%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET012-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 02:08:49 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 47 ( 8 unt; 5 def)
% Number of atoms : 101 ( 17 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 95 ( 41 ~; 49 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] :
( X = Y
| little_set(f1(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( X = Y
| member(f1(X,Y),Y)
| member(f1(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( X = Y
| ~ member(f1(X,Y),Y)
| ~ member(f1(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Z,X] :
( member(Z,X)
| ~ little_set(Z)
| member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
complement(as) = bs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
complement(bs) = cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
as != cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0,X1] :
( X0 = X1
| little_set(f1(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( X0 = X1
| member(f1(X0,X1),X1)
| member(f1(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
! [X0,X1] :
( X0 = X1
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f18,plain,
! [X0,X1] :
( member(X0,X1)
| ~ little_set(X0)
| member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
complement(as) = bs,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f22,plain,
complement(bs) = cs,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f23,plain,
as != cs,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f25,plain,
( ~ member(f1(cs,as),as)
| ~ member(f1(cs,as),cs) ),
inference(resolution,[status(thm)],[f16,f23]) ).
fof(f33,definition,
( sQ2_spl
<=> member(f1(cs,as),cs) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f35,plain,
( sQ2_spl
| ~ member(f1(cs,as),cs) ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,definition,
( sQ3_spl
<=> member(f1(cs,as),as) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f38,plain,
( sQ3_spl
| ~ member(f1(cs,as),as) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f25,f33,f36]) ).
fof(f40,plain,
! [X0] :
( ~ member(X0,bs)
| ~ member(X0,cs) ),
inference(paramodulation,[status(thm)],[f22,f17]) ).
fof(f41,plain,
! [X0] :
( ~ member(X0,as)
| ~ member(X0,bs) ),
inference(paramodulation,[status(thm)],[f21,f17]) ).
fof(f43,plain,
! [X0] :
( member(X0,bs)
| ~ little_set(X0)
| member(X0,cs) ),
inference(paramodulation,[status(thm)],[f22,f18]) ).
fof(f44,plain,
! [X0] :
( member(X0,as)
| ~ little_set(X0)
| member(X0,bs) ),
inference(paramodulation,[status(thm)],[f21,f18]) ).
fof(f45,plain,
( sQ2_spl
| member(f1(cs,as),bs)
| ~ little_set(f1(cs,as)) ),
inference(resolution,[status(thm)],[f43,f35]) ).
fof(f47,definition,
( sQ4_spl
<=> little_set(f1(cs,as)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( sQ4_spl
| ~ little_set(f1(cs,as)) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,definition,
( sQ5_spl
<=> member(f1(cs,as),bs) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( ~ sQ5_spl
| member(f1(cs,as),bs) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f52,plain,
( sQ5_spl
| ~ member(f1(cs,as),bs) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
( sQ2_spl
| sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f45,f47,f50,f33]) ).
fof(f57,plain,
! [X0] :
( ~ member(f1(cs,X0),bs)
| cs = X0
| member(f1(cs,X0),X0) ),
inference(resolution,[status(thm)],[f15,f40]) ).
fof(f60,definition,
( sQ6_spl
<=> as = cs ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ6_spl
| as = cs ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f64,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f23]) ).
fof(f65,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f64]) ).
fof(f134,plain,
( sQ3_spl
| ~ member(f1(cs,as),bs)
| cs = as ),
inference(resolution,[status(thm)],[f38,f57]) ).
fof(f135,plain,
( sQ3_spl
| ~ sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f134,f60,f50,f36]) ).
fof(f140,plain,
( sQ4_spl
| cs = as ),
inference(resolution,[status(thm)],[f49,f14]) ).
fof(f141,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f140,f60,f47]) ).
fof(f144,plain,
( sQ5_spl
| member(f1(cs,as),as)
| ~ little_set(f1(cs,as)) ),
inference(resolution,[status(thm)],[f52,f44]) ).
fof(f145,plain,
( sQ5_spl
| sQ3_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f144,f47,f36,f50]) ).
fof(f173,plain,
( ~ sQ5_spl
| ~ member(f1(cs,as),as) ),
inference(resolution,[status(thm)],[f41,f51]) ).
fof(f182,plain,
( ~ sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f173,f36,f50]) ).
fof(f191,plain,
$false,
inference(sat_refutation,[status(thm)],[f39,f53,f65,f135,f141,f145,f182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:36:57 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.38 % Refutation found
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.038150 seconds
% 0.14/0.41 % CPU time: 0.091541 seconds
% 0.14/0.41 % Total memory used: 19.352 MB
% 0.14/0.41 % Net memory used: 19.306 MB
%------------------------------------------------------------------------------