TSTP Solution File: SWC104+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWC104+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 20:44:32 EDT 2024
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 71 ( 16 unt; 0 def)
% Number of atoms : 266 ( 64 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 310 ( 115 ~; 109 |; 59 &)
% ( 13 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 70 ( 49 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( ssList(W)
& app(V,W) = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
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
| ~ neq(V,nil)
| ! [Y] :
( ssList(Y)
=> ( app(W,Y) != X
| ~ totalorderedP(W)
| ? [Z] :
( ssItem(Z)
& ? [X1] :
( ssList(X1)
& app(cons(Z,nil),X1) = Y
& ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& app(X3,cons(X2,nil)) = W
& leq(X2,Z) ) ) ) ) ) )
| ( nil != X
& nil = W )
| ( neq(U,nil)
& frontsegP(V,U) ) ) ) ) ) ),
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
| ~ neq(V,nil)
| ! [Y] :
( ssList(Y)
=> ( app(W,Y) != X
| ~ totalorderedP(W)
| ? [Z] :
( ssItem(Z)
& ? [X1] :
( ssList(X1)
& app(cons(Z,nil),X1) = Y
& ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& app(X3,cons(X2,nil)) = W
& leq(X2,Z) ) ) ) ) ) )
| ( nil != X
& nil = W )
| ( neq(U,nil)
& frontsegP(V,U) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f119,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( frontsegP(U,V)
<=> ? [W] :
( ssList(W)
& app(V,W) = U ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f120,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( ( ~ frontsegP(U,V)
| ? [W] :
( ssList(W)
& app(V,W) = U ) )
& ( frontsegP(U,V)
| ! [W] :
( ~ ssList(W)
| app(V,W) != U ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f119]) ).
fof(f121,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( ( ~ frontsegP(U,V)
| ( ssList(sk0_5(V,U))
& app(V,sk0_5(V,U)) = U ) )
& ( frontsegP(U,V)
| ! [W] :
( ~ ssList(W)
| app(V,W) != U ) ) ) ) ),
inference(skolemization,[status(esa)],[f120]) ).
fof(f124,plain,
! [X0,X1,X2] :
( ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(X0,X1)
| ~ ssList(X2)
| app(X1,X2) != X0 ),
inference(cnf_transformation,[status(esa)],[f121]) ).
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)
& app(W,Y) = X
& totalorderedP(W)
& ! [Z] :
( ~ ssItem(Z)
| ! [X1] :
( ~ ssList(X1)
| app(cons(Z,nil),X1) != Y
| ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X3,cons(X2,nil)) != W
| ~ leq(X2,Z) ) ) ) ) )
& ( nil = X
| nil != W )
& ( ~ neq(U,nil)
| ~ frontsegP(V,U) ) ) ) ) ),
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)
& app(W,Y) = X
& totalorderedP(W)
& ! [Z] :
( ~ ssItem(Z)
| ! [X1] :
( ~ ssList(X1)
| app(cons(Z,nil),X1) != Y )
| ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X3,cons(X2,nil)) != W )
| ~ leq(X2,Z) ) ) )
& ( nil = X
| nil != W )
& ( ~ neq(U,nil)
| ~ frontsegP(V,U) ) ) ) ) ),
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)
& app(sk0_49,sk0_51) = sk0_50
& totalorderedP(sk0_49)
& ! [Z] :
( ~ ssItem(Z)
| ! [X1] :
( ~ ssList(X1)
| app(cons(Z,nil),X1) != sk0_51 )
| ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X3,cons(X2,nil)) != sk0_49 )
| ~ leq(X2,Z) ) )
& ( nil = sk0_50
| nil != sk0_49 )
& ( ~ neq(sk0_47,nil)
| ~ frontsegP(sk0_48,sk0_47) ) ),
inference(skolemization,[status(esa)],[f416]) ).
fof(f418,plain,
ssList(sk0_47),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f419,plain,
ssList(sk0_48),
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(f425,plain,
ssList(sk0_51),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f426,plain,
app(sk0_49,sk0_51) = sk0_50,
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f429,plain,
( nil = sk0_50
| nil != sk0_49 ),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f430,plain,
( ~ neq(sk0_47,nil)
| ~ frontsegP(sk0_48,sk0_47) ),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f431,plain,
( spl0_0
<=> nil = sk0_50 ),
introduced(split_symbol_definition) ).
fof(f432,plain,
( nil = sk0_50
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f434,plain,
( spl0_1
<=> nil = sk0_49 ),
introduced(split_symbol_definition) ).
fof(f436,plain,
( nil != sk0_49
| spl0_1 ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f429,f431,f434]) ).
