TSTP Solution File: NUM414+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM414+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 12:29:03 EDT 2023
% Result : Theorem 0.10s 0.34s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 63 ( 14 unt; 0 def)
% Number of atoms : 183 ( 20 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 200 ( 80 ~; 80 |; 23 &)
% ( 9 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 7 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 51 (; 49 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] :
( ( epsilon_transitive(A)
& epsilon_connected(A) )
=> ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
| ordinal_subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( subset(A,B)
& A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ proper_subset(A,B)
& A != B
& ~ proper_subset(B,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ proper_subset(A,B)
& A != B
& ~ proper_subset(B,A) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f50,plain,
! [A] :
( ~ ordinal(A)
| ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f51,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f59,plain,
! [A] :
( ~ epsilon_transitive(A)
| ~ epsilon_connected(A)
| ordinal(A) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f60,plain,
! [X0] :
( ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0)
| ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f65,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ordinal_subset(A,B)
| ordinal_subset(B,A) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f66,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X0,X1)
| ordinal_subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f67,plain,
! [A,B] :
( ( ~ proper_subset(A,B)
| ( subset(A,B)
& A != B ) )
& ( proper_subset(A,B)
| ~ subset(A,B)
| A = B ) ),
inference(NNF_transformation,[status(esa)],[f10]) ).
fof(f68,plain,
( ! [A,B] :
( ~ proper_subset(A,B)
| ( subset(A,B)
& A != B ) )
& ! [A,B] :
( proper_subset(A,B)
| ~ subset(A,B)
| A = B ) ),
inference(miniscoping,[status(esa)],[f67]) ).
fof(f71,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f143,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f31]) ).
fof(f144,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ( ( ~ ordinal_subset(A,B)
| subset(A,B) )
& ( ordinal_subset(A,B)
| ~ subset(A,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f143]) ).
fof(f145,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ ordinal_subset(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f144]) ).
fof(f163,plain,
? [A] :
( ordinal(A)
& ? [B] :
( ordinal(B)
& ~ proper_subset(A,B)
& A != B
& ~ proper_subset(B,A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f39]) ).
fof(f164,plain,
( ordinal(sk0_15)
& ordinal(sk0_16)
& ~ proper_subset(sk0_15,sk0_16)
& sk0_15 != sk0_16
& ~ proper_subset(sk0_16,sk0_15) ),
inference(skolemization,[status(esa)],[f163]) ).
fof(f165,plain,
ordinal(sk0_15),
inference(cnf_transformation,[status(esa)],[f164]) ).
fof(f166,plain,
ordinal(sk0_16),
inference(cnf_transformation,[status(esa)],[f164]) ).
fof(f167,plain,
~ proper_subset(sk0_15,sk0_16),
inference(cnf_transformation,[status(esa)],[f164]) ).
fof(f168,plain,
sk0_15 != sk0_16,
inference(cnf_transformation,[status(esa)],[f164]) ).
fof(f169,plain,
~ proper_subset(sk0_16,sk0_15),
inference(cnf_transformation,[status(esa)],[f164]) ).
fof(f195,plain,
epsilon_transitive(sk0_16),
inference(resolution,[status(thm)],[f51,f166]) ).
fof(f196,plain,
epsilon_transitive(sk0_15),
inference(resolution,[status(thm)],[f51,f165]) ).
fof(f201,plain,
epsilon_connected(sk0_16),
inference(resolution,[status(thm)],[f52,f166]) ).
fof(f202,plain,
epsilon_connected(sk0_15),
inference(resolution,[status(thm)],[f52,f165]) ).
fof(f209,plain,
( spl0_2
<=> epsilon_transitive(sk0_16) ),
introduced(split_symbol_definition) ).
fof(f211,plain,
( ~ epsilon_transitive(sk0_16)
| spl0_2 ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,plain,
( spl0_3
<=> ordinal(sk0_16) ),
introduced(split_symbol_definition) ).
fof(f215,plain,
( ~ epsilon_transitive(sk0_16)
| ordinal(sk0_16) ),
inference(resolution,[status(thm)],[f201,f60]) ).
fof(f216,plain,
( ~ spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f215,f209,f212]) ).
fof(f217,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f211,f195]) ).
fof(f218,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f217]) ).
fof(f219,plain,
( spl0_4
<=> epsilon_transitive(sk0_15) ),
introduced(split_symbol_definition) ).
fof(f221,plain,
( ~ epsilon_transitive(sk0_15)
| spl0_4 ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( spl0_5
<=> ordinal(sk0_15) ),
introduced(split_symbol_definition) ).
fof(f225,plain,
( ~ epsilon_transitive(sk0_15)
| ordinal(sk0_15) ),
inference(resolution,[status(thm)],[f202,f60]) ).
fof(f226,plain,
( ~ spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f225,f219,f222]) ).
fof(f227,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f221,f196]) ).
fof(f228,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f227]) ).
fof(f241,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0) ),
inference(resolution,[status(thm)],[f145,f66]) ).
fof(f242,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1)
| ordinal_subset(X1,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f241]) ).
fof(f246,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X1,X0)
| proper_subset(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f242,f71]) ).
fof(f247,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| proper_subset(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ ordinal(X0)
| subset(X1,X0) ),
inference(resolution,[status(thm)],[f246,f145]) ).
fof(f248,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| proper_subset(X0,X1)
| X0 = X1
| subset(X1,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f247]) ).
fof(f251,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| proper_subset(X0,X1)
| X0 = X1
| proper_subset(X1,X0)
| X1 = X0 ),
inference(resolution,[status(thm)],[f248,f71]) ).
fof(f252,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| proper_subset(X0,X1)
| X0 = X1
| proper_subset(X1,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f251]) ).
fof(f253,plain,
( spl0_8
<=> proper_subset(sk0_15,sk0_16) ),
introduced(split_symbol_definition) ).
fof(f254,plain,
( proper_subset(sk0_15,sk0_16)
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,plain,
( spl0_9
<=> sk0_15 = sk0_16 ),
introduced(split_symbol_definition) ).
fof(f257,plain,
( sk0_15 = sk0_16
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f259,plain,
( ~ ordinal(sk0_15)
| ~ ordinal(sk0_16)
| proper_subset(sk0_15,sk0_16)
| sk0_15 = sk0_16 ),
inference(resolution,[status(thm)],[f252,f169]) ).
fof(f260,plain,
( ~ spl0_5
| ~ spl0_3
| spl0_8
| spl0_9 ),
inference(split_clause,[status(thm)],[f259,f222,f212,f253,f256]) ).
fof(f267,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f257,f168]) ).
fof(f268,plain,
~ spl0_9,
inference(contradiction_clause,[status(thm)],[f267]) ).
fof(f269,plain,
( $false
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f254,f167]) ).
fof(f270,plain,
~ spl0_8,
inference(contradiction_clause,[status(thm)],[f269]) ).
fof(f271,plain,
$false,
inference(sat_refutation,[status(thm)],[f216,f218,f226,f228,f260,f268,f270]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : NUM414+1 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n013.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Tue May 30 09:47:05 EDT 2023
% 0.10/0.33 % CPUTime :
% 0.10/0.33 % Drodi V3.5.1
% 0.10/0.34 % Refutation found
% 0.10/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.59 % Elapsed time: 0.038321 seconds
% 0.16/0.59 % CPU time: 0.022274 seconds
% 0.16/0.59 % Memory used: 3.195 MB
%------------------------------------------------------------------------------