%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP129-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 12:32:47 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.47s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 83
% Syntax : Number of formulae : 617 ( 21 unt; 64 def)
% Number of atoms : 1571 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1787 ( 833 ~; 890 |; 0 &)
% ( 64 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 68 ( 67 usr; 65 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 165 ( 165 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( product(e_4,X,Y)
| product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( product(X,e_4,Y)
| product(X,e_3,Y)
| product(X,e_2,Y)
| product(X,e_1,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [Y,X,Z1,Z2] :
( ~ product(X,Z1,Z2)
| ~ product(Z1,Y,Z2)
| product(Y,X,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [X,Z1,Z2,Y] :
( ~ product(Y,X,Z1)
| ~ product(Z1,Y,Z2)
| product(X,Z1,Z2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y] :
( product(X,Y,e_4)
| product(X,Y,e_3)
| product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
! [Y,X,Z1,Z2] :
( product(Z1,Y,Z2)
| ~ product(X,Z1,Z2)
| ~ product(Y,X,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [X0,X1] :
( product(e_4,X0,X1)
| product(e_3,X0,X1)
| product(e_2,X0,X1)
| product(e_1,X0,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f27,plain,
! [X0,X1] :
( product(X0,e_4,X1)
| product(X0,e_3,X1)
| product(X0,e_2,X1)
| product(X0,e_1,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f28,plain,
! [X,Z1,Z2] :
( ~ product(X,Z1,Z2)
| ! [Y] :
( ~ product(Z1,Y,Z2)
| product(Y,X,Z1) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ~ product(X1,X2,X3)
| ~ product(X2,X0,X3)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X,Z1,Y] :
( ~ product(Y,X,Z1)
| ! [Z2] :
( ~ product(Z1,Y,Z2)
| product(X,Z1,Z2) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,X0,X1)
| ~ product(X1,X3,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f33,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f34,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f35,plain,
group_element(e_4),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f37,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f38,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f40,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f41,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f44,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f48,plain,
! [X0,X1] :
( product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f49,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
! [Y,Z1,Z2] :
( product(Z1,Y,Z2)
| ! [X] :
( ~ product(X,Z1,Z2)
| ~ product(Y,X,Z1) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( product(X2,X0,X3)
| ~ product(X1,X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0] :
( product(X0,e_4,e_1)
| product(X0,e_3,e_1)
| product(X0,e_2,e_1)
| product(X0,e_1,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f32,f27]) ).
fof(f58,plain,
! [X0] :
( product(e_4,X0,e_1)
| product(e_3,X0,e_1)
| product(e_2,X0,e_1)
| product(e_1,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f32,f26]) ).
fof(f59,plain,
! [X0] :
( product(X0,e_4,e_2)
| product(X0,e_3,e_2)
| product(X0,e_2,e_2)
| product(X0,e_1,e_2)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f33,f27]) ).
fof(f60,plain,
! [X0] :
( product(e_4,X0,e_2)
| product(e_3,X0,e_2)
| product(e_2,X0,e_2)
| product(e_1,X0,e_2)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f33,f26]) ).
fof(f61,plain,
! [X0] :
( product(X0,e_4,e_3)
| product(X0,e_3,e_3)
| product(X0,e_2,e_3)
| product(X0,e_1,e_3)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f34,f27]) ).
fof(f62,plain,
! [X0] :
( product(e_4,X0,e_3)
| product(e_3,X0,e_3)
| product(e_2,X0,e_3)
| product(e_1,X0,e_3)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f34,f26]) ).
fof(f63,plain,
! [X0] :
( product(X0,e_4,e_4)
| product(X0,e_3,e_4)
| product(X0,e_2,e_4)
| product(X0,e_1,e_4)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f35,f27]) ).
fof(f64,plain,
! [X0] :
( product(e_4,X0,e_4)
| product(e_3,X0,e_4)
| product(e_2,X0,e_4)
| product(e_1,X0,e_4)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f35,f26]) ).
fof(f65,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f36,f54]) ).
fof(f66,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f36,f52]) ).
fof(f67,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f36,f50]) ).
fof(f68,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f37,f54]) ).
fof(f69,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f37,f52]) ).
fof(f70,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f37,f50]) ).
fof(f71,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f38,f54]) ).
fof(f72,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f38,f52]) ).
fof(f73,plain,
! [X0,X1] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f38,f50]) ).
fof(f77,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f40,f54]) ).
fof(f78,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f40,f52]) ).
fof(f79,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f40,f50]) ).
fof(f80,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f41,f54]) ).
fof(f81,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f41,f52]) ).
fof(f82,plain,
! [X0,X1] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f41,f50]) ).
fof(f89,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f44,f54]) ).
fof(f90,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f44,f52]) ).
fof(f91,plain,
! [X0,X1] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_3) ),
inference(resolution,[status(thm)],[f44,f50]) ).
fof(f101,plain,
! [X0] :
( product(X0,e_4,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f48,f35]) ).
fof(f102,plain,
! [X0] :
( product(X0,e_3,e_4)
| product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f48,f34]) ).
fof(f103,plain,
! [X0] :
( product(X0,e_2,e_4)
| product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f48,f33]) ).
fof(f104,plain,
! [X0] :
( product(X0,e_1,e_4)
| product(X0,e_1,e_3)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f48,f32]) ).
fof(f105,plain,
( product(e_4,e_4,e_1)
| product(e_4,e_3,e_1)
| product(e_4,e_2,e_1)
| product(e_4,e_1,e_1) ),
inference(resolution,[status(thm)],[f57,f35]) ).
fof(f106,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f57,f34]) ).
fof(f107,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f57,f33]) ).
fof(f108,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f57,f32]) ).
fof(f109,definition,
( sQ0_spl
<=> product(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ0_spl
| product(e_4,e_1,e_1) ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,definition,
( sQ1_spl
<=> product(e_4,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( ~ sQ1_spl
| product(e_4,e_2,e_1) ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,definition,
( sQ2_spl
<=> product(e_4,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ2_spl
| product(e_4,e_3,e_1) ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,definition,
( sQ3_spl
<=> product(e_4,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ3_spl
| product(e_4,e_4,e_1) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( sQ3_spl
| sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f105,f109,f112,f115,f118]) ).
fof(f122,definition,
( sQ4_spl
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( ~ sQ4_spl
| product(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,definition,
( sQ5_spl
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ5_spl
| product(e_3,e_2,e_1) ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,definition,
( sQ6_spl
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( ~ sQ6_spl
| product(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f131,definition,
( sQ7_spl
<=> product(e_3,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ7_spl
| product(e_3,e_4,e_1) ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,plain,
( sQ7_spl
| sQ6_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f106,f122,f125,f128,f131]) ).
