%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET640+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 02:10:19 PM UTC 2026
% Result : Theorem 0.03s 0.45s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 63 ( 9 unt; 0 def)
% Number of atoms : 256 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 318 ( 125 ~; 129 |; 29 &)
% ( 8 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 141 ( 135 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,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/sandbox/benchmark/theBenchmark.p') ).
fof(f6,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(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/sandbox/benchmark/theBenchmark.p') ).
fof(f11,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(f12,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,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/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(C,D))
=> ( subset(B,E)
=> subset(B,cross_product(C,D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(C,D))
=> ( subset(B,E)
=> subset(B,cross_product(C,D)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f35,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)],[f4]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f41,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)],[f6]) ).
fof(f42,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)],[f41]) ).
fof(f43,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK3_skl(C,B),C)
& member(sK3_skl(C,B),B)
& ilf_type(sK3_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,[sK3_skl]),skolemize(D,sK3_skl(C,B))],[f42]) ).
fof(f44,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)],[f43]) ).
fof(f46,plain,
! [X0,X1] :
( member(sK3_skl(X1,X0),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f47,plain,
! [X0,X1] :
( ~ member(sK3_skl(X1,X0),X1)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f50,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)],[f8]) ).
fof(f51,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)],[f50]) ).
fof(f52,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)],[f51]) ).
fof(f59,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)],[f11]) ).
fof(f60,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)],[f59]) ).
fof(f61,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))],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f66,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f67,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f69,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)],[f13]) ).
fof(f70,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)],[f69]) ).
fof(f71,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)],[f70]) ).
fof(f95,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f96,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ~ subset(B,cross_product(C,D))
& subset(B,E)
& ilf_type(E,relation_type(C,D)) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f97,plain,
( ~ subset(sK11_skl,cross_product(sK12_skl,sK13_skl))
& subset(sK11_skl,sK14_skl)
& ilf_type(sK14_skl,relation_type(sK12_skl,sK13_skl))
& ilf_type(sK13_skl,set_type)
& ilf_type(sK12_skl,set_type)
& ilf_type(sK11_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl,sK14_skl]),skolemize(B,sK11_skl),skolemize(C,sK12_skl),skolemize(D,sK13_skl),skolemize(E,sK14_skl)],[f96]) ).
fof(f101,plain,
ilf_type(sK14_skl,relation_type(sK12_skl,sK13_skl)),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f102,plain,
subset(sK11_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f103,plain,
~ subset(sK11_skl,cross_product(sK12_skl,sK13_skl)),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f37,f95]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f107,f95]) ).
fof(f113,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)],[f44,f95]) ).
fof(f115,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f67,f95]) ).
fof(f171,plain,
! [X0,X1] :
( member(sK3_skl(X0,X1),X1)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f46,f95]) ).
fof(f172,plain,
! [X0,X1] :
( member(sK3_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f171,f95]) ).
fof(f173,plain,
! [X0,X1,X2] :
( member(sK3_skl(X1,X0),X2)
| ~ ilf_type(sK3_skl(X1,X0),set_type)
| ~ subset(X0,X2)
| ~ ilf_type(X2,set_type)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f172,f113]) ).
fof(f174,plain,
! [X0,X1,X2] :
( member(sK3_skl(X1,X0),X2)
| ~ ilf_type(sK3_skl(X1,X0),set_type)
| ~ subset(X0,X2)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f95]) ).
fof(f175,plain,
! [X0,X1] :
( ~ member(sK3_skl(X0,X1),X0)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f47,f95]) ).
fof(f176,plain,
! [X0,X1] :
( ~ member(sK3_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f175,f95]) ).
fof(f234,plain,
! [X0,X1,X2] :
( member(sK3_skl(X1,X0),X2)
| ~ subset(X0,X2)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f174,f95]) ).
fof(f249,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)],[f71,f95]) ).
fof(f250,plain,
! [X0,X1] :
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[f249,f95]) ).
fof(f263,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)],[f52,f95]) ).
fof(f264,plain,
! [X0,X1] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[f263,f95]) ).
fof(f265,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| empty(power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[f264,f250]) ).
fof(f266,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f265,f115]) ).
fof(f268,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| member(X0,power_set(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f266,f108]) ).
fof(f273,plain,
member(sK14_skl,power_set(cross_product(sK12_skl,sK13_skl))),
inference(resolution,[status(thm)],[f268,f101]) ).
fof(f277,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f62,f95]) ).
fof(f278,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f277,f95]) ).
fof(f279,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f95]) ).
fof(f303,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ member(sK3_skl(X1,X2),X0)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f279,f176]) ).
fof(f310,plain,
! [X0,X1,X2] :
( ~ subset(X2,X0)
| subset(X2,X1)
| subset(X2,X1)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f303,f234]) ).
fof(f315,plain,
! [X0,X1,X2] :
( ~ subset(X2,X0)
| subset(X2,X1)
| ~ member(X0,power_set(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f310]) ).
fof(f346,plain,
! [X0] :
( subset(sK11_skl,X0)
| ~ member(sK14_skl,power_set(X0)) ),
inference(resolution,[status(thm)],[f315,f102]) ).
fof(f350,plain,
subset(sK11_skl,cross_product(sK12_skl,sK13_skl)),
inference(resolution,[status(thm)],[f346,f273]) ).
fof(f354,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f350,f103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET640+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:33:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.03/0.38 % Drodi V4.1.1
% 0.03/0.45 % Refutation found
% 0.03/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.03/0.47 % Elapsed time: 0.092870 seconds
% 0.03/0.47 % CPU time: 0.502899 seconds
% 0.03/0.47 % Total memory used: 89.963 MB
% 0.03/0.47 % Net memory used: 88.789 MB
%------------------------------------------------------------------------------