TSTP Solution File: SET811+4 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET811+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 12:35:14 EDT 2023
% Result : Theorem 0.10s 0.34s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 9 unt; 0 def)
% Number of atoms : 180 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 195 ( 71 ~; 72 |; 38 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 120 (; 114 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] :
( member(A,on)
<=> ( set(A)
& strict_well_order(member_predicate,A)
& ! [X] :
( member(X,A)
=> subset(X,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y] :
( apply(member_predicate,X,Y)
<=> member(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,R,A,Y] :
( member(Y,initial_segment(X,R,A))
<=> ( member(Y,A)
& apply(R,Y,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,conjecture,
! [A] :
( member(A,on)
=> ! [X] :
( member(X,A)
=> equal_set(X,initial_segment(X,member_predicate,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ! [A] :
( member(A,on)
=> ! [X] :
( member(X,A)
=> equal_set(X,initial_segment(X,member_predicate,A)) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( ~ member(X,A)
| member(X,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f23,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f22]) ).
fof(f24,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(miniscoping,[status(esa)],[f23]) ).
fof(f25,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ( member(sk0_0(B,A),A)
& ~ member(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f29,plain,
! [A,B] :
( ( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) )
& ( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f30,plain,
( ! [A,B] :
( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) )
& ! [A,B] :
( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(miniscoping,[status(esa)],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f76,plain,
! [A] :
( member(A,on)
<=> ( set(A)
& strict_well_order(member_predicate,A)
& ! [X] :
( ~ member(X,A)
| subset(X,A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f77,plain,
! [A] :
( ( ~ member(A,on)
| ( set(A)
& strict_well_order(member_predicate,A)
& ! [X] :
( ~ member(X,A)
| subset(X,A) ) ) )
& ( member(A,on)
| ~ set(A)
| ~ strict_well_order(member_predicate,A)
| ? [X] :
( member(X,A)
& ~ subset(X,A) ) ) ),
inference(NNF_transformation,[status(esa)],[f76]) ).
fof(f78,plain,
( ! [A] :
( ~ member(A,on)
| ( set(A)
& strict_well_order(member_predicate,A)
& ! [X] :
( ~ member(X,A)
| subset(X,A) ) ) )
& ! [A] :
( member(A,on)
| ~ set(A)
| ~ strict_well_order(member_predicate,A)
| ? [X] :
( member(X,A)
& ~ subset(X,A) ) ) ),
inference(miniscoping,[status(esa)],[f77]) ).
fof(f79,plain,
( ! [A] :
( ~ member(A,on)
| ( set(A)
& strict_well_order(member_predicate,A)
& ! [X] :
( ~ member(X,A)
| subset(X,A) ) ) )
& ! [A] :
( member(A,on)
| ~ set(A)
| ~ strict_well_order(member_predicate,A)
| ( member(sk0_3(A),A)
& ~ subset(sk0_3(A),A) ) ) ),
inference(skolemization,[status(esa)],[f78]) ).
fof(f82,plain,
! [X0,X1] :
( ~ member(X0,on)
| ~ member(X1,X0)
| subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f79]) ).
fof(f103,plain,
! [X,Y] :
( ( ~ apply(member_predicate,X,Y)
| member(X,Y) )
& ( apply(member_predicate,X,Y)
| ~ member(X,Y) ) ),
inference(NNF_transformation,[status(esa)],[f15]) ).
fof(f104,plain,
( ! [X,Y] :
( ~ apply(member_predicate,X,Y)
| member(X,Y) )
& ! [X,Y] :
( apply(member_predicate,X,Y)
| ~ member(X,Y) ) ),
inference(miniscoping,[status(esa)],[f103]) ).
fof(f105,plain,
! [X0,X1] :
( ~ apply(member_predicate,X0,X1)
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f104]) ).
fof(f106,plain,
! [X0,X1] :
( apply(member_predicate,X0,X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f104]) ).
fof(f123,plain,
! [X,R,A,Y] :
( ( ~ member(Y,initial_segment(X,R,A))
| ( member(Y,A)
& apply(R,Y,X) ) )
& ( member(Y,initial_segment(X,R,A))
| ~ member(Y,A)
| ~ apply(R,Y,X) ) ),
inference(NNF_transformation,[status(esa)],[f18]) ).
fof(f124,plain,
( ! [X,R,A,Y] :
( ~ member(Y,initial_segment(X,R,A))
| ( member(Y,A)
& apply(R,Y,X) ) )
& ! [X,R,A,Y] :
( member(Y,initial_segment(X,R,A))
| ~ member(Y,A)
| ~ apply(R,Y,X) ) ),
inference(miniscoping,[status(esa)],[f123]) ).
fof(f126,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,initial_segment(X1,X2,X3))
| apply(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( member(X0,initial_segment(X1,X2,X3))
| ~ member(X0,X3)
| ~ apply(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f132,plain,
? [A] :
( member(A,on)
& ? [X] :
( member(X,A)
& ~ equal_set(X,initial_segment(X,member_predicate,A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f133,plain,
( member(sk0_13,on)
& member(sk0_14,sk0_13)
& ~ equal_set(sk0_14,initial_segment(sk0_14,member_predicate,sk0_13)) ),
inference(skolemization,[status(esa)],[f132]) ).