fof(f135,definition,
( sQ8_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ8_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,definition,
( sQ9_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( ~ sQ9_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,definition,
( sQ10_spl
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ10_spl
| product(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,definition,
( sQ11_spl
<=> product(e_2,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( ~ sQ11_spl
| product(e_2,e_4,e_1) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( sQ11_spl
| sQ10_spl
| sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f107,f135,f138,f141,f144]) ).
fof(f148,definition,
( sQ12_spl
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f149,plain,
( ~ sQ12_spl
| product(e_1,e_1,e_1) ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f151,definition,
( sQ13_spl
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( ~ sQ13_spl
| product(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,definition,
( sQ14_spl
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( ~ sQ14_spl
| product(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
( sQ15_spl
<=> product(e_1,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ15_spl
| product(e_1,e_4,e_1) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f108,f148,f151,f154,f157]) ).
fof(f162,plain,
( product(e_4,e_3,e_1)
| product(e_3,e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f58,f34]) ).
fof(f163,plain,
( product(e_4,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f58,f33]) ).
fof(f164,plain,
( product(e_4,e_1,e_1)
| product(e_3,e_1,e_1)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f58,f32]) ).
fof(f166,plain,
( sQ2_spl
| sQ6_spl
| sQ10_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f162,f154,f141,f128,f115]) ).
fof(f167,plain,
( sQ1_spl
| sQ5_spl
| sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f163,f151,f138,f125,f112]) ).
fof(f168,plain,
( sQ0_spl
| sQ4_spl
| sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f164,f148,f135,f122,f109]) ).
fof(f169,plain,
( product(e_4,e_4,e_2)
| product(e_4,e_3,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_1,e_2) ),
inference(resolution,[status(thm)],[f59,f35]) ).
fof(f170,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_1,e_2) ),
inference(resolution,[status(thm)],[f59,f34]) ).
fof(f171,plain,
( product(e_2,e_4,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f59,f33]) ).
fof(f172,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f59,f32]) ).
fof(f173,definition,
( sQ16_spl
<=> product(e_4,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ16_spl
| product(e_4,e_1,e_2) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,definition,
( sQ17_spl
<=> product(e_4,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( ~ sQ17_spl
| product(e_4,e_2,e_2) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,definition,
( sQ18_spl
<=> product(e_4,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ18_spl
| product(e_4,e_3,e_2) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,definition,
( sQ19_spl
<=> product(e_4,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( ~ sQ19_spl
| product(e_4,e_4,e_2) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,plain,
( sQ19_spl
| sQ18_spl
| sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f169,f173,f176,f179,f182]) ).
fof(f186,definition,
( sQ20_spl
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( ~ sQ20_spl
| product(e_3,e_1,e_2) ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,definition,
( sQ21_spl
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ21_spl
| product(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,definition,
( sQ22_spl
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ22_spl
| product(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,definition,
( sQ23_spl
<=> product(e_3,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( ~ sQ23_spl
| product(e_3,e_4,e_2) ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,plain,
( sQ23_spl
| sQ22_spl
| sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f170,f186,f189,f192,f195]) ).
fof(f199,definition,
( sQ24_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( ~ sQ24_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,definition,
( sQ25_spl
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( ~ sQ25_spl
| product(e_2,e_2,e_2) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
( sQ26_spl
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( ~ sQ26_spl
| product(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
( sQ27_spl
<=> product(e_2,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( ~ sQ27_spl
| product(e_2,e_4,e_2) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,plain,
( sQ27_spl
| sQ26_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f171,f199,f202,f205,f208]) ).
fof(f212,definition,
( sQ28_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( ~ sQ28_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f215,definition,
( sQ29_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f216,plain,
( ~ sQ29_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,definition,
( sQ30_spl
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f219,plain,
( ~ sQ30_spl
| product(e_1,e_3,e_2) ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,definition,
( sQ31_spl
<=> product(e_1,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( ~ sQ31_spl
| product(e_1,e_4,e_2) ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,plain,
( sQ31_spl
| sQ30_spl
| sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f172,f212,f215,f218,f221]) ).
fof(f225,plain,
( product(e_4,e_4,e_2)
| product(e_3,e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_1,e_4,e_2) ),
inference(resolution,[status(thm)],[f60,f35]) ).
fof(f226,plain,
( product(e_4,e_3,e_2)
| product(e_3,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f60,f34]) ).
fof(f227,plain,
( product(e_4,e_2,e_2)
| product(e_3,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f60,f33]) ).
fof(f228,plain,
( product(e_4,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f60,f32]) ).
fof(f229,plain,
( sQ19_spl
| sQ23_spl
| sQ27_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f225,f221,f208,f195,f182]) ).
fof(f230,plain,
( sQ18_spl
| sQ22_spl
| sQ26_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f226,f218,f205,f192,f179]) ).
fof(f231,plain,
( sQ17_spl
| sQ21_spl
| sQ25_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f227,f215,f202,f189,f176]) ).
fof(f232,plain,
( sQ16_spl
| sQ20_spl
| sQ24_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f228,f212,f199,f186,f173]) ).
fof(f233,plain,
( product(e_4,e_4,e_3)
| product(e_4,e_3,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[f61,f35]) ).
fof(f235,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_3,e_3)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[f61,f33]) ).
fof(f236,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_3,e_3)
| product(e_1,e_2,e_3)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f61,f32]) ).
fof(f237,definition,
( sQ32_spl
<=> product(e_4,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( ~ sQ32_spl
| product(e_4,e_1,e_3) ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,definition,
( sQ33_spl
<=> product(e_4,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( ~ sQ33_spl
| product(e_4,e_2,e_3) ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,definition,
( sQ34_spl
<=> product(e_4,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( ~ sQ34_spl
| product(e_4,e_3,e_3) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f246,definition,
( sQ35_spl
<=> product(e_4,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( ~ sQ35_spl
| product(e_4,e_4,e_3) ),
inference(component_clause,[status(thm)],[f246]) ).
fof(f249,plain,
( sQ35_spl
| sQ34_spl
| sQ33_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f233,f237,f240,f243,f246]) ).
fof(f250,definition,
( sQ36_spl
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f251,plain,
( ~ sQ36_spl
| product(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f253,definition,
( sQ37_spl
<=> product(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( ~ sQ37_spl
| product(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,definition,
( sQ38_spl
<=> product(e_3,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( ~ sQ38_spl
| product(e_3,e_3,e_3) ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f259,definition,
( sQ39_spl
<=> product(e_3,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( ~ sQ39_spl
| product(e_3,e_4,e_3) ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f263,definition,
( sQ40_spl
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( ~ sQ40_spl
| product(e_2,e_1,e_3) ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,definition,
( sQ41_spl
<=> product(e_2,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( ~ sQ41_spl
| product(e_2,e_2,e_3) ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f269,definition,
( sQ42_spl
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f270,plain,
( ~ sQ42_spl
| product(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f272,definition,
( sQ43_spl
<=> product(e_2,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( ~ sQ43_spl
| product(e_2,e_4,e_3) ),
inference(component_clause,[status(thm)],[f272]) ).
