534,plain,
$false,
inference(sat_refutation,[status(thm)],[f438,f442,f486,f503,f527,f529,f531,f533]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWC086+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n005.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue May 30 11:19:36 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.15/0.32 % Drodi V3.5.1
% 0.15/0.32 % Refutation found
% 0.15/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.54 % Elapsed time: 0.019260 seconds
% 0.15/0.54 % CPU time: 0.019275 seconds
% 0.15/0.54 % Memory used: 4.087 MB
%------------------------------------------------------------------------------