TSTP Solution File: SWW101+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWW101+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n024.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 20:49:46 EDT 2024
% Result : Theorem 0.18s 0.41s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of formulae : 109 ( 35 unt; 0 def)
% Number of atoms : 247 ( 111 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 235 ( 97 ~; 89 |; 36 &)
% ( 12 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 53 ( 50 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] :
( bool(X)
<=> ( X = false
| X = true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
( true != false
& true != err
& false != err ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( d(true)
& d(false)
& d(err) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( forallprefers(X,Y)
<=> ( ( ~ d(X)
& d(Y) )
| ( d(X)
& d(Y)
& ~ bool(X)
& bool(Y) )
| ( X = false
& Y = true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] :
( ( d(X)
& phi(X) = X )
| ( ~ d(X)
& phi(X) = err ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( prop(X) = true
<=> bool(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] :
( prop(X) = false
<=> ~ bool(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [B] : lazy_impl(false,B) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [B] : lazy_impl(true,B) = phi(B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
false1 = false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [P] : f7(P) = lazy_impl(prop(P),P),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
? [P] :
( false2 = phi(f7(P))
& ~ ? [P1] : forallprefers(f7(P1),f7(P)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,conjecture,
false1 = false2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
false1 != false2,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
! [X] :
( ( ~ bool(X)
| X = false
| X = true )
& ( bool(X)
| ( X != false
& X != true ) ) ),
inference(NNF_transformation,[status(esa)],[f1]) ).
fof(f48,plain,
( ! [X] :
( ~ bool(X)
| X = false
| X = true )
& ! [X] :
( bool(X)
| ( X != false
& X != true ) ) ),
inference(miniscoping,[status(esa)],[f47]) ).
fof(f49,plain,
! [X0] :
( ~ bool(X0)
| X0 = false
| X0 = true ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f50,plain,
! [X0] :
( bool(X0)
| X0 != false ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f51,plain,
! [X0] :
( bool(X0)
| X0 != true ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f54,plain,
false != err,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f55,plain,
d(true),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f56,plain,
d(false),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f58,plain,
! [X,Y] :
( pd0_0(Y,X)
<=> ( ( ~ d(X)
& d(Y) )
| ( d(X)
& d(Y)
& ~ bool(X)
& bool(Y) ) ) ),
introduced(predicate_definition,[f4]) ).
fof(f59,plain,
! [X,Y] :
( forallprefers(X,Y)
<=> ( pd0_0(Y,X)
| ( X = false
& Y = true ) ) ),
inference(formula_renaming,[status(thm)],[f4,f58]) ).
fof(f60,plain,
! [X,Y] :
( ( ~ forallprefers(X,Y)
| pd0_0(Y,X)
| ( X = false
& Y = true ) )
& ( forallprefers(X,Y)
| ( ~ pd0_0(Y,X)
& ( X != false
| Y != true ) ) ) ),
inference(NNF_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
( ! [X,Y] :
( ~ forallprefers(X,Y)
| pd0_0(Y,X)
| ( X = false
& Y = true ) )
& ! [X,Y] :
( forallprefers(X,Y)
| ( ~ pd0_0(Y,X)
& ( X != false
| Y != true ) ) ) ),
inference(miniscoping,[status(esa)],[f60]) ).
fof(f65,plain,
! [X0,X1] :
( forallprefers(X0,X1)
| X0 != false
| X1 != true ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f74,plain,
! [X] :
( pd0_2(X)
=> ( d(X)
& phi(X) = X ) ),
introduced(predicate_definition,[f6]) ).
fof(f75,plain,
! [X] :
( pd0_2(X)
| ( ~ d(X)
& phi(X) = err ) ),
inference(formula_renaming,[status(thm)],[f6,f74]) ).
fof(f76,plain,
! [X0] :
( pd0_2(X0)
| ~ d(X0) ),
inference(cnf_transformation,[status(esa)],[f75]) ).
fof(f77,plain,
! [X0] :
( pd0_2(X0)
| phi(X0) = err ),
inference(cnf_transformation,[status(esa)],[f75]) ).
fof(f78,plain,
! [X] :
( ( prop(X) != true
| bool(X) )
& ( prop(X) = true
| ~ bool(X) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f79,plain,
( ! [X] :
( prop(X) != true
| bool(X) )
& ! [X] :
( prop(X) = true
| ~ bool(X) ) ),
inference(miniscoping,[status(esa)],[f78]) ).
fof(f81,plain,
! [X0] :
( prop(X0) = true
| ~ bool(X0) ),
inference(cnf_transformation,[status(esa)],[f79]) ).
fof(f82,plain,
! [X] :
( ( prop(X) != false
| ~ bool(X) )
& ( prop(X) = false
| bool(X) ) ),
inference(NNF_transformation,[status(esa)],[f8]) ).
fof(f83,plain,
( ! [X] :
( prop(X) != false
| ~ bool(X) )
& ! [X] :
( prop(X) = false
| bool(X) ) ),
inference(miniscoping,[status(esa)],[f82]) ).
