%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN007+1.014 : TPTP v9.3.1. Released v1.0.0.
% 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 03:14:54 PM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 65
% Syntax : Number of formulae : 327 ( 1 unt; 64 def)
% Number of atoms : 1497 ( 0 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 1613 ( 443 ~; 572 |; 78 &)
% ( 518 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 29 ( 5 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 79 ( 78 usr; 79 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> ( p_14
<=> ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> ( p_14
<=> ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( p_1
<~> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> ( p_14
<=> ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
( sP0_prd
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> ( p_14
<=> ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( p_1
<~> ( p_2
<=> sP0_prd ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ( ( ( sP0_prd
| p_2 )
& ( ~ sP0_prd
| ~ p_2 ) )
| ~ p_1 )
& ( ( ( ~ sP0_prd
| p_2 )
& ( sP0_prd
| ~ p_2 ) )
| p_1 ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
( sP0_prd
| ~ p_2
| p_1 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
( ~ sP0_prd
| p_2
| p_1 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
( ~ sP0_prd
| ~ p_2
| ~ p_1 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
( sP0_prd
| p_2
| ~ p_1 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,definition,
( sP1_prd
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> ( p_14
<=> ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f12,plain,
( sP0_prd
<=> ( p_3
<=> sP1_prd ) ),
inference(formula_renaming,[status(thm)],[f4,f11]) ).
fof(f13,plain,
( ( ( ( sP1_prd
| p_3 )
& ( ~ sP1_prd
| ~ p_3 ) )
| sP0_prd )
& ( ( ( ~ sP1_prd
| p_3 )
& ( sP1_prd
| ~ p_3 ) )
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
( sP1_prd
| ~ p_3
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
( ~ sP1_prd
| p_3
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
( ~ sP1_prd
| ~ p_3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,plain,
( sP1_prd
| p_3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f18,definition,
( sP2_prd
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> ( p_14
<=> ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f19,plain,
( sP1_prd
<=> ( p_4
<=> sP2_prd ) ),
inference(formula_renaming,[status(thm)],[f11,f18]) ).
fof(f20,plain,
( ( ( ( sP2_prd
| p_4 )
& ( ~ sP2_prd
| ~ p_4 ) )
| sP1_prd )
& ( ( ( ~ sP2_prd
| p_4 )
& ( sP2_prd
| ~ p_4 ) )
| ~ sP1_prd ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
( sP2_prd
| ~ p_4
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
( ~ sP2_prd
| p_4
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f23,plain,
( ~ sP2_prd
| ~ p_4
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f24,plain,
( sP2_prd
| p_4
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f25,definition,
( sP3_prd
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> ( p_14
<=> ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f26,plain,
( sP2_prd
<=> ( p_5
<=> sP3_prd ) ),
inference(formula_renaming,[status(thm)],[f18,f25]) ).
fof(f27,plain,
( ( ( ( sP3_prd
| p_5 )
& ( ~ sP3_prd
| ~ p_5 ) )
| sP2_prd )
& ( ( ( ~ sP3_prd
| p_5 )
& ( sP3_prd
| ~ p_5 ) )
| ~ sP2_prd ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
( sP3_prd
| ~ p_5
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
( ~ sP3_prd
| p_5
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
( ~ sP3_prd
| ~ p_5
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
( sP3_prd
| p_5
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f32,definition,
( sP4_prd
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> ( p_14
<=> ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f33,plain,
( sP3_prd
<=> ( p_6
<=> sP4_prd ) ),
inference(formula_renaming,[status(thm)],[f25,f32]) ).
fof(f34,plain,
( ( ( ( sP4_prd
| p_6 )
& ( ~ sP4_prd
| ~ p_6 ) )
| sP3_prd )
& ( ( ( ~ sP4_prd
| p_6 )
& ( sP4_prd
| ~ p_6 ) )
| ~ sP3_prd ) ),
inference(NNF_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
( sP4_prd
| ~ p_6
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
( ~ sP4_prd
| p_6
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
( ~ sP4_prd
| ~ p_6
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f38,plain,
( sP4_prd
| p_6
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f39,definition,
( sP5_prd
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> ( p_14
<=> ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f40,plain,
( sP4_prd
<=> ( p_7
<=> sP5_prd ) ),
inference(formula_renaming,[status(thm)],[f32,f39]) ).
fof(f41,plain,
( ( ( ( sP5_prd
| p_7 )
& ( ~ sP5_prd
| ~ p_7 ) )
| sP4_prd )
& ( ( ( ~ sP5_prd
| p_7 )
& ( sP5_prd
| ~ p_7 ) )
| ~ sP4_prd ) ),
inference(NNF_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
( sP5_prd
| ~ p_7
| ~ sP4_prd ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
( ~ sP5_prd
| p_7
| ~ sP4_prd ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f44,plain,
( ~ sP5_prd
| ~ p_7
| sP4_prd ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f45,plain,
( sP5_prd
| p_7
| sP4_prd ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f46,definition,
( sP6_prd
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> ( p_14
<=> ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6_prd])],[]) ).
