TSTP Solution File: SWC050+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWC050+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n016.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 12:39:02 EDT 2023
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 9 unt; 0 def)
% Number of atoms : 231 ( 21 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 280 ( 111 ~; 98 |; 50 &)
% ( 8 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-4 aty)
% Number of variables : 86 (; 73 !; 13 ?)
% 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)
& neq(Y,nil)
& rearsegP(V,Y)
& rearsegP(U,Y) )
| ! [Z] :
( ssList(Z)
=> ( ~ neq(Z,nil)
| ~ rearsegP(X,Z)
| ~ rearsegP(W,Z) ) ) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) ) ),
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)
& rearsegP(V,Y)
& rearsegP(U,Y) )
| ! [Z] :
( ssList(Z)
=> ( ~ neq(Z,nil)
| ~ rearsegP(X,Z)
| ~ rearsegP(W,Z) ) ) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) ) ),
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)
| ~ neq(Y,nil)
| ~ rearsegP(V,Y)
| ~ rearsegP(U,Y) )
& ? [Z] :
( ssList(Z)
& neq(Z,nil)
& rearsegP(X,Z)
& rearsegP(W,Z) ) )
| ( 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] :
( ~ ssList(Y)
| ~ neq(Y,nil)
| ~ rearsegP(V,Y)
| ~ rearsegP(U,Y) )
& ? [Z] :
( ssList(Z)
& neq(Z,nil)
& rearsegP(X,Z)
& rearsegP(W,Z) ) ) ),
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(f420,plain,
ssList(sk0_48),
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,
( 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] :
( ~ ssList(Y)
| ~ neq(Y,nil)
| ~ rearsegP(V,Y)
| ~ rearsegP(U,Y) )
& ? [Z] :
( ssList(Z)
& neq(Z,nil)
& rearsegP(X,Z)
& rearsegP(W,Z) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f416]) ).
fof(f428,plain,
! [U,V,W,X] :
( ~ pd0_0(X,W,V,U)
| ( neq(V,nil)
& ! [Y] :
( ~ ssList(Y)
| ~ neq(Y,nil)
| ~ rearsegP(V,Y)
| ~ rearsegP(U,Y) )
& ssList(sk0_51(X,W,V,U))
& neq(sk0_51(X,W,V,U),nil)
& rearsegP(X,sk0_51(X,W,V,U))
& rearsegP(W,sk0_51(X,W,V,U)) ) ),
inference(skolemization,[status(esa)],[f427]) ).
fof(f430,plain,
! [X0,X1,X2,X3,X4] :
( ~ pd0_0(X0,X1,X2,X3)
| ~ ssList(X4)
| ~ neq(X4,nil)
| ~ rearsegP(X2,X4)
| ~ rearsegP(X3,X4) ),
inference(cnf_transformation,[status(esa)],[f428]) ).
fof(f431,plain,
! [X0,X1,X2,X3] :
( ~ pd0_0(X0,X1,X2,X3)
| ssList(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)
| neq(sk0_51(X0,X1,X2,X3),nil) ),
inference(cnf_transformation,[status(esa)],[f428]) ).
fof(f433,plain,
! [X0,X1,X2,X3] :
( ~ pd0_0(X0,X1,X2,X3)
| rearsegP(X0,sk0_51(X0,X1,X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f428]) ).
fof(f434,plain,
! [X0,X1,X2,X3] :
( ~ pd0_0(X0,X1,X2,X3)
| rearsegP(X1,sk0_51(X0,X1,X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f428]) ).
fof(f435,plain,
( spl0_0
<=> pd0_0(sk0_50,sk0_49,sk0_48,sk0_47) ),
introduced(split_symbol_definition) ).
fof(f436,plain,
( pd0_0(sk0_50,sk0_49,sk0_48,sk0_47)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,plain,
( spl0_1
<=> neq(sk0_48,nil) ),
introduced(split_symbol_definition) ).
fof(f439,plain,
( neq(sk0_48,nil)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f425,f435,f438]) ).
fof(f442,plain,
( spl0_2
<=> neq(sk0_50,nil) ),
introduced(split_symbol_definition) ).
