TSTP Solution File: SWC076+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWC076+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 20:44:26 EDT 2024
% Result : Theorem 0.13s 0.34s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 79 ( 17 unt; 0 def)
% Number of atoms : 329 ( 87 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 393 ( 143 ~; 139 |; 79 &)
% ( 15 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 12 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 96 ( 64 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& app(app(W,V),X) = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,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
| ? [Y] :
( ssList(Y)
& neq(Y,nil)
& segmentP(V,Y)
& segmentP(U,Y) )
| ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( app(app(Z,W),X1) != X
| ~ equalelemsP(W)
| ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& app(X3,cons(X2,nil)) = Z
& ? [X4] :
( ssList(X4)
& app(cons(X2,nil),X4) = W ) ) )
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X1
& ? [X7] :
( ssList(X7)
& app(X7,cons(X5,nil)) = W ) ) ) ) ) )
| ( nil != X
& nil = W )
| ( nil = V
& nil = 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
| ? [Y] :
( ssList(Y)
& neq(Y,nil)
& segmentP(V,Y)
& segmentP(U,Y) )
| ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( app(app(Z,W),X1) != X
| ~ equalelemsP(W)
| ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& app(X3,cons(X2,nil)) = Z
& ? [X4] :
( ssList(X4)
& app(cons(X2,nil),X4) = W ) ) )
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X1
& ? [X7] :
( ssList(X7)
& app(X7,cons(X5,nil)) = W ) ) ) ) ) )
| ( nil != X
& nil = W )
| ( nil = V
& nil = U ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f131,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( segmentP(U,V)
<=> ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& app(app(W,V),X) = U ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f132,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( ( ~ segmentP(U,V)
| ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& app(app(W,V),X) = U ) ) )
& ( segmentP(U,V)
| ! [W] :
( ~ ssList(W)
| ! [X] :
( ~ ssList(X)
| app(app(W,V),X) != U ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f131]) ).
fof(f133,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( ( ~ segmentP(U,V)
| ( ssList(sk0_7(V,U))
& ssList(sk0_8(V,U))
& app(app(sk0_7(V,U),V),sk0_8(V,U)) = U ) )
& ( segmentP(U,V)
| ! [W] :
( ~ ssList(W)
| ! [X] :
( ~ ssList(X)
| app(app(W,V),X) != U ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f132]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X0)
| ~ ssList(X1)
| segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ),
inference(cnf_transformation,[status(esa)],[f133]) ).
fof(f217,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( neq(U,V)
<=> U != V ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f218,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( ( ~ neq(U,V)
| U != V )
& ( neq(U,V)
| U = V ) ) ) ),
inference(NNF_transformation,[status(esa)],[f217]) ).
fof(f220,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f218]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f318,plain,
! [U] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(pre_NNF_transformation,[status(esa)],[f55]) ).
fof(f319,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f318]) ).
fof(f415,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& ! [Y] :
( ~ ssList(Y)
| ~ neq(Y,nil)
| ~ segmentP(V,Y)
| ~ segmentP(U,Y) )
& ? [Z] :
( ssList(Z)
& ? [X1] :
( ssList(X1)
& app(app(Z,W),X1) = X
& equalelemsP(W)
& ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X3,cons(X2,nil)) != Z
| ! [X4] :
( ~ ssList(X4)
| app(cons(X2,nil),X4) != W ) ) )
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X1
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != W ) ) ) ) )
& ( nil = X
| nil != W )
& ( nil != V
| nil != 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
& ! [Y] :
( ~ ssList(Y)
| ~ neq(Y,nil)
| ~ segmentP(V,Y)
| ~ segmentP(U,Y) )
& ? [Z] :
( ssList(Z)
& ? [X1] :
( ssList(X1)
& app(app(Z,W),X1) = X
& equalelemsP(W)
& ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X3,cons(X2,nil)) != Z )
| ! [X4] :
( ~ ssList(X4)
| app(cons(X2,nil),X4) != W ) )
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X1 )
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != W ) ) ) )
& ( nil = X
| nil != W )
& ( nil != V
| nil != 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
& ! [Y] :
( ~ ssList(Y)
| ~ neq(Y,nil)
| ~ segmentP(sk0_48,Y)
| ~ segmentP(sk0_47,Y) )
& ssList(sk0_51)
& ssList(sk0_52)
& app(app(sk0_51,sk0_49),sk0_52) = sk0_50
& equalelemsP(sk0_49)
& ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X3,cons(X2,nil)) != sk0_51 )
| ! [X4] :
( ~ ssList(X4)
| app(cons(X2,nil),X4) != sk0_49 ) )
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != sk0_52 )
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != sk0_49 ) )
& ( nil = sk0_50
| nil != sk0_49 )
& ( nil != sk0_48
| nil != sk0_47 ) ),
inference(skolemization,[status(esa)],[f416]) ).
fof(f418,plain,
ssList(sk0_47),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f419,plain,
ssList(sk0_48),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f422,plain,
sk0_48 = sk0_50,
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f423,plain,
sk0_47 = sk0_49,
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f424,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk0_48,X0)
| ~ segmentP(sk0_47,X0) ),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f425,plain,
ssList(sk0_51),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f426,plain,
ssList(sk0_52),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f427,plain,
app(app(sk0_51,sk0_49),sk0_52) = sk0_50,
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f431,plain,
( nil = sk0_50
| nil != sk0_49 ),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f432,plain,
( nil != sk0_48
| nil != sk0_47 ),
inference(cnf_transformation,[status(esa)],[f417]) ).
fof(f433,plain,
( spl0_0
<=> nil = sk0_50 ),
introduced(split_symbol_definition) ).
