TSTP Solution File: SET162+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET162+3 : TPTP v8.1.2. Released v2.2.0.
% 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 12:34:09 EDT 2023
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 15 unt; 0 def)
% Number of atoms : 97 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 96 ( 37 ~; 39 |; 15 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 84 (; 81 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B] : union(B,empty_set) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B] : union(B,empty_set) = B,
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [B,C,D] :
( ( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) )
& ( member(D,union(B,C))
| ( ~ member(D,B)
& ~ member(D,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f1]) ).
fof(f12,plain,
( ! [B,C,D] :
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) )
& ! [B,C,D] :
( member(D,union(B,C))
| ( ~ member(D,B)
& ~ member(D,C) ) ) ),
inference(miniscoping,[status(esa)],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f15,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f16,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f17,plain,
! [B,C] :
( ( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f18,plain,
( ! [B,C] :
( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ! [B,C] :
( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(miniscoping,[status(esa)],[f17]) ).
fof(f21,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f22,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f23,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f24,plain,
! [B,C] :
( ( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ( subset(B,C)
| ? [D] :
( member(D,B)
& ~ member(D,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f23]) ).
fof(f25,plain,
( ! [B,C] :
( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ! [B,C] :
( subset(B,C)
| ? [D] :
( member(D,B)
& ~ member(D,C) ) ) ),
inference(miniscoping,[status(esa)],[f24]) ).
fof(f26,plain,
( ! [B,C] :
( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ! [B,C] :
( subset(B,C)
| ( member(sk0_0(C,B),B)
& ~ member(sk0_0(C,B),C) ) ) ),
inference(skolemization,[status(esa)],[f25]) ).
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(f43,plain,
? [B] : union(B,empty_set) != B,
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f44,plain,
union(sk0_3,empty_set) != sk0_3,
inference(skolemization,[status(esa)],[f43]) ).
fof(f45,plain,
union(sk0_3,empty_set) != sk0_3,
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f64,plain,
! [X0,X1,X2] :
( subset(union(X0,X1),X2)
| member(sk0_0(X2,union(X0,X1)),X0)
| member(sk0_0(X2,union(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f28,f13]) ).
fof(f75,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
| ~ member(sk0_0(union(X1,X2),X0),X2) ),
inference(resolution,[status(thm)],[f29,f15]) ).
fof(f99,plain,
! [X0,X1] :
( subset(union(X0,X1),X1)
| member(sk0_0(X1,union(X0,X1)),X0)
| subset(union(X0,X1),X1) ),
inference(resolution,[status(thm)],[f64,f29]) ).
fof(f100,plain,
! [X0,X1] :
( subset(union(X0,X1),X1)
| member(sk0_0(X1,union(X0,X1)),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f99]) ).
fof(f108,plain,
! [X0,X1] :
( subset(X0,union(X1,X0))
| subset(X0,union(X1,X0)) ),
inference(resolution,[status(thm)],[f75,f28]) ).
fof(f109,plain,
! [X0,X1] : subset(X0,union(X1,X0)),
inference(duplicate_literals_removal,[status(esa)],[f108]) ).
fof(f117,plain,
! [X0,X1] : subset(X0,union(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f109]) ).
fof(f121,plain,
! [X0,X1] :
( union(X0,X1) = X0
| ~ subset(union(X0,X1),X0) ),
inference(resolution,[status(thm)],[f117,f21]) ).
fof(f144,plain,
! [X0,X1] :
( union(X0,X1) = X0
| ~ subset(union(X1,X0),X0) ),
inference(paramodulation,[status(thm)],[f22,f121]) ).
fof(f447,plain,
! [X0] : subset(union(empty_set,X0),X0),
inference(resolution,[status(thm)],[f100,f16]) ).
fof(f562,plain,
! [X0] : union(X0,empty_set) = X0,
inference(resolution,[status(thm)],[f447,f144]) ).
fof(f574,plain,
sk0_3 != sk0_3,
inference(backward_demodulation,[status(thm)],[f562,f45]) ).
fof(f575,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f574]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET162+3 : TPTP v8.1.2. Released v2.2.0.
% 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 10:35:49 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.61 % Elapsed time: 0.043242 seconds
% 0.26/0.61 % CPU time: 0.054230 seconds
% 0.26/0.61 % Memory used: 5.682 MB
%------------------------------------------------------------------------------