TSTP Solution File: SWC200+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% 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 : n021.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 20:44:55 EDT 2024
% Result : Theorem 0.21s 0.56s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 9 unt; 0 def)
% Number of atoms : 193 ( 37 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 228 ( 89 ~; 88 |; 28 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 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(f441,plain,
singletonP(sk0_47),
inference(forward_demodulation,[status(thm)],[f422,f423]) ).
fof(f709,plain,
( spl0_14
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f711,plain,
( ~ ssList(sk0_47)
| spl0_14 ),
inference(component_clause,[status(thm)],[f709]) ).
fof(f712,plain,
( spl0_15
<=> cons(sk0_4(sk0_47),nil) = sk0_47 ),
introduced(split_symbol_definition) ).
fof(f713,plain,
( cons(sk0_4(sk0_47),nil) = sk0_47
| ~ spl0_15 ),
inference(component_clause,[status(thm)],[f712]) ).
fof(f715,plain,
( ~ ssList(sk0_47)
| cons(sk0_4(sk0_47),nil) = sk0_47 ),
inference(resolution,[status(thm)],[f117,f441]) ).
fof(f716,plain,
( ~ spl0_14
| spl0_15 ),
inference(split_clause,[status(thm)],[f715,f709,f712]) ).
fof(f719,plain,
( $false
| spl0_14 ),
inference(forward_subsumption_resolution,[status(thm)],[f711,f417]) ).
fof(f720,plain,
spl0_14,
inference(contradiction_clause,[status(thm)],[f719]) ).
fof(f734,plain,
( spl0_16
<=> ssItem(sk0_4(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f735,plain,
( ssItem(sk0_4(sk0_47))
| ~ spl0_16 ),
inference(component_clause,[status(thm)],[f734]) ).
fof(f736,plain,
( ~ ssItem(sk0_4(sk0_47))
| spl0_16 ),
inference(component_clause,[status(thm)],[f734]) ).
fof(f750,plain,
( spl0_20
<=> singletonP(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f752,plain,
( ~ singletonP(sk0_47)
| spl0_20 ),
inference(component_clause,[status(thm)],[f750]) ).
fof(f753,plain,
( ~ ssList(sk0_47)
| ~ singletonP(sk0_47)
| spl0_16 ),
inference(resolution,[status(thm)],[f736,f116]) ).
fof(f754,plain,
( ~ spl0_14
| ~ spl0_20
| spl0_16 ),
inference(split_clause,[status(thm)],[f753,f709,f750,f734]) ).
fof(f755,plain,
( $false
| spl0_20 ),
inference(forward_subsumption_resolution,[status(thm)],[f752,f441]) ).
fof(f756,plain,
spl0_20,
inference(contradiction_clause,[status(thm)],[f755]) ).
fof(f766,plain,
( sk0_4(sk0_47) != sk0_51(sk0_4(sk0_47))
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f735,f426]) ).
fof(f838,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(sk0_4(sk0_47),X1),X0)
| X0 = sk0_4(sk0_47)
| memberP(X1,X0)
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f275,f735]) ).
fof(f976,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(cons(sk0_4(sk0_47),nil),X0)
| X0 = sk0_4(sk0_47)
| memberP(nil,X0)
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f838,f223]) ).
fof(f977,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(sk0_47,X0)
| X0 = sk0_4(sk0_47)
| memberP(nil,X0)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[status(thm)],[f713,f976]) ).
fof(f978,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(sk0_47,X0)
| X0 = sk0_4(sk0_47)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f977,f279]) ).
fof(f983,plain,
! [X0] :
( ~ ssItem(sk0_51(X0))
| sk0_51(X0) = sk0_4(sk0_47)
| ~ ssItem(X0)
| ~ spl0_15
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f978,f425]) ).
fof(f984,plain,
! [X0] :
( sk0_51(X0) = sk0_4(sk0_47)
| ~ ssItem(X0)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f983,f424]) ).
fof(f985,plain,
( sk0_51(sk0_4(sk0_47)) = sk0_4(sk0_47)
| ~ spl0_15
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f984,f735]) ).
fof(f986,plain,
( $false
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f985,f766]) ).
fof(f987,plain,
( ~ spl0_15
| ~ spl0_16 ),
inference(contradiction_clause,[status(thm)],[f986]) ).
fof(f988,plain,
$false,
inference(sat_refutation,[status(thm)],[f716,f720,f754,f756,f987]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC200+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 00:13:25 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.38 % Drodi V3.6.0
% 0.21/0.56 % Refutation found
% 0.21/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.58 % Elapsed time: 0.212156 seconds
% 0.21/0.58 % CPU time: 1.461344 seconds
% 0.21/0.58 % Total memory used: 79.866 MB
% 0.21/0.58 % Net memory used: 79.124 MB
%------------------------------------------------------------------------------