TSTP Solution File: SWC271+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWC271+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 20:45:09 EDT 2024
% Result : Theorem 5.84s 1.03s
% Output : CNFRefutation 5.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 77 ( 9 unt; 0 def)
% Number of atoms : 337 ( 30 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 418 ( 158 ~; 160 |; 58 &)
% ( 18 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 13 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-2 aty)
% Number of variables : 100 ( 84 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [U] :
( ssList(U)
=> ( totalorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> leq(V,W) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [U] :
( ssList(U)
=> ( strictorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> lt(V,W) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( lt(U,V)
<=> ( U != V
& leq(U,V) ) ) ) ),
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
| ~ frontsegP(X,W)
| ~ strictorderedP(W)
| ? [Y] :
( ssList(Y)
& neq(W,Y)
& frontsegP(X,Y)
& segmentP(Y,W)
& strictorderedP(Y) )
| totalorderedP(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
| ~ frontsegP(X,W)
| ~ strictorderedP(W)
| ? [Y] :
( ssList(Y)
& neq(W,Y)
& frontsegP(X,Y)
& segmentP(Y,W)
& strictorderedP(Y) )
| totalorderedP(U) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f174,plain,
! [U] :
( ~ ssList(U)
| ( totalorderedP(U)
<=> ! [V] :
( ~ ssItem(V)
| ! [W] :
( ~ ssItem(W)
| ! [X] :
( ~ ssList(X)
| ! [Y] :
( ~ ssList(Y)
| ! [Z] :
( ~ ssList(Z)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| leq(V,W) ) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f175,plain,
! [U] :
( ~ ssList(U)
| ( ( ~ totalorderedP(U)
| ! [V] :
( ~ ssItem(V)
| ! [W] :
( ~ ssItem(W)
| ! [X] :
( ~ ssList(X)
| ! [Y] :
( ~ ssList(Y)
| ! [Z] :
( ~ ssList(Z)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| leq(V,W) ) ) ) ) ) )
& ( totalorderedP(U)
| ? [V] :
( ssItem(V)
& ? [W] :
( ssItem(W)
& ? [X] :
( ssList(X)
& ? [Y] :
( ssList(Y)
& ? [Z] :
( ssList(Z)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ~ leq(V,W) ) ) ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f174]) ).
fof(f176,plain,
! [U] :
( ~ ssList(U)
| ( ( ~ totalorderedP(U)
| ! [V] :
( ~ ssItem(V)
| ! [W] :
( ~ ssItem(W)
| ! [X] :
( ~ ssList(X)
| ! [Y] :
( ~ ssList(Y)
| ! [Z] :
( ~ ssList(Z)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| leq(V,W) ) ) ) ) ) )
& ( totalorderedP(U)
| ( ssItem(sk0_24(U))
& ssItem(sk0_25(U))
& ssList(sk0_26(U))
& ssList(sk0_27(U))
& ssList(sk0_28(U))
& app(app(sk0_26(U),cons(sk0_24(U),sk0_27(U))),cons(sk0_25(U),sk0_28(U))) = U
& ~ leq(sk0_24(U),sk0_25(U)) ) ) ) ),
inference(skolemization,[status(esa)],[f175]) ).
fof(f178,plain,
! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| ssItem(sk0_24(X0)) ),
inference(cnf_transformation,[status(esa)],[f176]) ).
fof(f179,plain,
! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| ssItem(sk0_25(X0)) ),
inference(cnf_transformation,[status(esa)],[f176]) ).
fof(f180,plain,
! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| ssList(sk0_26(X0)) ),
inference(cnf_transformation,[status(esa)],[f176]) ).
fof(f181,plain,
! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| ssList(sk0_27(X0)) ),
inference(cnf_transformation,[status(esa)],[f176]) ).
fof(f182,plain,
! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| ssList(sk0_28(X0)) ),
inference(cnf_transformation,[status(esa)],[f176]) ).
fof(f183,plain,
! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| app(app(sk0_26(X0),cons(sk0_24(X0),sk0_27(X0))),cons(sk0_25(X0),sk0_28(X0))) = X0 ),
inference(cnf_transformation,[status(esa)],[f176]) ).
