%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET643+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 : n006.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 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 49 ( 20 ~; 16 |; 4 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(B,B) ),
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)
=> ilf_type(cross_product(B,C),relation_type(B,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(cross_product(B,C),relation_type(B,C)) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,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)],[f1]) ).
fof(f23,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)],[f22]) ).
fof(f57,plain,
! [B] :
( subset(B,B)
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f58,plain,
! [X0] :
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f95,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f96,plain,
? [B] :
( ? [C] :
( ~ ilf_type(cross_product(B,C),relation_type(B,C))
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f97,plain,
( ~ ilf_type(cross_product(sK11_skl,sK12_skl),relation_type(sK11_skl,sK12_skl))
& ilf_type(sK12_skl,set_type)
& ilf_type(sK11_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl]),skolemize(B,sK11_skl),skolemize(C,sK12_skl)],[f96]) ).
fof(f100,plain,
~ ilf_type(cross_product(sK11_skl,sK12_skl),relation_type(sK11_skl,sK12_skl)),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f103,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)],[f23,f95]) ).
fof(f106,plain,
! [X0] : subset(X0,X0),
inference(forward_subsumption_resolution,[status(thm)],[f58,f95]) ).
fof(f107,plain,
! [X0,X1] :
( ilf_type(cross_product(X0,X1),relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f106,f103]) ).
fof(f108,plain,
! [X0,X1] :
( ilf_type(cross_product(X1,X0),relation_type(X1,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f107,f95]) ).
fof(f110,plain,
! [X0,X1] : ilf_type(cross_product(X0,X1),relation_type(X0,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f108,f95]) ).
fof(f111,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f100,f110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET643+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:30:58 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.052498 seconds
% 0.09/0.42 % CPU time: 0.146123 seconds
% 0.09/0.42 % Total memory used: 81.641 MB
% 0.09/0.42 % Net memory used: 81.508 MB
%------------------------------------------------------------------------------