TSTP Solution File: NUM412+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM412+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.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 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 10 unt; 0 def)
% Number of atoms : 169 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 186 ( 76 ~; 73 |; 20 &)
% ( 6 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 72 (; 69 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( ( epsilon_transitive(A)
& epsilon_connected(A) )
=> ordinal(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,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(f9,axiom,
! [A,B] :
( ( relation(A)
& function(A)
& transfinite_sequence(A)
& ordinal(B) )
=> transfinite_sequence_of(tseq_dom_restriction(A,B),relation_rng(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( transfinite_sequence_of(B,A)
=> ( relation(B)
& function(B)
& transfinite_sequence(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,conjecture,
! [A,B] :
( transfinite_sequence_of(B,A)
=> ! [C] :
( ordinal(C)
=> transfinite_sequence_of(tseq_dom_restriction(B,C),A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ ! [A,B] :
( transfinite_sequence_of(B,A)
=> ! [C] :
( ordinal(C)
=> transfinite_sequence_of(tseq_dom_restriction(B,C),A) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f54,plain,
! [A] :
( ~ ordinal(A)
| ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f55,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f56,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f63,plain,
! [A] :
( ~ epsilon_transitive(A)
| ~ epsilon_connected(A)
| ordinal(A) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f64,plain,
! [X0] :
( ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0)
| ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f69,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)],[f8]) ).
fof(f70,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)],[f69]) ).
fof(f71,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)],[f70]) ).
fof(f72,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)],[f71]) ).
fof(f74,plain,
! [A,B] :
( ~ relation(A)
| ~ function(A)
| ~ transfinite_sequence(A)
| ~ ordinal(B)
| transfinite_sequence_of(tseq_dom_restriction(A,B),relation_rng(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f75,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| ~ transfinite_sequence(X0)
| ~ ordinal(X1)
| transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0)) ),
inference(cnf_transformation,[status(esa)],[f74]) ).
fof(f79,plain,
! [A,B] :
( ~ transfinite_sequence_of(B,A)
| ( relation(B)
& function(B)
& transfinite_sequence(B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f80,plain,
! [B] :
( ! [A] : ~ transfinite_sequence_of(B,A)
| ( relation(B)
& function(B)
& transfinite_sequence(B) ) ),
inference(miniscoping,[status(esa)],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X0,X1)
| relation(X0) ),
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X0,X1)
| function(X0) ),
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f83,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X0,X1)
| transfinite_sequence(X0) ),
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f182,plain,
! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ transfinite_sequence_of(C,A)
| transfinite_sequence_of(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f42]) ).
fof(f183,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ transfinite_sequence_of(X2,X0)
| transfinite_sequence_of(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f182]) ).
fof(f184,plain,
? [A,B] :
( transfinite_sequence_of(B,A)
& ? [C] :
( ordinal(C)
& ~ transfinite_sequence_of(tseq_dom_restriction(B,C),A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f44]) ).
fof(f185,plain,
( transfinite_sequence_of(sk0_17,sk0_16)
& ordinal(sk0_18)
& ~ transfinite_sequence_of(tseq_dom_restriction(sk0_17,sk0_18),sk0_16) ),
inference(skolemization,[status(esa)],[f184]) ).
fof(f186,plain,
transfinite_sequence_of(sk0_17,sk0_16),
inference(cnf_transformation,[status(esa)],[f185]) ).
fof(f187,plain,
ordinal(sk0_18),
inference(cnf_transformation,[status(esa)],[f185]) ).
fof(f188,plain,
~ transfinite_sequence_of(tseq_dom_restriction(sk0_17,sk0_18),sk0_16),
inference(cnf_transformation,[status(esa)],[f185]) ).
fof(f211,plain,
epsilon_transitive(sk0_18),
inference(resolution,[status(thm)],[f55,f187]) ).
fof(f214,plain,
epsilon_connected(sk0_18),
inference(resolution,[status(thm)],[f56,f187]) ).
fof(f316,plain,
( spl0_18
<=> epsilon_transitive(sk0_18) ),
introduced(split_symbol_definition) ).
fof(f318,plain,
( ~ epsilon_transitive(sk0_18)
| spl0_18 ),
inference(component_clause,[status(thm)],[f316]) ).
fof(f319,plain,
( spl0_19
<=> ordinal(sk0_18) ),
introduced(split_symbol_definition) ).
