TSTP Solution File: SWC046+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWC046+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 20:44:18 EDT 2024
% Result : Theorem 12.09s 1.94s
% Output : CNFRefutation 12.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 11 unt; 0 def)
% Number of atoms : 226 ( 46 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 251 ( 90 ~; 93 |; 44 &)
% ( 9 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 59 ( 44 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [U] :
( ssItem(U)
& ? [V] :
( ssItem(V)
& U != V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [U] :
( ssList(U)
=> ( nil = U
| ? [V] :
( ssList(V)
& ? [W] :
( ssItem(W)
& cons(W,V) = U ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( nil != V
| V != X
| U != W
| nil = U
| ? [Y] :
( ssItem(Y)
& ( ( ~ memberP(W,Y)
& ! [Z] :
( ssList(Z)
=> ~ segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) )
& memberP(X,Y) )
| ( memberP(W,Y)
& ( ~ memberP(X,Y)
| ? [Z] :
( ssList(Z)
& segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( nil != V
| V != X
| U != W
| nil = U
| ? [Y] :
( ssItem(Y)
& ( ( ~ memberP(W,Y)
& ! [Z] :
( ssList(Z)
=> ~ segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) )
& memberP(X,Y) )
| ( memberP(W,Y)
& ( ~ memberP(X,Y)
| ? [Z] :
( ssList(Z)
& segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f102,plain,
( ssItem(sk0_0)
& ssItem(sk0_1)
& sk0_0 != sk0_1 ),
inference(skolemization,[status(esa)],[f2]) ).
fof(f103,plain,
ssItem(sk0_0),
inference(cnf_transformation,[status(esa)],[f102]) ).
fof(f229,plain,
! [U] :
( ~ ssList(U)
| nil = U
| ? [V] :
( ssList(V)
& ? [W] :
( ssItem(W)
& cons(W,V) = U ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f230,plain,
! [U] :
( ~ ssList(U)
| nil = U
| ( ssList(sk0_43(U))
& ssItem(sk0_44(U))
& cons(sk0_44(U),sk0_43(U)) = U ) ),
inference(skolemization,[status(esa)],[f229]) ).
fof(f231,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(sk0_43(X0)) ),
inference(cnf_transformation,[status(esa)],[f230]) ).
fof(f232,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(sk0_44(X0)) ),
inference(cnf_transformation,[status(esa)],[f230]) ).
fof(f233,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(sk0_44(X0),sk0_43(X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f230]) ).
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(f276,plain,
! [X0,X1,X2] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X0)
| X0 != X1 ),
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)
& nil = V
& V = X
& U = W
& nil != U
& ! [Y] :
( ~ ssItem(Y)
| ( ( memberP(W,Y)
| ? [Z] :
( ssList(Z)
& segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) )
| ~ memberP(X,Y) )
& ( ~ memberP(W,Y)
| ( memberP(X,Y)
& ! [Z] :
( ~ ssList(Z)
| ~ segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) ) ) ) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f97]) ).
fof(f416,plain,
( ssList(sk0_47)
& ssList(sk0_48)
& ssList(sk0_49)
& ssList(sk0_50)
& nil = sk0_48
& sk0_48 = sk0_50
& sk0_47 = sk0_49
& nil != sk0_47
& ! [Y] :
( ~ ssItem(Y)
| ( ( memberP(sk0_49,Y)
| ( ssList(sk0_51(Y))
& segmentP(sk0_50,app(app(cons(Y,nil),sk0_51(Y)),cons(Y,nil))) )
| ~ memberP(sk0_50,Y) )
& ( ~ memberP(sk0_49,Y)
| ( memberP(sk0_50,Y)
& ! [Z] :
( ~ ssList(Z)
| ~ segmentP(sk0_50,app(app(cons(Y,nil),Z),cons(Y,nil))) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f415]) ).
fof(f417,plain,
ssList(sk0_47),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f421,plain,
nil = sk0_48,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f422,plain,
sk0_48 = sk0_50,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f423,plain,
sk0_47 = sk0_49,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f424,plain,
nil != sk0_47,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f427,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(sk0_49,X0)
| memberP(sk0_50,X0) ),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f446,plain,
! [X1,X2] :
( ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(destructive_equality_resolution,[status(esa)],[f276]) ).
fof(f447,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| memberP(cons(X0,X1),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f446]) ).
fof(f459,plain,
nil = sk0_50,
inference(forward_demodulation,[status(thm)],[f421,f422]) ).
fof(f465,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(sk0_47,X0)
| memberP(sk0_50,X0) ),
inference(forward_demodulation,[status(thm)],[f423,f427]) ).
fof(f466,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(sk0_47,X0)
| memberP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f459,f465]) ).
fof(f467,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(sk0_47,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f466,f279]) ).
fof(f492,plain,
( spl0_3
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f494,plain,
( ~ ssList(sk0_47)
| spl0_3 ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f502,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f494,f417]) ).
fof(f503,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f502]) ).
