TSTP Solution File: SWC325+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWC325+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 12:40:03 EDT 2023
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of formulae : 87 ( 8 unt; 0 def)
% Number of atoms : 267 ( 77 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 298 ( 118 ~; 113 |; 33 &)
% ( 16 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 15 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 48 (; 38 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
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
| ? [Y] :
( ssList(Y)
& ? [Z] :
( ssList(Z)
& app(Y,Z) = V
& app(Z,Y) = U ) )
| ( nil != W
& nil = X )
| ( ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(cons(X1,nil),X2) != W
| app(X2,cons(X1,nil)) != X ) ) )
& neq(X,nil) ) ) ) ) ) ),
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
| ? [Y] :
( ssList(Y)
& ? [Z] :
( ssList(Z)
& app(Y,Z) = V
& app(Z,Y) = U ) )
| ( nil != W
& nil = X )
| ( ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(cons(X1,nil),X2) != W
| app(X2,cons(X1,nil)) != X ) ) )
& 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(f220,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f218]) ).
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(f248,plain,
! [U] :
( ~ ssList(U)
| app(nil,U) = U ),
inference(pre_NNF_transformation,[status(esa)],[f28]) ).
fof(f249,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[status(esa)],[f248]) ).
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)
& V = X
& U = W
& ! [Y] :
( ~ ssList(Y)
| ! [Z] :
( ~ ssList(Z)
| app(Y,Z) != V
| app(Z,Y) != U ) )
& ( nil = W
| nil != X )
& ( ? [X1] :
( ssItem(X1)
& ? [X2] :
( ssList(X2)
& app(cons(X1,nil),X2) = W
& app(X2,cons(X1,nil)) = X ) )
| ~ neq(X,nil) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f97]) ).
fof(f416,plain,
( ssList(sk0_47)
& ssList(sk0_48)
& ssList(sk0_49)
& ssList(sk0_50)
& sk0_48 = sk0_50
& sk0_47 = sk0_49
& ! [Y] :
( ~ ssList(Y)
| ! [Z] :
( ~ ssList(Z)
| app(Y,Z) != sk0_48
| app(Z,Y) != sk0_47 ) )
& ( nil = sk0_49
| nil != sk0_50 )
& ( ( ssItem(sk0_51)
& ssList(sk0_52)
& app(cons(sk0_51,nil),sk0_52) = sk0_49
& app(sk0_52,cons(sk0_51,nil)) = sk0_50 )
| ~ neq(sk0_50,nil) ) ),
inference(skolemization,[status(esa)],[f415]) ).
fof(f418,plain,
ssList(sk0_48),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f421,plain,
sk0_48 = sk0_50,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f422,plain,
sk0_47 = sk0_49,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f423,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != sk0_48
| app(X1,X0) != sk0_47 ),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f424,plain,
( nil = sk0_49
| nil != sk0_50 ),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f425,plain,
( ssItem(sk0_51)
| ~ neq(sk0_50,nil) ),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f426,plain,
( ssList(sk0_52)
| ~ neq(sk0_50,nil) ),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f427,plain,
( app(cons(sk0_51,nil),sk0_52) = sk0_49
| ~ neq(sk0_50,nil) ),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f428,plain,
( app(sk0_52,cons(sk0_51,nil)) = sk0_50
| ~ neq(sk0_50,nil) ),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f429,plain,
( spl0_0
<=> nil = sk0_49 ),
introduced(split_symbol_definition) ).
fof(f430,plain,
( nil = sk0_49
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,plain,
( spl0_1
<=> nil = sk0_50 ),
introduced(split_symbol_definition) ).
fof(f434,plain,
( nil != sk0_50
| spl0_1 ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f435,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f424,f429,f432]) ).
fof(f436,plain,
( spl0_2
<=> ssItem(sk0_51) ),
introduced(split_symbol_definition) ).
fof(f439,plain,
( spl0_3
<=> neq(sk0_50,nil) ),
introduced(split_symbol_definition) ).
fof(f441,plain,
( ~ neq(sk0_50,nil)
| spl0_3 ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,plain,
( spl0_2
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f425,f436,f439]) ).
fof(f443,plain,
( spl0_4
<=> ssList(sk0_52) ),
introduced(split_symbol_definition) ).
fof(f446,plain,
( spl0_4
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f426,f443,f439]) ).
fof(f447,plain,
( spl0_5
<=> app(cons(sk0_51,nil),sk0_52) = sk0_49 ),
introduced(split_symbol_definition) ).
fof(f448,plain,
( app(cons(sk0_51,nil),sk0_52) = sk0_49
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,plain,
( spl0_5
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f427,f447,f439]) ).
fof(f451,plain,
( spl0_6
<=> app(sk0_52,cons(sk0_51,nil)) = sk0_50 ),
introduced(split_symbol_definition) ).
fof(f452,plain,
( app(sk0_52,cons(sk0_51,nil)) = sk0_50
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,plain,
( spl0_6
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f428,f451,f439]) ).
fof(f504,plain,
( nil != sk0_48
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f421,f434]) ).
fof(f505,plain,
( ~ neq(sk0_48,nil)
| spl0_3 ),
inference(forward_demodulation,[status(thm)],[f421,f441]) ).
fof(f506,plain,
( spl0_11
<=> ssList(sk0_48) ),
introduced(split_symbol_definition) ).
fof(f508,plain,
( ~ ssList(sk0_48)
| spl0_11 ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f509,plain,
( spl0_12
<=> ssList(nil) ),
introduced(split_symbol_definition) ).
