TSTP Solution File: SWC200+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWC200+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n028.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 12:39:39 EDT 2023
% Result : Theorem 0.14s 0.52s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 10 unt; 0 def)
% Number of atoms : 200 ( 37 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 232 ( 90 ~; 90 |; 28 &)
% ( 9 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 55 (; 45 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& cons(V,nil) = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ( memberP(cons(V,W),U)
<=> ( U = V
| memberP(W,U) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(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
| ~ singletonP(W)
| ? [Y] :
( ssItem(Y)
& ! [Z] :
( ssItem(Z)
=> ( ~ memberP(U,Z)
| Y = Z ) ) ) ) ) ) ) ),
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
| ~ singletonP(W)
| ? [Y] :
( ssItem(Y)
& ! [Z] :
( ssItem(Z)
=> ( ~ memberP(U,Z)
| Y = Z ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f113,plain,
! [U] :
( ~ ssList(U)
| ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& cons(V,nil) = U ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f114,plain,
! [U] :
( ~ ssList(U)
| ( ( ~ singletonP(U)
| ? [V] :
( ssItem(V)
& cons(V,nil) = U ) )
& ( singletonP(U)
| ! [V] :
( ~ ssItem(V)
| cons(V,nil) != U ) ) ) ),
inference(NNF_transformation,[status(esa)],[f113]) ).
fof(f115,plain,
! [U] :
( ~ ssList(U)
| ( ( ~ singletonP(U)
| ( ssItem(sk0_4(U))
& cons(sk0_4(U),nil) = U ) )
& ( singletonP(U)
| ! [V] :
( ~ ssItem(V)
| cons(V,nil) != U ) ) ) ),
inference(skolemization,[status(esa)],[f114]) ).
fof(f116,plain,
! [X0] :
( ~ ssList(X0)
| ~ singletonP(X0)
| ssItem(sk0_4(X0)) ),
inference(cnf_transformation,[status(esa)],[f115]) ).
fof(f117,plain,
! [X0] :
( ~ ssList(X0)
| ~ singletonP(X0)
| cons(sk0_4(X0),nil) = X0 ),
inference(cnf_transformation,[status(esa)],[f115]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f273,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ~ ssItem(V)
| ! [W] :
( ~ ssList(W)
| ( memberP(cons(V,W),U)
<=> ( U = V
| memberP(W,U) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f37]) ).
fof(f274,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ~ ssItem(V)
| ! [W] :
( ~ ssList(W)
| ( ( ~ memberP(cons(V,W),U)
| U = V
| memberP(W,U) )
& ( memberP(cons(V,W),U)
| ( U != V
& ~ memberP(W,U) ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f273]) ).
fof(f275,plain,
! [X0,X1,X2] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X0)
| X0 = X1
| memberP(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f274]) ).
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(f415,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& singletonP(W)
& ! [Y] :
( ~ ssItem(Y)
| ? [Z] :
( ssItem(Z)
& memberP(U,Z)
& Y != Z ) ) ) ) ) ),
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
& singletonP(sk0_49)
& ! [Y] :
( ~ ssItem(Y)
| ( ssItem(sk0_51(Y))
& memberP(sk0_47,sk0_51(Y))
& Y != sk0_51(Y) ) ) ),
inference(skolemization,[status(esa)],[f415]) ).
fof(f417,plain,
ssList(sk0_47),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f422,plain,
sk0_47 = sk0_49,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f423,plain,
singletonP(sk0_49),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f424,plain,
! [X0] :
( ~ ssItem(X0)
| ssItem(sk0_51(X0)) ),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f425,plain,
! [X0] :
( ~ ssItem(X0)
| memberP(sk0_47,sk0_51(X0)) ),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f426,plain,
! [X0] :
( ~ ssItem(X0)
| X0 != sk0_51(X0) ),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f459,plain,
singletonP(sk0_47),
inference(forward_demodulation,[status(thm)],[f422,f423]) ).
fof(f728,plain,
( spl0_18
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f730,plain,
( ~ ssList(sk0_47)
| spl0_18 ),
inference(component_clause,[status(thm)],[f728]) ).
fof(f731,plain,
( spl0_19
<=> cons(sk0_4(sk0_47),nil) = sk0_47 ),
introduced(split_symbol_definition) ).
fof(f732,plain,
( cons(sk0_4(sk0_47),nil) = sk0_47
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f731]) ).
fof(f734,plain,
( ~ ssList(sk0_47)
| cons(sk0_4(sk0_47),nil) = sk0_47 ),
inference(resolution,[status(thm)],[f117,f459]) ).
