TSTP Solution File: SET587+3 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET587+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n010.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 20:39:53 EDT 2024
% Result : Theorem 0.11s 0.36s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 4 unt; 0 def)
% Number of atoms : 141 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 153 ( 61 ~; 64 |; 18 &)
% ( 8 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 85 ( 79 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f16,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(f17,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)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f20,plain,
! [X0,X1,X2] :
( member(X0,difference(X1,X2))
| ~ member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f21,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f22,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f23,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)],[f22]) ).
fof(f24,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)],[f23]) ).
fof(f25,plain,
( ! [B,C] :
( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ! [B,C] :
( subset(B,C)
| ( member(sk0_1(C,B),B)
& ~ member(sk0_1(C,B),C) ) ) ),
inference(skolemization,[status(esa)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_1(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f29,plain,
! [B,C] :
( ( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(NNF_transformation,[status(esa)],[f5]) ).
fof(f30,plain,
( ! [B,C] :
( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ! [B,C] :
( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(miniscoping,[status(esa)],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f47,plain,
? [B,C] :
( difference(B,C) = empty_set
<~> subset(B,C) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f48,plain,
? [B,C] :
( ( difference(B,C) = empty_set
| subset(B,C) )
& ( difference(B,C) != empty_set
| ~ subset(B,C) ) ),
inference(NNF_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
( ( difference(sk0_4,sk0_5) = empty_set
| subset(sk0_4,sk0_5) )
& ( difference(sk0_4,sk0_5) != empty_set
| ~ subset(sk0_4,sk0_5) ) ),
inference(skolemization,[status(esa)],[f48]) ).
fof(f50,plain,
( difference(sk0_4,sk0_5) = empty_set
| subset(sk0_4,sk0_5) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f51,plain,
( difference(sk0_4,sk0_5) != empty_set
| ~ subset(sk0_4,sk0_5) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f52,plain,
( spl0_0
<=> difference(sk0_4,sk0_5) = empty_set ),
introduced(split_symbol_definition) ).
fof(f53,plain,
( difference(sk0_4,sk0_5) = empty_set
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,plain,
( spl0_1
<=> subset(sk0_4,sk0_5) ),
introduced(split_symbol_definition) ).
fof(f56,plain,
( subset(sk0_4,sk0_5)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f50,f52,f55]) ).
fof(f59,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f51,f52,f55]) ).
fof(f63,plain,
! [X0,X1,X2] :
( subset(difference(X0,X1),X2)
| ~ member(sk0_1(X2,difference(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f27,f19]) ).
fof(f64,plain,
! [X0,X1,X2] :
( subset(difference(X0,X1),X2)
| member(sk0_1(X2,difference(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f27,f18]) ).
fof(f65,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[status(thm)],[f27,f21]) ).
fof(f70,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(resolution,[status(thm)],[f65,f33]) ).
fof(f234,plain,
! [X0] :
( member(X0,empty_set)
| ~ member(X0,sk0_4)
| member(X0,sk0_5)
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f53,f20]) ).
fof(f235,plain,
! [X0] :
( ~ member(X0,sk0_4)
| member(X0,sk0_5)
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f234,f21]) ).
fof(f241,plain,
! [X0] :
( member(sk0_1(X0,sk0_4),sk0_5)
| subset(sk0_4,X0)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f235,f27]) ).
fof(f278,plain,
( subset(sk0_4,sk0_5)
| subset(sk0_4,sk0_5)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f241,f28]) ).
fof(f279,plain,
( spl0_1
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f278,f55,f52]) ).
fof(f280,plain,
! [X0] :
( ~ member(X0,sk0_4)
| member(X0,sk0_5)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f56,f26]) ).
fof(f291,plain,
! [X0,X1] :
( member(sk0_1(X0,difference(sk0_4,X1)),sk0_5)
| subset(difference(sk0_4,X1),X0)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f280,f64]) ).
fof(f297,plain,
! [X0] :
( subset(difference(sk0_4,sk0_5),X0)
| subset(difference(sk0_4,sk0_5),X0)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f291,f63]) ).
fof(f298,plain,
! [X0] :
( subset(difference(sk0_4,sk0_5),X0)
| ~ spl0_1 ),
inference(duplicate_literals_removal,[status(esa)],[f297]) ).
fof(f303,plain,
( difference(sk0_4,sk0_5) = empty_set
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f298,f70]) ).
fof(f304,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f303,f52,f55]) ).
fof(f307,plain,
$false,
inference(sat_refutation,[status(thm)],[f58,f59,f279,f304]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET587+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Apr 29 21:13:50 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.34 % Drodi V3.6.0
% 0.11/0.36 % Refutation found
% 0.11/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.36 % Elapsed time: 0.024841 seconds
% 0.11/0.36 % CPU time: 0.088621 seconds
% 0.11/0.36 % Total memory used: 18.813 MB
% 0.11/0.36 % Net memory used: 18.668 MB
%------------------------------------------------------------------------------