fof(f47,plain,
( sP5_prd
<=> ( p_8
<=> sP6_prd ) ),
inference(formula_renaming,[status(thm)],[f39,f46]) ).
fof(f48,plain,
( ( ( ( sP6_prd
| p_8 )
& ( ~ sP6_prd
| ~ p_8 ) )
| sP5_prd )
& ( ( ( ~ sP6_prd
| p_8 )
& ( sP6_prd
| ~ p_8 ) )
| ~ sP5_prd ) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
( sP6_prd
| ~ p_8
| ~ sP5_prd ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
( ~ sP6_prd
| p_8
| ~ sP5_prd ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
( ~ sP6_prd
| ~ p_8
| sP5_prd ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f52,plain,
( sP6_prd
| p_8
| sP5_prd ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f53,definition,
( sP7_prd
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> ( p_14
<=> ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7_prd])],[]) ).
fof(f54,plain,
( sP6_prd
<=> ( p_9
<=> sP7_prd ) ),
inference(formula_renaming,[status(thm)],[f46,f53]) ).
fof(f55,plain,
( ( ( ( sP7_prd
| p_9 )
& ( ~ sP7_prd
| ~ p_9 ) )
| sP6_prd )
& ( ( ( ~ sP7_prd
| p_9 )
& ( sP7_prd
| ~ p_9 ) )
| ~ sP6_prd ) ),
inference(NNF_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
( sP7_prd
| ~ p_9
| ~ sP6_prd ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
( ~ sP7_prd
| p_9
| ~ sP6_prd ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f58,plain,
( ~ sP7_prd
| ~ p_9
| sP6_prd ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f59,plain,
( sP7_prd
| p_9
| sP6_prd ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f60,definition,
( sP8_prd
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> ( p_14
<=> ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8_prd])],[]) ).
fof(f61,plain,
( sP7_prd
<=> ( p_10
<=> sP8_prd ) ),
inference(formula_renaming,[status(thm)],[f53,f60]) ).
fof(f62,plain,
( ( ( ( sP8_prd
| p_10 )
& ( ~ sP8_prd
| ~ p_10 ) )
| sP7_prd )
& ( ( ( ~ sP8_prd
| p_10 )
& ( sP8_prd
| ~ p_10 ) )
| ~ sP7_prd ) ),
inference(NNF_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
( sP8_prd
| ~ p_10
| ~ sP7_prd ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
( ~ sP8_prd
| p_10
| ~ sP7_prd ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f65,plain,
( ~ sP8_prd
| ~ p_10
| sP7_prd ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f66,plain,
( sP8_prd
| p_10
| sP7_prd ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f67,definition,
( sP9_prd
<=> ( p_12
<=> ( p_13
<=> ( p_14
<=> ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9_prd])],[]) ).
fof(f68,plain,
( sP8_prd
<=> ( p_11
<=> sP9_prd ) ),
inference(formula_renaming,[status(thm)],[f60,f67]) ).
fof(f69,plain,
( ( ( ( sP9_prd
| p_11 )
& ( ~ sP9_prd
| ~ p_11 ) )
| sP8_prd )
& ( ( ( ~ sP9_prd
| p_11 )
& ( sP9_prd
| ~ p_11 ) )
| ~ sP8_prd ) ),
inference(NNF_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
( sP9_prd
| ~ p_11
| ~ sP8_prd ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
( ~ sP9_prd
| p_11
| ~ sP8_prd ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f72,plain,
( ~ sP9_prd
| ~ p_11
| sP8_prd ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f73,plain,
( sP9_prd
| p_11
| sP8_prd ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f74,definition,
( sP10_prd
<=> ( p_13
<=> ( p_14
<=> ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10_prd])],[]) ).
fof(f75,plain,
( sP9_prd
<=> ( p_12
<=> sP10_prd ) ),
inference(formula_renaming,[status(thm)],[f67,f74]) ).
fof(f76,plain,
( ( ( ( sP10_prd
| p_12 )
& ( ~ sP10_prd
| ~ p_12 ) )
| sP9_prd )
& ( ( ( ~ sP10_prd
| p_12 )
& ( sP10_prd
| ~ p_12 ) )
| ~ sP9_prd ) ),
inference(NNF_transformation,[status(thm)],[f75]) ).
