TSTP Solution File: SET603+3 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET603+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.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 20:39:56 EDT 2024
% Result : Theorem 0.10s 0.34s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 92 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 94 ( 36 ~; 37 |; 16 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 76 ( 73 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B] : difference(B,empty_set) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B] : difference(B,empty_set) = B,
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(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] :
( ( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f23,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)],[f22]) ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f34,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f35,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)],[f34]) ).
fof(f36,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)],[f35]) ).
fof(f37,plain,
( ! [B,C] :
( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ! [B,C] :
( subset(B,C)
| ( member(sk0_2(C,B),B)
& ~ member(sk0_2(C,B),C) ) ) ),
inference(skolemization,[status(esa)],[f36]) ).
fof(f39,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_2(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f40,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_2(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f47,plain,
? [B] : difference(B,empty_set) != B,
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f48,plain,
difference(sk0_4,empty_set) != sk0_4,
inference(skolemization,[status(esa)],[f47]) ).
fof(f49,plain,
difference(sk0_4,empty_set) != sk0_4,
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f183,plain,
! [X0,X1,X2] :
( subset(difference(X0,X1),X2)
| member(sk0_2(X2,difference(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f39,f18]) ).
fof(f185,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| member(sk0_2(X1,X0),difference(X0,X2))
| member(sk0_2(X1,X0),X2) ),
inference(resolution,[status(thm)],[f39,f20]) ).
fof(f265,plain,
! [X0,X1] :
( subset(difference(X0,X1),X0)
| subset(difference(X0,X1),X0) ),
inference(resolution,[status(thm)],[f183,f40]) ).
fof(f266,plain,
! [X0,X1] : subset(difference(X0,X1),X0),
inference(duplicate_literals_removal,[status(esa)],[f265]) ).
fof(f278,plain,
! [X0,X1] :
( X0 = difference(X0,X1)
| ~ subset(X0,difference(X0,X1)) ),
inference(resolution,[status(thm)],[f266,f26]) ).
fof(f349,plain,
! [X0,X1] :
( subset(X0,difference(X0,X1))
| member(sk0_2(difference(X0,X1),X0),X1)
| subset(X0,difference(X0,X1)) ),
inference(resolution,[status(thm)],[f185,f40]) ).
fof(f350,plain,
! [X0,X1] :
( subset(X0,difference(X0,X1))
| member(sk0_2(difference(X0,X1),X0),X1) ),
inference(duplicate_literals_removal,[status(esa)],[f349]) ).
fof(f359,plain,
! [X0] : subset(X0,difference(X0,empty_set)),
inference(resolution,[status(thm)],[f350,f21]) ).
fof(f365,plain,
! [X0] : X0 = difference(X0,empty_set),
inference(resolution,[status(thm)],[f359,f278]) ).
fof(f371,plain,
sk0_4 != sk0_4,
inference(backward_demodulation,[status(thm)],[f365,f49]) ).
fof(f372,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f371]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET603+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n002.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Apr 29 21:57:39 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.33 % Drodi V3.6.0
% 0.10/0.34 % Refutation found
% 0.10/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.35 % Elapsed time: 0.023669 seconds
% 0.10/0.35 % CPU time: 0.049245 seconds
% 0.10/0.35 % Total memory used: 13.487 MB
% 0.10/0.35 % Net memory used: 13.423 MB
%------------------------------------------------------------------------------