%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU165+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 02:19:30 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 64 ( 26 ~; 22 |; 12 &)
% ( 3 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 36 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,plain,
? [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<~> ( in(B,D)
& in(A,C) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f20,plain,
? [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
( ( ~ in(sK3_skl,sK5_skl)
| ~ in(sK2_skl,sK4_skl)
| ~ in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)) )
& ( ( in(sK3_skl,sK5_skl)
& in(sK2_skl,sK4_skl) )
| in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl),skolemize(D,sK5_skl)],[f20]) ).
fof(f22,plain,
( in(sK2_skl,sK4_skl)
| in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
( in(sK3_skl,sK5_skl)
| in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f24,plain,
( ~ in(sK3_skl,sK5_skl)
| ~ in(sK2_skl,sK4_skl)
| ~ in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f25,plain,
! [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f26,plain,
( ! [A,B,C,D] :
( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ! [A,B,C,D] :
( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f34,plain,
in(sK2_skl,sK4_skl),
inference(backward_subsumption_resolution,[status(thm)],[f22,f27]) ).
fof(f35,plain,
( ~ in(sK3_skl,sK5_skl)
| ~ in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)) ),
inference(backward_subsumption_resolution,[status(thm)],[f24,f27]) ).
fof(f38,plain,
in(sK3_skl,sK5_skl),
inference(backward_subsumption_resolution,[status(thm)],[f23,f28]) ).
fof(f43,plain,
~ in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f35,f28]) ).
fof(f44,plain,
( ~ in(sK3_skl,sK5_skl)
| ~ in(sK2_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f43,f29]) ).
fof(f45,plain,
~ in(sK3_skl,sK5_skl),
inference(forward_subsumption_resolution,[status(thm)],[f44,f34]) ).
fof(f46,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f45,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU165+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:53:50 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.051584 seconds
% 0.13/0.41 % CPU time: 0.156701 seconds
% 0.13/0.41 % Total memory used: 101.432 MB
% 0.13/0.41 % Net memory used: 100.967 MB
%------------------------------------------------------------------------------