fof(f77,plain,
( sP10_prd
| ~ p_12
| ~ sP9_prd ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
( ~ sP10_prd
| p_12
| ~ sP9_prd ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f79,plain,
( ~ sP10_prd
| ~ p_12
| sP9_prd ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f80,plain,
( sP10_prd
| p_12
| sP9_prd ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f81,definition,
( sP11_prd
<=> ( p_14
<=> ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11_prd])],[]) ).
fof(f82,plain,
( sP10_prd
<=> ( p_13
<=> sP11_prd ) ),
inference(formula_renaming,[status(thm)],[f74,f81]) ).
fof(f83,plain,
( ( ( ( sP11_prd
| p_13 )
& ( ~ sP11_prd
| ~ p_13 ) )
| sP10_prd )
& ( ( ( ~ sP11_prd
| p_13 )
& ( sP11_prd
| ~ p_13 ) )
| ~ sP10_prd ) ),
inference(NNF_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
( sP11_prd
| ~ p_13
| ~ sP10_prd ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f85,plain,
( ~ sP11_prd
| p_13
| ~ sP10_prd ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f86,plain,
( ~ sP11_prd
| ~ p_13
| sP10_prd ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f87,plain,
( sP11_prd
| p_13
| sP10_prd ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f88,definition,
( sP12_prd
<=> ( p_1
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12_prd])],[]) ).
fof(f89,plain,
( sP11_prd
<=> ( p_14
<=> sP12_prd ) ),
inference(formula_renaming,[status(thm)],[f81,f88]) ).
fof(f90,plain,
( ( ( ( sP12_prd
| p_14 )
& ( ~ sP12_prd
| ~ p_14 ) )
| sP11_prd )
& ( ( ( ~ sP12_prd
| p_14 )
& ( sP12_prd
| ~ p_14 ) )
| ~ sP11_prd ) ),
inference(NNF_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
( sP12_prd
| ~ p_14
| ~ sP11_prd ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f92,plain,
( ~ sP12_prd
| p_14
| ~ sP11_prd ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f93,plain,
( ~ sP12_prd
| ~ p_14
| sP11_prd ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f94,plain,
( sP12_prd
| p_14
| sP11_prd ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f95,definition,
( sP13_prd
<=> ( p_2
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13_prd])],[]) ).
fof(f96,plain,
( sP12_prd
<=> ( p_1
<=> sP13_prd ) ),
inference(formula_renaming,[status(thm)],[f88,f95]) ).
fof(f97,plain,
( ( ( ( sP13_prd
| p_1 )
& ( ~ sP13_prd
| ~ p_1 ) )
| sP12_prd )
& ( ( ( ~ sP13_prd
| p_1 )
& ( sP13_prd
| ~ p_1 ) )
| ~ sP12_prd ) ),
inference(NNF_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
( sP13_prd
| ~ p_1
| ~ sP12_prd ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
( ~ sP13_prd
| p_1
| ~ sP12_prd ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f100,plain,
( ~ sP13_prd
| ~ p_1
| sP12_prd ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f101,plain,
( sP13_prd
| p_1
| sP12_prd ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f102,definition,
( sP14_prd
<=> ( p_3
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14_prd])],[]) ).
fof(f103,plain,
( sP13_prd
<=> ( p_2
<=> sP14_prd ) ),
inference(formula_renaming,[status(thm)],[f95,f102]) ).
fof(f104,plain,
( ( ( ( sP14_prd
| p_2 )
& ( ~ sP14_prd
| ~ p_2 ) )
| sP13_prd )
& ( ( ( ~ sP14_prd
| p_2 )
& ( sP14_prd
| ~ p_2 ) )
| ~ sP13_prd ) ),
inference(NNF_transformation,[status(thm)],[f103]) ).
fof(f105,plain,
( sP14_prd
| ~ p_2
| ~ sP13_prd ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f106,plain,
( ~ sP14_prd
| p_2
| ~ sP13_prd ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f107,plain,
( ~ sP14_prd
| ~ p_2
| sP13_prd ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f108,plain,
( sP14_prd
| p_2
| sP13_prd ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f109,definition,
( sP15_prd
<=> ( p_4
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15_prd])],[]) ).
fof(f110,plain,
( sP14_prd
<=> ( p_3
<=> sP15_prd ) ),
inference(formula_renaming,[status(thm)],[f102,f109]) ).
fof(f111,plain,
( ( ( ( sP15_prd
| p_3 )
& ( ~ sP15_prd
| ~ p_3 ) )
| sP14_prd )
& ( ( ( ~ sP15_prd
| p_3 )
& ( sP15_prd
| ~ p_3 ) )
| ~ sP14_prd ) ),
inference(NNF_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
( sP15_prd
| ~ p_3
| ~ sP14_prd ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
( ~ sP15_prd
| p_3
| ~ sP14_prd ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f114,plain,
( ~ sP15_prd
| ~ p_3
| sP14_prd ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f115,plain,
( sP15_prd
| p_3
| sP14_prd ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f116,definition,
( sP16_prd
<=> ( p_5
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16_prd])],[]) ).