fof(f511,plain,
( ~ ssList(nil)
| spl0_12 ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,plain,
( spl0_13
<=> sk0_48 = nil ),
introduced(split_symbol_definition) ).
fof(f513,plain,
( sk0_48 = nil
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f512]) ).
fof(f515,plain,
( ~ ssList(sk0_48)
| ~ ssList(nil)
| sk0_48 = nil
| spl0_3 ),
inference(resolution,[status(thm)],[f505,f220]) ).
fof(f516,plain,
( ~ spl0_11
| ~ spl0_12
| spl0_13
| spl0_3 ),
inference(split_clause,[status(thm)],[f515,f506,f509,f512,f439]) ).
fof(f525,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f223]) ).
fof(f526,plain,
spl0_12,
inference(contradiction_clause,[status(thm)],[f525]) ).
fof(f527,plain,
( $false
| spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f508,f418]) ).
fof(f528,plain,
spl0_11,
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f529,plain,
( app(cons(sk0_51,nil),sk0_52) = sk0_47
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f422,f448]) ).
fof(f530,plain,
( app(sk0_52,cons(sk0_51,nil)) = sk0_48
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f421,f452]) ).
fof(f534,plain,
( spl0_16
<=> ssList(cons(sk0_51,nil)) ),
introduced(split_symbol_definition) ).
fof(f536,plain,
( ~ ssList(cons(sk0_51,nil))
| spl0_16 ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f537,plain,
( spl0_17
<=> app(cons(sk0_51,nil),sk0_52) = sk0_47 ),
introduced(split_symbol_definition) ).
fof(f539,plain,
( app(cons(sk0_51,nil),sk0_52) != sk0_47
| spl0_17 ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f540,plain,
( ~ ssList(sk0_52)
| ~ ssList(cons(sk0_51,nil))
| app(cons(sk0_51,nil),sk0_52) != sk0_47
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f423,f530]) ).
fof(f541,plain,
( ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f540,f443,f534,f537,f451]) ).
fof(f555,plain,
( sk0_47 != sk0_47
| ~ spl0_5
| spl0_17 ),
inference(forward_demodulation,[status(thm)],[f529,f539]) ).
fof(f556,plain,
( $false
| ~ spl0_5
| spl0_17 ),
inference(trivial_equality_resolution,[status(esa)],[f555]) ).
fof(f557,plain,
( ~ spl0_5
| spl0_17 ),
inference(contradiction_clause,[status(thm)],[f556]) ).
fof(f558,plain,
( spl0_21
<=> app(nil,sk0_48) = sk0_47 ),
introduced(split_symbol_definition) ).
fof(f561,plain,
( ~ ssList(sk0_48)
| ~ ssList(sk0_48)
| ~ ssList(nil)
| app(nil,sk0_48) != sk0_47 ),
inference(resolution,[status(thm)],[f389,f423]) ).
fof(f562,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_21 ),
inference(split_clause,[status(thm)],[f561,f506,f509,f558]) ).
fof(f570,plain,
( spl0_23
<=> app(sk0_48,nil) = sk0_47 ),
introduced(split_symbol_definition) ).
fof(f572,plain,
( app(sk0_48,nil) != sk0_47
| spl0_23 ),
inference(component_clause,[status(thm)],[f570]) ).
fof(f573,plain,
( ~ ssList(sk0_48)
| ~ ssList(nil)
| ~ ssList(sk0_48)
| app(sk0_48,nil) != sk0_47 ),
inference(resolution,[status(thm)],[f249,f423]) ).
fof(f574,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(split_clause,[status(thm)],[f573,f506,f509,f570]) ).
fof(f575,plain,
( ~ ssList(nil)
| ~ ssItem(sk0_51)
| spl0_16 ),
inference(resolution,[status(thm)],[f222,f536]) ).
fof(f576,plain,
( ~ spl0_12
| ~ spl0_2
| spl0_16 ),
inference(split_clause,[status(thm)],[f575,f509,f436,f534]) ).
fof(f577,plain,
( $false
| spl0_1
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f513,f504]) ).
fof(f578,plain,
( spl0_1
| ~ spl0_13 ),
inference(contradiction_clause,[status(thm)],[f577]) ).
fof(f580,plain,
( nil = sk0_47
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f422,f430]) ).
fof(f582,plain,
( app(sk0_48,nil) != nil
| ~ spl0_0
| spl0_23 ),
inference(backward_demodulation,[status(thm)],[f580,f572]) ).
fof(f604,plain,
( app(nil,nil) != nil
| ~ spl0_13
| ~ spl0_0
| spl0_23 ),
inference(forward_demodulation,[status(thm)],[f513,f582]) ).
fof(f605,plain,
( ~ ssList(nil)
| ~ spl0_13
| ~ spl0_0
| spl0_23 ),
inference(resolution,[status(thm)],[f604,f249]) ).
fof(f606,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_0
| spl0_23 ),
inference(split_clause,[status(thm)],[f605,f509,f512,f429,f570]) ).
fof(f609,plain,
$false,
inference(sat_refutation,[status(thm)],[f435,f442,f446,f450,f454,f516,f526,f528,f541,f557,f562,f574,f576,f578,f606]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC325+1 : TPTP v8.1.2. Released v2.4.0.
% 0.04/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue May 30 11:18:35 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.13/0.35 % Refutation found
% 0.13/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.57 % Elapsed time: 0.021902 seconds
% 0.26/0.57 % CPU time: 0.055862 seconds
% 0.26/0.57 % Memory used: 16.245 MB
%------------------------------------------------------------------------------