fof(f275,plain,
( sQ43_spl
| sQ42_spl
| sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f235,f263,f266,f269,f272]) ).
fof(f276,definition,
( sQ44_spl
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f277,plain,
( ~ sQ44_spl
| product(e_1,e_1,e_3) ),
inference(component_clause,[status(thm)],[f276]) ).
fof(f279,definition,
( sQ45_spl
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( ~ sQ45_spl
| product(e_1,e_2,e_3) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,definition,
( sQ46_spl
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f283,plain,
( ~ sQ46_spl
| product(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f285,definition,
( sQ47_spl
<=> product(e_1,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( ~ sQ47_spl
| product(e_1,e_4,e_3) ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,plain,
( sQ47_spl
| sQ46_spl
| sQ45_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f236,f276,f279,f282,f285]) ).
fof(f290,plain,
( product(e_4,e_3,e_3)
| product(e_3,e_3,e_3)
| product(e_2,e_3,e_3)
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f62,f34]) ).
fof(f292,plain,
( product(e_4,e_1,e_3)
| product(e_3,e_1,e_3)
| product(e_2,e_1,e_3)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f62,f32]) ).
fof(f294,plain,
( sQ34_spl
| sQ38_spl
| sQ42_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f290,f282,f269,f256,f243]) ).
fof(f296,plain,
( sQ32_spl
| sQ36_spl
| sQ40_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f292,f276,f263,f250,f237]) ).
fof(f297,plain,
( product(e_4,e_4,e_4)
| product(e_4,e_3,e_4)
| product(e_4,e_2,e_4)
| product(e_4,e_1,e_4) ),
inference(resolution,[status(thm)],[f63,f35]) ).
fof(f299,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_3,e_4)
| product(e_2,e_2,e_4)
| product(e_2,e_1,e_4) ),
inference(resolution,[status(thm)],[f63,f33]) ).
fof(f300,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_3,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_1,e_4) ),
inference(resolution,[status(thm)],[f63,f32]) ).
fof(f301,definition,
( sQ48_spl
<=> product(e_4,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f302,plain,
( ~ sQ48_spl
| product(e_4,e_1,e_4) ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f304,definition,
( sQ49_spl
<=> product(e_4,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f305,plain,
( ~ sQ49_spl
| product(e_4,e_2,e_4) ),
inference(component_clause,[status(thm)],[f304]) ).
fof(f307,definition,
( sQ50_spl
<=> product(e_4,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f308,plain,
( ~ sQ50_spl
| product(e_4,e_3,e_4) ),
inference(component_clause,[status(thm)],[f307]) ).
fof(f310,definition,
( sQ51_spl
<=> product(e_4,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( ~ sQ51_spl
| product(e_4,e_4,e_4) ),
inference(component_clause,[status(thm)],[f310]) ).
fof(f313,plain,
( sQ51_spl
| sQ50_spl
| sQ49_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f297,f301,f304,f307,f310]) ).
fof(f314,definition,
( sQ52_spl
<=> product(e_3,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( ~ sQ52_spl
| product(e_3,e_1,e_4) ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f317,definition,
( sQ53_spl
<=> product(e_3,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f318,plain,
( ~ sQ53_spl
| product(e_3,e_2,e_4) ),
inference(component_clause,[status(thm)],[f317]) ).
fof(f320,definition,
( sQ54_spl
<=> product(e_3,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f321,plain,
( ~ sQ54_spl
| product(e_3,e_3,e_4) ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,definition,
( sQ55_spl
<=> product(e_3,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f324,plain,
( ~ sQ55_spl
| product(e_3,e_4,e_4) ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f327,definition,
( sQ56_spl
<=> product(e_2,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f328,plain,
( ~ sQ56_spl
| product(e_2,e_1,e_4) ),
inference(component_clause,[status(thm)],[f327]) ).
fof(f330,definition,
( sQ57_spl
<=> product(e_2,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( ~ sQ57_spl
| product(e_2,e_2,e_4) ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f333,definition,
( sQ58_spl
<=> product(e_2,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( ~ sQ58_spl
| product(e_2,e_3,e_4) ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f336,definition,
( sQ59_spl
<=> product(e_2,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( ~ sQ59_spl
| product(e_2,e_4,e_4) ),
inference(component_clause,[status(thm)],[f336]) ).
fof(f339,plain,
( sQ59_spl
| sQ58_spl
| sQ57_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f299,f327,f330,f333,f336]) ).
fof(f340,definition,
( sQ60_spl
<=> product(e_1,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f341,plain,
( ~ sQ60_spl
| product(e_1,e_1,e_4) ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f343,definition,
( sQ61_spl
<=> product(e_1,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f344,plain,
( ~ sQ61_spl
| product(e_1,e_2,e_4) ),
inference(component_clause,[status(thm)],[f343]) ).
fof(f346,definition,
( sQ62_spl
<=> product(e_1,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f347,plain,
( ~ sQ62_spl
| product(e_1,e_3,e_4) ),
inference(component_clause,[status(thm)],[f346]) ).
fof(f349,definition,
( sQ63_spl
<=> product(e_1,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f350,plain,
( ~ sQ63_spl
| product(e_1,e_4,e_4) ),
inference(component_clause,[status(thm)],[f349]) ).
fof(f352,plain,
( sQ63_spl
| sQ62_spl
| sQ61_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f300,f340,f343,f346,f349]) ).
fof(f353,plain,
( product(e_4,e_4,e_4)
| product(e_3,e_4,e_4)
| product(e_2,e_4,e_4)
| product(e_1,e_4,e_4) ),
inference(resolution,[status(thm)],[f64,f35]) ).
fof(f354,plain,
( product(e_4,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[f64,f34]) ).
fof(f355,plain,
( product(e_4,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[f64,f33]) ).
fof(f356,plain,
( product(e_4,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_1,e_1,e_4) ),
inference(resolution,[status(thm)],[f64,f32]) ).
fof(f357,plain,
( sQ51_spl
| sQ55_spl
| sQ59_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f353,f349,f336,f323,f310]) ).
fof(f358,plain,
( sQ50_spl
| sQ54_spl
| sQ58_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f354,f346,f333,f320,f307]) ).
fof(f359,plain,
( sQ49_spl
| sQ53_spl
| sQ57_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f355,f343,f330,f317,f304]) ).
fof(f360,plain,
( sQ48_spl
| sQ52_spl
| sQ56_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f356,f340,f327,f314,f301]) ).
fof(f361,plain,
( product(e_4,e_4,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1) ),
inference(resolution,[status(thm)],[f101,f35]) ).
fof(f362,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[f101,f34]) ).
fof(f363,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[f101,f33]) ).
fof(f364,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(resolution,[status(thm)],[f101,f32]) ).