fof(f117,plain,
( sP15_prd
<=> ( p_4
<=> sP16_prd ) ),
inference(formula_renaming,[status(thm)],[f109,f116]) ).
fof(f118,plain,
( ( ( ( sP16_prd
| p_4 )
& ( ~ sP16_prd
| ~ p_4 ) )
| sP15_prd )
& ( ( ( ~ sP16_prd
| p_4 )
& ( sP16_prd
| ~ p_4 ) )
| ~ sP15_prd ) ),
inference(NNF_transformation,[status(thm)],[f117]) ).
fof(f119,plain,
( sP16_prd
| ~ p_4
| ~ sP15_prd ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f120,plain,
( ~ sP16_prd
| p_4
| ~ sP15_prd ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f121,plain,
( ~ sP16_prd
| ~ p_4
| sP15_prd ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f122,plain,
( sP16_prd
| p_4
| sP15_prd ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f123,definition,
( sP17_prd
<=> ( p_6
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17_prd])],[]) ).
fof(f124,plain,
( sP16_prd
<=> ( p_5
<=> sP17_prd ) ),
inference(formula_renaming,[status(thm)],[f116,f123]) ).
fof(f125,plain,
( ( ( ( sP17_prd
| p_5 )
& ( ~ sP17_prd
| ~ p_5 ) )
| sP16_prd )
& ( ( ( ~ sP17_prd
| p_5 )
& ( sP17_prd
| ~ p_5 ) )
| ~ sP16_prd ) ),
inference(NNF_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
( sP17_prd
| ~ p_5
| ~ sP16_prd ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
( ~ sP17_prd
| p_5
| ~ sP16_prd ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f128,plain,
( ~ sP17_prd
| ~ p_5
| sP16_prd ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f129,plain,
( sP17_prd
| p_5
| sP16_prd ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f130,definition,
( sP18_prd
<=> ( p_7
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18_prd])],[]) ).
fof(f131,plain,
( sP17_prd
<=> ( p_6
<=> sP18_prd ) ),
inference(formula_renaming,[status(thm)],[f123,f130]) ).
fof(f132,plain,
( ( ( ( sP18_prd
| p_6 )
& ( ~ sP18_prd
| ~ p_6 ) )
| sP17_prd )
& ( ( ( ~ sP18_prd
| p_6 )
& ( sP18_prd
| ~ p_6 ) )
| ~ sP17_prd ) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
( sP18_prd
| ~ p_6
| ~ sP17_prd ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
( ~ sP18_prd
| p_6
| ~ sP17_prd ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f135,plain,
( ~ sP18_prd
| ~ p_6
| sP17_prd ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f136,plain,
( sP18_prd
| p_6
| sP17_prd ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f137,definition,
( sP19_prd
<=> ( p_8
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19_prd])],[]) ).
fof(f138,plain,
( sP18_prd
<=> ( p_7
<=> sP19_prd ) ),
inference(formula_renaming,[status(thm)],[f130,f137]) ).
fof(f139,plain,
( ( ( ( sP19_prd
| p_7 )
& ( ~ sP19_prd
| ~ p_7 ) )
| sP18_prd )
& ( ( ( ~ sP19_prd
| p_7 )
& ( sP19_prd
| ~ p_7 ) )
| ~ sP18_prd ) ),
inference(NNF_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
( sP19_prd
| ~ p_7
| ~ sP18_prd ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
( ~ sP19_prd
| p_7
| ~ sP18_prd ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f142,plain,
( ~ sP19_prd
| ~ p_7
| sP18_prd ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f143,plain,
( sP19_prd
| p_7
| sP18_prd ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f144,definition,
( sP20_prd
<=> ( p_9
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20_prd])],[]) ).
fof(f145,plain,
( sP19_prd
<=> ( p_8
<=> sP20_prd ) ),
inference(formula_renaming,[status(thm)],[f137,f144]) ).
fof(f146,plain,
( ( ( ( sP20_prd
| p_8 )
& ( ~ sP20_prd
| ~ p_8 ) )
| sP19_prd )
& ( ( ( ~ sP20_prd
| p_8 )
& ( sP20_prd
| ~ p_8 ) )
| ~ sP19_prd ) ),
inference(NNF_transformation,[status(thm)],[f145]) ).
fof(f147,plain,
( sP20_prd
| ~ p_8
| ~ sP19_prd ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f148,plain,
( ~ sP20_prd
| p_8
| ~ sP19_prd ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f149,plain,
( ~ sP20_prd
| ~ p_8
| sP19_prd ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f150,plain,
( sP20_prd
| p_8
| sP19_prd ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f151,definition,
( sP21_prd
<=> ( p_10
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21_prd])],[]) ).
