TSTP Solution File: SWC264+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWC264+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n012.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 20:45:08 EDT 2024
% Result : Theorem 3.61s 0.88s
% Output : CNFRefutation 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 79 ( 8 unt; 0 def)
% Number of atoms : 334 ( 32 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 408 ( 153 ~; 163 |; 53 &)
% ( 17 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 12 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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f93,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( lt(U,V)
<=> ( U != V
& leq(U,V) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ~ ssList(X)
| V != X
| U != W
| ~ strictorderedP(W)
| totalorderedP(U) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ~ ssList(X)
| V != X
| U != 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
& 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
& 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
& 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(f424,plain,
strictorderedP(sk0_49),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f425,plain,
~ totalorderedP(sk0_47),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f437,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(f458,plain,
strictorderedP(sk0_47),
inference(forward_demodulation,[status(thm)],[f423,f424]) ).
fof(f524,plain,
( spl0_8
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f526,plain,
( ~ ssList(sk0_47)
| spl0_8 ),
inference(component_clause,[status(thm)],[f524]) ).
fof(f555,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f418]) ).
fof(f556,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f555]) ).
fof(f3426,plain,
( spl0_262
<=> 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(f3427,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_262 ),
inference(component_clause,[status(thm)],[f3426]) ).
fof(f3429,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,f425]) ).
fof(f3430,plain,
( ~ spl0_8
| spl0_262 ),
inference(split_clause,[status(thm)],[f3429,f524,f3426]) ).
fof(f3447,plain,
( spl0_266
<=> ssItem(sk0_24(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f3449,plain,
( ~ ssItem(sk0_24(sk0_47))
| spl0_266 ),
inference(component_clause,[status(thm)],[f3447]) ).
fof(f3450,plain,
( spl0_267
<=> ssItem(sk0_25(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f3452,plain,
( ~ ssItem(sk0_25(sk0_47))
| spl0_267 ),
inference(component_clause,[status(thm)],[f3450]) ).
fof(f3453,plain,
( spl0_268
<=> ssList(sk0_26(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f3455,plain,
( ~ ssList(sk0_26(sk0_47))
| spl0_268 ),
inference(component_clause,[status(thm)],[f3453]) ).
fof(f3456,plain,
( spl0_269
<=> ssList(sk0_27(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f3458,plain,
( ~ ssList(sk0_27(sk0_47))
| spl0_269 ),
inference(component_clause,[status(thm)],[f3456]) ).
fof(f3459,plain,
( spl0_270
<=> ssList(sk0_28(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f3461,plain,
( ~ ssList(sk0_28(sk0_47))
| spl0_270 ),
inference(component_clause,[status(thm)],[f3459]) ).
fof(f3462,plain,
( spl0_271
<=> lt(sk0_24(sk0_47),sk0_25(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f3463,plain,
( lt(sk0_24(sk0_47),sk0_25(sk0_47))
| ~ spl0_271 ),
inference(component_clause,[status(thm)],[f3462]) ).
fof(f3473,plain,
( spl0_274
<=> leq(sk0_24(sk0_47),sk0_25(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f3474,plain,
( leq(sk0_24(sk0_47),sk0_25(sk0_47))
| ~ spl0_274 ),
inference(component_clause,[status(thm)],[f3473]) ).
fof(f3486,plain,
( spl0_277
<=> strictorderedP(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(f3488,plain,
( ~ strictorderedP(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_277 ),
inference(component_clause,[status(thm)],[f3486]) ).
fof(f3489,plain,
( ~ ssList(sk0_47)
| ~ strictorderedP(app(app(sk0_26(sk0_47),cons(sk0_24(sk0_47),sk0_27(sk0_47))),cons(sk0_25(sk0_47),sk0_28(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_262 ),
inference(paramodulation,[status(thm)],[f3427,f437]) ).
fof(f3490,plain,
( ~ spl0_8
| ~ spl0_277
| ~ spl0_266
| ~ spl0_267
| ~ spl0_268
| ~ spl0_269
| ~ spl0_270
| spl0_271
| ~ spl0_262 ),
inference(split_clause,[status(thm)],[f3489,f524,f3486,f3447,f3450,f3453,f3456,f3459,f3462,f3426]) ).
fof(f3494,plain,
( spl0_279
<=> totalorderedP(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f3495,plain,
( totalorderedP(sk0_47)
| ~ spl0_279 ),
inference(component_clause,[status(thm)],[f3494]) ).
