TSTP Solution File: SET586+3 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET586+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n012.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 12:34:43 EDT 2023
% Result : Theorem 0.15s 0.32s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 8 unt; 0 def)
% Number of atoms : 89 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 87 ( 33 ~; 34 |; 14 &)
% ( 3 <=>; 3 =>; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 85 (; 77 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [B,C,D] :
( subset(B,C)
=> subset(intersection(B,D),intersection(C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [B,C,D] :
( subset(B,C)
=> subset(intersection(B,D),intersection(C,D)) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,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)],[f1]) ).
fof(f9,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)],[f8]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f12,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f13,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f14,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)],[f13]) ).
fof(f15,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)],[f14]) ).
fof(f16,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)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f20,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f29,plain,
? [B,C,D] :
( subset(B,C)
& ~ subset(intersection(B,D),intersection(C,D)) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f30,plain,
? [B,C] :
( subset(B,C)
& ? [D] : ~ subset(intersection(B,D),intersection(C,D)) ),
inference(miniscoping,[status(esa)],[f29]) ).
fof(f31,plain,
( subset(sk0_2,sk0_3)
& ~ subset(intersection(sk0_2,sk0_4),intersection(sk0_3,sk0_4)) ),
inference(skolemization,[status(esa)],[f30]) ).
fof(f32,plain,
subset(sk0_2,sk0_3),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
~ subset(intersection(sk0_2,sk0_4),intersection(sk0_3,sk0_4)),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f38,plain,
! [X0] :
( ~ member(X0,sk0_2)
| member(X0,sk0_3) ),
inference(resolution,[status(thm)],[f17,f32]) ).
fof(f42,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),X2)
| member(sk0_0(X2,intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f18,f11]) ).
fof(f43,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),X2)
| member(sk0_0(X2,intersection(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f18,f10]) ).
fof(f44,plain,
! [X0,X1] :
( subset(intersection(X0,sk0_2),X1)
| member(sk0_0(X1,intersection(X0,sk0_2)),sk0_3) ),
inference(resolution,[status(thm)],[f42,f38]) ).
fof(f84,plain,
! [X0,X1,X2] :
( subset(X0,intersection(X1,X2))
| ~ member(sk0_0(intersection(X1,X2),X0),X1)
| ~ member(sk0_0(intersection(X1,X2),X0),X2) ),
inference(resolution,[status(thm)],[f19,f12]) ).
fof(f123,plain,
! [X0,X1] :
( subset(intersection(X0,sk0_2),intersection(X1,sk0_3))
| ~ member(sk0_0(intersection(X1,sk0_3),intersection(X0,sk0_2)),X1)
| subset(intersection(X0,sk0_2),intersection(X1,sk0_3)) ),
inference(resolution,[status(thm)],[f84,f44]) ).
fof(f124,plain,
! [X0,X1] :
( subset(intersection(X0,sk0_2),intersection(X1,sk0_3))
| ~ member(sk0_0(intersection(X1,sk0_3),intersection(X0,sk0_2)),X1) ),
inference(duplicate_literals_removal,[status(esa)],[f123]) ).
fof(f345,plain,
! [X0] :
( subset(intersection(X0,sk0_2),intersection(X0,sk0_3))
| subset(intersection(X0,sk0_2),intersection(X0,sk0_3)) ),
inference(resolution,[status(thm)],[f124,f43]) ).
fof(f346,plain,
! [X0] : subset(intersection(X0,sk0_2),intersection(X0,sk0_3)),
inference(duplicate_literals_removal,[status(esa)],[f345]) ).
fof(f384,plain,
! [X0] : subset(intersection(sk0_2,X0),intersection(X0,sk0_3)),
inference(paramodulation,[status(thm)],[f20,f346]) ).
fof(f415,plain,
! [X0] : subset(intersection(sk0_2,X0),intersection(sk0_3,X0)),
inference(paramodulation,[status(thm)],[f20,f384]) ).
fof(f422,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f33,f415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET586+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n012.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue May 30 10:17:10 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.10/0.31 % Drodi V3.5.1
% 0.15/0.32 % Refutation found
% 0.15/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.54 % Elapsed time: 0.019064 seconds
% 0.15/0.54 % CPU time: 0.027353 seconds
% 0.15/0.54 % Memory used: 3.949 MB
%------------------------------------------------------------------------------