TSTP Solution File: SET666+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET666+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 0.15s 0.32s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 66 ( 10 unt; 0 def)
% Number of atoms : 240 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 294 ( 120 ~; 120 |; 22 &)
% ( 10 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 125 (; 122 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(identity_relation_of(B),cross_product(B,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,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/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,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/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,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/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ilf_type(identity_relation_of(B),identity_relation_of_type(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ilf_type(identity_relation_of(B),identity_relation_of_type(B)) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f27,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)],[f1]) ).
fof(f28,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)],[f27]) ).
fof(f33,plain,
! [B] :
( ~ ilf_type(B,set_type)
| subset(identity_relation_of(B),cross_product(B,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f34,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| subset(identity_relation_of(X0),cross_product(X0,X0)) ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f42,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f43,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ ilf_type(C,identity_relation_of_type(B))
| ilf_type(C,relation_type(B,B)) )
& ( ilf_type(C,identity_relation_of_type(B))
| ~ ilf_type(C,relation_type(B,B)) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f42]) ).
fof(f45,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,relation_type(X0,X0)) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f60,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)],[f12]) ).
fof(f61,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)],[f60]) ).
fof(f63,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)],[f61]) ).
fof(f67,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( subset(B,C)
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f68,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ subset(B,C)
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( subset(B,C)
| ? [D] :
( ilf_type(D,set_type)
& member(D,B)
& ~ member(D,C) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f67]) ).
fof(f69,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ subset(B,C)
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( subset(B,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)],[f68]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f76,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)],[f16]) ).
fof(f77,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)],[f76]) ).
fof(f78,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_5(C,B),set_type)
& member(sk0_5(C,B),B)
& ~ member(sk0_5(C,B),C) ) ) ) ) ),
inference(skolemization,[status(esa)],[f77]) ).
fof(f81,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1))
| member(sk0_5(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f78]) ).
fof(f82,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1))
| ~ member(sk0_5(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f78]) ).
fof(f83,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(pre_NNF_transformation,[status(esa)],[f17]) ).
fof(f84,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[status(esa)],[f83]) ).
fof(f86,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)],[f18]) ).
fof(f87,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)],[f86]) ).
fof(f89,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)],[f87]) ).
fof(f112,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f113,plain,
? [B] :
( ilf_type(B,set_type)
& ~ ilf_type(identity_relation_of(B),identity_relation_of_type(B)) ),
inference(pre_NNF_transformation,[status(esa)],[f26]) ).
fof(f114,plain,
( ilf_type(sk0_11,set_type)
& ~ ilf_type(identity_relation_of(sk0_11),identity_relation_of_type(sk0_11)) ),
inference(skolemization,[status(esa)],[f113]) ).
fof(f116,plain,
~ ilf_type(identity_relation_of(sk0_11),identity_relation_of_type(sk0_11)),
inference(cnf_transformation,[status(esa)],[f114]) ).
fof(f123,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ilf_type(X0,identity_relation_of_type(X1))
| ~ ilf_type(X0,relation_type(X1,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f45,f112]) ).
fof(f126,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f84,f112]) ).
fof(f133,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)],[f28,f112]) ).
fof(f146,plain,
! [X0] : subset(identity_relation_of(X0),cross_product(X0,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f34,f112]) ).
fof(f173,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| member(X1,power_set(X0))
| member(sk0_5(X0,X1),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f81,f112]) ).
fof(f174,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| member(X1,power_set(X0))
| ~ member(sk0_5(X0,X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f82,f112]) ).
fof(f175,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sk0_5(X1,X0),X1) ),
inference(resolution,[status(thm)],[f174,f112]) ).
fof(f190,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)],[f89,f112]) ).
fof(f191,plain,
! [X0,X1] :
( empty(X0)
| ilf_type(X1,member_type(X0))
| ~ member(X1,X0) ),
inference(resolution,[status(thm)],[f190,f112]) ).
fof(f192,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)],[f63,f112]) ).
fof(f193,plain,
! [X0,X1] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(resolution,[status(thm)],[f192,f112]) ).
fof(f196,plain,
! [X0,X1] :
( ilf_type(X0,subset_type(X1))
| empty(power_set(X1))
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f193,f191]) ).
fof(f197,plain,
! [X0,X1] :
( ilf_type(X0,subset_type(X1))
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f126]) ).
fof(f258,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ subset(X1,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| member(X2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f70,f112]) ).
fof(f259,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ subset(X1,X0)
| ~ member(X2,X1)
| member(X2,X0) ),
inference(resolution,[status(thm)],[f258,f112]) ).
fof(f260,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f112]) ).
fof(f261,plain,
! [X0,X1] :
( ~ member(X0,identity_relation_of(X1))
| member(X0,cross_product(X1,X1)) ),
inference(resolution,[status(thm)],[f260,f146]) ).
fof(f262,plain,
! [X0,X1] :
( ~ member(sk0_5(cross_product(X0,X0),X1),identity_relation_of(X0))
| member(X1,power_set(cross_product(X0,X0))) ),
inference(resolution,[status(thm)],[f261,f175]) ).
fof(f266,plain,
! [X0] :
( member(identity_relation_of(X0),power_set(cross_product(X0,X0)))
| ~ ilf_type(cross_product(X0,X0),set_type)
| member(identity_relation_of(X0),power_set(cross_product(X0,X0))) ),
inference(resolution,[status(thm)],[f262,f173]) ).
fof(f267,plain,
! [X0] :
( member(identity_relation_of(X0),power_set(cross_product(X0,X0)))
| ~ ilf_type(cross_product(X0,X0),set_type) ),
inference(duplicate_literals_removal,[status(esa)],[f266]) ).
fof(f268,plain,
! [X0] : member(identity_relation_of(X0),power_set(cross_product(X0,X0))),
inference(forward_subsumption_resolution,[status(thm)],[f267,f112]) ).
fof(f269,plain,
! [X0] : ilf_type(identity_relation_of(X0),subset_type(cross_product(X0,X0))),
inference(resolution,[status(thm)],[f268,f197]) ).
fof(f271,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ilf_type(identity_relation_of(X0),relation_type(X0,X0)) ),
inference(resolution,[status(thm)],[f269,f133]) ).
fof(f272,plain,
! [X0] : ilf_type(identity_relation_of(X0),relation_type(X0,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f271,f112]) ).
fof(f274,plain,
! [X0] :
( ~ ilf_type(identity_relation_of(X0),set_type)
| ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)) ),
inference(resolution,[status(thm)],[f272,f123]) ).
fof(f275,plain,
! [X0] : ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f274,f112]) ).
fof(f276,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f116,f275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SET666+3 : TPTP v8.1.2. Released v2.2.0.
% 0.05/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n017.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 09:44:25 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.15/0.31 % 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
% 0.16/0.54 % Elapsed time: 0.013748 seconds
% 0.16/0.54 % CPU time: 0.017104 seconds
% 0.16/0.54 % Memory used: 3.059 MB
%------------------------------------------------------------------------------