%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET012-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 0.13s 0.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 56 ( 11 unt; 6 def)
% Number of atoms : 118 ( 20 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 108 ( 46 ~; 56 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( little_set(X)
| ~ member(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f31,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [Z,X] :
( member(Z,X)
| ~ little_set(Z)
| member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,axiom,
member(empty_set,infinity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f142,hypothesis,
complement(as) = bs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f143,hypothesis,
complement(bs) = cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f144,negated_conjecture,
as != cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f145,plain,
! [X] :
( little_set(X)
| ! [Y] : ~ member(X,Y) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f146,plain,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f147,plain,
! [X0,X1] :
( X0 = X1
| little_set(f1(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f148,plain,
! [X0,X1] :
( X0 = X1
| member(f1(X0,X1),X1)
| member(f1(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f149,plain,
! [X0,X1] :
( X0 = X1
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f184,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f185,plain,
! [X0,X1] :
( member(X0,X1)
| ~ little_set(X0)
| member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f222,plain,
member(empty_set,infinity),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f322,plain,
complement(as) = bs,
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f323,plain,
complement(bs) = cs,
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f324,plain,
as != cs,
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f339,plain,
( ~ member(f1(as,cs),cs)
| ~ member(f1(as,cs),as) ),
inference(resolution,[status(thm)],[f149,f324]) ).
fof(f341,definition,
( sQ0_spl
<=> member(f1(as,cs),as) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f342,plain,
( ~ sQ0_spl
| member(f1(as,cs),as) ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f343,plain,
( sQ0_spl
| ~ member(f1(as,cs),as) ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f344,definition,
( sQ1_spl
<=> member(f1(as,cs),cs) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f347,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f339,f341,f344]) ).
fof(f393,definition,
( sQ4_spl
<=> cs = as ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f394,plain,
( ~ sQ4_spl
| cs = as ),
inference(component_clause,[status(thm)],[f393]) ).
fof(f397,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f394,f324]) ).
fof(f398,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f397]) ).
fof(f399,plain,
! [X0] :
( member(X0,bs)
| ~ little_set(X0)
| member(X0,cs) ),
inference(paramodulation,[status(thm)],[f323,f185]) ).
fof(f400,plain,
! [X0] :
( member(X0,as)
| ~ little_set(X0)
| member(X0,bs) ),
inference(paramodulation,[status(thm)],[f322,f185]) ).
fof(f404,definition,
( sQ5_spl
<=> little_set(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f406,plain,
( sQ5_spl
| ~ little_set(empty_set) ),
inference(component_clause,[status(thm)],[f404]) ).
fof(f416,plain,
( sQ0_spl
| ~ little_set(f1(as,cs))
| member(f1(as,cs),bs) ),
inference(resolution,[status(thm)],[f343,f400]) ).
fof(f418,definition,
( sQ7_spl
<=> member(f1(as,cs),bs) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f421,definition,
( sQ8_spl
<=> little_set(f1(as,cs)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f423,plain,
( sQ8_spl
| ~ little_set(f1(as,cs)) ),
inference(component_clause,[status(thm)],[f421]) ).
fof(f424,plain,
( sQ0_spl
| ~ sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f416,f418,f421,f341]) ).
fof(f437,plain,
! [X0] :
( sQ5_spl
| ~ member(empty_set,X0) ),
inference(resolution,[status(thm)],[f406,f146]) ).
fof(f438,plain,
( sQ5_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f222,f437]) ).
fof(f446,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f438]) ).
fof(f472,plain,
! [X0,X1] :
( X0 = complement(X1)
| member(f1(X0,complement(X1)),X0)
| ~ member(f1(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[f184,f148]) ).
fof(f482,plain,
! [X0] :
( ~ member(X0,as)
| ~ member(X0,bs) ),
inference(paramodulation,[status(thm)],[f322,f184]) ).
fof(f485,plain,
! [X0] :
( X0 = complement(bs)
| member(f1(X0,cs),X0)
| ~ member(f1(X0,complement(bs)),bs) ),
inference(paramodulation,[status(thm)],[f323,f472]) ).
fof(f487,plain,
! [X0] :
( X0 = complement(bs)
| member(f1(X0,cs),X0)
| ~ member(f1(X0,cs),bs) ),
inference(forward_demodulation,[status(thm)],[f323,f485]) ).
fof(f488,plain,
! [X0] :
( X0 = cs
| member(f1(X0,cs),X0)
| ~ member(f1(X0,cs),bs) ),
inference(forward_demodulation,[status(thm)],[f323,f487]) ).
fof(f637,plain,
( ~ sQ0_spl
| ~ member(f1(as,cs),bs) ),
inference(resolution,[status(thm)],[f482,f342]) ).
fof(f643,plain,
( as = cs
| ~ member(f1(as,cs),bs)
| ~ member(f1(as,cs),bs) ),
inference(resolution,[status(thm)],[f482,f488]) ).
fof(f710,plain,
( sQ4_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f643,f418,f393]) ).
fof(f752,plain,
( ~ sQ0_spl
| ~ little_set(f1(as,cs))
| member(f1(as,cs),cs) ),
inference(resolution,[status(thm)],[f637,f399]) ).
fof(f753,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f752,f344,f421,f341]) ).
fof(f765,plain,
( sQ8_spl
| as = cs ),
inference(resolution,[status(thm)],[f423,f147]) ).
fof(f769,plain,
( sQ8_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f765,f393,f421]) ).
fof(f770,plain,
$false,
inference(sat_refutation,[status(thm)],[f347,f398,f424,f446,f710,f753,f769]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % 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 04:43:16 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.46 % Refutation found
% 0.13/0.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.48 % Elapsed time: 0.120088 seconds
% 0.13/0.48 % CPU time: 0.651357 seconds
% 0.13/0.48 % Total memory used: 121.166 MB
% 0.13/0.48 % Net memory used: 120.599 MB
%------------------------------------------------------------------------------