fof(f580,plain,
( spl0_7
<=> nil = sk0_47 ),
introduced(split_symbol_definition) ).
fof(f581,plain,
( nil = sk0_47
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f580]) ).
fof(f1178,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f581,f424]) ).
fof(f1179,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f1178]) ).
fof(f1433,plain,
( spl0_66
<=> ssItem(sk0_0) ),
introduced(split_symbol_definition) ).
fof(f1435,plain,
( ~ ssItem(sk0_0)
| spl0_66 ),
inference(component_clause,[status(thm)],[f1433]) ).
fof(f1452,plain,
( $false
| spl0_66 ),
inference(forward_subsumption_resolution,[status(thm)],[f1435,f103]) ).
fof(f1453,plain,
spl0_66,
inference(contradiction_clause,[status(thm)],[f1452]) ).
fof(f2606,plain,
( spl0_151
<=> cons(sk0_44(sk0_47),sk0_43(sk0_47)) = sk0_47 ),
introduced(split_symbol_definition) ).
fof(f2607,plain,
( cons(sk0_44(sk0_47),sk0_43(sk0_47)) = sk0_47
| ~ spl0_151 ),
inference(component_clause,[status(thm)],[f2606]) ).
fof(f2609,plain,
( nil = sk0_47
| cons(sk0_44(sk0_47),sk0_43(sk0_47)) = sk0_47 ),
inference(resolution,[status(thm)],[f233,f417]) ).
fof(f2610,plain,
( spl0_7
| spl0_151 ),
inference(split_clause,[status(thm)],[f2609,f580,f2606]) ).
fof(f3175,plain,
( spl0_162
<=> ssList(sk0_43(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f3176,plain,
( ssList(sk0_43(sk0_47))
| ~ spl0_162 ),
inference(component_clause,[status(thm)],[f3175]) ).
fof(f3177,plain,
( ~ ssList(sk0_43(sk0_47))
| spl0_162 ),
inference(component_clause,[status(thm)],[f3175]) ).
fof(f3178,plain,
( spl0_163
<=> ssItem(sk0_44(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f3180,plain,
( ~ ssItem(sk0_44(sk0_47))
| spl0_163 ),
inference(component_clause,[status(thm)],[f3178]) ).
fof(f3202,plain,
( ~ ssList(sk0_47)
| nil = sk0_47
| spl0_163 ),
inference(resolution,[status(thm)],[f3180,f232]) ).
fof(f3203,plain,
( ~ spl0_3
| spl0_7
| spl0_163 ),
inference(split_clause,[status(thm)],[f3202,f492,f580,f3178]) ).
fof(f3204,plain,
( ~ ssList(sk0_47)
| nil = sk0_47
| spl0_162 ),
inference(resolution,[status(thm)],[f3177,f231]) ).
fof(f3205,plain,
( ~ spl0_3
| spl0_7
| spl0_162 ),
inference(split_clause,[status(thm)],[f3204,f492,f580,f3175]) ).
fof(f3322,plain,
! [X0] :
( ~ ssItem(X0)
| memberP(cons(X0,sk0_43(sk0_47)),X0)
| ~ spl0_162 ),
inference(resolution,[status(thm)],[f3176,f447]) ).
fof(f3513,plain,
( spl0_196
<=> memberP(sk0_47,sk0_44(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f3514,plain,
( memberP(sk0_47,sk0_44(sk0_47))
| ~ spl0_196 ),
inference(component_clause,[status(thm)],[f3513]) ).
fof(f3740,plain,
( ~ ssItem(sk0_44(sk0_47))
| ~ spl0_196 ),
inference(resolution,[status(thm)],[f3514,f467]) ).
fof(f3741,plain,
( ~ spl0_163
| ~ spl0_196 ),
inference(split_clause,[status(thm)],[f3740,f3178,f3513]) ).
fof(f3816,plain,
( ~ ssItem(sk0_44(sk0_47))
| memberP(sk0_47,sk0_44(sk0_47))
| ~ spl0_162
| ~ spl0_151 ),
inference(paramodulation,[status(thm)],[f2607,f3322]) ).
fof(f3817,plain,
( ~ spl0_163
| spl0_196
| ~ spl0_162
| ~ spl0_151 ),
inference(split_clause,[status(thm)],[f3816,f3178,f3513,f3175,f2606]) ).
fof(f3818,plain,
$false,
inference(sat_refutation,[status(thm)],[f503,f1179,f1453,f2610,f3203,f3205,f3741,f3817]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWC046+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 29 23:57:05 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 % Drodi V3.6.0
% 12.09/1.94 % Refutation found
% 12.09/1.94 % SZS status Theorem for theBenchmark: Theorem is valid
% 12.09/1.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.69/1.98 % Elapsed time: 1.625811 seconds
% 12.69/1.98 % CPU time: 12.773108 seconds
% 12.69/1.98 % Total memory used: 161.255 MB
% 12.69/1.98 % Net memory used: 156.423 MB
%------------------------------------------------------------------------------