TSTP Solution File: SWC270+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWC270+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n014.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 99.48s 12.96s
% Output : CNFRefutation 100.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 78 ( 9 unt; 0 def)
% Number of atoms : 326 ( 32 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 387 ( 139 ~; 152 |; 56 &)
% ( 18 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 13 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-2 aty)
% Number of variables : 100 ( 82 !; 18 ?)
% 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
| ~ segmentP(X,W)
| ~ strictorderedP(W)
| 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
| ~ segmentP(X,W)
| ~ strictorderedP(W)
| 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
& segmentP(X,W)
& strictorderedP(W)
& ~ totalorderedP(U) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f97]) ).
fof(f416,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& segmentP(X,W) )
& strictorderedP(W)
& ~ totalorderedP(U) ) ) ),
inference(miniscoping,[status(esa)],[f415]) ).
fof(f417,plain,
( ssList(sk0_47)
& ssList(sk0_48)
& ssList(sk0_49)
& ssList(sk0_50)
& sk0_48 = sk0_50
& sk0_47 = sk0_49
& segmentP(sk0_50,sk0_49)
& strictorderedP(sk0_49)
& ~ totalorderedP(sk0_47) ),
inference(skolemization,[status(esa)],[f416]) ).
fof(f418,plain,
ssList(sk0_47),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f423,plain,
sk0_47 = sk0_49,
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f425,plain,
strictorderedP(sk0_49),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f426,plain,
~ totalorderedP(sk0_47),
inference(cnf_transformation,[status(esa)],[f417]) ).
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)],[f423,f425]) ).
fof(f466,plain,
( spl0_0
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f468,plain,
( ~ ssList(sk0_47)
| spl0_0 ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f502,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f468,f418]) ).
fof(f503,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f502]) ).
fof(f3953,plain,
( spl0_678
<=> totalorderedP(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f3954,plain,
( totalorderedP(sk0_47)
| ~ spl0_678 ),
inference(component_clause,[status(thm)],[f3953]) ).
fof(f3956,plain,
( spl0_679
<=> ssList(sk0_26(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f3959,plain,
( totalorderedP(sk0_47)
| ssList(sk0_26(sk0_47)) ),
inference(resolution,[status(thm)],[f180,f418]) ).
fof(f3960,plain,
( spl0_678
| spl0_679 ),
inference(split_clause,[status(thm)],[f3959,f3953,f3956]) ).
fof(f3961,plain,
( $false
| ~ spl0_678 ),
inference(forward_subsumption_resolution,[status(thm)],[f3954,f426]) ).
fof(f3962,plain,
~ spl0_678,
inference(contradiction_clause,[status(thm)],[f3961]) ).
fof(f3973,plain,
( spl0_682
<=> ssList(sk0_27(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f3976,plain,
( totalorderedP(sk0_47)
| ssList(sk0_27(sk0_47)) ),
inference(resolution,[status(thm)],[f181,f418]) ).
fof(f3977,plain,
( spl0_678
| spl0_682 ),
inference(split_clause,[status(thm)],[f3976,f3953,f3973]) ).
fof(f3988,plain,
( spl0_685
<=> ssList(sk0_28(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f3991,plain,
( totalorderedP(sk0_47)
| ssList(sk0_28(sk0_47)) ),
inference(resolution,[status(thm)],[f182,f418]) ).
fof(f3992,plain,
( spl0_678
| spl0_685 ),
inference(split_clause,[status(thm)],[f3991,f3953,f3988]) ).
fof(f4006,plain,
( spl0_689
<=> strictorderedP(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f4008,plain,
( ~ strictorderedP(sk0_47)
| spl0_689 ),
inference(component_clause,[status(thm)],[f4006]) ).
fof(f43954,plain,
( spl0_8603
<=> ssItem(sk0_24(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f43957,plain,
( totalorderedP(sk0_47)
| ssItem(sk0_24(sk0_47)) ),
inference(resolution,[status(thm)],[f178,f418]) ).
fof(f43958,plain,
( spl0_678
| spl0_8603 ),
inference(split_clause,[status(thm)],[f43957,f3953,f43954]) ).
fof(f44094,plain,
( spl0_8631
<=> ssItem(sk0_25(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f44097,plain,
( totalorderedP(sk0_47)
| ssItem(sk0_25(sk0_47)) ),
inference(resolution,[status(thm)],[f179,f418]) ).
