%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET642+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 : n018.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 02:10:20 PM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 8 unt; 0 def)
% Number of atoms : 88 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 101 ( 38 ~; 34 |; 10 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 41 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [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/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( subset(B,cross_product(C,D))
=> ilf_type(B,relation_type(C,D)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/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)
=> ilf_type(B,relation_type(C,D)) ) ) ) ) ),
file('/export/starexec/sandbox2/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)
=> ilf_type(B,relation_type(C,D)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,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)],[f1]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( subset(X0,cross_product(X1,X2))
| ~ subset(X0,X3)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [B] :
( ! [C] :
( ! [D] :
( ilf_type(B,relation_type(C,D))
| ~ subset(B,cross_product(C,D))
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ilf_type(X0,relation_type(X1,X2))
| ~ subset(X0,cross_product(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f88,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f89,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ~ ilf_type(B,relation_type(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(f90,plain,
( ~ ilf_type(sK9_skl,relation_type(sK10_skl,sK11_skl))
& subset(sK9_skl,sK12_skl)
& ilf_type(sK12_skl,relation_type(sK10_skl,sK11_skl))
& ilf_type(sK11_skl,set_type)
& ilf_type(sK10_skl,set_type)
& ilf_type(sK9_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl,sK12_skl]),skolemize(B,sK9_skl),skolemize(C,sK10_skl),skolemize(D,sK11_skl),skolemize(E,sK12_skl)],[f89]) ).
fof(f94,plain,
ilf_type(sK12_skl,relation_type(sK10_skl,sK11_skl)),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f95,plain,
subset(sK9_skl,sK12_skl),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f96,plain,
~ ilf_type(sK9_skl,relation_type(sK10_skl,sK11_skl)),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f106,plain,
! [X0,X1,X2,X3] :
( subset(X3,cross_product(X0,X1))
| ~ subset(X3,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f23,f88]) ).
fof(f107,plain,
! [X0] :
( subset(X0,cross_product(sK10_skl,sK11_skl))
| ~ subset(X0,sK12_skl)
| ~ ilf_type(sK11_skl,set_type)
| ~ ilf_type(sK10_skl,set_type) ),
inference(resolution,[status(thm)],[f106,f94]) ).
fof(f108,plain,
! [X0] :
( subset(X0,cross_product(sK10_skl,sK11_skl))
| ~ subset(X0,sK12_skl)
| ~ ilf_type(sK11_skl,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f107,f88]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ilf_type(X2,relation_type(X0,X1))
| ~ subset(X2,cross_product(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f25,f88]) ).
fof(f120,plain,
! [X0] :
( subset(X0,cross_product(sK10_skl,sK11_skl))
| ~ subset(X0,sK12_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f88]) ).
fof(f121,plain,
subset(sK9_skl,cross_product(sK10_skl,sK11_skl)),
inference(resolution,[status(thm)],[f120,f95]) ).
fof(f127,plain,
( ilf_type(sK9_skl,relation_type(sK10_skl,sK11_skl))
| ~ ilf_type(sK11_skl,set_type)
| ~ ilf_type(sK10_skl,set_type) ),
inference(resolution,[status(thm)],[f121,f109]) ).
fof(f129,plain,
( ilf_type(sK9_skl,relation_type(sK10_skl,sK11_skl))
| ~ ilf_type(sK11_skl,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f127,f88]) ).
fof(f164,plain,
ilf_type(sK9_skl,relation_type(sK10_skl,sK11_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f129,f88]) ).
fof(f165,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f96,f164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET642+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 : n018.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 05:33:13 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.42 % Elapsed time: 0.048301 seconds
% 0.10/0.42 % CPU time: 0.137839 seconds
% 0.10/0.42 % Total memory used: 81.427 MB
% 0.10/0.42 % Net memory used: 81.262 MB
%------------------------------------------------------------------------------