%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET676+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 : n008.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 02:10:25 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 53 ( 23 ~; 19 |; 3 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 25 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [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(f4,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/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)
=> ilf_type(cross_product(B,B),identity_relation_of_type(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ilf_type(cross_product(B,B),identity_relation_of_type(B)) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,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)],[f1]) ).
fof(f23,plain,
! [X0,X1] :
( ilf_type(cross_product(X0,X1),relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f35,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)],[f4]) ).
fof(f36,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)],[f35]) ).
fof(f38,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)],[f36]) ).
fof(f93,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f94,plain,
? [B] :
( ~ ilf_type(cross_product(B,B),identity_relation_of_type(B))
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f95,plain,
( ~ ilf_type(cross_product(sK11_skl,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)],[f94]) ).
fof(f97,plain,
~ ilf_type(cross_product(sK11_skl,sK11_skl),identity_relation_of_type(sK11_skl)),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f100,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)],[f38,f93]) ).
fof(f107,plain,
! [X0,X1] :
( ilf_type(cross_product(X1,X0),relation_type(X1,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f23,f93]) ).
fof(f108,plain,
! [X0] :
( ilf_type(cross_product(X0,X0),identity_relation_of_type(X0))
| ~ ilf_type(cross_product(X0,X0),set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f107,f100]) ).
fof(f109,plain,
! [X0] :
( ilf_type(cross_product(X0,X0),identity_relation_of_type(X0))
| ~ ilf_type(cross_product(X0,X0),set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f93]) ).
fof(f116,plain,
! [X0] : ilf_type(cross_product(X0,X0),identity_relation_of_type(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f109,f93]) ).
fof(f117,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f97,f116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET676+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 : n008.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 05:32:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.044854 seconds
% 0.14/0.42 % CPU time: 0.071803 seconds
% 0.14/0.42 % Total memory used: 5.113 MB
% 0.14/0.42 % Net memory used: 5.109 MB
%------------------------------------------------------------------------------