TSTP Solution File: SET662+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET662+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n005.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 12:34:58 EDT 2023
% Result : Theorem 0.16s 0.34s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 9 unt; 0 def)
% Number of atoms : 189 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 235 ( 99 ~; 90 |; 19 &)
% ( 8 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 103 (; 99 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ~ member(B,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(empty_set,relation_type(B,C)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(empty_set,relation_type(B,C)) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f26,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f32,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ member(B,empty_set) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f33,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ member(X0,empty_set) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f38,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f39,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) )
& ( ilf_type(C,subset_type(B))
| ~ ilf_type(C,member_type(power_set(B))) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,subset_type(X0))
| ilf_type(X1,member_type(power_set(X0))) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f54,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( empty(B)
<=> ! [C] :
( ~ ilf_type(C,set_type)
| ~ member(C,B) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f55,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ( ~ empty(B)
| ! [C] :
( ~ ilf_type(C,set_type)
| ~ member(C,B) ) )
& ( empty(B)
| ? [C] :
( ilf_type(C,set_type)
& member(C,B) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f54]) ).
fof(f56,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ( ~ empty(B)
| ! [C] :
( ~ ilf_type(C,set_type)
| ~ member(C,B) ) )
& ( empty(B)
| ( ilf_type(sk0_3(B),set_type)
& member(sk0_3(B),B) ) ) ) ),
inference(skolemization,[status(esa)],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f60,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( member(B,power_set(C))
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f61,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ member(B,power_set(C))
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( member(B,power_set(C))
| ? [D] :
( ilf_type(D,set_type)
& member(D,B)
& ~ member(D,C) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f60]) ).
fof(f62,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ member(B,power_set(C))
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( member(B,power_set(C))
| ( ilf_type(sk0_4(C,B),set_type)
& member(sk0_4(C,B),B)
& ~ member(sk0_4(C,B),C) ) ) ) ) ),
inference(skolemization,[status(esa)],[f61]) ).
fof(f65,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1))
| member(sk0_4(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f70,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( empty(C)
| ~ ilf_type(C,set_type)
| ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f71,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( empty(C)
| ~ ilf_type(C,set_type)
| ( ( ~ ilf_type(B,member_type(C))
| member(B,C) )
& ( ilf_type(B,member_type(C))
| ~ member(B,C) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f70]) ).
fof(f73,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| empty(X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f71]) ).
fof(f92,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f93,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ~ ilf_type(empty_set,relation_type(B,C)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f23]) ).
fof(f94,plain,
( ilf_type(sk0_9,set_type)
& ilf_type(sk0_10,set_type)
& ~ ilf_type(empty_set,relation_type(sk0_9,sk0_10)) ),
inference(skolemization,[status(esa)],[f93]) ).
fof(f97,plain,
~ ilf_type(empty_set,relation_type(sk0_9,sk0_10)),
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f99,plain,
! [X0] : ~ member(X0,empty_set),
inference(forward_subsumption_resolution,[status(thm)],[f33,f92]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ilf_type(X1,relation_type(X2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f27,f92]) ).
fof(f120,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f57,f92]) ).
fof(f121,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ member(X1,X0) ),
inference(resolution,[status(thm)],[f120,f92]) ).
fof(f126,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f40,f92]) ).
fof(f127,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f41,f92]) ).
fof(f128,plain,
! [X0,X1] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(resolution,[status(thm)],[f127,f92]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,member_type(power_set(cross_product(X1,X2))))
| ~ ilf_type(X2,set_type)
| ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f128,f100]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,member_type(power_set(cross_product(X1,X2))))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f129,f92]) ).
fof(f133,plain,
! [X0,X1,X2] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f130,f126]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f92]) ).
fof(f135,plain,
~ ilf_type(empty_set,subset_type(cross_product(sk0_9,sk0_10))),
inference(resolution,[status(thm)],[f134,f97]) ).
fof(f136,plain,
~ ilf_type(empty_set,member_type(power_set(cross_product(sk0_9,sk0_10)))),
inference(resolution,[status(thm)],[f135,f128]) ).
fof(f149,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| member(X1,power_set(X0))
| member(sk0_4(X0,X1),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f65,f92]) ).
fof(f150,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sk0_4(X1,X0),X0) ),
inference(resolution,[status(thm)],[f149,f92]) ).
fof(f151,plain,
! [X0] : member(empty_set,power_set(X0)),
inference(resolution,[status(thm)],[f150,f99]) ).
fof(f183,plain,
! [X0,X1] :
( empty(X0)
| ~ ilf_type(X0,set_type)
| ilf_type(X1,member_type(X0))
| ~ member(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f73,f92]) ).
fof(f184,plain,
! [X0,X1] :
( empty(X0)
| ilf_type(X1,member_type(X0))
| ~ member(X1,X0) ),
inference(resolution,[status(thm)],[f183,f92]) ).
fof(f185,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f121]) ).
fof(f187,plain,
~ member(empty_set,power_set(cross_product(sk0_9,sk0_10))),
inference(resolution,[status(thm)],[f185,f136]) ).
fof(f188,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f187,f151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET662+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n005.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue May 30 10:12:06 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.32 % Drodi V3.5.1
% 0.16/0.34 % Refutation found
% 0.16/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.39 % Elapsed time: 0.079958 seconds
% 0.16/0.39 % CPU time: 0.047200 seconds
% 0.16/0.39 % Memory used: 4.547 MB
%------------------------------------------------------------------------------