TSTP Solution File: SET009+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% 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 : n022.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 12:33:29 EDT 2023
% Result : Theorem 0.14s 0.37s
% Output : CNFRefutation 0.22s
% 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(f132,plain,
( spl0_11
<=> member(sk0_0(difference(sk0_3,sk0_1),difference(sk0_3,sk0_2)),sk0_1) ),
introduced(split_symbol_definition) ).
fof(f133,plain,
( member(sk0_0(difference(sk0_3,sk0_1),difference(sk0_3,sk0_2)),sk0_1)
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f135,plain,
( spl0_12
<=> subset(difference(sk0_3,sk0_2),difference(sk0_3,sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f136,plain,
( subset(difference(sk0_3,sk0_2),difference(sk0_3,sk0_1))
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,plain,
( member(sk0_0(difference(sk0_3,sk0_1),difference(sk0_3,sk0_2)),sk0_1)
| subset(difference(sk0_3,sk0_2),difference(sk0_3,sk0_1)) ),
inference(resolution,[status(thm)],[f30,f17]) ).
fof(f139,plain,
( spl0_11
| spl0_12 ),
inference(split_clause,[status(thm)],[f138,f132,f135]) ).
fof(f146,plain,
! [X0] :
( ~ subset(sk0_1,X0)
| member(sk0_0(difference(sk0_3,sk0_1),difference(sk0_3,sk0_2)),X0)
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f133,f15]) ).
fof(f159,plain,
( member(sk0_0(difference(sk0_3,sk0_1),difference(sk0_3,sk0_2)),sk0_2)
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f146,f22]) ).
fof(f160,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f159,f25]) ).
fof(f161,plain,
~ spl0_11,
inference(contradiction_clause,[status(thm)],[f160]) ).
fof(f162,plain,
( $false
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f136,f23]) ).
fof(f163,plain,
~ spl0_12,
inference(contradiction_clause,[status(thm)],[f162]) ).
fof(f164,plain,
$false,
inference(sat_refutation,[status(thm)],[f139,f161,f163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET009+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue May 30 10:21:12 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.5.1
% 0.14/0.37 % Refutation found
% 0.14/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.30/0.64 % Elapsed time: 0.064411 seconds
% 0.30/0.64 % CPU time: 0.028388 seconds
% 0.30/0.64 % Memory used: 641.244 KB
%------------------------------------------------------------------------------