fof(f365,plain,
( sQ51_spl
| sQ35_spl
| sQ19_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f361,f118,f182,f246,f310]) ).
fof(f366,plain,
( sQ55_spl
| sQ39_spl
| sQ23_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f362,f131,f195,f259,f323]) ).
fof(f367,plain,
( sQ59_spl
| sQ43_spl
| sQ27_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f363,f144,f208,f272,f336]) ).
fof(f368,plain,
( sQ63_spl
| sQ47_spl
| sQ31_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f364,f157,f221,f285,f349]) ).
fof(f369,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolution,[status(thm)],[f102,f35]) ).
fof(f371,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f102,f33]) ).
fof(f372,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f102,f32]) ).
fof(f373,plain,
( sQ50_spl
| sQ34_spl
| sQ18_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f369,f115,f179,f243,f307]) ).
fof(f375,plain,
( sQ58_spl
| sQ42_spl
| sQ26_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f371,f141,f205,f269,f333]) ).
fof(f376,plain,
( sQ62_spl
| sQ46_spl
| sQ30_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f372,f154,f218,f282,f346]) ).
fof(f377,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[f103,f35]) ).
fof(f378,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f103,f34]) ).
fof(f379,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f103,f33]) ).
fof(f380,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f103,f32]) ).
fof(f381,plain,
( sQ49_spl
| sQ33_spl
| sQ17_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f377,f112,f176,f240,f304]) ).
fof(f382,plain,
( sQ53_spl
| sQ37_spl
| sQ21_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f378,f125,f189,f253,f317]) ).
fof(f383,plain,
( sQ57_spl
| sQ41_spl
| sQ25_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f379,f138,f202,f266,f330]) ).
fof(f384,plain,
( sQ61_spl
| sQ45_spl
| sQ29_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f380,f151,f215,f279,f343]) ).
fof(f385,plain,
( ~ sQ3_spl
| ~ product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[f119,f89]) ).
fof(f386,plain,
( ~ sQ3_spl
| ~ product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[f119,f80]) ).
fof(f387,plain,
( ~ sQ3_spl
| ~ product(e_1,e_4,e_1) ),
inference(resolution,[status(thm)],[f119,f71]) ).
fof(f397,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f385,f132]) ).
fof(f398,plain,
( ~ sQ3_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f397]) ).
fof(f399,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(resolution,[status(thm)],[f104,f35]) ).
fof(f400,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f104,f34]) ).
fof(f401,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f104,f33]) ).
fof(f402,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f104,f32]) ).
fof(f403,plain,
( sQ48_spl
| sQ32_spl
| sQ16_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f399,f109,f173,f237,f301]) ).
fof(f404,plain,
( sQ52_spl
| sQ36_spl
| sQ20_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f400,f122,f186,f250,f314]) ).
fof(f405,plain,
( sQ56_spl
| sQ40_spl
| sQ24_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f401,f135,f199,f263,f327]) ).
fof(f406,plain,
( sQ60_spl
| sQ44_spl
| sQ28_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f402,f148,f212,f276,f340]) ).
fof(f407,plain,
( ~ sQ0_spl
| ~ product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f110,f89]) ).
fof(f408,plain,
( ~ sQ0_spl
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f110,f80]) ).
fof(f409,plain,
( ~ sQ0_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f110,f71]) ).
fof(f411,plain,
! [X0] :
( ~ sQ0_spl
| ~ product(e_1,e_4,X0)
| product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f110,f31]) ).
fof(f414,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f407,f123]) ).
fof(f415,plain,
( ~ sQ0_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f414]) ).
fof(f416,plain,
( ~ sQ1_spl
| ~ product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f113,f89]) ).
fof(f417,plain,
( ~ sQ1_spl
| ~ product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f113,f80]) ).
fof(f418,plain,
( ~ sQ1_spl
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f113,f71]) ).
fof(f422,plain,
! [X0] :
( ~ sQ1_spl
| ~ product(e_2,X0,e_1)
| product(X0,e_4,e_2) ),
inference(resolution,[status(thm)],[f113,f29]) ).
fof(f424,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f416,f126]) ).
fof(f425,plain,
( ~ sQ1_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f424]) ).
fof(f426,plain,
( ~ sQ2_spl
| ~ product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f116,f89]) ).
fof(f427,plain,
( ~ sQ2_spl
| ~ product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f116,f80]) ).
fof(f428,plain,
( ~ sQ2_spl
| ~ product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f116,f71]) ).
fof(f429,plain,
( ~ sQ2_spl
| ~ product(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[f116,f78]) ).
fof(f431,plain,
! [X0] :
( ~ sQ2_spl
| product(e_3,X0,e_1)
| ~ product(X0,e_4,e_3) ),
inference(resolution,[status(thm)],[f116,f56]) ).
fof(f432,plain,
! [X0] :
( ~ sQ2_spl
| ~ product(e_1,e_4,X0)
| product(e_3,e_1,X0) ),
inference(resolution,[status(thm)],[f116,f31]) ).
fof(f435,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f426,f129]) ).
fof(f436,plain,
( ~ sQ2_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f435]) ).
fof(f437,plain,
( ~ sQ2_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f427,f142]) ).
fof(f438,plain,
( ~ sQ2_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f437]) ).
fof(f439,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f417,f139]) ).
fof(f440,plain,
( ~ sQ1_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f439]) ).
fof(f441,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f386,f145]) ).
fof(f442,plain,
( ~ sQ3_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f441]) ).
fof(f443,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f387,f158]) ).
fof(f444,plain,
( ~ sQ3_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f443]) ).
fof(f445,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f408,f136]) ).
fof(f446,plain,
( ~ sQ0_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f445]) ).
fof(f447,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f409,f149]) ).
fof(f448,plain,
( ~ sQ0_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f447]) ).
fof(f449,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f428,f155]) ).
fof(f450,plain,
( ~ sQ2_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( ~ sQ31_spl
| ~ product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f222,f90]) ).
fof(f454,plain,
( ~ sQ31_spl
| ~ product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f222,f72]) ).
fof(f460,plain,
( ~ sQ31_spl
| ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f452,f219]) ).
fof(f461,plain,
( ~ sQ31_spl
| ~ sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f460]) ).
fof(f462,plain,
( ~ sQ29_spl
| ~ product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f216,f66]) ).
fof(f463,plain,
( ~ sQ29_spl
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f216,f67]) ).
fof(f465,plain,
! [X0] :
( ~ sQ29_spl
| ~ product(e_2,e_1,X0)
| product(e_2,e_2,X0) ),
inference(resolution,[status(thm)],[f216,f31]) ).
fof(f468,plain,
( ~ sQ29_spl
| ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f462,f213]) ).
fof(f469,plain,
( ~ sQ29_spl
| ~ sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f468]) ).
fof(f470,plain,
( ~ sQ29_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f463,f152]) ).
