TSTP Solution File: NUM410+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 12:29:02 EDT 2023
% Result : Theorem 0.16s 0.34s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 11 unt; 0 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 117 ( 46 ~; 43 |; 14 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 23 (; 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( transfinite_sequence(A)
<=> ordinal(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( ( relation(B)
& function(B)
& transfinite_sequence(B) )
=> ( transfinite_sequence_of(B,A)
<=> subset(relation_rng(B),A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,conjecture,
! [A] :
( ( relation(A)
& function(A) )
=> ( ordinal(relation_dom(A))
=> transfinite_sequence_of(A,relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
~ ! [A] :
( ( relation(A)
& function(A) )
=> ( ordinal(relation_dom(A))
=> transfinite_sequence_of(A,relation_rng(A)) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f66,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( transfinite_sequence(A)
<=> ordinal(relation_dom(A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f67,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( ( ~ transfinite_sequence(A)
| ordinal(relation_dom(A)) )
& ( transfinite_sequence(A)
| ~ ordinal(relation_dom(A)) ) ) ),
inference(NNF_transformation,[status(esa)],[f66]) ).
fof(f69,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| transfinite_sequence(X0)
| ~ ordinal(relation_dom(X0)) ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f70,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ~ transfinite_sequence(B)
| ( transfinite_sequence_of(B,A)
<=> subset(relation_rng(B),A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f71,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ~ transfinite_sequence(B)
| ( ( ~ transfinite_sequence_of(B,A)
| subset(relation_rng(B),A) )
& ( transfinite_sequence_of(B,A)
| ~ subset(relation_rng(B),A) ) ) ),
inference(NNF_transformation,[status(esa)],[f70]) ).
fof(f72,plain,
! [B] :
( ~ relation(B)
| ~ function(B)
| ~ transfinite_sequence(B)
| ( ! [A] :
( ~ transfinite_sequence_of(B,A)
| subset(relation_rng(B),A) )
& ! [A] :
( transfinite_sequence_of(B,A)
| ~ subset(relation_rng(B),A) ) ) ),
inference(miniscoping,[status(esa)],[f71]) ).
fof(f74,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| ~ transfinite_sequence(X0)
| transfinite_sequence_of(X0,X1)
| ~ subset(relation_rng(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f72]) ).
fof(f163,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(esa)],[f36]) ).
fof(f164,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f163]) ).
fof(f173,plain,
? [A] :
( relation(A)
& function(A)
& ordinal(relation_dom(A))
& ~ transfinite_sequence_of(A,relation_rng(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f41]) ).
fof(f174,plain,
( relation(sk0_16)
& function(sk0_16)
& ordinal(relation_dom(sk0_16))
& ~ transfinite_sequence_of(sk0_16,relation_rng(sk0_16)) ),
inference(skolemization,[status(esa)],[f173]) ).
fof(f175,plain,
relation(sk0_16),
inference(cnf_transformation,[status(esa)],[f174]) ).
fof(f176,plain,
function(sk0_16),
inference(cnf_transformation,[status(esa)],[f174]) ).
fof(f177,plain,
ordinal(relation_dom(sk0_16)),
inference(cnf_transformation,[status(esa)],[f174]) ).
fof(f178,plain,
~ transfinite_sequence_of(sk0_16,relation_rng(sk0_16)),
inference(cnf_transformation,[status(esa)],[f174]) ).
fof(f193,plain,
( spl0_0
<=> relation(sk0_16) ),
introduced(split_symbol_definition) ).
fof(f195,plain,
( ~ relation(sk0_16)
| spl0_0 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( spl0_1
<=> transfinite_sequence(sk0_16) ),
introduced(split_symbol_definition) ).
fof(f199,plain,
( spl0_2
<=> ordinal(relation_dom(sk0_16)) ),
introduced(split_symbol_definition) ).
fof(f201,plain,
( ~ ordinal(relation_dom(sk0_16))
| spl0_2 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,plain,
( ~ relation(sk0_16)
| transfinite_sequence(sk0_16)
| ~ ordinal(relation_dom(sk0_16)) ),
inference(resolution,[status(thm)],[f69,f176]) ).
fof(f203,plain,
( ~ spl0_0
| spl0_1
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f202,f193,f196,f199]) ).
fof(f206,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f201,f177]) ).
fof(f207,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f206]) ).
fof(f208,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f175]) ).
fof(f209,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f208]) ).
fof(f501,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ transfinite_sequence(X0)
| transfinite_sequence_of(X0,relation_rng(X0)) ),
inference(resolution,[status(thm)],[f164,f74]) ).
fof(f1160,plain,
( spl0_81
<=> function(sk0_16) ),
introduced(split_symbol_definition) ).
fof(f1162,plain,
( ~ function(sk0_16)
| spl0_81 ),
inference(component_clause,[status(thm)],[f1160]) ).
fof(f1163,plain,
( ~ relation(sk0_16)
| ~ function(sk0_16)
| ~ transfinite_sequence(sk0_16) ),
inference(resolution,[status(thm)],[f501,f178]) ).
fof(f1164,plain,
( ~ spl0_0
| ~ spl0_81
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f1163,f193,f1160,f196]) ).
fof(f1176,plain,
( $false
| spl0_81 ),
inference(forward_subsumption_resolution,[status(thm)],[f1162,f176]) ).
fof(f1177,plain,
spl0_81,
inference(contradiction_clause,[status(thm)],[f1176]) ).
fof(f1178,plain,
$false,
inference(sat_refutation,[status(thm)],[f203,f207,f209,f1164,f1177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.08/0.30 % Computer : n017.cluster.edu
% 0.08/0.30 % Model : x86_64 x86_64
% 0.08/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.30 % Memory : 8042.1875MB
% 0.08/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.30 % CPULimit : 300
% 0.08/0.30 % WCLimit : 300
% 0.08/0.30 % DateTime : Tue May 30 09:17:55 EDT 2023
% 0.08/0.31 % CPUTime :
% 0.16/0.31 % Drodi V3.5.1
% 0.16/0.34 % Refutation found
% 0.16/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.58 % Elapsed time: 0.051717 seconds
% 0.26/0.58 % CPU time: 0.061213 seconds
% 0.26/0.58 % Memory used: 11.426 MB
%------------------------------------------------------------------------------