TSTP Solution File: NUM414+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% 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 : n014.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 20:34:37 EDT 2024
% Result : Theorem 0.11s 0.34s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 10 unt; 0 def)
% Number of atoms : 140 ( 20 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 162 ( 66 ~; 63 |; 20 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 40 ( 38 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
| ordinal_subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( subset(A,B)
& A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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(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(f204,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ ordinal_subset(X0,X1)
| proper_subset(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f145,f71]) ).
fof(f207,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| proper_subset(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0) ),
inference(resolution,[status(thm)],[f204,f66]) ).
fof(f208,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| proper_subset(X0,X1)
| X0 = X1
| ordinal_subset(X1,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f207]) ).
fof(f209,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| proper_subset(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ ordinal(X0)
| proper_subset(X1,X0)
| X1 = X0 ),
inference(resolution,[status(thm)],[f208,f204]) ).
fof(f210,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| proper_subset(X0,X1)
| X0 = X1
| proper_subset(X1,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f209]) ).
fof(f211,plain,
( spl0_2
<=> ordinal(sk0_15) ),
introduced(split_symbol_definition) ).
fof(f213,plain,
( ~ ordinal(sk0_15)
| spl0_2 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( spl0_3
<=> ordinal(sk0_16) ),
introduced(split_symbol_definition) ).
fof(f216,plain,
( ~ ordinal(sk0_16)
| spl0_3 ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,plain,
( spl0_4
<=> proper_subset(sk0_15,sk0_16) ),
introduced(split_symbol_definition) ).
fof(f218,plain,
( proper_subset(sk0_15,sk0_16)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,plain,
( spl0_5
<=> sk0_15 = sk0_16 ),
introduced(split_symbol_definition) ).
fof(f221,plain,
( sk0_15 = sk0_16
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,plain,
( ~ ordinal(sk0_15)
| ~ ordinal(sk0_16)
| proper_subset(sk0_15,sk0_16)
| sk0_15 = sk0_16 ),
inference(resolution,[status(thm)],[f210,f169]) ).
fof(f224,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f223,f211,f214,f217,f220]) ).
fof(f230,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f165]) ).
fof(f231,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f230]) ).
fof(f232,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f216,f166]) ).
fof(f233,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f232]) ).
fof(f234,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f221,f168]) ).
fof(f235,plain,
~ spl0_5,
inference(contradiction_clause,[status(thm)],[f234]) ).
fof(f236,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f218,f167]) ).
fof(f237,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f238,plain,
$false,
inference(sat_refutation,[status(thm)],[f224,f231,f233,f235,f237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM414+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Apr 29 20:33:34 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % Drodi V3.6.0
% 0.11/0.34 % Refutation found
% 0.11/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.35 % Elapsed time: 0.026792 seconds
% 0.11/0.35 % CPU time: 0.068048 seconds
% 0.11/0.35 % Total memory used: 15.298 MB
% 0.11/0.35 % Net memory used: 15.258 MB
%------------------------------------------------------------------------------