TSTP Solution File: RNG047+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : RNG047+1 : TPTP v8.1.2. Released v4.0.0.
% 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 12:32:42 EDT 2023
% Result : Theorem 0.14s 0.36s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 67 ( 12 unt; 1 def)
% Number of atoms : 187 ( 78 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 197 ( 77 ~; 85 |; 19 &)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 36 (; 34 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
=> W0 = W1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [W0] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,definition,
! [W0] :
( aVector0(W0)
=> ( aDimensionOf0(W0) != sz00
=> ! [W1] :
( W1 = sziznziztdt0(W0)
<=> ( aVector0(W1)
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& ! [W2] :
( aNaturalNumber0(W2)
=> sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,hypothesis,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
( aDimensionOf0(xs) = aDimensionOf0(xt)
& aDimensionOf0(xt) != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f48,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| szszuzczcdt0(W0) != szszuzczcdt0(W1)
| W0 = W1 ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f49,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f112,plain,
! [W0] :
( ~ aVector0(W0)
| aNaturalNumber0(aDimensionOf0(W0)) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f113,plain,
! [X0] :
( ~ aVector0(X0)
| aNaturalNumber0(aDimensionOf0(X0)) ),
inference(cnf_transformation,[status(esa)],[f112]) ).
fof(f116,plain,
! [W0] :
( ~ aVector0(W0)
| aDimensionOf0(W0) = sz00
| ! [W1] :
( W1 = sziznziztdt0(W0)
<=> ( aVector0(W1)
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& ! [W2] :
( ~ aNaturalNumber0(W2)
| sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f32]) ).
fof(f117,plain,
! [W0] :
( ~ aVector0(W0)
| aDimensionOf0(W0) = sz00
| ! [W1] :
( ( W1 != sziznziztdt0(W0)
| ( aVector0(W1)
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& ! [W2] :
( ~ aNaturalNumber0(W2)
| sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) )
& ( W1 = sziznziztdt0(W0)
| ~ aVector0(W1)
| szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0)
| ? [W2] :
( aNaturalNumber0(W2)
& sdtlbdtrb0(W1,W2) != sdtlbdtrb0(W0,W2) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f116]) ).
fof(f118,plain,
! [W0] :
( ~ aVector0(W0)
| aDimensionOf0(W0) = sz00
| ( ! [W1] :
( W1 != sziznziztdt0(W0)
| ( aVector0(W1)
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& ! [W2] :
( ~ aNaturalNumber0(W2)
| sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) )
& ! [W1] :
( W1 = sziznziztdt0(W0)
| ~ aVector0(W1)
| szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0)
| ? [W2] :
( aNaturalNumber0(W2)
& sdtlbdtrb0(W1,W2) != sdtlbdtrb0(W0,W2) ) ) ) ),
inference(miniscoping,[status(esa)],[f117]) ).
fof(f119,plain,
! [W0] :
( ~ aVector0(W0)
| aDimensionOf0(W0) = sz00
| ( ! [W1] :
( W1 != sziznziztdt0(W0)
| ( aVector0(W1)
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& ! [W2] :
( ~ aNaturalNumber0(W2)
| sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) )
& ! [W1] :
( W1 = sziznziztdt0(W0)
| ~ aVector0(W1)
| szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0)
| ( aNaturalNumber0(sk0_1(W1,W0))
& sdtlbdtrb0(W1,sk0_1(W1,W0)) != sdtlbdtrb0(W0,sk0_1(W1,W0)) ) ) ) ),
inference(skolemization,[status(esa)],[f118]) ).
fof(f120,plain,
! [X0,X1] :
( ~ aVector0(X0)
| aDimensionOf0(X0) = sz00
| X1 != sziznziztdt0(X0)
| aVector0(X1) ),
inference(cnf_transformation,[status(esa)],[f119]) ).
fof(f121,plain,
! [X0,X1] :
( ~ aVector0(X0)
| aDimensionOf0(X0) = sz00
| X1 != sziznziztdt0(X0)
| szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0) ),
inference(cnf_transformation,[status(esa)],[f119]) ).
fof(f125,plain,
aVector0(xs),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f126,plain,
aVector0(xt),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f127,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f128,plain,
aDimensionOf0(xt) != sz00,
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f129,plain,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f145,plain,
! [X0] :
( ~ aVector0(X0)
| aDimensionOf0(X0) = sz00
| aVector0(sziznziztdt0(X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f120]) ).
fof(f146,plain,
! [X0] :
( ~ aVector0(X0)
| aDimensionOf0(X0) = sz00
| szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0))) = aDimensionOf0(X0) ),
inference(destructive_equality_resolution,[status(esa)],[f121]) ).
fof(f148,plain,
aDimensionOf0(xs) != sz00,
inference(forward_demodulation,[status(thm)],[f127,f128]) ).
fof(f149,plain,
( spl0_4
<=> aDimensionOf0(xt) = sz00 ),
introduced(split_symbol_definition) ).