fof(f184,plain,
! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| ~ leq(sk0_24(X0),sk0_25(X0)) ),
inference(cnf_transformation,[status(esa)],[f176]) ).
fof(f185,plain,
! [U] :
( ~ ssList(U)
| ( strictorderedP(U)
<=> ! [V] :
( ~ ssItem(V)
| ! [W] :
( ~ ssItem(W)
| ! [X] :
( ~ ssList(X)
| ! [Y] :
( ~ ssList(Y)
| ! [Z] :
( ~ ssList(Z)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| lt(V,W) ) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f186,plain,
! [U] :
( ~ ssList(U)
| ( ( ~ strictorderedP(U)
| ! [V] :
( ~ ssItem(V)
| ! [W] :
( ~ ssItem(W)
| ! [X] :
( ~ ssList(X)
| ! [Y] :
( ~ ssList(Y)
| ! [Z] :
( ~ ssList(Z)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| lt(V,W) ) ) ) ) ) )
& ( strictorderedP(U)
| ? [V] :
( ssItem(V)
& ? [W] :
( ssItem(W)
& ? [X] :
( ssList(X)
& ? [Y] :
( ssList(Y)
& ? [Z] :
( ssList(Z)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ~ lt(V,W) ) ) ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f185]) ).
fof(f187,plain,
! [U] :
( ~ ssList(U)
| ( ( ~ strictorderedP(U)
| ! [V] :
( ~ ssItem(V)
| ! [W] :
( ~ ssItem(W)
| ! [X] :
( ~ ssList(X)
| ! [Y] :
( ~ ssList(Y)
| ! [Z] :
( ~ ssList(Z)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| lt(V,W) ) ) ) ) ) )
& ( strictorderedP(U)
| ( ssItem(sk0_29(U))
& ssItem(sk0_30(U))
& ssList(sk0_31(U))
& ssList(sk0_32(U))
& ssList(sk0_33(U))
& app(app(sk0_31(U),cons(sk0_29(U),sk0_32(U))),cons(sk0_30(U),sk0_33(U))) = U
& ~ lt(sk0_29(U),sk0_30(U)) ) ) ) ),
inference(skolemization,[status(esa)],[f186]) ).
fof(f188,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ ssList(X0)
| ~ strictorderedP(X0)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| lt(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f187]) ).
fof(f406,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ~ ssItem(V)
| ( lt(U,V)
<=> ( U != V
& leq(U,V) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f93]) ).
fof(f407,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ~ ssItem(V)
| ( ( ~ lt(U,V)
| ( U != V
& leq(U,V) ) )
& ( lt(U,V)
| U = V
| ~ leq(U,V) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f406]) ).
fof(f409,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f407]) ).
fof(f415,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& frontsegP(X,W)
& strictorderedP(W)
& ! [Y] :
( ~ ssList(Y)
| ~ neq(W,Y)
| ~ frontsegP(X,Y)
| ~ segmentP(Y,W)
| ~ strictorderedP(Y) )
& ~ totalorderedP(U) ) ) ) ),
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
& frontsegP(sk0_50,sk0_49)
& strictorderedP(sk0_49)
& ! [Y] :
( ~ ssList(Y)
| ~ neq(sk0_49,Y)
| ~ frontsegP(sk0_50,Y)
| ~ segmentP(Y,sk0_49)
| ~ strictorderedP(Y) )
& ~ totalorderedP(sk0_47) ),
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(f424,plain,
strictorderedP(sk0_49),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f426,plain,
~ totalorderedP(sk0_47),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f438,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| lt(X1,X3) ),
inference(destructive_equality_resolution,[status(esa)],[f188]) ).
fof(f459,plain,
strictorderedP(sk0_47),
inference(forward_demodulation,[status(thm)],[f422,f424]) ).
fof(f465,plain,
( spl0_0
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f467,plain,
( ~ ssList(sk0_47)
| spl0_0 ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f474,plain,
( spl0_3
<=> strictorderedP(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f476,plain,
( ~ strictorderedP(sk0_47)
| spl0_3 ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f479,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f476,f459]) ).
fof(f480,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f479]) ).
fof(f483,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f467,f417]) ).
fof(f484,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f483]) ).