fof(f85,plain,
! [X0] :
( prop(X0) = false
| bool(X0) ),
inference(cnf_transformation,[status(esa)],[f83]) ).
fof(f98,plain,
! [X0] : lazy_impl(false,X0) = true,
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f99,plain,
! [X0] : lazy_impl(true,X0) = phi(X0),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f152,plain,
false1 = false,
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f153,plain,
! [X0] : f7(X0) = lazy_impl(prop(X0),X0),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f154,plain,
? [P] :
( false2 = phi(f7(P))
& ! [P1] : ~ forallprefers(f7(P1),f7(P)) ),
inference(pre_NNF_transformation,[status(esa)],[f40]) ).
fof(f155,plain,
( false2 = phi(f7(sk0_6))
& ! [P1] : ~ forallprefers(f7(P1),f7(sk0_6)) ),
inference(skolemization,[status(esa)],[f154]) ).
fof(f156,plain,
false2 = phi(f7(sk0_6)),
inference(cnf_transformation,[status(esa)],[f155]) ).
fof(f157,plain,
! [X0] : ~ forallprefers(f7(X0),f7(sk0_6)),
inference(cnf_transformation,[status(esa)],[f155]) ).
fof(f163,plain,
false1 != false2,
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f184,plain,
! [X] :
( ~ pd0_2(X)
| ( d(X)
& phi(X) = X ) ),
inference(pre_NNF_transformation,[status(esa)],[f74]) ).
fof(f186,plain,
! [X0] :
( ~ pd0_2(X0)
| phi(X0) = X0 ),
inference(cnf_transformation,[status(esa)],[f184]) ).
fof(f197,plain,
bool(false),
inference(destructive_equality_resolution,[status(esa)],[f50]) ).
fof(f198,plain,
bool(true),
inference(destructive_equality_resolution,[status(esa)],[f51]) ).
fof(f199,plain,
forallprefers(false,true),
inference(destructive_equality_resolution,[status(esa)],[f65]) ).
fof(f201,plain,
false != false2,
inference(backward_demodulation,[status(thm)],[f152,f163]) ).
fof(f215,plain,
! [X0] :
( phi(X0) = X0
| ~ d(X0) ),
inference(resolution,[status(thm)],[f186,f76]) ).
fof(f217,plain,
phi(false) = false,
inference(resolution,[status(thm)],[f215,f56]) ).
fof(f218,plain,
phi(true) = true,
inference(resolution,[status(thm)],[f215,f55]) ).
fof(f222,plain,
! [X0] :
( phi(X0) = err
| phi(X0) = X0 ),
inference(resolution,[status(thm)],[f77,f186]) ).
fof(f226,plain,
prop(true) = true,
inference(resolution,[status(thm)],[f81,f198]) ).
fof(f227,plain,
prop(false) = true,
inference(resolution,[status(thm)],[f81,f197]) ).
fof(f234,plain,
! [X0] :
( prop(X0) = false
| X0 = false
| X0 = true ),
inference(resolution,[status(thm)],[f85,f49]) ).
fof(f259,plain,
f7(false) = lazy_impl(true,false),
inference(paramodulation,[status(thm)],[f227,f153]) ).
fof(f260,plain,
f7(false) = phi(false),
inference(forward_demodulation,[status(thm)],[f99,f259]) ).
fof(f261,plain,
f7(false) = false,
inference(forward_demodulation,[status(thm)],[f217,f260]) ).
fof(f262,plain,
f7(true) = lazy_impl(true,true),
inference(paramodulation,[status(thm)],[f226,f153]) ).
fof(f263,plain,
f7(true) = phi(true),
inference(forward_demodulation,[status(thm)],[f99,f262]) ).
fof(f264,plain,
f7(true) = true,
inference(forward_demodulation,[status(thm)],[f218,f263]) ).
fof(f267,plain,
~ forallprefers(false,f7(sk0_6)),
inference(paramodulation,[status(thm)],[f261,f157]) ).
fof(f273,plain,
( spl0_4
<=> f7(sk0_6) = true ),
introduced(split_symbol_definition) ).
fof(f274,plain,
( f7(sk0_6) = true
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f275,plain,
( f7(sk0_6) != true
| spl0_4 ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f314,plain,
( spl0_6
<=> false2 = err ),
introduced(split_symbol_definition) ).
fof(f315,plain,
( false2 = err
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f317,plain,
( spl0_7
<=> phi(f7(sk0_6)) = f7(sk0_6) ),
introduced(split_symbol_definition) ).
fof(f318,plain,
( phi(f7(sk0_6)) = f7(sk0_6)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f317]) ).
fof(f320,plain,
( false2 = err
| phi(f7(sk0_6)) = f7(sk0_6) ),
inference(paramodulation,[status(thm)],[f156,f222]) ).
fof(f321,plain,
( spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f320,f314,f317]) ).
fof(f536,plain,
( err = phi(f7(sk0_6))
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f315,f156]) ).