fof(f471,plain,
( ~ sQ29_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f470]) ).
fof(f472,plain,
( ~ sQ27_spl
| ~ product(e_1,e_4,e_2) ),
inference(resolution,[status(thm)],[f209,f65]) ).
fof(f474,plain,
( ~ sQ27_spl
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f209,f81]) ).
fof(f478,plain,
! [X0] :
( ~ sQ27_spl
| ~ product(e_2,e_2,X0)
| product(e_4,e_2,X0) ),
inference(resolution,[status(thm)],[f209,f31]) ).
fof(f481,plain,
( ~ sQ27_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f472,f222]) ).
fof(f482,plain,
( ~ sQ27_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f481]) ).
fof(f483,plain,
( ~ sQ8_spl
| ~ sQ29_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f136,f488]) ).
fof(f484,plain,
( ~ sQ56_spl
| ~ sQ29_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f328,f488]) ).
fof(f485,plain,
( ~ sQ40_spl
| ~ sQ29_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f264,f488]) ).
fof(f486,plain,
( ~ sQ24_spl
| ~ sQ29_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f200,f488]) ).
fof(f488,plain,
! [X0] :
( ~ sQ29_spl
| ~ product(e_2,e_1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f465,f66]) ).
fof(f489,plain,
( ~ sQ8_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f483]) ).
fof(f491,plain,
( ~ sQ26_spl
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f206,f78]) ).
fof(f495,plain,
! [X0] :
( ~ sQ26_spl
| ~ product(e_2,e_2,X0)
| product(e_3,e_2,X0) ),
inference(resolution,[status(thm)],[f206,f31]) ).
fof(f498,plain,
( ~ sQ26_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f203]) ).
fof(f499,plain,
( ~ sQ26_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f498]) ).
fof(f500,plain,
( ~ sQ23_spl
| ~ product(e_2,e_4,e_2) ),
inference(resolution,[status(thm)],[f196,f77]) ).
fof(f501,plain,
( ~ sQ23_spl
| ~ product(e_1,e_4,e_2) ),
inference(resolution,[status(thm)],[f196,f68]) ).
fof(f503,plain,
( ~ sQ23_spl
| ~ product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f196,f81]) ).
fof(f505,plain,
( ~ sQ23_spl
| ~ product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[f196,f67]) ).
fof(f510,plain,
( ~ sQ23_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f501,f222]) ).
fof(f511,plain,
( ~ sQ23_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f512,plain,
( ~ sQ56_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f484]) ).
fof(f513,plain,
( ~ sQ40_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f485]) ).
fof(f515,plain,
( ~ sQ22_spl
| ~ product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f193,f68]) ).
fof(f516,plain,
( ~ sQ22_spl
| ~ product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f193,f78]) ).
fof(f518,plain,
( ~ sQ22_spl
| ~ product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f193,f67]) ).
fof(f519,plain,
! [X0] :
( ~ sQ22_spl
| product(e_3,X0,e_2)
| ~ product(X0,e_3,e_3) ),
inference(resolution,[status(thm)],[f193,f56]) ).
fof(f523,plain,
( ~ sQ22_spl
| product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f193,f29]) ).
fof(f525,plain,
( ~ sQ22_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f516,f190]) ).
fof(f526,plain,
( ~ sQ22_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f525]) ).
fof(f527,plain,
( ~ sQ20_spl
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f187,f77]) ).
fof(f528,plain,
( ~ sQ20_spl
| ~ product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f187,f68]) ).
fof(f529,plain,
( ~ sQ20_spl
| ~ product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f187,f67]) ).
fof(f534,plain,
( ~ sQ20_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f200]) ).
fof(f535,plain,
( ~ sQ20_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f536,plain,
( ~ sQ9_spl
| ~ sQ26_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f139,f539]) ).
fof(f537,plain,
( ~ sQ57_spl
| ~ sQ26_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f331,f539]) ).
fof(f538,plain,
( ~ sQ41_spl
| ~ sQ26_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f267,f539]) ).
fof(f539,plain,
! [X0] :
( ~ sQ26_spl
| ~ product(e_2,e_2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f495,f77]) ).
fof(f541,plain,
( ~ sQ9_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f536]) ).
fof(f542,plain,
( ~ sQ4_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f123,f529]) ).
fof(f543,plain,
( ~ sQ4_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f542]) ).
fof(f544,plain,
( ~ sQ24_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f486]) ).
fof(f545,plain,
( ~ sQ6_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f129,f518]) ).
fof(f546,plain,
( ~ sQ6_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f545]) ).
fof(f547,plain,
( ~ sQ1_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f418,f151,f112]) ).
fof(f548,plain,
( ~ sQ23_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f500,f208,f195]) ).
fof(f549,plain,
( ~ sQ41_spl
| ~ sQ27_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f267,f551]) ).
fof(f550,plain,
( ~ sQ57_spl
| ~ sQ27_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f331,f551]) ).
fof(f551,plain,
! [X0] :
( ~ sQ27_spl
| ~ product(e_2,e_2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f478,f80]) ).
fof(f552,plain,
( ~ sQ15_spl
| ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f158,f555]) ).
fof(f553,plain,
( ~ sQ47_spl
| ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f286,f555]) ).
fof(f554,plain,
( ~ sQ63_spl
| ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f350,f555]) ).
fof(f555,plain,
! [X0] :
( ~ sQ0_spl
| ~ product(e_1,e_4,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f411,f72]) ).
fof(f556,plain,
( ~ sQ41_spl
| ~ sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f549]) ).
fof(f557,plain,
( ~ sQ15_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f558,plain,
( ~ sQ20_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f528,f212,f186]) ).
fof(f559,plain,
( ~ sQ57_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f537]) ).
fof(f560,plain,
( ~ sQ22_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f515,f218,f192]) ).
fof(f561,plain,
( ~ sQ16_spl
| ~ product(e_3,e_1,e_2) ),
inference(resolution,[status(thm)],[f174,f89]) ).
fof(f562,plain,
( ~ sQ16_spl
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f174,f80]) ).
fof(f563,plain,
( ~ sQ16_spl
| ~ product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f174,f71]) ).
fof(f569,plain,
( ~ sQ16_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f563,f212,f173]) ).
fof(f570,plain,
( ~ sQ17_spl
| ~ product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f177,f89]) ).
fof(f576,plain,
! [X0] :
( ~ sQ17_spl
| ~ product(e_2,e_4,X0)
| product(e_2,e_2,X0) ),
inference(resolution,[status(thm)],[f177,f31]) ).
fof(f579,plain,
( ~ sQ17_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f570,f189,f176]) ).
fof(f581,plain,
( ~ sQ59_spl
| ~ sQ17_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f337,f584]) ).
fof(f582,plain,
( ~ sQ11_spl
| ~ sQ17_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f145,f584]) ).
