%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET666+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:10:24 PM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 9 unt; 0 def)
% Number of atoms : 263 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 332 ( 138 ~; 135 |; 24 &)
% ( 12 <=>; 23 =>; 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 : 12 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 136 ( 132 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) )
& ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(identity_relation_of(B),cross_product(B,B)) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,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(f24,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/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/sandbox2/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] :
( ! [C] :
( ( ! [E] :
( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ! [D] :
( ilf_type(D,relation_type(B,C))
| ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f33,plain,
! [B] :
( subset(identity_relation_of(B),cross_product(B,B))
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f34,plain,
! [X0] :
( subset(identity_relation_of(X0),cross_product(X0,X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f42,plain,
! [B] :
( ! [C] :
( ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f43,plain,
! [B] :
( ! [C] :
( ( ( ~ ilf_type(C,relation_type(B,B))
| 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,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
! [X0,X1] :
( ~ ilf_type(X1,relation_type(X0,X0))
| ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f60,plain,
! [B] :
( ! [C] :
( ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f61,plain,
! [B] :
( ! [C] :
( ( ( ~ ilf_type(C,member_type(power_set(B)))
| ilf_type(C,subset_type(B)) )
& ( ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,subset_type(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f60]) ).
fof(f63,plain,
! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f67,plain,
! [B] :
( ! [C] :
( ( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f68,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK4_skl(C,B),C)
& member(sK4_skl(C,B),B)
& ilf_type(sK4_skl(C,B),set_type) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(D,sK4_skl(C,B))],[f68]) ).
fof(f70,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f76,plain,
! [B] :
( ! [C] :
( ( member(B,power_set(C))
<=> ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f77,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| member(B,power_set(C)) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK5_skl(C,B),C)
& member(sK5_skl(C,B),B)
& ilf_type(sK5_skl(C,B),set_type) )
| member(B,power_set(C)) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(D,sK5_skl(C,B))],[f77]) ).
fof(f81,plain,
! [X0,X1] :
( member(sK5_skl(X1,X0),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f82,plain,
! [X0,X1] :
( ~ member(sK5_skl(X1,X0),X1)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f86,plain,
! [B] :
( ! [C] :
( ( ilf_type(B,member_type(C))
<=> member(B,C) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f87,plain,
! [B] :
( ! [C] :
( ( ( ~ member(B,C)
| ilf_type(B,member_type(C)) )
& ( member(B,C)
| ~ ilf_type(B,member_type(C)) ) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f86]) ).
fof(f89,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f104,plain,
! [B] :
( ( empty(B)
<=> ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) ) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f105,plain,
! [B] :
( ( ( ? [C] :
( member(C,B)
& ilf_type(C,set_type) )
| empty(B) )
& ( ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f104]) ).
fof(f106,plain,
! [B] :
( ( ( ( member(sK10_skl(B),B)
& ilf_type(sK10_skl(B),set_type) )
| empty(B) )
& ( ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(C,sK10_skl(B))],[f105]) ).
fof(f107,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f112,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f113,plain,
? [B] :
( ~ ilf_type(identity_relation_of(B),identity_relation_of_type(B))
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f114,plain,
( ~ ilf_type(identity_relation_of(sK11_skl),identity_relation_of_type(sK11_skl))
& ilf_type(sK11_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(B,sK11_skl)],[f113]) ).
fof(f116,plain,
~ ilf_type(identity_relation_of(sK11_skl),identity_relation_of_type(sK11_skl)),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f122,plain,
! [X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X1))
| ilf_type(X0,identity_relation_of_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f45,f112]) ).
fof(f138,plain,
! [X0,X1,X2] :
( ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X0,set_type) ),
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(f150,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f107,f112]) ).
fof(f168,plain,
! [X0,X1] :
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f63,f112]) ).
fof(f172,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f70,f112]) ).
fof(f176,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f172,f112]) ).
fof(f182,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f112]) ).
fof(f187,plain,
! [X0,X1] :
( member(X0,cross_product(X1,X1))
| ~ member(X0,identity_relation_of(X1)) ),
inference(resolution,[status(thm)],[f182,f146]) ).
fof(f267,plain,
! [X0,X1] :
( member(sK5_skl(X0,X1),X1)
| member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f81,f112]) ).
fof(f268,plain,
! [X0,X1] :
( ~ member(sK5_skl(X0,X1),X0)
| member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f82,f112]) ).
fof(f271,plain,
! [X0,X1] :
( ~ member(sK5_skl(cross_product(X0,X0),X1),identity_relation_of(X0))
| member(X1,power_set(cross_product(X0,X0)))
| ~ ilf_type(cross_product(X0,X0),set_type) ),
inference(resolution,[status(thm)],[f268,f187]) ).
fof(f275,plain,
! [X0,X1] :
( ~ member(sK5_skl(cross_product(X1,X1),X0),identity_relation_of(X1))
| member(X0,power_set(cross_product(X1,X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f271,f112]) ).
fof(f276,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)],[f275,f267]) ).
fof(f277,plain,
! [X0] :
( ~ ilf_type(cross_product(X0,X0),set_type)
| member(identity_relation_of(X0),power_set(cross_product(X0,X0))) ),
inference(duplicate_literals_removal,[status(thm)],[f276]) ).
fof(f278,plain,
! [X0] : member(identity_relation_of(X0),power_set(cross_product(X0,X0))),
inference(forward_subsumption_resolution,[status(thm)],[f277,f112]) ).
fof(f633,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f112]) ).
fof(f972,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f150,f112]) ).
fof(f975,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f633,f972]) ).
fof(f987,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f975,f112]) ).
fof(f1024,plain,
! [X0,X1] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f987,f168]) ).
fof(f1026,plain,
! [X0,X1] :
( ilf_type(X0,subset_type(X1))
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1024,f112]) ).
fof(f1049,plain,
! [X0] : ilf_type(identity_relation_of(X0),subset_type(cross_product(X0,X0))),
inference(resolution,[status(thm)],[f1026,f278]) ).
fof(f1111,plain,
! [X0] :
( ilf_type(identity_relation_of(X0),relation_type(X0,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f1049,f138]) ).
fof(f1113,plain,
! [X0] : ilf_type(identity_relation_of(X0),relation_type(X0,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f1111,f112]) ).
fof(f1115,plain,
! [X0] :
( ilf_type(identity_relation_of(X0),identity_relation_of_type(X0))
| ~ ilf_type(identity_relation_of(X0),set_type) ),
inference(resolution,[status(thm)],[f1113,f122]) ).
fof(f1116,plain,
! [X0] : ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f1115,f112]) ).
fof(f1118,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f116,f1116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET666+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:36:38 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.061746 seconds
% 0.14/0.43 % CPU time: 0.227634 seconds
% 0.14/0.43 % Total memory used: 84.508 MB
% 0.14/0.43 % Net memory used: 84.096 MB
%------------------------------------------------------------------------------