TSTP Solution File: SEU238+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU238+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.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 12:36:25 EDT 2023
% Result : Theorem 2.89s 0.82s
% Output : CNFRefutation 2.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 83 ( 5 unt; 0 def)
% Number of atoms : 322 ( 31 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 424 ( 185 ~; 172 |; 40 &)
% ( 11 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 110 (; 103 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( subset(A,B)
& A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( ordinal(A)
=> ( ~ empty(succ(A))
& epsilon_transitive(succ(A))
& epsilon_connected(succ(A))
& ordinal(succ(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A] : in(A,succ(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ( proper_subset(A,B)
=> in(A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [A] :
( ordinal(A)
=> ( being_limit_ordinal(A)
<=> ! [B] :
( ordinal(B)
=> ( in(B,A)
=> in(succ(B),A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,conjecture,
! [A] :
( ordinal(A)
=> ( ~ ( ~ being_limit_ordinal(A)
& ! [B] :
( ordinal(B)
=> A != succ(B) ) )
& ~ ( ? [B] :
( ordinal(B)
& A = succ(B) )
& being_limit_ordinal(A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ( ~ ( ~ being_limit_ordinal(A)
& ! [B] :
( ordinal(B)
=> A != succ(B) ) )
& ~ ( ? [B] :
( ordinal(B)
& A = succ(B) )
& being_limit_ordinal(A) ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f56,plain,
! [A,B] :
( ~ in(A,B)
| ~ in(B,A) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f57,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f81,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)],[f12]) ).
fof(f82,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)],[f81]) ).
fof(f85,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f82]) ).
fof(f106,plain,
! [A] :
( ~ ordinal(A)
| ( ~ empty(succ(A))
& epsilon_transitive(succ(A))
& epsilon_connected(succ(A))
& ordinal(succ(A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f108,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(succ(X0)) ),
inference(cnf_transformation,[status(esa)],[f106]) ).
fof(f110,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(succ(X0)) ),
inference(cnf_transformation,[status(esa)],[f106]) ).
fof(f169,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f38]) ).
fof(f170,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)],[f169]) ).
fof(f171,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ ordinal_subset(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f170]) ).
fof(f178,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f182,plain,
! [A] :
( ~ epsilon_transitive(A)
| ! [B] :
( ~ ordinal(B)
| ~ proper_subset(A,B)
| in(A,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f44]) ).
fof(f183,plain,
! [X0,X1] :
( ~ epsilon_transitive(X0)
| ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f182]) ).
fof(f186,plain,
! [A] :
( ~ ordinal(A)
| ! [B] :
( ~ ordinal(B)
| ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f46]) ).
fof(f187,plain,
! [A] :
( ~ ordinal(A)
| ! [B] :
( ~ ordinal(B)
| ( ( ~ in(A,B)
| ordinal_subset(succ(A),B) )
& ( in(A,B)
| ~ ordinal_subset(succ(A),B) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f186]) ).
fof(f188,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal_subset(succ(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f187]) ).
fof(f194,plain,
! [A] :
( ~ ordinal(A)
| ( being_limit_ordinal(A)
<=> ! [B] :
( ~ ordinal(B)
| ~ in(B,A)
| in(succ(B),A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f48]) ).
fof(f195,plain,
! [A] :
( ~ ordinal(A)
| ( ( ~ being_limit_ordinal(A)
| ! [B] :
( ~ ordinal(B)
| ~ in(B,A)
| in(succ(B),A) ) )
& ( being_limit_ordinal(A)
| ? [B] :
( ordinal(B)
& in(B,A)
& ~ in(succ(B),A) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f194]) ).
fof(f196,plain,
! [A] :
( ~ ordinal(A)
| ( ( ~ being_limit_ordinal(A)
| ! [B] :
( ~ ordinal(B)
| ~ in(B,A)
| in(succ(B),A) ) )
& ( being_limit_ordinal(A)
| ( ordinal(sk0_14(A))
& in(sk0_14(A),A)
& ~ in(succ(sk0_14(A)),A) ) ) ) ),
inference(skolemization,[status(esa)],[f195]) ).
fof(f197,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X1)
| ~ in(X1,X0)
| in(succ(X1),X0) ),
inference(cnf_transformation,[status(esa)],[f196]) ).
fof(f198,plain,
! [X0] :
( ~ ordinal(X0)
| being_limit_ordinal(X0)
| ordinal(sk0_14(X0)) ),
inference(cnf_transformation,[status(esa)],[f196]) ).
fof(f199,plain,
! [X0] :
( ~ ordinal(X0)
| being_limit_ordinal(X0)
| in(sk0_14(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f196]) ).
fof(f200,plain,
! [X0] :
( ~ ordinal(X0)
| being_limit_ordinal(X0)
| ~ in(succ(sk0_14(X0)),X0) ),
inference(cnf_transformation,[status(esa)],[f196]) ).