fof(f583,plain,
( ~ sQ43_spl
| ~ sQ17_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f273,f584]) ).
fof(f584,plain,
! [X0] :
( ~ sQ17_spl
| ~ product(e_2,e_4,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f576,f81]) ).
fof(f585,plain,
( ~ sQ59_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f581]) ).
fof(f586,plain,
( ~ sQ11_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f582]) ).
fof(f589,plain,
( ~ sQ18_spl
| ~ product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f180,f71]) ).
fof(f590,plain,
( ~ sQ18_spl
| ~ product(e_4,e_2,e_2) ),
inference(resolution,[status(thm)],[f180,f78]) ).
fof(f591,plain,
( ~ sQ18_spl
| ~ product(e_4,e_1,e_2) ),
inference(resolution,[status(thm)],[f180,f69]) ).
fof(f592,plain,
( ~ sQ18_spl
| ~ product(e_4,e_3,e_1) ),
inference(resolution,[status(thm)],[f180,f67]) ).
fof(f595,plain,
! [X0] :
( ~ sQ18_spl
| ~ product(e_3,X0,e_2)
| product(X0,e_4,e_3) ),
inference(resolution,[status(thm)],[f180,f29]) ).
fof(f596,plain,
! [X0] :
( ~ sQ18_spl
| ~ product(X0,e_4,e_2)
| product(e_3,X0,e_4) ),
inference(resolution,[status(thm)],[f180,f29]) ).
fof(f597,plain,
( ~ sQ18_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f589,f218,f179]) ).
fof(f598,plain,
( ~ sQ18_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f592,f115,f179]) ).
fof(f599,plain,
( ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f590,f176,f179]) ).
fof(f600,plain,
( ~ sQ43_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f583]) ).
fof(f601,plain,
( ~ sQ47_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f553]) ).
fof(f602,plain,
( ~ sQ22_spl
| ~ sQ46_spl
| product(e_3,e_1,e_2) ),
inference(resolution,[status(thm)],[f283,f519]) ).
fof(f603,plain,
( ~ sQ46_spl
| ~ product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[f283,f78]) ).
fof(f605,plain,
( ~ sQ46_spl
| ~ product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f283,f79]) ).
fof(f606,plain,
( ~ sQ46_spl
| ~ product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f283,f70]) ).
fof(f608,plain,
! [X0] :
( ~ sQ46_spl
| ~ product(e_3,e_1,X0)
| product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f283,f31]) ).
fof(f611,plain,
( ~ sQ22_spl
| ~ sQ46_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f602,f186,f282,f192]) ).
fof(f612,plain,
( ~ sQ46_spl
| ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f603,f280]) ).
fof(f613,plain,
( ~ sQ46_spl
| ~ sQ45_spl ),
inference(contradiction_clause,[status(thm)],[f612]) ).
fof(f615,plain,
( ~ sQ44_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f277,f70]) ).
fof(f620,plain,
( ~ sQ44_spl
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f277,f29]) ).
fof(f623,plain,
( ~ sQ44_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f615,f148,f276]) ).
fof(f628,plain,
( ~ sQ42_spl
| ~ product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f270,f70]) ).
fof(f630,plain,
! [X0] :
( ~ sQ42_spl
| ~ product(e_3,e_2,X0)
| product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f270,f31]) ).
fof(f634,plain,
( ~ sQ21_spl
| ~ sQ42_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f190,f637]) ).
fof(f635,plain,
( ~ sQ53_spl
| ~ sQ42_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f318,f637]) ).
fof(f636,plain,
( ~ sQ37_spl
| ~ sQ42_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f254,f637]) ).
fof(f637,plain,
! [X0] :
( ~ sQ42_spl
| ~ product(e_3,e_2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f630,f78]) ).
fof(f638,plain,
( ~ sQ21_spl
| ~ sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f634]) ).
fof(f639,plain,
( ~ sQ23_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f505,f131,f195]) ).
fof(f640,plain,
( ~ sQ24_spl
| ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f200,f562]) ).
fof(f641,plain,
( ~ sQ24_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f640]) ).
fof(f644,plain,
( ~ sQ38_spl
| ~ product(e_3,e_2,e_3) ),
inference(resolution,[status(thm)],[f257,f78]) ).
fof(f645,plain,
( ~ sQ38_spl
| ~ product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[f257,f69]) ).
fof(f646,plain,
( ~ sQ38_spl
| ~ product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[f257,f79]) ).
fof(f654,plain,
( ~ sQ38_spl
| ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f644,f254]) ).
fof(f655,plain,
( ~ sQ38_spl
| ~ sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f654]) ).
fof(f656,plain,
( ~ sQ38_spl
| ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f645,f251]) ).
fof(f657,plain,
( ~ sQ38_spl
| ~ sQ36_spl ),
inference(contradiction_clause,[status(thm)],[f656]) ).
fof(f658,plain,
( ~ sQ57_spl
| ~ sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f550]) ).
fof(f659,plain,
( ~ sQ32_spl
| ~ product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[f238,f89]) ).
fof(f660,plain,
( ~ sQ32_spl
| ~ product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[f238,f80]) ).
fof(f662,plain,
( ~ sQ32_spl
| ~ product(e_4,e_1,e_2) ),
inference(resolution,[status(thm)],[f238,f79]) ).
fof(f669,plain,
( ~ sQ33_spl
| ~ product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f241,f80]) ).
fof(f670,plain,
( ~ sQ33_spl
| ~ product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[f241,f71]) ).
fof(f671,plain,
( ~ sQ33_spl
| ~ product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[f241,f66]) ).
fof(f672,plain,
( ~ sQ33_spl
| ~ product(e_4,e_2,e_2) ),
inference(resolution,[status(thm)],[f241,f79]) ).
fof(f673,plain,
( ~ sQ33_spl
| ~ product(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[f241,f70]) ).
fof(f678,plain,
( ~ sQ33_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f669,f266,f240]) ).
fof(f679,plain,
( ~ sQ33_spl
| ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f671,f238]) ).
fof(f680,plain,
( ~ sQ33_spl
| ~ sQ32_spl ),
inference(contradiction_clause,[status(thm)],[f679]) ).
fof(f681,plain,
( ~ sQ63_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f554]) ).
fof(f682,plain,
( ~ sQ44_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f620,f148,f276]) ).
fof(f690,plain,
( ~ sQ34_spl
| ~ product(e_4,e_3,e_1) ),
inference(resolution,[status(thm)],[f244,f70]) ).
fof(f692,plain,
! [X0] :
( ~ sQ34_spl
| ~ product(e_3,e_4,X0)
| product(e_3,e_3,X0) ),
inference(resolution,[status(thm)],[f244,f31]) ).
fof(f695,plain,
( ~ sQ34_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f690,f115,f243]) ).
fof(f696,plain,
( ~ sQ55_spl
| ~ sQ34_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f324,f699]) ).
