TSTP Solution File: NUM388+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM388+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 12:29:00 EDT 2023
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 6 unt; 0 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 148 ( 56 ~; 52 |; 25 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 86 (; 81 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( epsilon_transitive(C)
=> ( ( in(C,A)
& in(A,B) )
=> in(C,B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( epsilon_transitive(C)
=> ( ( in(C,A)
& in(A,B) )
=> in(C,B) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f27,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A,B,C] :
~ ( in(A,B)
& element(B,powerset(C))
& empty(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,plain,
! [A] :
( ~ ordinal(A)
| ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f39,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f49,plain,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( ~ in(B,A)
| subset(B,A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f50,plain,
! [A] :
( ( ~ epsilon_transitive(A)
| ! [B] :
( ~ in(B,A)
| subset(B,A) ) )
& ( epsilon_transitive(A)
| ? [B] :
( in(B,A)
& ~ subset(B,A) ) ) ),
inference(NNF_transformation,[status(esa)],[f49]) ).
fof(f51,plain,
( ! [A] :
( ~ epsilon_transitive(A)
| ! [B] :
( ~ in(B,A)
| subset(B,A) ) )
& ! [A] :
( epsilon_transitive(A)
| ? [B] :
( in(B,A)
& ~ subset(B,A) ) ) ),
inference(miniscoping,[status(esa)],[f50]) ).
fof(f52,plain,
( ! [A] :
( ~ epsilon_transitive(A)
| ! [B] :
( ~ in(B,A)
| subset(B,A) ) )
& ! [A] :
( epsilon_transitive(A)
| ( in(sk0_0(A),A)
& ~ subset(sk0_0(A),A) ) ) ),
inference(skolemization,[status(esa)],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( ~ epsilon_transitive(X0)
| ~ in(X1,X0)
| subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f102,plain,
? [A] :
( ordinal(A)
& ? [B] :
( ordinal(B)
& ? [C] :
( epsilon_transitive(C)
& in(C,A)
& in(A,B)
& ~ in(C,B) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f25]) ).
fof(f103,plain,
( ordinal(sk0_13)
& ordinal(sk0_14)
& epsilon_transitive(sk0_15)
& in(sk0_15,sk0_13)
& in(sk0_13,sk0_14)
& ~ in(sk0_15,sk0_14) ),
inference(skolemization,[status(esa)],[f102]) ).
fof(f105,plain,
ordinal(sk0_14),
inference(cnf_transformation,[status(esa)],[f103]) ).
fof(f107,plain,
in(sk0_15,sk0_13),
inference(cnf_transformation,[status(esa)],[f103]) ).
fof(f108,plain,
in(sk0_13,sk0_14),
inference(cnf_transformation,[status(esa)],[f103]) ).
fof(f109,plain,
~ in(sk0_15,sk0_14),
inference(cnf_transformation,[status(esa)],[f103]) ).
fof(f112,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f27]) ).
fof(f113,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f112]) ).
fof(f114,plain,
! [A,B] :
( ( ~ element(A,powerset(B))
| subset(A,B) )
& ( element(A,powerset(B))
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f28]) ).
fof(f115,plain,
( ! [A,B] :
( ~ element(A,powerset(B))
| subset(A,B) )
& ! [A,B] :
( element(A,powerset(B))
| ~ subset(A,B) ) ),
inference(miniscoping,[status(esa)],[f114]) ).
fof(f117,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f115]) ).
fof(f118,plain,
! [A,B,C] :
( ~ in(A,B)
| ~ element(B,powerset(C))
| element(A,C) ),
inference(pre_NNF_transformation,[status(esa)],[f29]) ).
fof(f119,plain,
! [A,C] :
( ! [B] :
( ~ in(A,B)
| ~ element(B,powerset(C)) )
| element(A,C) ),
inference(miniscoping,[status(esa)],[f118]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| element(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f119]) ).
fof(f121,plain,
! [A,B,C] :
( ~ in(A,B)
| ~ element(B,powerset(C))
| ~ empty(C) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f122,plain,
! [C] :
( ! [B] :
( ! [A] : ~ in(A,B)
| ~ element(B,powerset(C)) )
| ~ empty(C) ),
inference(miniscoping,[status(esa)],[f121]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(cnf_transformation,[status(esa)],[f122]) ).
fof(f175,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| empty(X2)
| in(X0,X2) ),
inference(resolution,[status(thm)],[f120,f113]) ).
fof(f264,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| in(X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f175,f123]) ).
fof(f266,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,X2)
| ~ subset(X1,X2) ),
inference(resolution,[status(thm)],[f264,f117]) ).
fof(f274,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,X2)
| ~ epsilon_transitive(X2)
| ~ in(X1,X2) ),
inference(resolution,[status(thm)],[f266,f53]) ).
fof(f281,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,X2)
| ~ in(X1,X2)
| ~ ordinal(X2) ),
inference(resolution,[status(thm)],[f274,f39]) ).
fof(f522,plain,
! [X0,X1] :
( ~ in(X0,X1)
| in(X0,sk0_14)
| ~ in(X1,sk0_14) ),
inference(resolution,[status(thm)],[f281,f105]) ).
fof(f540,plain,
! [X0] :
( ~ in(X0,sk0_13)
| in(X0,sk0_14) ),
inference(resolution,[status(thm)],[f522,f108]) ).
fof(f557,plain,
in(sk0_15,sk0_14),
inference(resolution,[status(thm)],[f540,f107]) ).
fof(f558,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f557,f109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM388+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n011.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 09:58:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38 % Elapsed time: 0.028979 seconds
% 0.13/0.38 % CPU time: 0.077196 seconds
% 0.13/0.38 % Memory used: 12.290 MB
%------------------------------------------------------------------------------