fof(f438,plain,
( spl0_2
<=> neq(sk0_47,nil) ),
introduced(split_symbol_definition) ).
fof(f440,plain,
( ~ neq(sk0_47,nil)
| spl0_2 ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,plain,
( spl0_3
<=> frontsegP(sk0_48,sk0_47) ),
introduced(split_symbol_definition) ).
fof(f444,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f430,f438,f441]) ).
fof(f449,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(X0)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(esa)],[f124]) ).
fof(f460,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f219]) ).
fof(f461,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f460]) ).
fof(f478,plain,
( nil != sk0_47
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f423,f436]) ).
fof(f485,plain,
( spl0_6
<=> sk0_47 = nil ),
introduced(split_symbol_definition) ).
fof(f486,plain,
( sk0_47 = nil
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f485]) ).
fof(f490,plain,
app(sk0_47,sk0_51) = sk0_50,
inference(forward_demodulation,[status(thm)],[f423,f426]) ).
fof(f491,plain,
app(sk0_47,sk0_51) = sk0_48,
inference(forward_demodulation,[status(thm)],[f422,f490]) ).
fof(f492,plain,
( spl0_7
<=> ssList(app(sk0_47,sk0_51)) ),
introduced(split_symbol_definition) ).
fof(f494,plain,
( ~ ssList(app(sk0_47,sk0_51))
| spl0_7 ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f495,plain,
( spl0_8
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f497,plain,
( ~ ssList(sk0_47)
| spl0_8 ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f498,plain,
( spl0_9
<=> ssList(sk0_51) ),
introduced(split_symbol_definition) ).
fof(f500,plain,
( ~ ssList(sk0_51)
| spl0_9 ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,plain,
( ~ ssList(app(sk0_47,sk0_51))
| ~ ssList(sk0_47)
| frontsegP(sk0_48,sk0_47)
| ~ ssList(sk0_51) ),
inference(paramodulation,[status(thm)],[f491,f449]) ).
fof(f502,plain,
( ~ spl0_7
| ~ spl0_8
| spl0_3
| ~ spl0_9 ),
inference(split_clause,[status(thm)],[f501,f492,f495,f441,f498]) ).
fof(f503,plain,
( $false
| spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f425]) ).
fof(f504,plain,
spl0_9,
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f505,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f497,f418]) ).
fof(f506,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f507,plain,
( ~ ssList(sk0_48)
| spl0_7 ),
inference(forward_demodulation,[status(thm)],[f491,f494]) ).
fof(f508,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f507,f419]) ).
fof(f509,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f508]) ).
fof(f514,plain,
( spl0_10
<=> ssList(nil) ),
introduced(split_symbol_definition) ).
fof(f516,plain,
( ~ ssList(nil)
| spl0_10 ),
inference(component_clause,[status(thm)],[f514]) ).
fof(f524,plain,
( $false
| spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f516,f223]) ).
fof(f525,plain,
spl0_10,
inference(contradiction_clause,[status(thm)],[f524]) ).
fof(f526,plain,
( ~ ssList(sk0_47)
| ~ ssList(nil)
| sk0_47 = nil
| spl0_2 ),
inference(resolution,[status(thm)],[f220,f440]) ).
fof(f527,plain,
( ~ spl0_8
| ~ spl0_10
| spl0_6
| spl0_2 ),
inference(split_clause,[status(thm)],[f526,f495,f514,f485,f438]) ).
fof(f528,plain,
( $false
| spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f486,f478]) ).
fof(f529,plain,
( spl0_1
| ~ spl0_6 ),
inference(contradiction_clause,[status(thm)],[f528]) ).
fof(f530,plain,
( nil = sk0_48
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f422,f432]) ).
fof(f534,plain,
( neq(nil,nil)
| ~ spl0_0 ),
inference(backward_demodulation,[status(thm)],[f530,f424]) ).
fof(f545,plain,
( ~ ssList(nil)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f534,f461]) ).
fof(f546,plain,
( ~ spl0_10
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f545,f514,f431]) ).
fof(f548,plain,
$false,
inference(sat_refutation,[status(thm)],[f437,f444,f502,f504,f506,f509,f525,f527,f529,f546]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC104+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.35 % Computer : n007.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Tue Apr 30 00:04:32 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.37 % Drodi V3.6.0
% 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
% 0.12/0.38 % Elapsed time: 0.028384 seconds
% 0.12/0.38 % CPU time: 0.043147 seconds
% 0.12/0.38 % Total memory used: 14.767 MB
% 0.12/0.38 % Net memory used: 14.742 MB
%------------------------------------------------------------------------------