TSTP Solution File: SET593+3 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET593+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 12:34:44 EDT 2023
% Result : Theorem 0.18s 0.37s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 4 unt; 0 def)
% Number of atoms : 121 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 128 ( 48 ~; 52 |; 19 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 84 (; 79 !; 5 ?)
% 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,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [B,C,D] :
( subset(B,union(C,D))
=> ( subset(difference(B,C),D)
& subset(difference(B,D),C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B,C,D] :
( subset(B,union(C,D))
=> ( subset(difference(B,C),D)
& subset(difference(B,D),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(f14,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)],[f2]) ).
fof(f15,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)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f19,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f20,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)],[f19]) ).
fof(f21,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)],[f20]) ).
fof(f22,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)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f35,plain,
? [B,C,D] :
( subset(B,union(C,D))
& ( ~ subset(difference(B,C),D)
| ~ subset(difference(B,D),C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f36,plain,
( subset(sk0_2,union(sk0_3,sk0_4))
& ( ~ subset(difference(sk0_2,sk0_3),sk0_4)
| ~ subset(difference(sk0_2,sk0_4),sk0_3) ) ),
inference(skolemization,[status(esa)],[f35]) ).
fof(f37,plain,
subset(sk0_2,union(sk0_3,sk0_4)),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
( ~ subset(difference(sk0_2,sk0_3),sk0_4)
| ~ subset(difference(sk0_2,sk0_4),sk0_3) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f39,plain,
( spl0_0
<=> subset(difference(sk0_2,sk0_3),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f42,plain,
( spl0_1
<=> subset(difference(sk0_2,sk0_4),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f45,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f38,f39,f42]) ).
fof(f52,plain,
! [X0] :
( ~ member(X0,sk0_2)
| member(X0,union(sk0_3,sk0_4)) ),
inference(resolution,[status(thm)],[f23,f37]) ).
fof(f53,plain,
! [X0] :
( ~ member(X0,sk0_2)
| member(X0,sk0_3)
| member(X0,sk0_4) ),
inference(resolution,[status(thm)],[f52,f11]) ).
fof(f54,plain,
! [X0,X1,X2] :
( subset(difference(X0,X1),X2)
| ~ member(sk0_0(X2,difference(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f24,f17]) ).
fof(f55,plain,
! [X0,X1,X2] :
( subset(difference(X0,X1),X2)
| member(sk0_0(X2,difference(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f24,f16]) ).
fof(f85,plain,
! [X0] :
( subset(X0,sk0_4)
| ~ member(sk0_0(sk0_4,X0),sk0_2)
| member(sk0_0(sk0_4,X0),sk0_3) ),
inference(resolution,[status(thm)],[f25,f53]) ).
fof(f86,plain,
! [X0] :
( subset(X0,sk0_3)
| ~ member(sk0_0(sk0_3,X0),sk0_2)
| member(sk0_0(sk0_3,X0),sk0_4) ),
inference(resolution,[status(thm)],[f25,f53]) ).
fof(f485,plain,
! [X0] :
( subset(difference(X0,sk0_3),sk0_4)
| ~ member(sk0_0(sk0_4,difference(X0,sk0_3)),sk0_2)
| subset(difference(X0,sk0_3),sk0_4) ),
inference(resolution,[status(thm)],[f85,f54]) ).
fof(f486,plain,
! [X0] :
( subset(difference(X0,sk0_3),sk0_4)
| ~ member(sk0_0(sk0_4,difference(X0,sk0_3)),sk0_2) ),
inference(duplicate_literals_removal,[status(esa)],[f485]) ).
fof(f487,plain,
( subset(difference(sk0_2,sk0_3),sk0_4)
| subset(difference(sk0_2,sk0_3),sk0_4) ),
inference(resolution,[status(thm)],[f486,f55]) ).
fof(f488,plain,
spl0_0,
inference(split_clause,[status(thm)],[f487,f39]) ).
fof(f489,plain,
! [X0] :
( subset(difference(X0,sk0_4),sk0_3)
| ~ member(sk0_0(sk0_3,difference(X0,sk0_4)),sk0_2)
| subset(difference(X0,sk0_4),sk0_3) ),
inference(resolution,[status(thm)],[f86,f54]) ).
fof(f490,plain,
! [X0] :
( subset(difference(X0,sk0_4),sk0_3)
| ~ member(sk0_0(sk0_3,difference(X0,sk0_4)),sk0_2) ),
inference(duplicate_literals_removal,[status(esa)],[f489]) ).
fof(f491,plain,
( subset(difference(sk0_2,sk0_4),sk0_3)
| subset(difference(sk0_2,sk0_4),sk0_3) ),
inference(resolution,[status(thm)],[f490,f55]) ).
fof(f492,plain,
spl0_1,
inference(split_clause,[status(thm)],[f491,f42]) ).
fof(f493,plain,
$false,
inference(sat_refutation,[status(thm)],[f45,f488,f492]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET593+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 10:03:47 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.34 % Drodi V3.5.1
% 0.18/0.37 % Refutation found
% 0.18/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.38 % Elapsed time: 0.043793 seconds
% 0.18/0.38 % CPU time: 0.201912 seconds
% 0.18/0.38 % Memory used: 21.549 MB
%------------------------------------------------------------------------------