%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : PUZ016-2.005 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 01:59:52 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.36s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 92
% Syntax : Number of formulae : 205 ( 7 unt; 38 def)
% Number of atoms : 442 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 487 ( 250 ~; 199 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 77 ( 76 usr; 77 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,negated_conjecture,
~ vertical_1_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ horizontal_1_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( vertical_1_1
| horizontal_1_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( horizontal_1_4
| vertical_1_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( vertical_1_2
| horizontal_2_1
| vertical_2_2
| horizontal_2_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( vertical_1_4
| horizontal_2_3
| vertical_2_4
| horizontal_2_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( vertical_2_1
| vertical_3_1
| horizontal_3_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( vertical_2_3
| horizontal_3_2
| vertical_3_3
| horizontal_3_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( vertical_2_5
| horizontal_3_4
| vertical_3_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( vertical_3_2
| horizontal_4_1
| vertical_4_2
| horizontal_4_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( vertical_3_4
| horizontal_4_3
| vertical_4_4
| horizontal_4_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( vertical_4_1
| horizontal_5_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( vertical_4_3
| horizontal_5_2
| horizontal_5_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( vertical_4_5
| horizontal_5_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( ~ vertical_1_4
| ~ horizontal_1_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( ~ vertical_1_1
| ~ horizontal_2_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( ~ vertical_1_1
| ~ vertical_2_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( ~ vertical_2_3
| ~ horizontal_2_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( ~ horizontal_2_2
| ~ horizontal_2_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( ~ horizontal_2_2
| ~ vertical_2_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( ~ vertical_1_3
| ~ horizontal_2_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
( ~ horizontal_2_4
| ~ vertical_2_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
( ~ vertical_1_5
| ~ vertical_2_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,negated_conjecture,
( ~ vertical_3_1
| ~ horizontal_3_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,negated_conjecture,
( ~ vertical_3_2
| ~ horizontal_3_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,negated_conjecture,
( ~ horizontal_3_1
| ~ horizontal_3_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,negated_conjecture,
( ~ vertical_2_2
| ~ horizontal_3_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,negated_conjecture,
( ~ horizontal_3_1
| ~ vertical_3_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,negated_conjecture,
( ~ vertical_2_2
| ~ vertical_3_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,negated_conjecture,
( ~ vertical_2_2
| ~ horizontal_3_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,negated_conjecture,
( ~ vertical_3_3
| ~ horizontal_3_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,negated_conjecture,
( ~ vertical_3_4
| ~ horizontal_3_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,negated_conjecture,
( ~ horizontal_3_3
| ~ horizontal_3_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f77,negated_conjecture,
( ~ horizontal_3_3
| ~ vertical_3_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,negated_conjecture,
( ~ vertical_2_4
| ~ vertical_3_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f79,negated_conjecture,
( ~ vertical_2_4
| ~ horizontal_3_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f83,negated_conjecture,
( ~ vertical_4_1
| ~ horizontal_4_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,negated_conjecture,
( ~ vertical_3_1
| ~ horizontal_4_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,negated_conjecture,
( ~ vertical_3_1
| ~ vertical_4_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
( ~ vertical_4_3
| ~ horizontal_4_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
( ~ horizontal_4_2
| ~ horizontal_4_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
( ~ vertical_3_3
| ~ horizontal_4_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,negated_conjecture,
( ~ horizontal_4_2
| ~ vertical_4_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
( ~ vertical_3_3
| ~ vertical_4_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
( ~ vertical_3_3
| ~ horizontal_4_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f104,negated_conjecture,
( ~ horizontal_4_4
| ~ vertical_4_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f105,negated_conjecture,
( ~ vertical_3_5
| ~ vertical_4_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f106,negated_conjecture,
( ~ vertical_3_5
| ~ horizontal_4_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f108,negated_conjecture,
( ~ horizontal_5_1
| ~ horizontal_5_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f109,negated_conjecture,
( ~ vertical_4_2
| ~ horizontal_5_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f110,negated_conjecture,
( ~ vertical_4_2
| ~ horizontal_5_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
( ~ horizontal_5_3
| ~ horizontal_5_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f115,negated_conjecture,
( ~ vertical_4_4
| ~ horizontal_5_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f116,negated_conjecture,
( ~ vertical_4_4
| ~ horizontal_5_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f120,plain,