fof(f201,plain,
? [A] :
( ordinal(A)
& ( ( ~ being_limit_ordinal(A)
& ! [B] :
( ~ ordinal(B)
| A != succ(B) ) )
| ( ? [B] :
( ordinal(B)
& A = succ(B) )
& being_limit_ordinal(A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f50]) ).
fof(f202,plain,
! [A] :
( pd0_0(A)
=> ( ~ being_limit_ordinal(A)
& ! [B] :
( ~ ordinal(B)
| A != succ(B) ) ) ),
introduced(predicate_definition,[f201]) ).
fof(f203,plain,
? [A] :
( ordinal(A)
& ( pd0_0(A)
| ( ? [B] :
( ordinal(B)
& A = succ(B) )
& being_limit_ordinal(A) ) ) ),
inference(formula_renaming,[status(thm)],[f201,f202]) ).
fof(f204,plain,
( ordinal(sk0_15)
& ( pd0_0(sk0_15)
| ( ordinal(sk0_16)
& sk0_15 = succ(sk0_16)
& being_limit_ordinal(sk0_15) ) ) ),
inference(skolemization,[status(esa)],[f203]) ).
fof(f205,plain,
ordinal(sk0_15),
inference(cnf_transformation,[status(esa)],[f204]) ).
fof(f206,plain,
( pd0_0(sk0_15)
| ordinal(sk0_16) ),
inference(cnf_transformation,[status(esa)],[f204]) ).
fof(f207,plain,
( pd0_0(sk0_15)
| sk0_15 = succ(sk0_16) ),
inference(cnf_transformation,[status(esa)],[f204]) ).
fof(f208,plain,
( pd0_0(sk0_15)
| being_limit_ordinal(sk0_15) ),
inference(cnf_transformation,[status(esa)],[f204]) ).
fof(f223,plain,
! [A] :
( ~ pd0_0(A)
| ( ~ being_limit_ordinal(A)
& ! [B] :
( ~ ordinal(B)
| A != succ(B) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f202]) ).
fof(f224,plain,
! [X0] :
( ~ pd0_0(X0)
| ~ being_limit_ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f223]) ).
fof(f225,plain,
! [X0,X1] :
( ~ pd0_0(X0)
| ~ ordinal(X1)
| X0 != succ(X1) ),
inference(cnf_transformation,[status(esa)],[f223]) ).
fof(f233,plain,
( spl0_2
<=> pd0_0(sk0_15) ),
introduced(split_symbol_definition) ).
fof(f234,plain,
( pd0_0(sk0_15)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f233]) ).
fof(f236,plain,
( spl0_3
<=> ordinal(sk0_16) ),
introduced(split_symbol_definition) ).
fof(f239,plain,
( spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f206,f233,f236]) ).
fof(f240,plain,
( spl0_4
<=> sk0_15 = succ(sk0_16) ),
introduced(split_symbol_definition) ).
fof(f241,plain,
( sk0_15 = succ(sk0_16)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,plain,
( spl0_2
| spl0_4 ),
inference(split_clause,[status(thm)],[f207,f233,f240]) ).
fof(f244,plain,
( spl0_5
<=> being_limit_ordinal(sk0_15) ),
introduced(split_symbol_definition) ).
fof(f247,plain,
( spl0_2
| spl0_5 ),
inference(split_clause,[status(thm)],[f208,f233,f244]) ).
fof(f250,plain,
! [X0,X1] :
( ~ in(X0,succ(X1))
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X1)
| ~ in(X1,X0) ),
inference(resolution,[status(thm)],[f57,f197]) ).
fof(f252,plain,
! [X0,X1] :
( ~ ordinal(succ(X0))
| ~ being_limit_ordinal(succ(X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| ~ ordinal(succ(X1))
| ~ being_limit_ordinal(succ(X1))
| ~ ordinal(X0)
| ~ in(X0,succ(X1)) ),
inference(resolution,[status(thm)],[f250,f197]) ).
fof(f253,plain,
! [X0,X1] :
( ~ ordinal(succ(X0))
| ~ being_limit_ordinal(succ(X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| ~ being_limit_ordinal(succ(X1))
| ~ ordinal(X0)
| ~ in(X0,succ(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f252,f110]) ).
fof(f267,plain,
! [X0,X1] :
( ~ being_limit_ordinal(succ(X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| ~ being_limit_ordinal(succ(X1))
| ~ ordinal(X0)
| ~ in(X0,succ(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f110]) ).
fof(f271,plain,
! [X0] :
( ~ being_limit_ordinal(succ(X0))
| ~ ordinal(X0)
| ~ being_limit_ordinal(succ(X0))
| ~ ordinal(X0)
| ~ in(X0,succ(X0)) ),
inference(resolution,[status(thm)],[f267,f178]) ).
