TSTP Solution File: SWC218+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWC218+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 : Wed May 31 12:39:42 EDT 2023
% Result : Theorem 0.19s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 21
% Syntax : Number of formulae : 95 ( 18 unt; 0 def)
% Number of atoms : 275 ( 66 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 296 ( 116 ~; 111 |; 27 &)
% ( 17 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 14 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 58 (; 51 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = V
& nil = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = 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)
=> ! [Z] :
( ssList(Z)
=> ( app(Y,Z) != X
| ! [X1] :
( ssItem(X1)
=> app(app(Y,cons(X1,nil)),Z) != W ) ) ) )
| neq(U,nil) ) ) ) ) ),
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)
=> ! [Z] :
( ssList(Z)
=> ( app(Y,Z) != X
| ! [X1] :
( ssItem(X1)
=> app(app(Y,cons(X1,nil)),Z) != W ) ) ) )
| neq(U,nil) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
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(f221,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssItem(V)
| ssList(cons(V,U)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f222,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f221]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f234,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssItem(V)
| nil != cons(V,U) ) ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f235,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != cons(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f234]) ).
fof(f244,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ssList(app(U,V)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f244]) ).
fof(f383,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( nil = app(U,V)
<=> ( nil = V
& nil = U ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f83]) ).
fof(f384,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( ( nil != app(U,V)
| ( nil = V
& nil = U ) )
& ( nil = app(U,V)
| nil != V
| nil != U ) ) ) ),
inference(NNF_transformation,[status(esa)],[f383]) ).
fof(f385,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X1 ),
inference(cnf_transformation,[status(esa)],[f384]) ).
fof(f388,plain,
! [U] :
( ~ ssList(U)
| app(U,nil) = U ),
inference(pre_NNF_transformation,[status(esa)],[f84]) ).
fof(f389,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[status(esa)],[f388]) ).
fof(f415,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& ? [Y] :
( ssList(Y)
& ? [Z] :
( ssList(Z)
& app(Y,Z) = X
& ? [X1] :
( ssItem(X1)
& app(app(Y,cons(X1,nil)),Z) = W ) ) )
& ~ neq(U,nil) ) ) ) ),
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
& ssList(sk0_51)
& ssList(sk0_52)
& app(sk0_51,sk0_52) = sk0_50
& ssItem(sk0_53)
& app(app(sk0_51,cons(sk0_53,nil)),sk0_52) = sk0_49
& ~ neq(sk0_47,nil) ),
inference(skolemization,[status(esa)],[f415]) ).
fof(f417,plain,
ssList(sk0_47),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f421,plain,
sk0_48 = sk0_50,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f422,plain,
sk0_47 = sk0_49,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f423,plain,
ssList(sk0_51),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f424,plain,
ssList(sk0_52),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f425,plain,
app(sk0_51,sk0_52) = sk0_50,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f426,plain,
ssItem(sk0_53),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f427,plain,
app(app(sk0_51,cons(sk0_53,nil)),sk0_52) = sk0_49,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f428,plain,
~ neq(sk0_47,nil),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f461,plain,
app(sk0_51,sk0_52) = sk0_48,
inference(forward_demodulation,[status(thm)],[f421,f425]) ).
fof(f468,plain,
( spl0_2
<=> sk0_47 = nil ),
introduced(split_symbol_definition) ).
fof(f469,plain,
( sk0_47 = nil
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f473,plain,
( spl0_3
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f475,plain,
( ~ ssList(sk0_47)
| spl0_3 ),
inference(component_clause,[status(thm)],[f473]) ).
fof(f476,plain,
( spl0_4
<=> ssList(nil) ),
introduced(split_symbol_definition) ).
fof(f478,plain,
( ~ ssList(nil)
| spl0_4 ),
inference(component_clause,[status(thm)],[f476]) ).
fof(f479,plain,
( ~ ssList(sk0_47)
| ~ ssList(nil)
| sk0_47 = nil ),
inference(resolution,[status(thm)],[f220,f428]) ).
fof(f480,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_2 ),
inference(split_clause,[status(thm)],[f479,f473,f476,f468]) ).
fof(f481,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f478,f223]) ).
fof(f482,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f481]) ).
fof(f483,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f475,f417]) ).
fof(f484,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f483]) ).
fof(f486,plain,
( nil = sk0_49
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f469,f422]) ).
fof(f495,plain,
( app(app(sk0_51,cons(sk0_53,nil)),sk0_52) = nil
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f486,f427]) ).
fof(f496,plain,
( spl0_6
<=> ssList(app(sk0_51,cons(sk0_53,nil))) ),
introduced(split_symbol_definition) ).
fof(f498,plain,
( ~ ssList(app(sk0_51,cons(sk0_53,nil)))
| spl0_6 ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f499,plain,
( spl0_7
<=> ssList(sk0_52) ),
introduced(split_symbol_definition) ).
fof(f501,plain,
( ~ ssList(sk0_52)
| spl0_7 ),
inference(component_clause,[status(thm)],[f499]) ).
fof(f504,plain,
( spl0_8
<=> ssList(sk0_51) ),
introduced(split_symbol_definition) ).
fof(f506,plain,
( ~ ssList(sk0_51)
| spl0_8 ),
inference(component_clause,[status(thm)],[f504]) ).
fof(f507,plain,
( spl0_9
<=> ssList(sk0_48) ),
introduced(split_symbol_definition) ).
fof(f512,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f506,f423]) ).
fof(f513,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f512]) ).
fof(f514,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f501,f424]) ).
fof(f515,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f514]) ).
fof(f516,plain,
( spl0_10
<=> nil = sk0_52 ),
introduced(split_symbol_definition) ).