~ vertical_1_2,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f122,plain,
~ horizontal_1_1,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f124,plain,
( vertical_1_1
| horizontal_1_1 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f126,plain,
( horizontal_1_4
| vertical_1_5 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f128,plain,
( vertical_1_2
| horizontal_2_1
| vertical_2_2
| horizontal_2_2 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f130,plain,
( vertical_1_4
| horizontal_2_3
| vertical_2_4
| horizontal_2_4 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f132,plain,
( vertical_2_1
| vertical_3_1
| horizontal_3_1 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f134,plain,
( vertical_2_3
| horizontal_3_2
| vertical_3_3
| horizontal_3_3 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f136,plain,
( vertical_2_5
| horizontal_3_4
| vertical_3_5 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f138,plain,
( vertical_3_2
| horizontal_4_1
| vertical_4_2
| horizontal_4_2 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f140,plain,
( vertical_3_4
| horizontal_4_3
| vertical_4_4
| horizontal_4_4 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f142,plain,
( vertical_4_1
| horizontal_5_1 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f144,plain,
( vertical_4_3
| horizontal_5_2
| horizontal_5_3 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f146,plain,
( vertical_4_5
| horizontal_5_4 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f148,plain,
( ~ vertical_1_4
| ~ horizontal_1_4 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f153,plain,
( ~ vertical_1_1
| ~ horizontal_2_1 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f154,plain,
( ~ vertical_1_1
| ~ vertical_2_1 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f161,plain,
( ~ vertical_2_3
| ~ horizontal_2_3 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f162,plain,
( ~ horizontal_2_2
| ~ horizontal_2_3 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f164,plain,
( ~ horizontal_2_2
| ~ vertical_2_3 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f166,plain,
( ~ vertical_1_3
| ~ horizontal_2_2 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f173,plain,
( ~ horizontal_2_4
| ~ vertical_2_5 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f174,plain,
( ~ vertical_1_5
| ~ vertical_2_5 ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f176,plain,
( ~ vertical_3_1
| ~ horizontal_3_1 ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f179,plain,
( ~ vertical_3_2
| ~ horizontal_3_2 ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f180,plain,
( ~ horizontal_3_1
| ~ horizontal_3_2 ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f181,plain,
( ~ vertical_2_2
| ~ horizontal_3_2 ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f182,plain,
( ~ horizontal_3_1
| ~ vertical_3_2 ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f183,plain,
( ~ vertical_2_2
| ~ vertical_3_2 ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f184,plain,
( ~ vertical_2_2
| ~ horizontal_3_1 ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f185,plain,
( ~ vertical_3_3
| ~ horizontal_3_3 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f191,plain,
( ~ vertical_3_4
| ~ horizontal_3_4 ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f192,plain,
( ~ horizontal_3_3
| ~ horizontal_3_4 ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f194,plain,
( ~ horizontal_3_3
| ~ vertical_3_4 ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f195,plain,
( ~ vertical_2_4
| ~ vertical_3_4 ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f196,plain,
( ~ vertical_2_4
| ~ horizontal_3_3 ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f200,plain,
( ~ vertical_4_1
| ~ horizontal_4_1 ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f201,plain,
( ~ vertical_3_1
| ~ horizontal_4_1 ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f202,plain,
( ~ vertical_3_1
| ~ vertical_4_1 ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f209,plain,
( ~ vertical_4_3
| ~ horizontal_4_3 ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f210,plain,
( ~ horizontal_4_2
| ~ horizontal_4_3 ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f211,plain,
( ~ vertical_3_3
| ~ horizontal_4_3 ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f212,plain,
( ~ horizontal_4_2
| ~ vertical_4_3 ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f213,plain,
( ~ vertical_3_3
| ~ vertical_4_3 ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f214,plain,
( ~ vertical_3_3
| ~ horizontal_4_2 ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f221,plain,
( ~ horizontal_4_4
| ~ vertical_4_5 ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f222,plain,
( ~ vertical_3_5
| ~ vertical_4_5 ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f223,plain,
( ~ vertical_3_5
| ~ horizontal_4_4 ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f225,plain,
( ~ horizontal_5_1
| ~ horizontal_5_2 ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f226,plain,
( ~ vertical_4_2
| ~ horizontal_5_2 ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f227,plain,
( ~ vertical_4_2
| ~ horizontal_5_1 ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f231,plain,
( ~ horizontal_5_3
| ~ horizontal_5_4 ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f232,plain,
( ~ vertical_4_4
| ~ horizontal_5_4 ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f233,plain,
( ~ vertical_4_4
| ~ horizontal_5_3 ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f235,definition,
( sQ0_spl
<=> horizontal_1_1 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f236,plain,
( ~ sQ0_spl
| horizontal_1_1 ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,definition,
( sQ1_spl
<=> vertical_1_1 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f124,f235,f238]) ).