fof(f152,plain,
( sP20_prd
<=> ( p_9
<=> sP21_prd ) ),
inference(formula_renaming,[status(thm)],[f144,f151]) ).
fof(f153,plain,
( ( ( ( sP21_prd
| p_9 )
& ( ~ sP21_prd
| ~ p_9 ) )
| sP20_prd )
& ( ( ( ~ sP21_prd
| p_9 )
& ( sP21_prd
| ~ p_9 ) )
| ~ sP20_prd ) ),
inference(NNF_transformation,[status(thm)],[f152]) ).
fof(f154,plain,
( sP21_prd
| ~ p_9
| ~ sP20_prd ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f155,plain,
( ~ sP21_prd
| p_9
| ~ sP20_prd ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f156,plain,
( ~ sP21_prd
| ~ p_9
| sP20_prd ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f157,plain,
( sP21_prd
| p_9
| sP20_prd ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f158,definition,
( sP22_prd
<=> ( p_11
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22_prd])],[]) ).
fof(f159,plain,
( sP21_prd
<=> ( p_10
<=> sP22_prd ) ),
inference(formula_renaming,[status(thm)],[f151,f158]) ).
fof(f160,plain,
( ( ( ( sP22_prd
| p_10 )
& ( ~ sP22_prd
| ~ p_10 ) )
| sP21_prd )
& ( ( ( ~ sP22_prd
| p_10 )
& ( sP22_prd
| ~ p_10 ) )
| ~ sP21_prd ) ),
inference(NNF_transformation,[status(thm)],[f159]) ).
fof(f161,plain,
( sP22_prd
| ~ p_10
| ~ sP21_prd ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f162,plain,
( ~ sP22_prd
| p_10
| ~ sP21_prd ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f163,plain,
( ~ sP22_prd
| ~ p_10
| sP21_prd ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f164,plain,
( sP22_prd
| p_10
| sP21_prd ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f165,definition,
( sP23_prd
<=> ( p_12
<=> ( p_13
<=> p_14 ) ) ),
introduced(definition,[new_symbols(definition,[sP23_prd])],[]) ).
fof(f166,plain,
( sP22_prd
<=> ( p_11
<=> sP23_prd ) ),
inference(formula_renaming,[status(thm)],[f158,f165]) ).
fof(f167,plain,
( ( ( ( sP23_prd
| p_11 )
& ( ~ sP23_prd
| ~ p_11 ) )
| sP22_prd )
& ( ( ( ~ sP23_prd
| p_11 )
& ( sP23_prd
| ~ p_11 ) )
| ~ sP22_prd ) ),
inference(NNF_transformation,[status(thm)],[f166]) ).
fof(f168,plain,
( sP23_prd
| ~ p_11
| ~ sP22_prd ),
inference(cnf_transformation,[status(thm)],[f167]) ).
fof(f169,plain,
( ~ sP23_prd
| p_11
| ~ sP22_prd ),
inference(cnf_transformation,[status(thm)],[f167]) ).
fof(f170,plain,
( ~ sP23_prd
| ~ p_11
| sP22_prd ),
inference(cnf_transformation,[status(thm)],[f167]) ).
fof(f171,plain,
( sP23_prd
| p_11
| sP22_prd ),
inference(cnf_transformation,[status(thm)],[f167]) ).
fof(f172,definition,
( sP24_prd
<=> ( p_13
<=> p_14 ) ),
introduced(definition,[new_symbols(definition,[sP24_prd])],[]) ).
fof(f173,plain,
( sP23_prd
<=> ( p_12
<=> sP24_prd ) ),
inference(formula_renaming,[status(thm)],[f165,f172]) ).
fof(f174,plain,
( ( ( ( sP24_prd
| p_12 )
& ( ~ sP24_prd
| ~ p_12 ) )
| sP23_prd )
& ( ( ( ~ sP24_prd
| p_12 )
& ( sP24_prd
| ~ p_12 ) )
| ~ sP23_prd ) ),
inference(NNF_transformation,[status(thm)],[f173]) ).
fof(f175,plain,
( sP24_prd
| ~ p_12
| ~ sP23_prd ),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f176,plain,
( ~ sP24_prd
| p_12
| ~ sP23_prd ),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f177,plain,
( ~ sP24_prd
| ~ p_12
| sP23_prd ),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f178,plain,
( sP24_prd
| p_12
| sP23_prd ),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f179,plain,
( ( ( ( p_14
| p_13 )
& ( ~ p_14
| ~ p_13 ) )
| sP24_prd )
& ( ( ( ~ p_14
| p_13 )
& ( p_14
| ~ p_13 ) )
| ~ sP24_prd ) ),
inference(NNF_transformation,[status(thm)],[f172]) ).