fof(f996,plain,
( spl0_88
<=> ssList(sk0_26(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f999,plain,
( ~ ssList(sk0_47)
| ssList(sk0_26(sk0_47)) ),
inference(resolution,[status(thm)],[f180,f426]) ).
fof(f1000,plain,
( ~ spl0_0
| spl0_88 ),
inference(split_clause,[status(thm)],[f999,f465,f996]) ).
fof(f1131,plain,
( spl0_107
<=> ssList(sk0_27(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f1134,plain,
( ~ ssList(sk0_47)
| ssList(sk0_27(sk0_47)) ),
inference(resolution,[status(thm)],[f181,f426]) ).
fof(f1135,plain,
( ~ spl0_0
| spl0_107 ),
inference(split_clause,[status(thm)],[f1134,f465,f1131]) ).
fof(f1266,plain,
( spl0_126
<=> ssList(sk0_28(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f1269,plain,
( ~ ssList(sk0_47)
| ssList(sk0_28(sk0_47)) ),
inference(resolution,[status(thm)],[f182,f426]) ).
fof(f1270,plain,
( ~ spl0_0
| spl0_126 ),
inference(split_clause,[status(thm)],[f1269,f465,f1266]) ).
fof(f7224,plain,
( spl0_799
<=> ssItem(sk0_24(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f7227,plain,
( ~ ssList(sk0_47)
| ssItem(sk0_24(sk0_47)) ),
inference(resolution,[status(thm)],[f178,f426]) ).
fof(f7228,plain,
( ~ spl0_0
| spl0_799 ),
inference(split_clause,[status(thm)],[f7227,f465,f7224]) ).
fof(f7241,plain,
( spl0_802
<=> ssItem(sk0_25(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f7244,plain,
( ~ ssList(sk0_47)
| ssItem(sk0_25(sk0_47)) ),
inference(resolution,[status(thm)],[f179,f426]) ).
fof(f7245,plain,
( ~ spl0_0
| spl0_802 ),
inference(split_clause,[status(thm)],[f7244,f465,f7241]) ).
fof(f7258,plain,
( spl0_805
<=> app(app(sk0_26(sk0_47),cons(sk0_24(sk0_47),sk0_27(sk0_47))),cons(sk0_25(sk0_47),sk0_28(sk0_47))) = sk0_47 ),
introduced(split_symbol_definition) ).
fof(f7259,plain,
( app(app(sk0_26(sk0_47),cons(sk0_24(sk0_47),sk0_27(sk0_47))),cons(sk0_25(sk0_47),sk0_28(sk0_47))) = sk0_47
| ~ spl0_805 ),
inference(component_clause,[status(thm)],[f7258]) ).
fof(f7261,plain,
( ~ ssList(sk0_47)
| app(app(sk0_26(sk0_47),cons(sk0_24(sk0_47),sk0_27(sk0_47))),cons(sk0_25(sk0_47),sk0_28(sk0_47))) = sk0_47 ),
inference(resolution,[status(thm)],[f183,f426]) ).
fof(f7262,plain,
( ~ spl0_0
| spl0_805 ),
inference(split_clause,[status(thm)],[f7261,f465,f7258]) ).
fof(f7321,plain,
( spl0_812
<=> ssList(app(app(sk0_26(sk0_47),cons(sk0_24(sk0_47),sk0_27(sk0_47))),cons(sk0_25(sk0_47),sk0_28(sk0_47)))) ),
introduced(split_symbol_definition) ).
fof(f7323,plain,
( ~ ssList(app(app(sk0_26(sk0_47),cons(sk0_24(sk0_47),sk0_27(sk0_47))),cons(sk0_25(sk0_47),sk0_28(sk0_47))))
| spl0_812 ),
inference(component_clause,[status(thm)],[f7321]) ).
fof(f7327,plain,
( spl0_814
<=> lt(sk0_24(sk0_47),sk0_25(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f7328,plain,
( lt(sk0_24(sk0_47),sk0_25(sk0_47))
| ~ spl0_814 ),
inference(component_clause,[status(thm)],[f7327]) ).
