TSTP Solution File: SET185+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET185+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.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 12:34:13 EDT 2023
% Result : Theorem 0.20s 0.36s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 7 unt; 0 def)
% Number of atoms : 124 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 122 ( 44 ~; 51 |; 17 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 78 (; 74 !; 4 ?)
% 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,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
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(f7,conjecture,
! [B,C] :
( subset(B,C)
=> union(B,C) = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B,C] :
( subset(B,C)
=> union(B,C) = C ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,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(f10,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)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f14,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f15,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)],[f14]) ).
fof(f16,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)],[f15]) ).
fof(f17,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)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f21,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(f22,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)],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f35,plain,
? [B,C] :
( subset(B,C)
& union(B,C) != C ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f36,plain,
( subset(sk0_2,sk0_3)
& union(sk0_2,sk0_3) != sk0_3 ),
inference(skolemization,[status(esa)],[f35]) ).
fof(f37,plain,
subset(sk0_2,sk0_3),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
union(sk0_2,sk0_3) != sk0_3,
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f55,plain,
! [X0] :
( ~ member(X0,sk0_2)
| member(X0,sk0_3) ),
inference(resolution,[status(thm)],[f18,f37]) ).
fof(f57,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)],[f19,f11]) ).
fof(f66,plain,
! [X0,X1] :
( subset(union(X0,X1),X1)
| subset(union(X0,X1),X1)
| member(sk0_0(X1,union(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f20,f57]) ).
fof(f67,plain,
! [X0,X1] :
( subset(union(X0,X1),X1)
| member(sk0_0(X1,union(X0,X1)),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f66]) ).
fof(f75,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
| ~ member(sk0_0(union(X1,X2),X0),X2) ),
inference(resolution,[status(thm)],[f20,f13]) ).
fof(f83,plain,
! [X0] :
( subset(union(sk0_2,X0),X0)
| member(sk0_0(X0,union(sk0_2,X0)),sk0_3) ),
inference(resolution,[status(thm)],[f67,f55]) ).
fof(f101,plain,
! [X0,X1] :
( subset(X0,union(X1,X0))
| subset(X0,union(X1,X0)) ),
inference(resolution,[status(thm)],[f75,f19]) ).
fof(f102,plain,
! [X0,X1] : subset(X0,union(X1,X0)),
inference(duplicate_literals_removal,[status(esa)],[f101]) ).
fof(f213,plain,
( spl0_4
<=> subset(union(sk0_2,sk0_3),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f214,plain,
( subset(union(sk0_2,sk0_3),sk0_3)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,plain,
( subset(union(sk0_2,sk0_3),sk0_3)
| subset(union(sk0_2,sk0_3),sk0_3) ),
inference(resolution,[status(thm)],[f83,f20]) ).
fof(f217,plain,
spl0_4,
inference(split_clause,[status(thm)],[f216,f213]) ).
fof(f230,plain,
( spl0_7
<=> sk0_3 = union(sk0_2,sk0_3) ),
introduced(split_symbol_definition) ).
fof(f231,plain,
( sk0_3 = union(sk0_2,sk0_3)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f233,plain,
( spl0_8
<=> subset(sk0_3,union(sk0_2,sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f235,plain,
( ~ subset(sk0_3,union(sk0_2,sk0_3))
| spl0_8 ),
inference(component_clause,[status(thm)],[f233]) ).
fof(f236,plain,
( sk0_3 = union(sk0_2,sk0_3)
| ~ subset(sk0_3,union(sk0_2,sk0_3))
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f214,f25]) ).
fof(f237,plain,
( spl0_7
| ~ spl0_8
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f236,f230,f233,f213]) ).
fof(f238,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f235,f102]) ).
fof(f239,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f240,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f38]) ).
fof(f241,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f240]) ).
fof(f242,plain,
$false,
inference(sat_refutation,[status(thm)],[f217,f237,f239,f241]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET185+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.33 % Computer : n027.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 30 10:34:33 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.35 % Drodi V3.5.1
% 0.20/0.36 % Refutation found
% 0.20/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.61 % Elapsed time: 0.054799 seconds
% 0.24/0.61 % CPU time: 0.030435 seconds
% 0.24/0.61 % Memory used: 3.718 MB
%------------------------------------------------------------------------------