fof(f697,plain,
( ~ sQ7_spl
| ~ sQ34_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f132,f699]) ).
fof(f698,plain,
( ~ sQ39_spl
| ~ sQ34_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f260,f699]) ).
fof(f699,plain,
! [X0] :
( ~ sQ34_spl
| ~ product(e_3,e_4,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f692,f90]) ).
fof(f700,plain,
( ~ sQ55_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f696]) ).
fof(f701,plain,
( ~ sQ46_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f605,f218,f282]) ).
fof(f702,plain,
( ~ sQ46_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f606,f154,f282]) ).
fof(f703,plain,
( ~ sQ36_spl
| ~ sQ46_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f251,f706]) ).
fof(f704,plain,
( ~ sQ52_spl
| ~ sQ46_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f315,f706]) ).
fof(f705,plain,
( ~ sQ20_spl
| ~ sQ46_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f187,f706]) ).
fof(f706,plain,
! [X0] :
( ~ sQ46_spl
| ~ product(e_3,e_1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f608,f69]) ).
fof(f707,plain,
( ~ sQ36_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f703]) ).
fof(f709,plain,
( ~ sQ37_spl
| ~ sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f636]) ).
fof(f710,plain,
( ~ sQ41_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f538]) ).
fof(f711,plain,
( ~ sQ39_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f698]) ).
fof(f712,plain,
( ~ sQ36_spl
| ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f251,f659]) ).
fof(f713,plain,
( ~ sQ36_spl
| ~ sQ32_spl ),
inference(contradiction_clause,[status(thm)],[f712]) ).
fof(f714,plain,
( ~ sQ53_spl
| ~ sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f635]) ).
fof(f715,plain,
( ~ sQ42_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f628,f141,f269]) ).
fof(f716,plain,
( ~ sQ5_spl
| ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f126,f637]) ).
fof(f717,plain,
( ~ sQ5_spl
| ~ sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f716]) ).
fof(f718,plain,
( ~ sQ22_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f523,f256,f192]) ).
fof(f730,plain,
! [X0] :
( ~ sQ49_spl
| ~ product(e_4,e_4,X0)
| product(e_2,e_4,X0) ),
inference(resolution,[status(thm)],[f305,f31]) ).
fof(f736,plain,
( ~ sQ33_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f670,f279,f240]) ).
fof(f739,plain,
( ~ sQ51_spl
| ~ sQ49_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f311,f742]) ).
fof(f740,plain,
( ~ sQ35_spl
| ~ sQ49_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f247,f742]) ).
fof(f741,plain,
( ~ sQ19_spl
| ~ sQ49_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f183,f742]) ).
fof(f742,plain,
! [X0] :
( ~ sQ49_spl
| ~ product(e_4,e_4,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f730,f80]) ).
fof(f743,plain,
( ~ sQ51_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f739]) ).
fof(f744,plain,
( ~ sQ35_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f740]) ).
fof(f745,plain,
( ~ sQ33_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f672,f176,f240]) ).
fof(f746,plain,
( ~ sQ27_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f209,f584]) ).
fof(f747,plain,
( ~ sQ27_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f746]) ).
fof(f748,plain,
( ~ sQ38_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f646,f192,f256]) ).
fof(f749,plain,
( ~ sQ33_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f673,f112,f240]) ).
fof(f750,plain,
( ~ sQ19_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f741]) ).
fof(f753,plain,
( ~ sQ60_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f341,f73]) ).
fof(f756,plain,
( ~ sQ60_spl
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f341,f29]) ).
fof(f760,plain,
( ~ sQ60_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f756,f148,f340]) ).
fof(f762,plain,
( ~ sQ60_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f753,f148,f340]) ).
fof(f763,plain,
( ~ sQ52_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f704]) ).
fof(f764,plain,
( ~ sQ62_spl
| ~ product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[f347,f78]) ).
fof(f767,plain,
( ~ sQ62_spl
| ~ product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f347,f82]) ).
fof(f768,plain,
( ~ sQ62_spl
| ~ product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f347,f73]) ).
fof(f773,plain,
( ~ sQ62_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f764,f343,f346]) ).
fof(f774,plain,
( ~ sQ62_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f767,f218,f346]) ).
fof(f775,plain,
( ~ sQ50_spl
| ~ product(e_3,e_3,e_4) ),
inference(resolution,[status(thm)],[f308,f89]) ).
fof(f776,plain,
( ~ sQ50_spl
| ~ product(e_2,e_3,e_4) ),
inference(resolution,[status(thm)],[f308,f80]) ).
fof(f779,plain,
( ~ sQ50_spl
| ~ product(e_4,e_1,e_4) ),
inference(resolution,[status(thm)],[f308,f69]) ).
fof(f780,plain,
( ~ sQ50_spl
| ~ product(e_4,e_3,e_3) ),
inference(resolution,[status(thm)],[f308,f91]) ).
fof(f781,plain,
( ~ sQ50_spl
| ~ product(e_4,e_3,e_2) ),
inference(resolution,[status(thm)],[f308,f82]) ).
fof(f784,plain,
! [X0] :
( ~ sQ50_spl
| ~ product(e_4,e_4,X0)
| product(e_3,e_4,X0) ),
inference(resolution,[status(thm)],[f308,f31]) ).
fof(f787,plain,
( ~ sQ50_spl
| ~ sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f775,f321]) ).
fof(f788,plain,
( ~ sQ50_spl
| ~ sQ54_spl ),
inference(contradiction_clause,[status(thm)],[f787]) ).
fof(f789,plain,
( ~ sQ4_spl
| ~ sQ46_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f123,f706]) ).
fof(f790,plain,
( ~ sQ4_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f789]) ).
fof(f791,plain,
( ~ sQ50_spl
| ~ sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f776,f334]) ).
fof(f792,plain,
( ~ sQ50_spl
| ~ sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f791]) ).
fof(f793,plain,
( ~ sQ19_spl
| ~ product(e_3,e_4,e_2) ),
inference(resolution,[status(thm)],[f183,f89]) ).
fof(f794,plain,
( ~ sQ19_spl
| ~ product(e_2,e_4,e_2) ),
inference(resolution,[status(thm)],[f183,f80]) ).
fof(f796,plain,
( ~ sQ19_spl
| ~ product(e_4,e_3,e_2) ),
inference(resolution,[status(thm)],[f183,f90]) ).
fof(f799,plain,
( ~ sQ19_spl
| ~ product(e_4,e_4,e_1) ),
inference(resolution,[status(thm)],[f183,f67]) ).
fof(f806,plain,
( ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f796,f179,f182]) ).
fof(f807,plain,
( ~ sQ19_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f799,f118,f182]) ).
fof(f809,plain,
( ~ sQ27_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f474,f202,f208]) ).
fof(f810,plain,
( ~ sQ50_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f779,f301,f307]) ).