fof(f7338,plain,
( spl0_817
<=> leq(sk0_24(sk0_47),sk0_25(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f7339,plain,
( leq(sk0_24(sk0_47),sk0_25(sk0_47))
| ~ spl0_817 ),
inference(component_clause,[status(thm)],[f7338]) ).
fof(f7381,plain,
( ~ ssList(app(app(sk0_26(sk0_47),cons(sk0_24(sk0_47),sk0_27(sk0_47))),cons(sk0_25(sk0_47),sk0_28(sk0_47))))
| ~ strictorderedP(sk0_47)
| ~ ssItem(sk0_24(sk0_47))
| ~ ssItem(sk0_25(sk0_47))
| ~ ssList(sk0_26(sk0_47))
| ~ ssList(sk0_27(sk0_47))
| ~ ssList(sk0_28(sk0_47))
| lt(sk0_24(sk0_47),sk0_25(sk0_47))
| ~ spl0_805 ),
inference(paramodulation,[status(thm)],[f7259,f438]) ).
fof(f7382,plain,
( ~ spl0_812
| ~ spl0_3
| ~ spl0_799
| ~ spl0_802
| ~ spl0_88
| ~ spl0_107
| ~ spl0_126
| spl0_814
| ~ spl0_805 ),
inference(split_clause,[status(thm)],[f7381,f7321,f474,f7224,f7241,f996,f1131,f1266,f7327,f7258]) ).
fof(f7383,plain,
( spl0_826
<=> totalorderedP(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f7384,plain,
( totalorderedP(sk0_47)
| ~ spl0_826 ),
inference(component_clause,[status(thm)],[f7383]) ).
fof(f7565,plain,
( ~ ssList(sk0_47)
| ~ spl0_805
| spl0_812 ),
inference(forward_demodulation,[status(thm)],[f7259,f7323]) ).
fof(f7566,plain,
( $false
| ~ spl0_805
| spl0_812 ),
inference(forward_subsumption_resolution,[status(thm)],[f7565,f417]) ).
fof(f7567,plain,
( ~ spl0_805
| spl0_812 ),
inference(contradiction_clause,[status(thm)],[f7566]) ).
fof(f9277,plain,
( ~ ssItem(sk0_24(sk0_47))
| ~ ssItem(sk0_25(sk0_47))
| leq(sk0_24(sk0_47),sk0_25(sk0_47))
| ~ spl0_814 ),
inference(resolution,[status(thm)],[f7328,f409]) ).
fof(f9278,plain,
( ~ spl0_799
| ~ spl0_802
| spl0_817
| ~ spl0_814 ),
inference(split_clause,[status(thm)],[f9277,f7224,f7241,f7338,f7327]) ).
fof(f9286,plain,
( ~ ssList(sk0_47)
| totalorderedP(sk0_47)
| ~ spl0_817 ),
inference(resolution,[status(thm)],[f7339,f184]) ).
fof(f9287,plain,
( ~ spl0_0
| spl0_826
| ~ spl0_817 ),
inference(split_clause,[status(thm)],[f9286,f465,f7383,f7338]) ).
fof(f9300,plain,
( $false
| ~ spl0_826 ),
inference(forward_subsumption_resolution,[status(thm)],[f7384,f426]) ).
fof(f9301,plain,
~ spl0_826,
inference(contradiction_clause,[status(thm)],[f9300]) ).
fof(f9302,plain,
$false,
inference(sat_refutation,[status(thm)],[f480,f484,f1000,f1135,f1270,f7228,f7245,f7262,f7382,f7567,f9278,f9287,f9301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.07 % Problem : SWC271+1 : TPTP v8.1.2. Released v2.4.0.
% 0.01/0.08 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26 % Computer : n029.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Tue Apr 30 00:31:49 EDT 2024
% 0.07/0.26 % CPUTime :
% 0.11/0.27 % Drodi V3.6.0
% 5.84/1.03 % Refutation found
% 5.84/1.03 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.84/1.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.84/1.05 % Elapsed time: 0.781035 seconds
% 5.84/1.05 % CPU time: 6.105774 seconds
% 5.84/1.05 % Total memory used: 114.105 MB
% 5.84/1.05 % Net memory used: 111.986 MB
%------------------------------------------------------------------------------