fof(f44098,plain,
( spl0_678
| spl0_8631 ),
inference(split_clause,[status(thm)],[f44097,f3953,f44094]) ).
fof(f44234,plain,
( spl0_8659
<=> 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(f44235,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_8659 ),
inference(component_clause,[status(thm)],[f44234]) ).
fof(f44237,plain,
( totalorderedP(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,f418]) ).
fof(f44238,plain,
( spl0_678
| spl0_8659 ),
inference(split_clause,[status(thm)],[f44237,f3953,f44234]) ).
fof(f44559,plain,
( spl0_8720
<=> 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(f44561,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_8720 ),
inference(component_clause,[status(thm)],[f44559]) ).
fof(f44562,plain,
( spl0_8721
<=> lt(sk0_24(sk0_47),sk0_25(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f44563,plain,
( lt(sk0_24(sk0_47),sk0_25(sk0_47))
| ~ spl0_8721 ),
inference(component_clause,[status(thm)],[f44562]) ).
fof(f44570,plain,
( spl0_8723
<=> leq(sk0_24(sk0_47),sk0_25(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f44571,plain,
( leq(sk0_24(sk0_47),sk0_25(sk0_47))
| ~ spl0_8723 ),
inference(component_clause,[status(thm)],[f44570]) ).
fof(f44580,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_8659 ),
inference(paramodulation,[status(thm)],[f44235,f438]) ).
fof(f44581,plain,
( ~ spl0_8720
| ~ spl0_689
| ~ spl0_8603
| ~ spl0_8631
| ~ spl0_679
| ~ spl0_682
| ~ spl0_685
| spl0_8721
| ~ spl0_8659 ),
inference(split_clause,[status(thm)],[f44580,f44559,f4006,f43954,f44094,f3956,f3973,f3988,f44562,f44234]) ).
fof(f44633,plain,
( ~ ssList(sk0_47)
| ~ spl0_8659
| spl0_8720 ),
inference(forward_demodulation,[status(thm)],[f44235,f44561]) ).
fof(f44634,plain,
( $false
| ~ spl0_8659
| spl0_8720 ),
inference(forward_subsumption_resolution,[status(thm)],[f44633,f418]) ).
fof(f44635,plain,
( ~ spl0_8659
| spl0_8720 ),
inference(contradiction_clause,[status(thm)],[f44634]) ).
fof(f44637,plain,
( $false
| spl0_689 ),
inference(forward_subsumption_resolution,[status(thm)],[f4008,f459]) ).
fof(f44638,plain,
spl0_689,
inference(contradiction_clause,[status(thm)],[f44637]) ).
fof(f44649,plain,
( ~ ssItem(sk0_24(sk0_47))
| ~ ssItem(sk0_25(sk0_47))
| leq(sk0_24(sk0_47),sk0_25(sk0_47))
| ~ spl0_8721 ),
inference(resolution,[status(thm)],[f44563,f409]) ).
fof(f44650,plain,
( ~ spl0_8603
| ~ spl0_8631
| spl0_8723
| ~ spl0_8721 ),
inference(split_clause,[status(thm)],[f44649,f43954,f44094,f44570,f44562]) ).
fof(f44678,plain,
( ~ ssList(sk0_47)
| totalorderedP(sk0_47)
| ~ spl0_8723 ),
inference(resolution,[status(thm)],[f44571,f184]) ).
fof(f44679,plain,
( ~ spl0_0
| spl0_678
| ~ spl0_8723 ),
inference(split_clause,[status(thm)],[f44678,f466,f3953,f44570]) ).
fof(f44690,plain,
$false,
inference(sat_refutation,[status(thm)],[f503,f3960,f3962,f3977,f3992,f43958,f44098,f44238,f44581,f44635,f44638,f44650,f44679]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SWC270+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 30 00:01:34 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.37 % Drodi V3.6.0
% 99.48/12.96 % Refutation found
% 99.48/12.96 % SZS status Theorem for theBenchmark: Theorem is valid
% 99.48/12.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 100.24/13.02 % Elapsed time: 12.653068 seconds
% 100.24/13.02 % CPU time: 100.404848 seconds
% 100.24/13.02 % Total memory used: 288.860 MB
% 100.24/13.02 % Net memory used: 283.148 MB
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