fof(f322,plain,
( ~ epsilon_transitive(sk0_18)
| ordinal(sk0_18) ),
inference(resolution,[status(thm)],[f64,f214]) ).
fof(f323,plain,
( ~ spl0_18
| spl0_19 ),
inference(split_clause,[status(thm)],[f322,f316,f319]) ).
fof(f346,plain,
( $false
| spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f318,f211]) ).
fof(f347,plain,
spl0_18,
inference(contradiction_clause,[status(thm)],[f346]) ).
fof(f364,plain,
! [X0,X1] :
( ~ function(X0)
| ~ transfinite_sequence(X0)
| ~ transfinite_sequence_of(X0,X1)
| subset(relation_rng(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f72,f81]) ).
fof(f430,plain,
! [X0,X1] :
( ~ function(X0)
| ~ transfinite_sequence_of(X0,X1)
| subset(relation_rng(X0),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f364,f83]) ).
fof(f431,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X0,X1)
| subset(relation_rng(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f430,f82]) ).
fof(f433,plain,
transfinite_sequence(sk0_17),
inference(resolution,[status(thm)],[f83,f186]) ).
fof(f490,plain,
! [X0,X1,X2] :
( ~ transfinite_sequence_of(X0,relation_rng(X1))
| transfinite_sequence_of(X0,X2)
| ~ transfinite_sequence_of(X1,X2) ),
inference(resolution,[status(thm)],[f183,f431]) ).
fof(f492,plain,
! [X0,X1,X2] :
( transfinite_sequence_of(tseq_dom_restriction(X0,X1),X2)
| ~ transfinite_sequence_of(X0,X2)
| ~ relation(X0)
| ~ function(X0)
| ~ transfinite_sequence(X0)
| ~ ordinal(X1) ),
inference(resolution,[status(thm)],[f490,f75]) ).
fof(f493,plain,
! [X0,X1,X2] :
( transfinite_sequence_of(tseq_dom_restriction(X0,X1),X2)
| ~ transfinite_sequence_of(X0,X2)
| ~ function(X0)
| ~ transfinite_sequence(X0)
| ~ ordinal(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f492,f81]) ).
fof(f502,plain,
! [X0,X1,X2] :
( transfinite_sequence_of(tseq_dom_restriction(X0,X1),X2)
| ~ transfinite_sequence_of(X0,X2)
| ~ transfinite_sequence(X0)
| ~ ordinal(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f493,f82]) ).
fof(f503,plain,
( spl0_38
<=> transfinite_sequence_of(sk0_17,sk0_16) ),
introduced(split_symbol_definition) ).
fof(f505,plain,
( ~ transfinite_sequence_of(sk0_17,sk0_16)
| spl0_38 ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,plain,
( spl0_39
<=> transfinite_sequence(sk0_17) ),
introduced(split_symbol_definition) ).
fof(f508,plain,
( ~ transfinite_sequence(sk0_17)
| spl0_39 ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f509,plain,
( ~ transfinite_sequence_of(sk0_17,sk0_16)
| ~ transfinite_sequence(sk0_17)
| ~ ordinal(sk0_18) ),
inference(resolution,[status(thm)],[f502,f188]) ).
fof(f510,plain,
( ~ spl0_38
| ~ spl0_39
| ~ spl0_19 ),
inference(split_clause,[status(thm)],[f509,f503,f506,f319]) ).
fof(f519,plain,
( $false
| spl0_38 ),
inference(forward_subsumption_resolution,[status(thm)],[f505,f186]) ).
fof(f520,plain,
spl0_38,
inference(contradiction_clause,[status(thm)],[f519]) ).
fof(f521,plain,
( $false
| spl0_39 ),
inference(forward_subsumption_resolution,[status(thm)],[f508,f433]) ).
fof(f522,plain,
spl0_39,
inference(contradiction_clause,[status(thm)],[f521]) ).
fof(f523,plain,
$false,
inference(sat_refutation,[status(thm)],[f323,f347,f510,f520,f522]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM412+1 : 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 : n015.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 10:11:19 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.13/0.36 % Refutation found
% 0.13/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38 % Elapsed time: 0.027836 seconds
% 0.13/0.38 % CPU time: 0.054551 seconds
% 0.13/0.38 % Memory used: 12.374 MB
%------------------------------------------------------------------------------