fof(f242,definition,
( sQ2_spl
<=> horizontal_1_4 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f245,definition,
( sQ3_spl
<=> vertical_1_4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f252,definition,
( sQ5_spl
<=> vertical_1_5 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( sQ2_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f126,f252,f242]) ).
fof(f256,definition,
( sQ6_spl
<=> horizontal_2_1 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f259,definition,
( sQ7_spl
<=> vertical_2_1 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f263,definition,
( sQ8_spl
<=> horizontal_2_2 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f266,definition,
( sQ9_spl
<=> vertical_2_2 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f269,definition,
( sQ10_spl
<=> vertical_1_2 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f270,plain,
( ~ sQ10_spl
| vertical_1_2 ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f272,plain,
( sQ10_spl
| sQ6_spl
| sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f128,f263,f266,f256,f269]) ).
fof(f273,definition,
( sQ11_spl
<=> horizontal_2_3 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f276,definition,
( sQ12_spl
<=> vertical_2_3 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f279,definition,
( sQ13_spl
<=> vertical_1_3 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f283,definition,
( sQ14_spl
<=> horizontal_2_4 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f286,definition,
( sQ15_spl
<=> vertical_2_4 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f289,plain,
( sQ3_spl
| sQ11_spl
| sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f130,f283,f286,f273,f245]) ).
fof(f290,definition,
( sQ16_spl
<=> vertical_2_5 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f294,definition,
( sQ17_spl
<=> horizontal_3_1 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f297,definition,
( sQ18_spl
<=> vertical_3_1 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f300,plain,
( sQ7_spl
| sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f132,f294,f297,f259]) ).
fof(f301,definition,
( sQ19_spl
<=> horizontal_3_2 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f304,definition,
( sQ20_spl
<=> vertical_3_2 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f308,definition,
( sQ21_spl
<=> horizontal_3_3 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f311,definition,
( sQ22_spl
<=> vertical_3_3 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f314,plain,
( sQ12_spl
| sQ19_spl
| sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f134,f308,f311,f301,f276]) ).
fof(f315,definition,
( sQ23_spl
<=> horizontal_3_4 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f318,definition,
( sQ24_spl
<=> vertical_3_4 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f322,definition,
( sQ25_spl
<=> vertical_3_5 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f325,plain,
( sQ16_spl
| sQ23_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f136,f322,f315,f290]) ).
fof(f326,definition,
( sQ26_spl
<=> horizontal_4_1 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f329,definition,
( sQ27_spl
<=> vertical_4_1 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f333,definition,
( sQ28_spl
<=> horizontal_4_2 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f336,definition,
( sQ29_spl
<=> vertical_4_2 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( sQ20_spl
| sQ26_spl
| sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f138,f333,f336,f326,f304]) ).
fof(f340,definition,
( sQ30_spl
<=> horizontal_4_3 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f343,definition,
( sQ31_spl
<=> vertical_4_3 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f347,definition,
( sQ32_spl
<=> horizontal_4_4 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f350,definition,
( sQ33_spl
<=> vertical_4_4 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( sQ24_spl
| sQ30_spl
| sQ33_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f140,f347,f350,f340,f318]) ).
fof(f354,definition,
( sQ34_spl
<=> vertical_4_5 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f358,definition,
( sQ35_spl
<=> horizontal_5_1 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f361,plain,
( sQ27_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f142,f358,f329]) ).
fof(f362,definition,
( sQ36_spl
<=> horizontal_5_2 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f366,definition,
( sQ37_spl
<=> horizontal_5_3 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f369,plain,
( sQ31_spl
| sQ36_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f144,f366,f362,f343]) ).
fof(f370,definition,
( sQ38_spl
<=> horizontal_5_4 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f374,plain,
( sQ34_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f146,f370,f354]) ).
