%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET662+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 : n017.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 02:10:23 PM UTC 2026
% Result : Theorem 0.14s 5.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 9 unt; 0 def)
% Number of atoms : 174 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 212 ( 86 ~; 80 |; 19 &)
% ( 8 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 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 : 92 ( 88 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,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(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] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ( 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] :
( ! [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)],[f2]) ).
fof(f27,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)],[f26]) ).
fof(f32,plain,
! [B] :
( ~ member(B,empty_set)
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f33,plain,
! [X0] :
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f38,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(f39,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)],[f38]) ).
fof(f41,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)],[f39]) ).
fof(f54,plain,
! [B] :
( ( empty(B)
<=> ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) ) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f55,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)],[f54]) ).
fof(f56,plain,
! [B] :
( ( ( ( member(sK3_skl(B),B)
& ilf_type(sK3_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,[sK3_skl]),skolemize(C,sK3_skl(B))],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f60,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)],[f13]) ).
fof(f61,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)],[f60]) ).
fof(f62,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK4_skl(C,B),C)
& member(sK4_skl(C,B),B)
& ilf_type(sK4_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,[sK4_skl]),skolemize(D,sK4_skl(C,B))],[f61]) ).
fof(f65,plain,
! [X0,X1] :
( member(sK4_skl(X1,X0),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f70,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)],[f15]) ).
fof(f71,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)],[f70]) ).
fof(f73,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)],[f71]) ).
fof(f92,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f93,plain,
? [B] :
( ? [C] :
( ~ ilf_type(empty_set,relation_type(B,C))
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f94,plain,
( ~ ilf_type(empty_set,relation_type(sK9_skl,sK10_skl))
& ilf_type(sK10_skl,set_type)
& ilf_type(sK9_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(B,sK9_skl),skolemize(C,sK10_skl)],[f93]) ).
fof(f97,plain,
~ ilf_type(empty_set,relation_type(sK9_skl,sK10_skl)),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f98,plain,
! [X0] : ~ member(X0,empty_set),
inference(forward_subsumption_resolution,[status(thm)],[f33,f92]) ).
fof(f101,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)],[f27,f92]) ).
fof(f121,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f57,f92]) ).
fof(f122,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f121,f92]) ).
fof(f143,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)],[f41,f92]) ).
fof(f162,plain,
! [X0,X1] :
( member(sK4_skl(X0,X1),X1)
| member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f65,f92]) ).
fof(f163,plain,
! [X0,X1] :
( member(sK4_skl(X1,X0),X0)
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f162,f92]) ).
fof(f164,plain,
! [X0] : member(empty_set,power_set(X0)),
inference(resolution,[status(thm)],[f163,f98]) ).
fof(f191,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)],[f73,f92]) ).
fof(f192,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[f191,f92]) ).
fof(f193,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f122]) ).
fof(f198,plain,
! [X0] : ilf_type(empty_set,member_type(power_set(X0))),
inference(resolution,[status(thm)],[f193,f164]) ).
fof(f215,plain,
! [X0] :
( ilf_type(empty_set,subset_type(X0))
| ~ ilf_type(empty_set,set_type) ),
inference(resolution,[status(thm)],[f198,f143]) ).
fof(f217,plain,
! [X0] : ilf_type(empty_set,subset_type(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f215,f92]) ).
fof(f219,plain,
! [X0,X1] :
( ilf_type(empty_set,relation_type(X1,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f217,f101]) ).
fof(f221,plain,
! [X0,X1] : ilf_type(empty_set,relation_type(X0,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f219,f92]) ).
fof(f223,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f97,f221]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET662+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.41 % Computer : n017.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.41 % DateTime : Mon Sep 21 05:27:17 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.43 % Drodi V4.1.1
% 0.14/5.48 % Refutation found
% 0.14/5.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/5.52 % Elapsed time: 0.094185 seconds
% 0.19/5.52 % CPU time: 0.268677 seconds
% 0.19/5.52 % Total memory used: 52.907 MB
% 0.19/5.52 % Net memory used: 52.697 MB
%------------------------------------------------------------------------------