TSTP Solution File: SET812+4 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET812+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n010.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 20:40:24 EDT 2024
% Result : Theorem 0.20s 0.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 7 unt; 0 def)
% Number of atoms : 186 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 205 ( 77 ~; 80 |; 36 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 121 ( 116 !; 5 ?)
% 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(f3,axiom,
! [X,A] :
( member(X,power_set(A))
<=> subset(X,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,A)
& member(X,B) ) ),
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(f20,conjecture,
! [A] :
( member(A,on)
=> equal_set(A,intersection(A,power_set(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ! [A] :
( member(A,on)
=> equal_set(A,intersection(A,power_set(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(f34,plain,
! [X,A] :
( ( ~ member(X,power_set(A))
| subset(X,A) )
& ( member(X,power_set(A))
| ~ subset(X,A) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f35,plain,
( ! [X,A] :
( ~ member(X,power_set(A))
| subset(X,A) )
& ! [X,A] :
( member(X,power_set(A))
| ~ subset(X,A) ) ),
inference(miniscoping,[status(esa)],[f34]) ).
fof(f37,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f38,plain,
! [X,A,B] :
( ( ~ member(X,intersection(A,B))
| ( member(X,A)
& member(X,B) ) )
& ( member(X,intersection(A,B))
| ~ member(X,A)
| ~ member(X,B) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f39,plain,
( ! [X,A,B] :
( ~ member(X,intersection(A,B))
| ( member(X,A)
& member(X,B) ) )
& ! [X,A,B] :
( member(X,intersection(A,B))
| ~ member(X,A)
| ~ member(X,B) ) ),
inference(miniscoping,[status(esa)],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f42,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
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(f132,plain,
? [A] :
( member(A,on)
& ~ equal_set(A,intersection(A,power_set(A))) ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f133,plain,
( member(sk0_13,on)
& ~ equal_set(sk0_13,intersection(sk0_13,power_set(sk0_13))) ),
inference(skolemization,[status(esa)],[f132]) ).
fof(f134,plain,
member(sk0_13,on),
inference(cnf_transformation,[status(esa)],[f133]) ).
fof(f135,plain,
~ equal_set(sk0_13,intersection(sk0_13,power_set(sk0_13))),
inference(cnf_transformation,[status(esa)],[f133]) ).
fof(f146,plain,
! [X0] :
( ~ member(X0,sk0_13)
| subset(X0,sk0_13) ),
inference(resolution,[status(thm)],[f82,f134]) ).
fof(f149,plain,
! [X0,X1,X2,X3] :
( ~ subset(intersection(X0,X1),X2)
| member(X3,X2)
| ~ member(X3,X0)
| ~ member(X3,X1) ),
inference(resolution,[status(thm)],[f26,f42]) ).
fof(f163,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),X2)
| member(sk0_0(X2,intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f27,f41]) ).
fof(f164,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),X2)
| member(sk0_0(X2,intersection(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f27,f40]) ).
fof(f169,plain,
! [X0,X1] :
( subset(X0,power_set(X1))
| ~ subset(sk0_0(power_set(X1),X0),X1) ),
inference(resolution,[status(thm)],[f28,f37]) ).
fof(f170,plain,
! [X0,X1,X2] :
( subset(X0,intersection(X1,X2))
| ~ member(sk0_0(intersection(X1,X2),X0),X1)
| ~ member(sk0_0(intersection(X1,X2),X0),X2) ),
inference(resolution,[status(thm)],[f28,f42]) ).
fof(f201,plain,
! [X0,X1] :
( subset(intersection(X0,sk0_13),X1)
| subset(sk0_0(X1,intersection(X0,sk0_13)),sk0_13) ),
inference(resolution,[status(thm)],[f163,f146]) ).
fof(f209,plain,
! [X0] :
( subset(intersection(X0,sk0_13),power_set(sk0_13))
| subset(intersection(X0,sk0_13),power_set(sk0_13)) ),
inference(resolution,[status(thm)],[f201,f169]) ).
fof(f210,plain,
! [X0] : subset(intersection(X0,sk0_13),power_set(sk0_13)),
inference(duplicate_literals_removal,[status(esa)],[f209]) ).
fof(f212,plain,
! [X0,X1] :
( member(X0,power_set(sk0_13))
| ~ member(X0,X1)
| ~ member(X0,sk0_13) ),
inference(resolution,[status(thm)],[f210,f149]) ).
fof(f227,plain,
! [X0,X1] :
( subset(intersection(X0,X1),X0)
| subset(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[f164,f28]) ).
fof(f228,plain,
! [X0,X1] : subset(intersection(X0,X1),X0),
inference(duplicate_literals_removal,[status(esa)],[f227]) ).
fof(f247,plain,
! [X0,X1] :
( equal_set(X0,intersection(X0,X1))
| ~ subset(X0,intersection(X0,X1)) ),
inference(resolution,[status(thm)],[f228,f33]) ).
fof(f270,plain,
! [X0,X1,X2] :
( subset(X0,intersection(X1,power_set(sk0_13)))
| ~ member(sk0_0(intersection(X1,power_set(sk0_13)),X0),X1)
| ~ member(sk0_0(intersection(X1,power_set(sk0_13)),X0),X2)
| ~ member(sk0_0(intersection(X1,power_set(sk0_13)),X0),sk0_13) ),
inference(resolution,[status(thm)],[f170,f212]) ).
fof(f281,plain,
! [X0] :
( subset(sk0_13,intersection(X0,power_set(sk0_13)))
| ~ member(sk0_0(intersection(X0,power_set(sk0_13)),sk0_13),X0)
| subset(sk0_13,intersection(X0,power_set(sk0_13))) ),
inference(resolution,[status(thm)],[f270,f27]) ).
fof(f282,plain,
! [X0] :
( subset(sk0_13,intersection(X0,power_set(sk0_13)))
| ~ member(sk0_0(intersection(X0,power_set(sk0_13)),sk0_13),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f281]) ).
fof(f657,plain,
( spl0_8
<=> subset(sk0_13,intersection(sk0_13,power_set(sk0_13))) ),
introduced(split_symbol_definition) ).
fof(f658,plain,
( subset(sk0_13,intersection(sk0_13,power_set(sk0_13)))
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f657]) ).
fof(f660,plain,
( subset(sk0_13,intersection(sk0_13,power_set(sk0_13)))
| subset(sk0_13,intersection(sk0_13,power_set(sk0_13))) ),
inference(resolution,[status(thm)],[f282,f27]) ).
fof(f661,plain,
spl0_8,
inference(split_clause,[status(thm)],[f660,f657]) ).
fof(f708,plain,
( equal_set(sk0_13,intersection(sk0_13,power_set(sk0_13)))
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f658,f247]) ).
fof(f709,plain,
( $false
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f708,f135]) ).
fof(f710,plain,
~ spl0_8,
inference(contradiction_clause,[status(thm)],[f709]) ).
fof(f711,plain,
$false,
inference(sat_refutation,[status(thm)],[f661,f710]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET812+4 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 29 21:22:50 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.6.0
% 0.20/0.52 % Refutation found
% 0.20/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.55 % Elapsed time: 0.195202 seconds
% 0.20/0.55 % CPU time: 1.403827 seconds
% 0.20/0.55 % Total memory used: 67.551 MB
% 0.20/0.55 % Net memory used: 66.851 MB
%------------------------------------------------------------------------------