fof(f272,plain,
! [X0] :
( ~ being_limit_ordinal(succ(X0))
| ~ ordinal(X0)
| ~ in(X0,succ(X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f271]) ).
fof(f273,plain,
! [X0] :
( ~ being_limit_ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f272,f178]) ).
fof(f276,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ ordinal_subset(X0,X1)
| proper_subset(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f171,f85]) ).
fof(f487,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1)
| ~ ordinal(succ(X0))
| ~ ordinal(X1)
| proper_subset(succ(X0),X1)
| succ(X0) = X1 ),
inference(resolution,[status(thm)],[f188,f276]) ).
fof(f488,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1)
| ~ ordinal(succ(X0))
| proper_subset(succ(X0),X1)
| succ(X0) = X1 ),
inference(duplicate_literals_removal,[status(esa)],[f487]) ).
fof(f489,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1)
| proper_subset(succ(X0),X1)
| succ(X0) = X1 ),
inference(forward_subsumption_resolution,[status(thm)],[f488,f110]) ).
fof(f493,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1)
| succ(X0) = X1
| ~ epsilon_transitive(succ(X0))
| ~ ordinal(X1)
| in(succ(X0),X1) ),
inference(resolution,[status(thm)],[f489,f183]) ).
fof(f494,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1)
| succ(X0) = X1
| ~ epsilon_transitive(succ(X0))
| in(succ(X0),X1) ),
inference(duplicate_literals_removal,[status(esa)],[f493]) ).
fof(f495,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1)
| succ(X0) = X1
| in(succ(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f494,f108]) ).
fof(f497,plain,
! [X0] :
( ~ ordinal(sk0_14(X0))
| ~ ordinal(X0)
| ~ in(sk0_14(X0),X0)
| succ(sk0_14(X0)) = X0
| ~ ordinal(X0)
| being_limit_ordinal(X0) ),
inference(resolution,[status(thm)],[f495,f200]) ).
fof(f498,plain,
! [X0] :
( ~ ordinal(sk0_14(X0))
| ~ ordinal(X0)
| ~ in(sk0_14(X0),X0)
| succ(sk0_14(X0)) = X0
| being_limit_ordinal(X0) ),
inference(duplicate_literals_removal,[status(esa)],[f497]) ).
fof(f499,plain,
! [X0] :
( ~ ordinal(X0)
| ~ in(sk0_14(X0),X0)
| succ(sk0_14(X0)) = X0
| being_limit_ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f498,f198]) ).
fof(f690,plain,
! [X0] :
( ~ ordinal(X0)
| succ(sk0_14(X0)) = X0
| being_limit_ordinal(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f499,f199]) ).
fof(f779,plain,
! [X0] :
( ~ ordinal(X0)
| being_limit_ordinal(X0)
| ~ pd0_0(X0)
| ~ ordinal(sk0_14(X0)) ),
inference(resolution,[status(thm)],[f690,f225]) ).
fof(f780,plain,
! [X0] :
( ~ ordinal(X0)
| ~ pd0_0(X0)
| ~ ordinal(sk0_14(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f779,f224]) ).
fof(f782,plain,
! [X0] :
( ~ ordinal(X0)
| ~ pd0_0(X0)
| ~ ordinal(X0)
| being_limit_ordinal(X0) ),
inference(resolution,[status(thm)],[f780,f198]) ).
fof(f783,plain,
! [X0] :
( ~ ordinal(X0)
| ~ pd0_0(X0)
| being_limit_ordinal(X0) ),
inference(duplicate_literals_removal,[status(esa)],[f782]) ).
fof(f784,plain,
! [X0] :
( ~ ordinal(X0)
| ~ pd0_0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f783,f224]) ).
fof(f786,plain,
( ~ ordinal(sk0_15)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f784,f234]) ).
fof(f787,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f786,f205]) ).
fof(f788,plain,
~ spl0_2,
inference(contradiction_clause,[status(thm)],[f787]) ).
fof(f975,plain,
( ~ being_limit_ordinal(sk0_15)
| ~ ordinal(sk0_16)
| ~ spl0_4 ),
inference(paramodulation,[status(thm)],[f241,f273]) ).
fof(f976,plain,
( ~ spl0_5
| ~ spl0_3
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f975,f244,f236,f240]) ).
fof(f999,plain,
$false,
inference(sat_refutation,[status(thm)],[f239,f243,f247,f788,f976]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU238+3 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 09:26:28 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.5.1
% 2.89/0.82 % Refutation found
% 2.89/0.82 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.89/0.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.89/0.84 % Elapsed time: 0.486424 seconds
% 2.89/0.84 % CPU time: 2.977648 seconds
% 2.89/0.84 % Memory used: 85.119 MB
%------------------------------------------------------------------------------