fof(f444,plain,
( ~ neq(sk0_50,nil)
| spl0_2 ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( spl0_0
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f426,f435,f442]) ).
fof(f461,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f219]) ).
fof(f462,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f461]) ).
fof(f478,plain,
( spl0_3
<=> ssList(nil) ),
introduced(split_symbol_definition) ).
fof(f480,plain,
( ~ ssList(nil)
| spl0_3 ),
inference(component_clause,[status(thm)],[f478]) ).
fof(f488,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f223]) ).
fof(f489,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f488]) ).
fof(f498,plain,
( ~ neq(sk0_48,nil)
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f423,f444]) ).
fof(f499,plain,
( spl0_6
<=> ssList(sk0_48) ),
introduced(split_symbol_definition) ).
fof(f501,plain,
( ~ ssList(sk0_48)
| spl0_6 ),
inference(component_clause,[status(thm)],[f499]) ).
fof(f502,plain,
( spl0_7
<=> sk0_48 = nil ),
introduced(split_symbol_definition) ).
fof(f503,plain,
( sk0_48 = nil
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f502]) ).
fof(f505,plain,
( ~ ssList(sk0_48)
| ~ ssList(nil)
| sk0_48 = nil
| spl0_2 ),
inference(resolution,[status(thm)],[f498,f220]) ).
fof(f506,plain,
( ~ spl0_6
| ~ spl0_3
| spl0_7
| spl0_2 ),
inference(split_clause,[status(thm)],[f505,f499,f478,f502,f442]) ).
fof(f515,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f501,f420]) ).
fof(f516,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f526,plain,
( neq(nil,nil)
| ~ spl0_7
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f503,f439]) ).
fof(f531,plain,
( ~ ssList(nil)
| ~ spl0_7
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f526,f462]) ).
fof(f532,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f531,f478,f502,f438]) ).
fof(f534,plain,
( pd0_0(sk0_50,sk0_47,sk0_48,sk0_47)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f424,f436]) ).
fof(f536,plain,
( pd0_0(sk0_48,sk0_47,sk0_48,sk0_47)
| ~ spl0_0 ),
inference(backward_demodulation,[status(thm)],[f423,f534]) ).
fof(f546,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ rearsegP(sk0_48,X0)
| ~ rearsegP(sk0_47,X0)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f430,f536]) ).
fof(f549,plain,
! [X0,X1,X2] :
( ~ ssList(sk0_51(sk0_48,X0,X1,X2))
| ~ neq(sk0_51(sk0_48,X0,X1,X2),nil)
| ~ rearsegP(sk0_47,sk0_51(sk0_48,X0,X1,X2))
| ~ pd0_0(sk0_48,X0,X1,X2)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f546,f433]) ).
fof(f550,plain,
! [X0,X1,X2] :
( ~ neq(sk0_51(sk0_48,X0,X1,X2),nil)
| ~ rearsegP(sk0_47,sk0_51(sk0_48,X0,X1,X2))
| ~ pd0_0(sk0_48,X0,X1,X2)
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f549,f431]) ).
fof(f822,plain,
! [X0,X1,X2] :
( ~ rearsegP(sk0_47,sk0_51(sk0_48,X0,X1,X2))
| ~ pd0_0(sk0_48,X0,X1,X2)
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f550,f432]) ).
fof(f838,plain,
! [X0,X1] :
( ~ pd0_0(sk0_48,sk0_47,X0,X1)
| ~ pd0_0(sk0_48,sk0_47,X0,X1)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f822,f434]) ).
fof(f839,plain,
! [X0,X1] :
( ~ pd0_0(sk0_48,sk0_47,X0,X1)
| ~ spl0_0 ),
inference(duplicate_literals_removal,[status(esa)],[f838]) ).
fof(f844,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f839]) ).
fof(f845,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f844]) ).
fof(f846,plain,
$false,
inference(sat_refutation,[status(thm)],[f441,f445,f489,f506,f516,f532,f845]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC050+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n016.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 11:52:14 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.39 % Elapsed time: 0.042652 seconds
% 0.12/0.39 % CPU time: 0.134239 seconds
% 0.12/0.39 % Memory used: 18.485 MB
%------------------------------------------------------------------------------