fof(f434,plain,
( nil = sk0_50
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f436,plain,
( spl0_1
<=> nil = sk0_49 ),
introduced(split_symbol_definition) ).
fof(f438,plain,
( nil != sk0_49
| spl0_1 ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f431,f433,f436]) ).
fof(f440,plain,
( spl0_2
<=> nil = sk0_48 ),
introduced(split_symbol_definition) ).
fof(f442,plain,
( nil != sk0_48
| spl0_2 ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,plain,
( spl0_3
<=> nil = sk0_47 ),
introduced(split_symbol_definition) ).
fof(f444,plain,
( nil = sk0_47
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f432,f440,f443]) ).
fof(f453,plain,
! [X0,X1,X2] :
( ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X1)
| segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X0)
| ~ ssList(X2) ),
inference(destructive_equality_resolution,[status(esa)],[f137]) ).
fof(f480,plain,
( nil != sk0_47
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f423,f438]) ).
fof(f481,plain,
app(app(sk0_51,sk0_47),sk0_52) = sk0_50,
inference(forward_demodulation,[status(thm)],[f423,f427]) ).
fof(f482,plain,
app(app(sk0_51,sk0_47),sk0_52) = sk0_48,
inference(forward_demodulation,[status(thm)],[f422,f481]) ).
fof(f483,plain,
( spl0_4
<=> ssList(app(app(sk0_51,sk0_47),sk0_52)) ),
introduced(split_symbol_definition) ).
fof(f485,plain,
( ~ ssList(app(app(sk0_51,sk0_47),sk0_52))
| spl0_4 ),
inference(component_clause,[status(thm)],[f483]) ).
fof(f486,plain,
( spl0_5
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f488,plain,
( ~ ssList(sk0_47)
| spl0_5 ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f489,plain,
( spl0_6
<=> segmentP(sk0_48,sk0_47) ),
introduced(split_symbol_definition) ).
fof(f492,plain,
( spl0_7
<=> ssList(sk0_51) ),
introduced(split_symbol_definition) ).
fof(f494,plain,
( ~ ssList(sk0_51)
| spl0_7 ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f495,plain,
( spl0_8
<=> ssList(sk0_52) ),
introduced(split_symbol_definition) ).
fof(f497,plain,
( ~ ssList(sk0_52)
| spl0_8 ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f498,plain,
( ~ ssList(app(app(sk0_51,sk0_47),sk0_52))
| ~ ssList(sk0_47)
| segmentP(sk0_48,sk0_47)
| ~ ssList(sk0_51)
| ~ ssList(sk0_52) ),
inference(paramodulation,[status(thm)],[f482,f453]) ).
fof(f499,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f498,f483,f486,f489,f492,f495]) ).
fof(f508,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f494,f425]) ).
fof(f509,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f508]) ).
fof(f510,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f488,f418]) ).
fof(f511,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f512,plain,
( ~ ssList(sk0_48)
| spl0_4 ),
inference(forward_demodulation,[status(thm)],[f482,f485]) ).
fof(f513,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f512,f419]) ).
fof(f514,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f513]) ).
fof(f515,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f497,f426]) ).
fof(f516,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f518,plain,
( spl0_11
<=> neq(sk0_47,nil) ),
introduced(split_symbol_definition) ).
fof(f520,plain,
( ~ neq(sk0_47,nil)
| spl0_11 ),
inference(component_clause,[status(thm)],[f518]) ).
fof(f526,plain,
( spl0_13
<=> ssList(nil) ),
introduced(split_symbol_definition) ).
fof(f528,plain,
( ~ ssList(nil)
| spl0_13 ),
inference(component_clause,[status(thm)],[f526]) ).
fof(f553,plain,
( ~ ssList(sk0_47)
| ~ neq(sk0_47,nil)
| ~ segmentP(sk0_48,sk0_47)
| ~ ssList(sk0_47) ),
inference(resolution,[status(thm)],[f424,f319]) ).
fof(f554,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f553,f486,f518,f489]) ).
fof(f558,plain,
( $false
| spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f223]) ).
fof(f559,plain,
spl0_13,
inference(contradiction_clause,[status(thm)],[f558]) ).
fof(f579,plain,
( ~ ssList(sk0_47)
| ~ ssList(nil)
| sk0_47 = nil
| spl0_11 ),
inference(resolution,[status(thm)],[f220,f520]) ).
fof(f580,plain,
( ~ spl0_5
| ~ spl0_13
| spl0_3
| spl0_11 ),
inference(split_clause,[status(thm)],[f579,f486,f526,f443,f518]) ).
fof(f581,plain,
( $false
| spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f444,f480]) ).
fof(f582,plain,
( spl0_1
| ~ spl0_3 ),
inference(contradiction_clause,[status(thm)],[f581]) ).
fof(f583,plain,
( nil = sk0_48
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f422,f434]) ).
fof(f584,plain,
( $false
| spl0_2
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f583,f442]) ).
fof(f585,plain,
( spl0_2
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f584]) ).
fof(f586,plain,
$false,
inference(sat_refutation,[status(thm)],[f439,f446,f499,f509,f511,f514,f516,f554,f559,f580,f582,f585]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC076+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.32 % Computer : n006.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon Apr 29 23:57:50 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % Drodi V3.6.0
% 0.13/0.34 % Refutation found
% 0.13/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.36 % Elapsed time: 0.027149 seconds
% 0.13/0.36 % CPU time: 0.046107 seconds
% 0.13/0.36 % Total memory used: 14.915 MB
% 0.13/0.36 % Net memory used: 14.888 MB
%------------------------------------------------------------------------------