TSTP Solution File: SET200+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET200+3 : TPTP v8.1.2. Released v2.2.0.
% 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 12:34:16 EDT 2023
% Result : Theorem 0.09s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 10 unt; 0 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 101 ( 40 ~; 37 |; 16 &)
% ( 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 72 (; 66 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [B,C,D,E] :
( ( subset(B,C)
& subset(D,E) )
=> subset(union(B,D),union(C,E)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [B,C,D,E] :
( ( subset(B,C)
& subset(D,E) )
=> subset(union(B,D),union(C,E)) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,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(f9,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)],[f8]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f12,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f13,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f14,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)],[f13]) ).
fof(f15,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)],[f14]) ).
fof(f16,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)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f29,plain,
? [B,C,D,E] :
( subset(B,C)
& subset(D,E)
& ~ subset(union(B,D),union(C,E)) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f30,plain,
( subset(sk0_2,sk0_3)
& subset(sk0_4,sk0_5)
& ~ subset(union(sk0_2,sk0_4),union(sk0_3,sk0_5)) ),
inference(skolemization,[status(esa)],[f29]) ).
fof(f31,plain,
subset(sk0_2,sk0_3),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
subset(sk0_4,sk0_5),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f33,plain,
~ subset(union(sk0_2,sk0_4),union(sk0_3,sk0_5)),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f40,plain,
! [X0] :
( ~ member(X0,sk0_4)
| member(X0,sk0_5) ),
inference(resolution,[status(thm)],[f17,f32]) ).
fof(f41,plain,
! [X0] :
( ~ member(X0,sk0_2)
| member(X0,sk0_3) ),
inference(resolution,[status(thm)],[f17,f31]) ).
fof(f42,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)],[f18,f10]) ).
fof(f43,plain,
( spl0_0
<=> member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f44,plain,
( member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_2)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f46,plain,
( spl0_1
<=> member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f47,plain,
( member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_4)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,plain,
( member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_2)
| member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_4) ),
inference(resolution,[status(thm)],[f42,f33]) ).
fof(f50,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f49,f43,f46]) ).
fof(f89,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
| ~ member(sk0_0(union(X1,X2),X0),X2) ),
inference(resolution,[status(thm)],[f19,f12]) ).
fof(f90,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
| ~ member(sk0_0(union(X1,X2),X0),X1) ),
inference(resolution,[status(thm)],[f19,f11]) ).
fof(f124,plain,
~ member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_5),
inference(resolution,[status(thm)],[f89,f33]) ).
fof(f128,plain,
~ member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_3),
inference(resolution,[status(thm)],[f90,f33]) ).
fof(f142,plain,
~ member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_4),
inference(resolution,[status(thm)],[f124,f40]) ).
fof(f146,plain,
~ member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_2),
inference(resolution,[status(thm)],[f128,f41]) ).
fof(f147,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f146,f44]) ).
fof(f148,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f149,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f47,f142]) ).
fof(f150,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f151,plain,
$false,
inference(sat_refutation,[status(thm)],[f50,f148,f150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SET200+3 : TPTP v8.1.2. Released v2.2.0.
% 0.09/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31 % Computer : n031.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Tue May 30 10:42:37 EDT 2023
% 0.09/0.32 % CPUTime :
% 0.09/0.32 % Drodi V3.5.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.43 % Elapsed time: 0.109570 seconds
% 0.15/0.43 % CPU time: 0.317172 seconds
% 0.15/0.43 % Memory used: 53.226 MB
%------------------------------------------------------------------------------