fof(f376,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f148,f242,f245]) ).
fof(f381,plain,
( ~ sQ1_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f153,f256,f238]) ).
fof(f382,plain,
( ~ sQ1_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f154,f259,f238]) ).
fof(f389,plain,
( ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f161,f273,f276]) ).
fof(f390,plain,
( ~ sQ8_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f162,f273,f263]) ).
fof(f392,plain,
( ~ sQ8_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f164,f276,f263]) ).
fof(f394,plain,
( ~ sQ13_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f166,f263,f279]) ).
fof(f401,plain,
( ~ sQ14_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f173,f290,f283]) ).
fof(f402,plain,
( ~ sQ5_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f174,f290,f252]) ).
fof(f404,plain,
( ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f176,f294,f297]) ).
fof(f407,plain,
( ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f179,f301,f304]) ).
fof(f408,plain,
( ~ sQ17_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f180,f301,f294]) ).
fof(f409,plain,
( ~ sQ9_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f181,f301,f266]) ).
fof(f410,plain,
( ~ sQ17_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f182,f304,f294]) ).
fof(f411,plain,
( ~ sQ9_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f183,f304,f266]) ).
fof(f412,plain,
( ~ sQ9_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f184,f294,f266]) ).
fof(f413,plain,
( ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f185,f308,f311]) ).
fof(f419,plain,
( ~ sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f191,f315,f318]) ).
fof(f420,plain,
( ~ sQ21_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f192,f315,f308]) ).
fof(f422,plain,
( ~ sQ21_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f194,f318,f308]) ).
fof(f423,plain,
( ~ sQ15_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f195,f318,f286]) ).
fof(f424,plain,
( ~ sQ15_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f196,f308,f286]) ).
fof(f428,plain,
( ~ sQ27_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f200,f326,f329]) ).
fof(f429,plain,
( ~ sQ18_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f201,f326,f297]) ).
fof(f430,plain,
( ~ sQ18_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f202,f329,f297]) ).
fof(f437,plain,
( ~ sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f209,f340,f343]) ).
fof(f438,plain,
( ~ sQ28_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f210,f340,f333]) ).
fof(f439,plain,
( ~ sQ22_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f211,f340,f311]) ).
fof(f440,plain,
( ~ sQ28_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f212,f343,f333]) ).
fof(f441,plain,
( ~ sQ22_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f213,f343,f311]) ).
fof(f442,plain,
( ~ sQ22_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f214,f333,f311]) ).
fof(f449,plain,
( ~ sQ32_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f221,f354,f347]) ).
fof(f450,plain,
( ~ sQ25_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f222,f354,f322]) ).
fof(f451,plain,
( ~ sQ25_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f223,f347,f322]) ).
fof(f453,plain,
( ~ sQ35_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f225,f362,f358]) ).
fof(f454,plain,
( ~ sQ29_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f226,f362,f336]) ).
fof(f455,plain,
( ~ sQ29_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f227,f358,f336]) ).
fof(f459,plain,
( ~ sQ37_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f231,f370,f366]) ).
fof(f460,plain,
( ~ sQ33_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f232,f370,f350]) ).
fof(f461,plain,
( ~ sQ33_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f233,f366,f350]) ).
fof(f463,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f236,f122]) ).
fof(f464,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f463]) ).
fof(f465,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f270,f120]) ).
fof(f466,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f465]) ).
fof(f467,plain,
$false,
inference(sat_refutation,[status(thm)],[f241,f255,f272,f289,f300,f314,f325,f339,f353,f361,f369,f374,f376,f381,f382,f389,f390,f392,f394,f401,f402,f404,f407,f408,f409,f410,f411,f412,f413,f419,f420,f422,f423,f424,f428,f429,f430,f437,f438,f439,f440,f441,f442,f449,f450,f451,f453,f454,f455,f459,f460,f461,f464,f466]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ016-2.005 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 03:45:18 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.09/0.36 % Refutation found
% 0.09/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.39 % Elapsed time: 0.030675 seconds
% 0.13/0.39 % CPU time: 0.051197 seconds
% 0.13/0.39 % Total memory used: 4.341 MB
% 0.13/0.39 % Net memory used: 4.339 MB
%------------------------------------------------------------------------------