TSTP Solution File: SET626+3 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET626+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 20:40:01 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 7 unt; 0 def)
% Number of atoms : 80 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 83 ( 34 ~; 29 |; 15 &)
% ( 2 <=>; 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 : 77 ( 68 !; 9 ?)
% 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] :
( intersect(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(f4,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [B,C,D] :
( intersect(B,intersection(C,D))
=> intersect(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [B,C,D] :
( intersect(B,intersection(C,D))
=> intersect(B,C) ),
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(f11,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f13,plain,
! [B,C] :
( ( ~ intersect(B,C)
| ? [D] :
( member(D,B)
& member(D,C) ) )
& ( intersect(B,C)
| ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f14,plain,
( ! [B,C] :
( ~ intersect(B,C)
| ? [D] :
( member(D,B)
& member(D,C) ) )
& ! [B,C] :
( intersect(B,C)
| ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ) ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f15,plain,
( ! [B,C] :
( ~ intersect(B,C)
| ( member(sk0_0(C,B),B)
& member(sk0_0(C,B),C) ) )
& ! [B,C] :
( intersect(B,C)
| ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ) ),
inference(skolemization,[status(esa)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f18,plain,
! [X0,X1,X2] :
( intersect(X0,X1)
| ~ member(X2,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f19,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f20,plain,
! [B,C] :
( ~ intersect(B,C)
| intersect(C,B) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f21,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| intersect(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f29,plain,
? [B,C,D] :
( intersect(B,intersection(C,D))
& ~ intersect(B,C) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f30,plain,
? [B,C] :
( ? [D] : intersect(B,intersection(C,D))
& ~ intersect(B,C) ),
inference(miniscoping,[status(esa)],[f29]) ).
fof(f31,plain,
( intersect(sk0_2,intersection(sk0_3,sk0_4))
& ~ intersect(sk0_2,sk0_3) ),
inference(skolemization,[status(esa)],[f30]) ).
fof(f32,plain,
intersect(sk0_2,intersection(sk0_3,sk0_4)),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
~ intersect(sk0_2,sk0_3),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ intersect(X0,X1)
| intersect(X2,X0)
| ~ member(sk0_0(X1,X0),X2) ),
inference(resolution,[status(thm)],[f16,f18]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ intersect(X0,intersection(X1,X2))
| member(sk0_0(intersection(X1,X2),X0),X2) ),
inference(resolution,[status(thm)],[f17,f11]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ~ intersect(X0,intersection(X1,X2))
| ~ intersect(X0,intersection(X1,X2))
| intersect(X2,X0) ),
inference(resolution,[status(thm)],[f77,f51]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ~ intersect(X0,intersection(X1,X2))
| intersect(X2,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f126]) ).
fof(f139,plain,
! [X0,X1,X2] :
( ~ intersect(X0,intersection(X1,X2))
| intersect(X1,X0) ),
inference(paramodulation,[status(thm)],[f19,f127]) ).
fof(f160,plain,
intersect(sk0_3,sk0_2),
inference(resolution,[status(thm)],[f139,f32]) ).
fof(f165,plain,
intersect(sk0_2,sk0_3),
inference(resolution,[status(thm)],[f160,f21]) ).
fof(f166,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f165,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SET626+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.15 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.36 % Computer : n029.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Mon Apr 29 22:10:49 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % Drodi V3.6.0
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.39 % Elapsed time: 0.022289 seconds
% 0.13/0.39 % CPU time: 0.040768 seconds
% 0.13/0.39 % Total memory used: 13.071 MB
% 0.13/0.39 % Net memory used: 13.032 MB
%------------------------------------------------------------------------------