fof(f517,plain,
( nil = sk0_52
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f516]) ).
fof(f519,plain,
( ~ ssList(app(sk0_51,cons(sk0_53,nil)))
| ~ ssList(sk0_52)
| nil = sk0_52
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f385,f495]) ).
fof(f520,plain,
( ~ spl0_6
| ~ spl0_7
| spl0_10
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f519,f496,f499,f516,f468]) ).
fof(f537,plain,
( spl0_13
<=> ssList(cons(sk0_53,nil)) ),
introduced(split_symbol_definition) ).
fof(f539,plain,
( ~ ssList(cons(sk0_53,nil))
| spl0_13 ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f540,plain,
( ~ ssList(sk0_51)
| ~ ssList(cons(sk0_53,nil))
| spl0_6 ),
inference(resolution,[status(thm)],[f498,f245]) ).
fof(f541,plain,
( ~ spl0_8
| ~ spl0_13
| spl0_6 ),
inference(split_clause,[status(thm)],[f540,f504,f537,f496]) ).
fof(f542,plain,
( spl0_14
<=> ssItem(sk0_53) ),
introduced(split_symbol_definition) ).
fof(f544,plain,
( ~ ssItem(sk0_53)
| spl0_14 ),
inference(component_clause,[status(thm)],[f542]) ).
fof(f545,plain,
( ~ ssList(nil)
| ~ ssItem(sk0_53)
| spl0_13 ),
inference(resolution,[status(thm)],[f539,f222]) ).
fof(f546,plain,
( ~ spl0_4
| ~ spl0_14
| spl0_13 ),
inference(split_clause,[status(thm)],[f545,f476,f542,f537]) ).
fof(f547,plain,
( $false
| spl0_14 ),
inference(forward_subsumption_resolution,[status(thm)],[f544,f426]) ).
fof(f548,plain,
spl0_14,
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f549,plain,
( app(app(sk0_51,cons(sk0_53,nil)),nil) = nil
| ~ spl0_10
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f517,f495]) ).
fof(f550,plain,
( app(sk0_51,nil) = sk0_48
| ~ spl0_10 ),
inference(backward_demodulation,[status(thm)],[f517,f461]) ).
fof(f552,plain,
( spl0_15
<=> sk0_48 = sk0_51 ),
introduced(split_symbol_definition) ).
fof(f553,plain,
( sk0_48 = sk0_51
| ~ spl0_15 ),
inference(component_clause,[status(thm)],[f552]) ).
fof(f555,plain,
( ~ ssList(sk0_51)
| sk0_48 = sk0_51
| ~ spl0_10 ),
inference(paramodulation,[status(thm)],[f550,f389]) ).
fof(f556,plain,
( ~ spl0_8
| spl0_15
| ~ spl0_10 ),
inference(split_clause,[status(thm)],[f555,f504,f552,f516]) ).
fof(f559,plain,
( ~ ssList(sk0_51)
| ~ ssList(nil)
| ssList(sk0_48)
| ~ spl0_10 ),
inference(paramodulation,[status(thm)],[f550,f245]) ).
fof(f560,plain,
( ~ spl0_8
| ~ spl0_4
| spl0_9
| ~ spl0_10 ),
inference(split_clause,[status(thm)],[f559,f504,f476,f507,f516]) ).
fof(f563,plain,
( spl0_16
<=> nil = app(sk0_51,cons(sk0_53,nil)) ),
introduced(split_symbol_definition) ).
fof(f564,plain,
( nil = app(sk0_51,cons(sk0_53,nil))
| ~ spl0_16 ),
inference(component_clause,[status(thm)],[f563]) ).
fof(f566,plain,
( ~ ssList(app(sk0_51,cons(sk0_53,nil)))
| nil = app(sk0_51,cons(sk0_53,nil))
| ~ spl0_10
| ~ spl0_2 ),
inference(paramodulation,[status(thm)],[f549,f389]) ).
fof(f567,plain,
( ~ spl0_6
| spl0_16
| ~ spl0_10
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f566,f496,f563,f516,f468]) ).
fof(f588,plain,
( nil = app(sk0_48,cons(sk0_53,nil))
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[status(thm)],[f553,f564]) ).
fof(f590,plain,
( spl0_18
<=> nil = cons(sk0_53,nil) ),
introduced(split_symbol_definition) ).
fof(f591,plain,
( nil = cons(sk0_53,nil)
| ~ spl0_18 ),
inference(component_clause,[status(thm)],[f590]) ).
fof(f593,plain,
( ~ ssList(sk0_48)
| ~ ssList(cons(sk0_53,nil))
| nil = cons(sk0_53,nil)
| ~ spl0_15
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f588,f385]) ).
fof(f594,plain,
( ~ spl0_9
| ~ spl0_13
| spl0_18
| ~ spl0_15
| ~ spl0_16 ),
inference(split_clause,[status(thm)],[f593,f507,f537,f590,f552,f563]) ).
fof(f602,plain,
( ~ ssList(nil)
| ~ ssItem(sk0_53)
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f591,f235]) ).
fof(f603,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_18 ),
inference(split_clause,[status(thm)],[f602,f476,f542,f590]) ).
fof(f612,plain,
$false,
inference(sat_refutation,[status(thm)],[f480,f482,f484,f513,f515,f520,f541,f546,f548,f556,f560,f567,f594,f603]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC218+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n029.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 : Tue May 30 11:39:52 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.35 % Drodi V3.5.1
% 0.19/0.36 % Refutation found
% 0.19/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.37 % Elapsed time: 0.031075 seconds
% 0.19/0.37 % CPU time: 0.054906 seconds
% 0.19/0.37 % Memory used: 16.211 MB
%------------------------------------------------------------------------------