fof(f735,plain,
( ~ spl0_18
| spl0_19 ),
inference(split_clause,[status(thm)],[f734,f728,f731]) ).
fof(f736,plain,
( $false
| spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f730,f417]) ).
fof(f737,plain,
spl0_18,
inference(contradiction_clause,[status(thm)],[f736]) ).
fof(f756,plain,
( spl0_20
<=> ssItem(sk0_4(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f757,plain,
( ssItem(sk0_4(sk0_47))
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f756]) ).
fof(f758,plain,
( ~ ssItem(sk0_4(sk0_47))
| spl0_20 ),
inference(component_clause,[status(thm)],[f756]) ).
fof(f767,plain,
( spl0_23
<=> singletonP(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f769,plain,
( ~ singletonP(sk0_47)
| spl0_23 ),
inference(component_clause,[status(thm)],[f767]) ).
fof(f775,plain,
( spl0_25
<=> ssList(nil) ),
introduced(split_symbol_definition) ).
fof(f777,plain,
( ~ ssList(nil)
| spl0_25 ),
inference(component_clause,[status(thm)],[f775]) ).
fof(f780,plain,
( ~ ssList(sk0_47)
| ~ singletonP(sk0_47)
| spl0_20 ),
inference(resolution,[status(thm)],[f758,f116]) ).
fof(f781,plain,
( ~ spl0_18
| ~ spl0_23
| spl0_20 ),
inference(split_clause,[status(thm)],[f780,f728,f767,f756]) ).
fof(f782,plain,
( $false
| spl0_23 ),
inference(forward_subsumption_resolution,[status(thm)],[f769,f459]) ).
fof(f783,plain,
spl0_23,
inference(contradiction_clause,[status(thm)],[f782]) ).
fof(f784,plain,
( $false
| spl0_25 ),
inference(forward_subsumption_resolution,[status(thm)],[f777,f223]) ).
fof(f785,plain,
spl0_25,
inference(contradiction_clause,[status(thm)],[f784]) ).
fof(f793,plain,
( sk0_4(sk0_47) != sk0_51(sk0_4(sk0_47))
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f757,f426]) ).
fof(f939,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(sk0_4(sk0_47),X1),X0)
| X0 = sk0_4(sk0_47)
| memberP(X1,X0)
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f275,f757]) ).
fof(f1138,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(cons(sk0_4(sk0_47),nil),X0)
| X0 = sk0_4(sk0_47)
| memberP(nil,X0)
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f939,f223]) ).
fof(f1139,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(sk0_47,X0)
| X0 = sk0_4(sk0_47)
| memberP(nil,X0)
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[status(thm)],[f732,f1138]) ).
fof(f1140,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(sk0_47,X0)
| X0 = sk0_4(sk0_47)
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[status(thm)],[f1139,f279]) ).
fof(f1152,plain,
! [X0] :
( ~ ssItem(sk0_51(X0))
| sk0_51(X0) = sk0_4(sk0_47)
| ~ ssItem(X0)
| ~ spl0_19
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f1140,f425]) ).
fof(f1153,plain,
! [X0] :
( sk0_51(X0) = sk0_4(sk0_47)
| ~ ssItem(X0)
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[status(thm)],[f1152,f424]) ).
fof(f1162,plain,
( sk0_51(sk0_4(sk0_47)) = sk0_4(sk0_47)
| ~ spl0_19
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f1153,f757]) ).
fof(f1163,plain,
( $false
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[status(thm)],[f1162,f793]) ).
fof(f1164,plain,
( ~ spl0_19
| ~ spl0_20 ),
inference(contradiction_clause,[status(thm)],[f1163]) ).
fof(f1165,plain,
$false,
inference(sat_refutation,[status(thm)],[f735,f737,f781,f783,f785,f1164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SWC200+1 : TPTP v8.1.2. Released v2.4.0.
% 0.05/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.33 % Computer : n028.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8042.1875MB
% 0.09/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.33 % CPULimit : 300
% 0.09/0.33 % WCLimit : 300
% 0.09/0.33 % DateTime : Tue May 30 11:36:47 EDT 2023
% 0.09/0.33 % CPUTime :
% 0.09/0.34 % Drodi V3.5.1
% 0.14/0.52 % Refutation found
% 0.14/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.93/0.54 % Elapsed time: 0.208377 seconds
% 0.93/0.54 % CPU time: 1.023656 seconds
% 0.93/0.54 % Memory used: 72.649 MB
%------------------------------------------------------------------------------