%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU083+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 02:19:11 PM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 9 unt; 2 def)
% Number of atoms : 46 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 15 ~; 10 |; 7 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f33,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(set_union2(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,conjecture,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(set_union2(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,negated_conjecture,
~ ! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(set_union2(A,B)) ),
inference(negated_conjecture,[status(cth)],[f61]) ).
fof(f152,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f155,plain,
! [A,B] :
( finite(set_union2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f156,plain,
! [X0,X1] :
( finite(set_union2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f269,plain,
? [A,B] :
( ~ finite(set_union2(A,B))
& finite(B)
& finite(A) ),
inference(pre_NNF_transformation,[status(thm)],[f62]) ).
fof(f270,plain,
( ~ finite(set_union2(sK26_skl,sK27_skl))
& finite(sK27_skl)
& finite(sK26_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26_skl,sK27_skl]),skolemize(A,sK26_skl),skolemize(B,sK27_skl)],[f269]) ).
fof(f271,plain,
finite(sK26_skl),
inference(cnf_transformation,[status(thm)],[f270]) ).
fof(f272,plain,
finite(sK27_skl),
inference(cnf_transformation,[status(thm)],[f270]) ).
fof(f273,plain,
~ finite(set_union2(sK26_skl,sK27_skl)),
inference(cnf_transformation,[status(thm)],[f270]) ).
fof(f284,plain,
~ finite(set_union2(sK27_skl,sK26_skl)),
inference(paramodulation,[status(thm)],[f152,f273]) ).
fof(f330,plain,
( ~ finite(sK26_skl)
| ~ finite(sK27_skl) ),
inference(resolution,[status(thm)],[f156,f284]) ).
fof(f337,definition,
( sQ4_spl
<=> finite(sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( sQ4_spl
| ~ finite(sK27_skl) ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f340,definition,
( sQ5_spl
<=> finite(sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f342,plain,
( sQ5_spl
| ~ finite(sK26_skl) ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f343,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f330,f337,f340]) ).
fof(f355,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f339,f272]) ).
fof(f356,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f355]) ).
fof(f357,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f342,f271]) ).
fof(f358,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f357]) ).
fof(f359,plain,
$false,
inference(sat_refutation,[status(thm)],[f343,f356,f358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU083+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36 % Computer : n020.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8046.5625MB
% 0.13/0.36 % OS : Linux 6.8.0-71-generic
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Mon Sep 21 05:50:47 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.41 % Drodi V4.1.1
% 0.13/0.44 % Refutation found
% 0.13/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.50 % Elapsed time: 0.105391 seconds
% 0.17/0.50 % CPU time: 0.098628 seconds
% 0.17/0.50 % Total memory used: 3.337 MB
% 0.17/0.50 % Net memory used: 3.336 MB
%------------------------------------------------------------------------------