fof(f180,plain,
( p_14
| ~ p_13
| ~ sP24_prd ),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f181,plain,
( ~ p_14
| p_13
| ~ sP24_prd ),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f182,plain,
( ~ p_14
| ~ p_13
| sP24_prd ),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f183,plain,
( p_14
| p_13
| sP24_prd ),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f184,definition,
( sQ0_spl
<=> p_1 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f187,definition,
( sQ1_spl
<=> p_2 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f190,definition,
( sQ2_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f7,f184,f187,f190]) ).
fof(f194,plain,
( ~ sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f8,f184,f187,f190]) ).
fof(f195,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f9,f184,f187,f190]) ).
fof(f196,plain,
( sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f184,f187,f190]) ).
fof(f197,definition,
( sQ3_spl
<=> p_3 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f200,definition,
( sQ4_spl
<=> sP1_prd ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f14,f190,f197,f200]) ).
fof(f204,plain,
( ~ sQ4_spl
| sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f15,f190,f197,f200]) ).
fof(f205,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f16,f190,f197,f200]) ).
fof(f206,plain,
( sQ4_spl
| sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f17,f190,f197,f200]) ).
fof(f207,definition,
( sQ5_spl
<=> p_4 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f210,definition,
( sQ6_spl
<=> sP2_prd ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f21,f200,f207,f210]) ).
fof(f214,plain,
( ~ sQ6_spl
| sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f22,f200,f207,f210]) ).
fof(f215,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f23,f200,f207,f210]) ).
fof(f216,plain,
( sQ6_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f24,f200,f207,f210]) ).
fof(f217,definition,
( sQ7_spl
<=> p_5 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f220,definition,
( sQ8_spl
<=> sP3_prd ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f223,plain,
( sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f28,f210,f217,f220]) ).
fof(f224,plain,
( ~ sQ8_spl
| sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f29,f210,f217,f220]) ).
fof(f225,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f30,f210,f217,f220]) ).
fof(f226,plain,
( sQ8_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f31,f210,f217,f220]) ).
fof(f227,definition,
( sQ9_spl
<=> p_6 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f230,definition,
( sQ10_spl
<=> sP4_prd ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f35,f220,f227,f230]) ).
fof(f234,plain,
( ~ sQ10_spl
| sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f36,f220,f227,f230]) ).
fof(f235,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f37,f220,f227,f230]) ).
fof(f236,plain,
( sQ10_spl
| sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f38,f220,f227,f230]) ).
fof(f237,definition,
( sQ11_spl
<=> p_7 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f240,definition,
( sQ12_spl
<=> sP5_prd ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f42,f230,f237,f240]) ).
fof(f244,plain,
( ~ sQ12_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f43,f230,f237,f240]) ).
fof(f245,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f44,f230,f237,f240]) ).
fof(f246,plain,
( sQ12_spl
| sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f45,f230,f237,f240]) ).
fof(f247,definition,
( sQ13_spl
<=> p_8 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f250,definition,
( sQ14_spl
<=> sP6_prd ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f253,plain,
( sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f49,f240,f247,f250]) ).
fof(f254,plain,
( ~ sQ14_spl
| sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f50,f240,f247,f250]) ).
fof(f255,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f51,f240,f247,f250]) ).
fof(f256,plain,
( sQ14_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f52,f240,f247,f250]) ).
fof(f257,definition,
( sQ15_spl
<=> p_9 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f260,definition,
( sQ16_spl
<=> sP7_prd ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( sQ16_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f56,f250,f257,f260]) ).
fof(f264,plain,
( ~ sQ16_spl
| sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f57,f250,f257,f260]) ).
fof(f265,plain,
( ~ sQ16_spl
| ~ sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f58,f250,f257,f260]) ).
fof(f266,plain,
( sQ16_spl
| sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f59,f250,f257,f260]) ).
fof(f267,definition,
( sQ17_spl
<=> p_10 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f270,definition,
( sQ18_spl
<=> sP8_prd ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( sQ18_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f63,f260,f267,f270]) ).
fof(f274,plain,
( ~ sQ18_spl
| sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f64,f260,f267,f270]) ).
fof(f275,plain,
( ~ sQ18_spl
| ~ sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f65,f260,f267,f270]) ).
fof(f276,plain,
( sQ18_spl
| sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f66,f260,f267,f270]) ).
fof(f277,definition,
( sQ19_spl
<=> p_11 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f280,definition,
( sQ20_spl
<=> sP9_prd ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f283,plain,
( sQ20_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f70,f270,f277,f280]) ).
fof(f284,plain,
( ~ sQ20_spl
| sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f71,f270,f277,f280]) ).
fof(f285,plain,
( ~ sQ20_spl
| ~ sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f72,f270,f277,f280]) ).