fof(f3566,plain,
( ~ strictorderedP(sk0_47)
| ~ spl0_262
| spl0_277 ),
inference(forward_demodulation,[status(thm)],[f3427,f3488]) ).
fof(f3567,plain,
( $false
| ~ spl0_262
| spl0_277 ),
inference(forward_subsumption_resolution,[status(thm)],[f3566,f458]) ).
fof(f3568,plain,
( ~ spl0_262
| spl0_277 ),
inference(contradiction_clause,[status(thm)],[f3567]) ).
fof(f3667,plain,
( ~ ssList(sk0_47)
| totalorderedP(sk0_47)
| spl0_269 ),
inference(resolution,[status(thm)],[f3458,f181]) ).
fof(f3668,plain,
( ~ spl0_8
| spl0_279
| spl0_269 ),
inference(split_clause,[status(thm)],[f3667,f524,f3494,f3456]) ).
fof(f3669,plain,
( ~ ssList(sk0_47)
| totalorderedP(sk0_47)
| spl0_266 ),
inference(resolution,[status(thm)],[f3449,f178]) ).
fof(f3670,plain,
( ~ spl0_8
| spl0_279
| spl0_266 ),
inference(split_clause,[status(thm)],[f3669,f524,f3494,f3447]) ).
fof(f3671,plain,
( ~ ssList(sk0_47)
| totalorderedP(sk0_47)
| spl0_268 ),
inference(resolution,[status(thm)],[f3455,f180]) ).
fof(f3672,plain,
( ~ spl0_8
| spl0_279
| spl0_268 ),
inference(split_clause,[status(thm)],[f3671,f524,f3494,f3453]) ).
fof(f3748,plain,
( ~ ssList(sk0_47)
| totalorderedP(sk0_47)
| spl0_270 ),
inference(resolution,[status(thm)],[f3461,f182]) ).
fof(f3749,plain,
( ~ spl0_8
| spl0_279
| spl0_270 ),
inference(split_clause,[status(thm)],[f3748,f524,f3494,f3459]) ).
fof(f3776,plain,
( ~ ssList(sk0_47)
| totalorderedP(sk0_47)
| spl0_267 ),
inference(resolution,[status(thm)],[f3452,f179]) ).
fof(f3777,plain,
( ~ spl0_8
| spl0_279
| spl0_267 ),
inference(split_clause,[status(thm)],[f3776,f524,f3494,f3450]) ).
fof(f3778,plain,
( $false
| ~ spl0_279 ),
inference(forward_subsumption_resolution,[status(thm)],[f3495,f425]) ).
fof(f3779,plain,
~ spl0_279,
inference(contradiction_clause,[status(thm)],[f3778]) ).
fof(f4573,plain,
( ~ ssItem(sk0_24(sk0_47))
| ~ ssItem(sk0_25(sk0_47))
| leq(sk0_24(sk0_47),sk0_25(sk0_47))
| ~ spl0_271 ),
inference(resolution,[status(thm)],[f3463,f409]) ).
fof(f4574,plain,
( ~ spl0_266
| ~ spl0_267
| spl0_274
| ~ spl0_271 ),
inference(split_clause,[status(thm)],[f4573,f3447,f3450,f3473,f3462]) ).
fof(f4582,plain,
( ~ ssList(sk0_47)
| totalorderedP(sk0_47)
| ~ spl0_274 ),
inference(resolution,[status(thm)],[f3474,f184]) ).
fof(f4583,plain,
( ~ spl0_8
| spl0_279
| ~ spl0_274 ),
inference(split_clause,[status(thm)],[f4582,f524,f3494,f3473]) ).
fof(f4584,plain,
$false,
inference(sat_refutation,[status(thm)],[f556,f3430,f3490,f3568,f3668,f3670,f3672,f3749,f3777,f3779,f4574,f4583]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC264+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 30 00:01:12 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 3.61/0.88 % Refutation found
% 3.61/0.88 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.61/0.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.13/0.90 % Elapsed time: 0.551768 seconds
% 4.13/0.90 % CPU time: 4.210233 seconds
% 4.13/0.90 % Total memory used: 99.519 MB
% 4.13/0.90 % Net memory used: 98.006 MB
%------------------------------------------------------------------------------