TSTP Solution File: SET635+3 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET635+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 12:34:53 EDT 2023
% Result : Theorem 2.13s 0.69s
% Output : CNFRefutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 35 unt; 0 def)
% Number of atoms : 128 ( 38 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 121 ( 55 ~; 41 |; 19 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 125 (; 118 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [B] : union(B,empty_set) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C,D] : difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),D),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,conjecture,
! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),intersection(B,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ ! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),intersection(B,D)),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f23,plain,
! [X0] : union(X0,empty_set) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f24,plain,
! [X0,X1,X2] : difference(X0,intersection(X1,X2)) = union(difference(X0,X1),difference(X0,X2)),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f25,plain,
! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f31,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)],[f7]) ).
fof(f32,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)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f36,plain,
! [B,C] :
( ( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(NNF_transformation,[status(esa)],[f8]) ).
fof(f37,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)],[f36]) ).
fof(f40,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f41,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f42,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f43,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f44,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f45,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)],[f44]) ).
fof(f46,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)],[f45]) ).
fof(f47,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)],[f46]) ).
fof(f49,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f59,plain,
! [B] :
( ( ~ empty(B)
| ! [C] : ~ member(C,B) )
& ( empty(B)
| ? [C] : member(C,B) ) ),
inference(NNF_transformation,[status(esa)],[f15]) ).
fof(f60,plain,
( ! [B] :
( ~ empty(B)
| ! [C] : ~ member(C,B) )
& ! [B] :
( empty(B)
| ? [C] : member(C,B) ) ),
inference(miniscoping,[status(esa)],[f59]) ).
fof(f61,plain,
( ! [B] :
( ~ empty(B)
| ! [C] : ~ member(C,B) )
& ! [B] :
( empty(B)
| member(sk0_2(B),B) ) ),
inference(skolemization,[status(esa)],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ member(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f63,plain,
! [X0] :
( empty(X0)
| member(sk0_2(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f64,plain,
? [B,C,D] : intersection(B,difference(C,D)) != difference(intersection(B,C),intersection(B,D)),
inference(pre_NNF_transformation,[status(esa)],[f17]) ).
fof(f65,plain,
intersection(sk0_3,difference(sk0_4,sk0_5)) != difference(intersection(sk0_3,sk0_4),intersection(sk0_3,sk0_5)),
inference(skolemization,[status(esa)],[f64]) ).
fof(f66,plain,
intersection(sk0_3,difference(sk0_4,sk0_5)) != difference(intersection(sk0_3,sk0_4),intersection(sk0_3,sk0_5)),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f73,plain,
intersection(sk0_3,difference(sk0_4,sk0_5)) != intersection(sk0_3,difference(sk0_4,intersection(sk0_3,sk0_5))),
inference(backward_demodulation,[status(thm)],[f25,f66]) ).
fof(f74,plain,
intersection(difference(sk0_4,sk0_5),sk0_3) != intersection(sk0_3,difference(sk0_4,intersection(sk0_3,sk0_5))),
inference(forward_demodulation,[status(thm)],[f43,f73]) ).
fof(f75,plain,
intersection(difference(sk0_4,sk0_5),sk0_3) != intersection(difference(sk0_4,intersection(sk0_3,sk0_5)),sk0_3),
inference(forward_demodulation,[status(thm)],[f43,f74]) ).
fof(f76,plain,
! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X1,X0),X2),
inference(paramodulation,[status(thm)],[f43,f25]) ).
fof(f77,plain,
! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = intersection(X1,difference(X0,X2)),
inference(forward_demodulation,[status(thm)],[f25,f76]) ).
fof(f82,plain,
! [X0,X1,X2] : intersection(difference(X0,X1),X2) = intersection(X0,difference(X2,X1)),
inference(paramodulation,[status(thm)],[f43,f77]) ).
fof(f138,plain,
! [X0] : X0 = union(empty_set,X0),
inference(paramodulation,[status(thm)],[f23,f41]) ).
fof(f147,plain,
! [X0,X1] :
( empty(difference(X0,X1))
| ~ member(sk0_2(difference(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f63,f34]) ).
fof(f148,plain,
! [X0,X1] :
( empty(difference(X0,X1))
| member(sk0_2(difference(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f63,f33]) ).
fof(f171,plain,
intersection(difference(sk0_4,sk0_5),sk0_3) != intersection(sk0_3,difference(sk0_4,intersection(sk0_3,sk0_5))),
inference(paramodulation,[status(thm)],[f43,f75]) ).
fof(f172,plain,
intersection(difference(sk0_4,sk0_5),sk0_3) != intersection(difference(sk0_3,intersection(sk0_3,sk0_5)),sk0_4),
inference(forward_demodulation,[status(thm)],[f82,f171]) ).
fof(f277,plain,
! [X0] :
( empty(difference(X0,X0))
| empty(difference(X0,X0)) ),
inference(resolution,[status(thm)],[f148,f147]) ).
fof(f278,plain,
! [X0] : empty(difference(X0,X0)),
inference(duplicate_literals_removal,[status(esa)],[f277]) ).
fof(f398,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[status(thm)],[f49,f42]) ).
fof(f408,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f49,f62]) ).
fof(f409,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(resolution,[status(thm)],[f398,f40]) ).
fof(f417,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f409,f408]) ).
fof(f426,plain,
! [X0] : difference(X0,X0) = empty_set,
inference(resolution,[status(thm)],[f417,f278]) ).
fof(f471,plain,
! [X0,X1] : difference(X0,intersection(X0,X1)) = union(empty_set,difference(X0,X1)),
inference(paramodulation,[status(thm)],[f426,f24]) ).
fof(f472,plain,
! [X0,X1] : difference(X0,intersection(X0,X1)) = difference(X0,X1),
inference(forward_demodulation,[status(thm)],[f138,f471]) ).
fof(f1297,plain,
intersection(difference(sk0_4,sk0_5),sk0_3) != intersection(difference(sk0_3,sk0_5),sk0_4),
inference(backward_demodulation,[status(thm)],[f472,f172]) ).
fof(f2379,plain,
intersection(sk0_3,difference(sk0_4,sk0_5)) != intersection(difference(sk0_3,sk0_5),sk0_4),
inference(paramodulation,[status(thm)],[f43,f1297]) ).
fof(f2380,plain,
intersection(difference(sk0_3,sk0_5),sk0_4) != intersection(difference(sk0_3,sk0_5),sk0_4),
inference(forward_demodulation,[status(thm)],[f82,f2379]) ).
fof(f2381,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f2380]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SET635+3 : TPTP v8.1.2. Released v2.2.0.
% 0.05/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue May 30 10:16:42 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % Drodi V3.5.1
% 2.13/0.69 % Refutation found
% 2.13/0.69 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.13/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.13/0.72 % Elapsed time: 0.389993 seconds
% 2.13/0.72 % CPU time: 2.282022 seconds
% 2.13/0.72 % Memory used: 82.989 MB
%------------------------------------------------------------------------------