fof(f286,plain,
( sQ20_spl
| sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f73,f270,f277,f280]) ).
fof(f287,definition,
( sQ21_spl
<=> p_12 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f290,definition,
( sQ22_spl
<=> sP10_prd ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f293,plain,
( sQ22_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f77,f280,f287,f290]) ).
fof(f294,plain,
( ~ sQ22_spl
| sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f78,f280,f287,f290]) ).
fof(f295,plain,
( ~ sQ22_spl
| ~ sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f79,f280,f287,f290]) ).
fof(f296,plain,
( sQ22_spl
| sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f80,f280,f287,f290]) ).
fof(f297,definition,
( sQ23_spl
<=> p_13 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f300,definition,
( sQ24_spl
<=> sP11_prd ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( sQ24_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f84,f290,f297,f300]) ).
fof(f304,plain,
( ~ sQ24_spl
| sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f85,f290,f297,f300]) ).
fof(f305,plain,
( ~ sQ24_spl
| ~ sQ23_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f86,f290,f297,f300]) ).
fof(f306,plain,
( sQ24_spl
| sQ23_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f87,f290,f297,f300]) ).
fof(f307,definition,
( sQ25_spl
<=> p_14 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f310,definition,
( sQ26_spl
<=> sP12_prd ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f313,plain,
( sQ26_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f91,f300,f307,f310]) ).
fof(f314,plain,
( ~ sQ26_spl
| sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f92,f300,f307,f310]) ).
fof(f315,plain,
( ~ sQ26_spl
| ~ sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f93,f300,f307,f310]) ).
fof(f316,plain,
( sQ26_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f94,f300,f307,f310]) ).
fof(f317,definition,
( sQ27_spl
<=> sP13_prd ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f320,plain,
( sQ27_spl
| ~ sQ0_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f98,f310,f184,f317]) ).
fof(f321,plain,
( ~ sQ27_spl
| sQ0_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f99,f310,f184,f317]) ).
fof(f322,plain,
( ~ sQ27_spl
| ~ sQ0_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f100,f310,f184,f317]) ).
fof(f323,plain,
( sQ27_spl
| sQ0_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f101,f310,f184,f317]) ).
fof(f324,definition,
( sQ28_spl
<=> sP14_prd ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f327,plain,
( sQ28_spl
| ~ sQ1_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f105,f317,f187,f324]) ).
fof(f328,plain,
( ~ sQ28_spl
| sQ1_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f106,f317,f187,f324]) ).
fof(f329,plain,
( ~ sQ28_spl
| ~ sQ1_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f107,f317,f187,f324]) ).
fof(f330,plain,
( sQ28_spl
| sQ1_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f108,f317,f187,f324]) ).
fof(f331,definition,
( sQ29_spl
<=> sP15_prd ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( sQ29_spl
| ~ sQ3_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f112,f324,f197,f331]) ).
fof(f335,plain,
( ~ sQ29_spl
| sQ3_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f113,f324,f197,f331]) ).
fof(f336,plain,
( ~ sQ29_spl
| ~ sQ3_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f114,f324,f197,f331]) ).
fof(f337,plain,
( sQ29_spl
| sQ3_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f115,f324,f197,f331]) ).
fof(f338,definition,
( sQ30_spl
<=> sP16_prd ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f341,plain,
( sQ30_spl
| ~ sQ5_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f119,f331,f207,f338]) ).
fof(f342,plain,
( ~ sQ30_spl
| sQ5_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f120,f331,f207,f338]) ).
fof(f343,plain,
( ~ sQ30_spl
| ~ sQ5_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f121,f331,f207,f338]) ).
fof(f344,plain,
( sQ30_spl
| sQ5_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f122,f331,f207,f338]) ).
fof(f345,definition,
( sQ31_spl
<=> sP17_prd ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f348,plain,
( sQ31_spl
| ~ sQ7_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f126,f338,f217,f345]) ).
fof(f349,plain,
( ~ sQ31_spl
| sQ7_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f127,f338,f217,f345]) ).
fof(f350,plain,
( ~ sQ31_spl
| ~ sQ7_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f128,f338,f217,f345]) ).
fof(f351,plain,
( sQ31_spl
| sQ7_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f129,f338,f217,f345]) ).
fof(f352,definition,
( sQ32_spl
<=> sP18_prd ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f355,plain,
( sQ32_spl
| ~ sQ9_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f133,f345,f227,f352]) ).
fof(f356,plain,
( ~ sQ32_spl
| sQ9_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f134,f345,f227,f352]) ).
fof(f357,plain,
( ~ sQ32_spl
| ~ sQ9_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f135,f345,f227,f352]) ).
fof(f358,plain,
( sQ32_spl
| sQ9_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f136,f345,f227,f352]) ).