fof(f150,plain,
( aDimensionOf0(xt) = sz00
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( spl0_5
<=> aVector0(sziznziztdt0(xt)) ),
introduced(split_symbol_definition) ).
fof(f153,plain,
( aVector0(sziznziztdt0(xt))
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,plain,
( aDimensionOf0(xt) = sz00
| aVector0(sziznziztdt0(xt)) ),
inference(resolution,[status(thm)],[f145,f126]) ).
fof(f156,plain,
( spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f155,f149,f152]) ).
fof(f157,plain,
( spl0_6
<=> aDimensionOf0(xs) = sz00 ),
introduced(split_symbol_definition) ).
fof(f158,plain,
( aDimensionOf0(xs) = sz00
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( spl0_7
<=> aVector0(sziznziztdt0(xs)) ),
introduced(split_symbol_definition) ).
fof(f161,plain,
( aVector0(sziznziztdt0(xs))
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,plain,
( aDimensionOf0(xs) = sz00
| aVector0(sziznziztdt0(xs)) ),
inference(resolution,[status(thm)],[f145,f125]) ).
fof(f164,plain,
( spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f163,f157,f160]) ).
fof(f165,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f158,f148]) ).
fof(f166,plain,
~ spl0_6,
inference(contradiction_clause,[status(thm)],[f165]) ).
fof(f167,plain,
( aDimensionOf0(xs) = sz00
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f127,f150]) ).
fof(f168,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f167,f148]) ).
fof(f169,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f168]) ).
fof(f221,plain,
( spl0_19
<=> szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt) ),
introduced(split_symbol_definition) ).
fof(f222,plain,
( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,plain,
( aDimensionOf0(xt) = sz00
| szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt) ),
inference(resolution,[status(thm)],[f146,f126]) ).
fof(f225,plain,
( spl0_4
| spl0_19 ),
inference(split_clause,[status(thm)],[f224,f149,f221]) ).
fof(f226,plain,
( spl0_20
<=> szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) ),
introduced(split_symbol_definition) ).
fof(f227,plain,
( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,plain,
( aDimensionOf0(xs) = sz00
| szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) ),
inference(resolution,[status(thm)],[f146,f125]) ).
fof(f230,plain,
( spl0_6
| spl0_20 ),
inference(split_clause,[status(thm)],[f229,f157,f226]) ).
fof(f282,plain,
( aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f113,f153]) ).
fof(f284,plain,
( aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f113,f161]) ).
fof(f327,plain,
( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xs)
| ~ spl0_19 ),
inference(forward_demodulation,[status(thm)],[f127,f222]) ).
fof(f494,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(X0)
| aDimensionOf0(sziznziztdt0(xs)) = X0
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f49,f284]) ).
fof(f495,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| aDimensionOf0(xs) != szszuzczcdt0(X0)
| aDimensionOf0(sziznziztdt0(xs)) = X0
| ~ spl0_20
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f227,f494]) ).
fof(f606,plain,
( spl0_55
<=> aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ),
introduced(split_symbol_definition) ).
fof(f608,plain,
( aDimensionOf0(xs) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt)))
| spl0_55 ),
inference(component_clause,[status(thm)],[f606]) ).
fof(f609,plain,
( spl0_56
<=> aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ),
introduced(split_symbol_definition) ).
fof(f610,plain,
( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt))
| ~ spl0_56 ),
inference(component_clause,[status(thm)],[f609]) ).
fof(f612,plain,
( aDimensionOf0(xs) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt)))
| aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt))
| ~ spl0_20
| ~ spl0_7
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f495,f282]) ).
fof(f613,plain,
( ~ spl0_55
| spl0_56
| ~ spl0_20
| ~ spl0_7
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f612,f606,f609,f226,f160,f152]) ).
fof(f619,plain,
( aDimensionOf0(xs) != aDimensionOf0(xs)
| ~ spl0_19
| spl0_55 ),
inference(forward_demodulation,[status(thm)],[f327,f608]) ).
fof(f620,plain,
( $false
| ~ spl0_19
| spl0_55 ),
inference(trivial_equality_resolution,[status(esa)],[f619]) ).
fof(f621,plain,
( ~ spl0_19
| spl0_55 ),
inference(contradiction_clause,[status(thm)],[f620]) ).
fof(f626,plain,
( $false
| ~ spl0_56 ),
inference(forward_subsumption_resolution,[status(thm)],[f610,f129]) ).
fof(f627,plain,
~ spl0_56,
inference(contradiction_clause,[status(thm)],[f626]) ).
fof(f628,plain,
$false,
inference(sat_refutation,[status(thm)],[f156,f164,f166,f169,f225,f230,f613,f621,f627]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : RNG047+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n029.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 10:51:37 EDT 2023
% 0.09/0.31 % CPUTime :
% 0.14/0.31 % Drodi V3.5.1
% 0.14/0.36 % Refutation found
% 0.14/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.38 % Elapsed time: 0.072188 seconds
% 0.14/0.38 % CPU time: 0.183373 seconds
% 0.14/0.38 % Memory used: 31.568 MB
%------------------------------------------------------------------------------