%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU165+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 02:19:29 PM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 1 unt; 3 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 97 ( 38 ~; 40 |; 12 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 38 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,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(f12,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)],[f11]) ).
fof(f13,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(f23,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)],[f12]) ).
fof(f24,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)],[f23]) ).
fof(f25,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)],[f24]) ).
fof(f26,plain,
( in(sK2_skl,sK4_skl)
| in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
( in(sK3_skl,sK5_skl)
| in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,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)],[f25]) ).
fof(f29,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)],[f13]) ).
fof(f30,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)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,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)],[f30]) ).
fof(f34,definition,
( sQ0_spl
<=> in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f35,plain,
( ~ sQ0_spl
| in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)) ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f37,definition,
( sQ1_spl
<=> in(sK2_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f38,plain,
( ~ sQ1_spl
| in(sK2_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f37]) ).
fof(f39,plain,
( sQ1_spl
| ~ in(sK2_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f37]) ).
fof(f40,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f26,f34,f37]) ).
fof(f41,definition,
( sQ2_spl
<=> in(sK3_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f42,plain,
( ~ sQ2_spl
| in(sK3_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f27,f34,f41]) ).
fof(f45,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f28,f34,f37,f41]) ).
fof(f47,plain,
( ~ sQ0_spl
| in(sK2_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f31,f35]) ).
fof(f48,plain,
( ~ sQ0_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f47,f39]) ).
fof(f49,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f48]) ).
fof(f52,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ in(X0,X1)
| in(ordered_pair(X0,sK3_skl),cartesian_product2(X1,sK5_skl)) ),
inference(resolution,[status(thm)],[f33,f42]) ).
fof(f55,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f52,f38]) ).
fof(f56,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f55,f34,f41,f37]) ).
fof(f57,plain,
( ~ sQ0_spl
| in(sK3_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f35,f32]) ).
fof(f61,plain,
( ~ sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f57,f41,f34]) ).
fof(f62,plain,
$false,
inference(sat_refutation,[status(thm)],[f40,f44,f45,f49,f56,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU165+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 05:57:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.43 % Elapsed time: 0.045968 seconds
% 0.11/0.43 % CPU time: 0.120958 seconds
% 0.11/0.43 % Total memory used: 50.731 MB
% 0.11/0.43 % Net memory used: 50.529 MB
%------------------------------------------------------------------------------