TSTP Solution File: SET009+3 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET009+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 20:38:35 EDT 2024
% Result : Theorem 0.11s 0.34s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 8 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 95 ( 39 ~; 34 |; 14 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 55 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,difference(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(f4,conjecture,
! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ ! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [B,C,D] :
( ( ~ member(D,difference(B,C))
| ( member(D,B)
& ~ member(D,C) ) )
& ( member(D,difference(B,C))
| ~ member(D,B)
| member(D,C) ) ),
inference(NNF_transformation,[status(esa)],[f1]) ).
fof(f7,plain,
( ! [B,C,D] :
( ~ member(D,difference(B,C))
| ( member(D,B)
& ~ member(D,C) ) )
& ! [B,C,D] :
( member(D,difference(B,C))
| ~ member(D,B)
| member(D,C) ) ),
inference(miniscoping,[status(esa)],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f9,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f10,plain,
! [X0,X1,X2] :
( member(X0,difference(X1,X2))
| ~ member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f11,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f12,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)],[f11]) ).
fof(f13,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)],[f12]) ).
fof(f14,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)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f19,plain,
? [B,C,D] :
( subset(B,C)
& ~ subset(difference(D,C),difference(D,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f20,plain,
? [B,C] :
( subset(B,C)
& ? [D] : ~ subset(difference(D,C),difference(D,B)) ),
inference(miniscoping,[status(esa)],[f19]) ).
fof(f21,plain,
( subset(sk0_1,sk0_2)
& ~ subset(difference(sk0_3,sk0_2),difference(sk0_3,sk0_1)) ),
inference(skolemization,[status(esa)],[f20]) ).
fof(f22,plain,
subset(sk0_1,sk0_2),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f23,plain,
~ subset(difference(sk0_3,sk0_2),difference(sk0_3,sk0_1)),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f24,plain,
member(sk0_0(difference(sk0_3,sk0_1),difference(sk0_3,sk0_2)),difference(sk0_3,sk0_2)),
inference(resolution,[status(thm)],[f16,f23]) ).
fof(f25,plain,
~ member(sk0_0(difference(sk0_3,sk0_1),difference(sk0_3,sk0_2)),sk0_2),
inference(resolution,[status(thm)],[f24,f9]) ).
fof(f26,plain,
member(sk0_0(difference(sk0_3,sk0_1),difference(sk0_3,sk0_2)),sk0_3),
inference(resolution,[status(thm)],[f24,f8]) ).
fof(f30,plain,
! [X0] :
( member(sk0_0(difference(sk0_3,sk0_1),difference(sk0_3,sk0_2)),difference(sk0_3,X0))
| member(sk0_0(difference(sk0_3,sk0_1),difference(sk0_3,sk0_2)),X0) ),
inference(resolution,[status(thm)],[f26,f10]) ).
fof(f60,plain,
( spl0_3
<=> subset(difference(sk0_3,sk0_2),difference(sk0_3,sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f61,plain,
( subset(difference(sk0_3,sk0_2),difference(sk0_3,sk0_1))
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,plain,
( spl0_4
<=> member(sk0_0(difference(sk0_3,sk0_1),difference(sk0_3,sk0_2)),sk0_1) ),
introduced(split_symbol_definition) ).
fof(f64,plain,
( member(sk0_0(difference(sk0_3,sk0_1),difference(sk0_3,sk0_2)),sk0_1)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( subset(difference(sk0_3,sk0_2),difference(sk0_3,sk0_1))
| member(sk0_0(difference(sk0_3,sk0_1),difference(sk0_3,sk0_2)),sk0_1) ),
inference(resolution,[status(thm)],[f17,f30]) ).
fof(f67,plain,
( spl0_3
| spl0_4 ),
inference(split_clause,[status(thm)],[f66,f60,f63]) ).
fof(f78,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f23]) ).
fof(f79,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f78]) ).
fof(f172,plain,
! [X0] :
( ~ subset(sk0_1,X0)
| member(sk0_0(difference(sk0_3,sk0_1),difference(sk0_3,sk0_2)),X0)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f64,f15]) ).
fof(f187,plain,
( member(sk0_0(difference(sk0_3,sk0_1),difference(sk0_3,sk0_2)),sk0_2)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f172,f22]) ).
fof(f326,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f25,f187]) ).
fof(f327,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f326]) ).
fof(f328,plain,
$false,
inference(sat_refutation,[status(thm)],[f67,f79,f327]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET009+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Apr 29 21:55:46 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % Drodi V3.6.0
% 0.11/0.34 % Refutation found
% 0.11/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.35 % Elapsed time: 0.022510 seconds
% 0.11/0.35 % CPU time: 0.089641 seconds
% 0.11/0.35 % Total memory used: 5.351 MB
% 0.11/0.35 % Net memory used: 5.278 MB
%------------------------------------------------------------------------------