TSTP Solution File: SET814+4 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET814+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n031.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 65.58s 8.55s
% Output : CNFRefutation 65.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 136 ( 51 ~; 45 |; 31 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 71 (; 63 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(Y,A)
& member(X,Y) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
! [A] :
( member(A,on)
=> subset(sum(A),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [A] :
( member(A,on)
=> subset(sum(A),A) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( ~ member(X,A)
| member(X,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f24,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)],[f23]) ).
fof(f25,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)],[f24]) ).
fof(f26,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)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f29,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f64,plain,
! [X,A] :
( ( ~ member(X,sum(A))
| ? [Y] :
( member(Y,A)
& member(X,Y) ) )
& ( member(X,sum(A))
| ! [Y] :
( ~ member(Y,A)
| ~ member(X,Y) ) ) ),
inference(NNF_transformation,[status(esa)],[f10]) ).
fof(f65,plain,
( ! [X,A] :
( ~ member(X,sum(A))
| ? [Y] :
( member(Y,A)
& member(X,Y) ) )
& ! [X,A] :
( member(X,sum(A))
| ! [Y] :
( ~ member(Y,A)
| ~ member(X,Y) ) ) ),
inference(miniscoping,[status(esa)],[f64]) ).
fof(f66,plain,
( ! [X,A] :
( ~ member(X,sum(A))
| ( member(sk0_1(A,X),A)
& member(X,sk0_1(A,X)) ) )
& ! [X,A] :
( member(X,sum(A))
| ! [Y] :
( ~ member(Y,A)
| ~ member(X,Y) ) ) ),
inference(skolemization,[status(esa)],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ~ member(X0,sum(X1))
| member(sk0_1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ~ member(X0,sum(X1))
| member(X0,sk0_1(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f77,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(f78,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)],[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)
| ? [X] :
( member(X,A)
& ~ subset(X,A) ) ) ),
inference(miniscoping,[status(esa)],[f78]) ).
fof(f80,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)],[f79]) ).
fof(f83,plain,
! [X0,X1] :
( ~ member(X0,on)
| ~ member(X1,X0)
| subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f136,plain,
? [A] :
( member(A,on)
& ~ subset(sum(A),A) ),
inference(pre_NNF_transformation,[status(esa)],[f22]) ).
fof(f137,plain,
( member(sk0_13,on)
& ~ subset(sum(sk0_13),sk0_13) ),
inference(skolemization,[status(esa)],[f136]) ).
fof(f138,plain,
member(sk0_13,on),
inference(cnf_transformation,[status(esa)],[f137]) ).
fof(f139,plain,
~ subset(sum(sk0_13),sk0_13),
inference(cnf_transformation,[status(esa)],[f137]) ).
fof(f168,plain,
~ member(sk0_0(sk0_13,sum(sk0_13)),sk0_13),
inference(resolution,[status(thm)],[f29,f139]) ).
fof(f176,plain,
! [X0] :
( ~ subset(X0,sk0_13)
| ~ member(sk0_0(sk0_13,sum(sk0_13)),X0) ),
inference(resolution,[status(thm)],[f168,f27]) ).
fof(f1878,plain,
! [X0] :
( ~ member(X0,sk0_13)
| subset(X0,sk0_13) ),
inference(resolution,[status(thm)],[f83,f138]) ).
fof(f2053,plain,
member(sk0_0(sk0_13,sum(sk0_13)),sum(sk0_13)),
inference(resolution,[status(thm)],[f28,f139]) ).
fof(f2390,plain,
member(sk0_0(sk0_13,sum(sk0_13)),sk0_1(sk0_13,sk0_0(sk0_13,sum(sk0_13)))),
inference(resolution,[status(thm)],[f2053,f68]) ).
fof(f2477,plain,
member(sk0_1(sk0_13,sk0_0(sk0_13,sum(sk0_13))),sk0_13),
inference(resolution,[status(thm)],[f67,f2053]) ).
fof(f4672,plain,
subset(sk0_1(sk0_13,sk0_0(sk0_13,sum(sk0_13))),sk0_13),
inference(resolution,[status(thm)],[f2477,f1878]) ).
fof(f5177,plain,
~ member(sk0_0(sk0_13,sum(sk0_13)),sk0_1(sk0_13,sk0_0(sk0_13,sum(sk0_13)))),
inference(resolution,[status(thm)],[f4672,f176]) ).
fof(f5178,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5177,f2390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SET814+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.25 % Computer : n031.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue May 30 10:40:22 EDT 2023
% 0.07/0.25 % CPUTime :
% 0.07/0.26 % Drodi V3.5.1
% 65.58/8.55 % Refutation found
% 65.58/8.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 65.58/8.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 66.15/8.62 % Elapsed time: 8.359443 seconds
% 66.15/8.62 % CPU time: 66.392899 seconds
% 66.15/8.62 % Memory used: 333.639 MB
%------------------------------------------------------------------------------