TSTP Solution File: SET594+3 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET594+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n025.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 20:39:54 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 7 unt; 0 def)
% Number of atoms : 113 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 40 ~; 47 |; 17 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 81 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B,C,D] :
( union(intersection(B,C),intersection(B,D)) = B
=> subset(B,union(C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B,C,D] :
( union(intersection(B,C),intersection(B,D)) = B
=> subset(B,union(C,D)) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
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(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(f18,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)],[f2]) ).
fof(f19,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)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f22,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f23,plain,
! [B,C,D] :
( ( ~ member(D,intersection(B,C))
| ( member(D,B)
& member(D,C) ) )
& ( member(D,intersection(B,C))
| ~ member(D,B)
| ~ member(D,C) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f24,plain,
( ! [B,C,D] :
( ~ member(D,intersection(B,C))
| ( member(D,B)
& member(D,C) ) )
& ! [B,C,D] :
( member(D,intersection(B,C))
| ~ member(D,B)
| ~ member(D,C) ) ),
inference(miniscoping,[status(esa)],[f23]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f33,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f43,plain,
? [B,C,D] :
( union(intersection(B,C),intersection(B,D)) = B
& ~ subset(B,union(C,D)) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f44,plain,
( union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)) = sk0_2
& ~ subset(sk0_2,union(sk0_3,sk0_4)) ),
inference(skolemization,[status(esa)],[f43]) ).
fof(f45,plain,
union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)) = sk0_2,
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f46,plain,
~ subset(sk0_2,union(sk0_3,sk0_4)),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f61,plain,
! [X0] :
( ~ member(X0,sk0_2)
| member(X0,intersection(sk0_2,sk0_3))
| member(X0,intersection(sk0_2,sk0_4)) ),
inference(paramodulation,[status(thm)],[f45,f20]) ).
fof(f76,plain,
! [X0] :
( ~ member(X0,sk0_2)
| member(X0,intersection(sk0_2,sk0_3))
| member(X0,sk0_4) ),
inference(resolution,[status(thm)],[f61,f26]) ).
fof(f90,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
| ~ member(sk0_0(union(X1,X2),X0),X2) ),
inference(resolution,[status(thm)],[f17,f22]) ).
fof(f91,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
| ~ member(sk0_0(union(X1,X2),X0),X1) ),
inference(resolution,[status(thm)],[f17,f21]) ).
fof(f249,plain,
! [X0] :
( ~ member(X0,sk0_2)
| member(X0,sk0_4)
| member(X0,sk0_3) ),
inference(resolution,[status(thm)],[f76,f26]) ).
fof(f256,plain,
! [X0] :
( member(sk0_0(X0,sk0_2),sk0_4)
| member(sk0_0(X0,sk0_2),sk0_3)
| subset(sk0_2,X0) ),
inference(resolution,[status(thm)],[f249,f16]) ).
fof(f306,plain,
! [X0] :
( member(sk0_0(union(sk0_4,X0),sk0_2),sk0_3)
| subset(sk0_2,union(sk0_4,X0))
| subset(sk0_2,union(sk0_4,X0)) ),
inference(resolution,[status(thm)],[f256,f91]) ).
fof(f307,plain,
! [X0] :
( member(sk0_0(union(sk0_4,X0),sk0_2),sk0_3)
| subset(sk0_2,union(sk0_4,X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f306]) ).
fof(f478,plain,
( spl0_27
<=> subset(sk0_2,union(sk0_4,sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f479,plain,
( subset(sk0_2,union(sk0_4,sk0_3))
| ~ spl0_27 ),
inference(component_clause,[status(thm)],[f478]) ).
fof(f481,plain,
( subset(sk0_2,union(sk0_4,sk0_3))
| subset(sk0_2,union(sk0_4,sk0_3)) ),
inference(resolution,[status(thm)],[f307,f90]) ).
fof(f482,plain,
spl0_27,
inference(split_clause,[status(thm)],[f481,f478]) ).
fof(f486,plain,
( subset(sk0_2,union(sk0_3,sk0_4))
| ~ spl0_27 ),
inference(forward_demodulation,[status(thm)],[f33,f479]) ).
fof(f487,plain,
( $false
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[status(thm)],[f486,f46]) ).
fof(f488,plain,
~ spl0_27,
inference(contradiction_clause,[status(thm)],[f487]) ).
fof(f489,plain,
$false,
inference(sat_refutation,[status(thm)],[f482,f488]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET594+3 : TPTP v8.1.2. Released v2.2.0.
% 0.02/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31 % Computer : n025.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 : Mon Apr 29 21:43:40 EDT 2024
% 0.09/0.31 % CPUTime :
% 0.15/0.31 % Drodi V3.6.0
% 0.15/0.39 % Refutation found
% 0.15/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.41 % Elapsed time: 0.085856 seconds
% 0.15/0.41 % CPU time: 0.600292 seconds
% 0.15/0.41 % Total memory used: 65.106 MB
% 0.15/0.41 % Net memory used: 64.610 MB
%------------------------------------------------------------------------------