fof(f359,definition,
( sQ33_spl
<=> sP19_prd ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f362,plain,
( sQ33_spl
| ~ sQ11_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f140,f352,f237,f359]) ).
fof(f363,plain,
( ~ sQ33_spl
| sQ11_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f141,f352,f237,f359]) ).
fof(f364,plain,
( ~ sQ33_spl
| ~ sQ11_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f142,f352,f237,f359]) ).
fof(f365,plain,
( sQ33_spl
| sQ11_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f143,f352,f237,f359]) ).
fof(f366,definition,
( sQ34_spl
<=> sP20_prd ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f369,plain,
( sQ34_spl
| ~ sQ13_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f147,f359,f247,f366]) ).
fof(f370,plain,
( ~ sQ34_spl
| sQ13_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f148,f359,f247,f366]) ).
fof(f371,plain,
( ~ sQ34_spl
| ~ sQ13_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f149,f359,f247,f366]) ).
fof(f372,plain,
( sQ34_spl
| sQ13_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f150,f359,f247,f366]) ).
fof(f373,definition,
( sQ35_spl
<=> sP21_prd ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f376,plain,
( sQ35_spl
| ~ sQ15_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f154,f366,f257,f373]) ).
fof(f377,plain,
( ~ sQ35_spl
| sQ15_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f155,f366,f257,f373]) ).
fof(f378,plain,
( ~ sQ35_spl
| ~ sQ15_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f156,f366,f257,f373]) ).
fof(f379,plain,
( sQ35_spl
| sQ15_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f157,f366,f257,f373]) ).
fof(f380,definition,
( sQ36_spl
<=> sP22_prd ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f383,plain,
( sQ36_spl
| ~ sQ17_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f161,f373,f267,f380]) ).
fof(f384,plain,
( ~ sQ36_spl
| sQ17_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f162,f373,f267,f380]) ).
fof(f385,plain,
( ~ sQ36_spl
| ~ sQ17_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f163,f373,f267,f380]) ).
fof(f386,plain,
( sQ36_spl
| sQ17_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f164,f373,f267,f380]) ).
fof(f387,definition,
( sQ37_spl
<=> sP23_prd ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f390,plain,
( sQ37_spl
| ~ sQ19_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f168,f380,f277,f387]) ).
fof(f391,plain,
( ~ sQ37_spl
| sQ19_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f169,f380,f277,f387]) ).
fof(f392,plain,
( ~ sQ37_spl
| ~ sQ19_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f170,f380,f277,f387]) ).
fof(f393,plain,
( sQ37_spl
| sQ19_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f171,f380,f277,f387]) ).
fof(f394,definition,
( sQ38_spl
<=> sP24_prd ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f397,plain,
( sQ38_spl
| ~ sQ21_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f175,f387,f287,f394]) ).
fof(f398,plain,
( ~ sQ38_spl
| sQ21_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f176,f387,f287,f394]) ).
fof(f399,plain,
( ~ sQ38_spl
| ~ sQ21_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f177,f387,f287,f394]) ).
fof(f400,plain,
( sQ38_spl
| sQ21_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f178,f387,f287,f394]) ).
fof(f401,plain,
( sQ25_spl
| ~ sQ23_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f180,f394,f297,f307]) ).
fof(f402,plain,
( ~ sQ25_spl
| sQ23_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f181,f394,f297,f307]) ).
fof(f403,plain,
( ~ sQ25_spl
| ~ sQ23_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f182,f394,f297,f307]) ).
fof(f404,plain,
( sQ25_spl
| sQ23_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f183,f394,f297,f307]) ).
fof(f405,plain,
$false,
inference(sat_refutation,[status(thm)],[f193,f194,f195,f196,f203,f204,f205,f206,f213,f214,f215,f216,f223,f224,f225,f226,f233,f234,f235,f236,f243,f244,f245,f246,f253,f254,f255,f256,f263,f264,f265,f266,f273,f274,f275,f276,f283,f284,f285,f286,f293,f294,f295,f296,f303,f304,f305,f306,f313,f314,f315,f316,f320,f321,f322,f323,f327,f328,f329,f330,f334,f335,f336,f337,f341,f342,f343,f344,f348,f349,f350,f351,f355,f356,f357,f358,f362,f363,f364,f365,f369,f370,f371,f372,f376,f377,f378,f379,f383,f384,f385,f386,f390,f391,f392,f393,f397,f398,f399,f400,f401,f402,f403,f404]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN007+1.014 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 10:39:47 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.13/0.43 % Refutation found
% 0.13/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.075745 seconds
% 0.13/0.44 % CPU time: 0.409547 seconds
% 0.13/0.44 % Total memory used: 20.860 MB
% 0.13/0.44 % Net memory used: 20.795 MB
%------------------------------------------------------------------------------