fof(f541,plain,
( ~ forallprefers(false,true)
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f274,f267]) ).
fof(f542,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f541,f199]) ).
fof(f543,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f542]) ).
fof(f599,plain,
( false2 = f7(sk0_6)
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f318,f156]) ).
fof(f744,plain,
~ forallprefers(false,f7(sk0_6)),
inference(paramodulation,[status(thm)],[f261,f157]) ).
fof(f1080,plain,
( spl0_57
<=> prop(sk0_6) = false ),
introduced(split_symbol_definition) ).
fof(f1081,plain,
( prop(sk0_6) = false
| ~ spl0_57 ),
inference(component_clause,[status(thm)],[f1080]) ).
fof(f1082,plain,
( prop(sk0_6) != false
| spl0_57 ),
inference(component_clause,[status(thm)],[f1080]) ).
fof(f1186,plain,
( spl0_69
<=> sk0_6 = false ),
introduced(split_symbol_definition) ).
fof(f1187,plain,
( sk0_6 = false
| ~ spl0_69 ),
inference(component_clause,[status(thm)],[f1186]) ).
fof(f1189,plain,
( spl0_70
<=> sk0_6 = true ),
introduced(split_symbol_definition) ).
fof(f1190,plain,
( sk0_6 = true
| ~ spl0_70 ),
inference(component_clause,[status(thm)],[f1189]) ).
fof(f1225,plain,
( f7(sk0_6) = lazy_impl(false,sk0_6)
| ~ spl0_57 ),
inference(paramodulation,[status(thm)],[f1081,f153]) ).
fof(f1226,plain,
( f7(sk0_6) = true
| ~ spl0_57 ),
inference(forward_demodulation,[status(thm)],[f98,f1225]) ).
fof(f1227,plain,
( $false
| spl0_4
| ~ spl0_57 ),
inference(forward_subsumption_resolution,[status(thm)],[f1226,f275]) ).
fof(f1228,plain,
( spl0_4
| ~ spl0_57 ),
inference(contradiction_clause,[status(thm)],[f1227]) ).
fof(f1238,plain,
( sk0_6 = false
| sk0_6 = true
| spl0_57 ),
inference(resolution,[status(thm)],[f1082,f234]) ).
fof(f1239,plain,
( spl0_69
| spl0_70
| spl0_57 ),
inference(split_clause,[status(thm)],[f1238,f1186,f1189,f1080]) ).
fof(f1318,plain,
( err = phi(f7(false))
| ~ spl0_69
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f1187,f536]) ).
fof(f1319,plain,
( err = phi(false)
| ~ spl0_69
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f261,f1318]) ).
fof(f1320,plain,
( err = false
| ~ spl0_69
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f217,f1319]) ).
fof(f1321,plain,
( $false
| ~ spl0_69
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f1320,f54]) ).
fof(f1322,plain,
( ~ spl0_69
| ~ spl0_6 ),
inference(contradiction_clause,[status(thm)],[f1321]) ).
fof(f1325,plain,
( false2 = f7(false)
| ~ spl0_69
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f1187,f599]) ).
fof(f1326,plain,
( false2 = false
| ~ spl0_69
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f261,f1325]) ).
fof(f1336,plain,
( false != false
| ~ spl0_69
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f1326,f201]) ).
fof(f1337,plain,
( $false
| ~ spl0_69
| ~ spl0_7 ),
inference(trivial_equality_resolution,[status(esa)],[f1336]) ).
fof(f1338,plain,
( ~ spl0_69
| ~ spl0_7 ),
inference(contradiction_clause,[status(thm)],[f1337]) ).
fof(f1602,plain,
( ~ forallprefers(false,f7(true))
| ~ spl0_70 ),
inference(backward_demodulation,[status(thm)],[f1190,f744]) ).
fof(f1603,plain,
( ~ forallprefers(false,true)
| ~ spl0_70 ),
inference(forward_demodulation,[status(thm)],[f264,f1602]) ).
fof(f1604,plain,
( $false
| ~ spl0_70 ),
inference(forward_subsumption_resolution,[status(thm)],[f1603,f199]) ).
fof(f1605,plain,
~ spl0_70,
inference(contradiction_clause,[status(thm)],[f1604]) ).
fof(f1606,plain,
$false,
inference(sat_refutation,[status(thm)],[f321,f543,f1228,f1239,f1322,f1338,f1605]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWW101+1 : TPTP v8.1.2. Released v5.2.0.
% 0.06/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33 % Computer : n024.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Apr 29 23:57:06 EDT 2024
% 0.11/0.34 % CPUTime :
% 0.11/0.35 % Drodi V3.6.0
% 0.18/0.41 % Refutation found
% 0.18/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.43 % Elapsed time: 0.082607 seconds
% 0.18/0.43 % CPU time: 0.545792 seconds
% 0.18/0.43 % Total memory used: 70.275 MB
% 0.18/0.43 % Net memory used: 69.703 MB
%------------------------------------------------------------------------------