fof(f134,plain,
member(sk0_13,on),
inference(cnf_transformation,[status(esa)],[f133]) ).
fof(f135,plain,
member(sk0_14,sk0_13),
inference(cnf_transformation,[status(esa)],[f133]) ).
fof(f136,plain,
~ equal_set(sk0_14,initial_segment(sk0_14,member_predicate,sk0_13)),
inference(cnf_transformation,[status(esa)],[f133]) ).
fof(f147,plain,
! [X0] :
( ~ member(X0,sk0_13)
| subset(X0,sk0_13) ),
inference(resolution,[status(thm)],[f82,f134]) ).
fof(f148,plain,
subset(sk0_14,sk0_13),
inference(resolution,[status(thm)],[f147,f135]) ).
fof(f157,plain,
! [X0,X1,X2] :
( member(X0,initial_segment(X1,member_predicate,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f127,f106]) ).
fof(f159,plain,
! [X0] :
( ~ member(X0,sk0_14)
| member(X0,sk0_13) ),
inference(resolution,[status(thm)],[f26,f148]) ).
fof(f167,plain,
! [X0] :
( subset(sk0_14,X0)
| member(sk0_0(X0,sk0_14),sk0_13) ),
inference(resolution,[status(thm)],[f27,f159]) ).
fof(f172,plain,
! [X0,X1,X2,X3] :
( subset(initial_segment(X0,X1,X2),X3)
| apply(X1,sk0_0(X3,initial_segment(X0,X1,X2)),X0) ),
inference(resolution,[status(thm)],[f27,f126]) ).
fof(f177,plain,
! [X0,X1,X2] :
( subset(X0,initial_segment(X1,member_predicate,X2))
| ~ member(sk0_0(initial_segment(X1,member_predicate,X2),X0),X2)
| ~ member(sk0_0(initial_segment(X1,member_predicate,X2),X0),X1) ),
inference(resolution,[status(thm)],[f28,f157]) ).
fof(f282,plain,
! [X0,X1,X2] :
( subset(initial_segment(X0,member_predicate,X1),X2)
| member(sk0_0(X2,initial_segment(X0,member_predicate,X1)),X0) ),
inference(resolution,[status(thm)],[f172,f105]) ).
fof(f302,plain,
! [X0] :
( subset(sk0_14,initial_segment(X0,member_predicate,sk0_13))
| ~ member(sk0_0(initial_segment(X0,member_predicate,sk0_13),sk0_14),X0)
| subset(sk0_14,initial_segment(X0,member_predicate,sk0_13)) ),
inference(resolution,[status(thm)],[f177,f167]) ).
fof(f303,plain,
! [X0] :
( subset(sk0_14,initial_segment(X0,member_predicate,sk0_13))
| ~ member(sk0_0(initial_segment(X0,member_predicate,sk0_13),sk0_14),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f302]) ).
fof(f362,plain,
( spl0_4
<=> subset(sk0_14,initial_segment(sk0_14,member_predicate,sk0_13)) ),
introduced(split_symbol_definition) ).
fof(f363,plain,
( subset(sk0_14,initial_segment(sk0_14,member_predicate,sk0_13))
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f365,plain,
( subset(sk0_14,initial_segment(sk0_14,member_predicate,sk0_13))
| subset(sk0_14,initial_segment(sk0_14,member_predicate,sk0_13)) ),
inference(resolution,[status(thm)],[f303,f27]) ).
fof(f366,plain,
spl0_4,
inference(split_clause,[status(thm)],[f365,f362]) ).
fof(f556,plain,
! [X0,X1] :
( subset(initial_segment(X0,member_predicate,X1),X0)
| subset(initial_segment(X0,member_predicate,X1),X0) ),
inference(resolution,[status(thm)],[f282,f28]) ).
fof(f557,plain,
! [X0,X1] : subset(initial_segment(X0,member_predicate,X1),X0),
inference(duplicate_literals_removal,[status(esa)],[f556]) ).
fof(f604,plain,
! [X0,X1] :
( equal_set(X0,initial_segment(X0,member_predicate,X1))
| ~ subset(X0,initial_segment(X0,member_predicate,X1)) ),
inference(resolution,[status(thm)],[f557,f33]) ).
fof(f619,plain,
~ subset(sk0_14,initial_segment(sk0_14,member_predicate,sk0_13)),
inference(resolution,[status(thm)],[f604,f136]) ).
fof(f620,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f619,f363]) ).
fof(f621,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f620]) ).
fof(f622,plain,
$false,
inference(sat_refutation,[status(thm)],[f366,f621]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SET811+4 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n007.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue May 30 10:04:17 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.10/0.32 % 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
% 0.16/0.56 % Elapsed time: 0.028571 seconds
% 0.16/0.56 % CPU time: 0.038448 seconds
% 0.16/0.56 % Memory used: 4.904 MB
%------------------------------------------------------------------------------