fof(f811,plain,
( ~ sQ50_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f780,f243,f307]) ).
fof(f812,plain,
( ~ sQ51_spl
| ~ sQ50_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f311,f813]) ).
fof(f813,plain,
! [X0] :
( ~ sQ50_spl
| ~ product(e_4,e_4,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f784,f89]) ).
fof(f814,plain,
( ~ sQ7_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f697]) ).
fof(f815,plain,
( ~ sQ16_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f561,f186,f173]) ).
fof(f817,plain,
( ~ sQ20_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f705]) ).
fof(f818,plain,
( ~ sQ31_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f454,f212,f221]) ).
fof(f820,plain,
( ~ sQ43_spl
| ~ product(e_1,e_4,e_3) ),
inference(resolution,[status(thm)],[f273,f65]) ).
fof(f821,plain,
( ~ sQ2_spl
| ~ sQ43_spl
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f273,f431]) ).
fof(f825,plain,
( ~ sQ43_spl
| ~ product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[f273,f72]) ).
fof(f827,plain,
( ~ sQ43_spl
| ~ product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[f273,f70]) ).
fof(f832,plain,
( ~ sQ43_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f820,f285,f272]) ).
fof(f833,plain,
( ~ sQ43_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f825,f263,f272]) ).
fof(f834,plain,
( ~ sQ43_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f827,f144,f272]) ).
fof(f836,plain,
( ~ sQ32_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f660,f263,f237]) ).
fof(f837,plain,
( ~ sQ23_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f793]) ).
fof(f838,plain,
( ~ sQ23_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f837]) ).
fof(f839,plain,
( ~ sQ62_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f768,f154,f346]) ).
fof(f840,plain,
( ~ sQ2_spl
| ~ sQ43_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f821,f125,f272,f115]) ).
fof(f841,plain,
( ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f429,f112,f115]) ).
fof(f842,plain,
( ~ sQ32_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f662,f173,f237]) ).
fof(f843,plain,
( ~ sQ23_spl
| ~ sQ34_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f196,f699]) ).
fof(f844,plain,
( ~ sQ23_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f843]) ).
fof(f845,plain,
( ~ sQ51_spl
| ~ sQ50_spl ),
inference(contradiction_clause,[status(thm)],[f812]) ).
fof(f853,plain,
! [X0] :
( ~ sQ63_spl
| ~ product(e_4,e_1,X0)
| product(e_4,e_4,X0) ),
inference(resolution,[status(thm)],[f350,f31]) ).
fof(f857,plain,
( ~ sQ48_spl
| ~ sQ63_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f302,f859]) ).
fof(f858,plain,
( ~ sQ32_spl
| ~ sQ63_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f238,f859]) ).
fof(f859,plain,
! [X0] :
( ~ sQ63_spl
| ~ product(e_4,e_1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f853,f72]) ).
fof(f860,plain,
( ~ sQ48_spl
| ~ sQ63_spl ),
inference(contradiction_clause,[status(thm)],[f857]) ).
fof(f861,plain,
( ~ sQ35_spl
| ~ sQ50_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f247,f813]) ).
fof(f862,plain,
( ~ sQ50_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f781,f179,f307]) ).
fof(f863,plain,
( ~ sQ35_spl
| ~ sQ50_spl ),
inference(contradiction_clause,[status(thm)],[f861]) ).
fof(f871,plain,
( ~ sQ53_spl
| ~ product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[f318,f68]) ).
fof(f872,plain,
( ~ sQ53_spl
| ~ product(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[f318,f66]) ).
fof(f877,plain,
! [X0] :
( ~ sQ53_spl
| ~ product(e_4,e_3,X0)
| product(e_2,e_4,X0) ),
inference(resolution,[status(thm)],[f318,f31]) ).
fof(f880,plain,
( ~ sQ53_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f871,f343,f317]) ).
fof(f881,plain,
( ~ sQ53_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f872,f314,f317]) ).
fof(f886,plain,
( ~ sQ25_spl
| ~ product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f203,f67]) ).
fof(f893,plain,
( ~ sQ25_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f886,f138,f202]) ).
fof(f894,plain,
( ~ sQ19_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f794,f208,f182]) ).
fof(f895,plain,
( ~ sQ9_spl
| ~ sQ27_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f139,f551]) ).
fof(f896,plain,
( ~ sQ9_spl
| ~ sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f895]) ).
fof(f919,plain,
( ~ sQ61_spl
| ~ product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[f344,f91]) ).
fof(f921,plain,
( ~ sQ61_spl
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f344,f73]) ).
fof(f926,plain,
( ~ sQ61_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f921,f151,f343]) ).
fof(f928,plain,
( ~ sQ32_spl
| ~ sQ63_spl ),
inference(contradiction_clause,[status(thm)],[f858]) ).
fof(f930,plain,
( ~ sQ18_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f591,f173,f179]) ).
fof(f931,plain,
( ~ sQ16_spl
| ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f174,f859]) ).
fof(f932,plain,
( ~ sQ16_spl
| ~ sQ63_spl ),
inference(contradiction_clause,[status(thm)],[f931]) ).
fof(f959,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| product(e_3,e_4,e_2) ),
inference(resolution,[status(thm)],[f142,f422]) ).
fof(f960,plain,
( ~ sQ10_spl
| ~ product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f142,f65]) ).
fof(f968,plain,
( ~ sQ53_spl
| ~ sQ18_spl
| product(e_2,e_4,e_2) ),
inference(resolution,[status(thm)],[f180,f877]) ).
fof(f982,plain,
( ~ sQ53_spl
| ~ sQ18_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f968,f208,f179,f317]) ).
fof(f983,plain,
( ~ sQ61_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f919,f279,f343]) ).
fof(f984,plain,
( ~ sQ10_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f960,f154,f141]) ).
fof(f985,plain,
( ~ sQ21_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f503]) ).
fof(f986,plain,
( ~ sQ21_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f985]) ).
fof(f987,plain,
( ~ sQ3_spl
| ~ sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f742]) ).
fof(f988,plain,
( ~ sQ3_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f987]) ).
fof(f990,plain,
( ~ sQ59_spl
| ~ product(e_2,e_3,e_4) ),
inference(resolution,[status(thm)],[f337,f90]) ).
fof(f997,plain,
! [X0] :
( ~ sQ59_spl
| ~ product(e_4,e_2,X0)
| product(e_4,e_4,X0) ),
inference(resolution,[status(thm)],[f337,f31]) ).
fof(f1000,plain,
( ~ sQ59_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f990,f333,f336]) ).
fof(f1001,plain,
( ~ sQ33_spl
| ~ sQ59_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f241,f1003]) ).
fof(f1003,plain,
! [X0] :
( ~ sQ59_spl
| ~ product(e_4,e_2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f997,f81]) ).
fof(f1004,plain,
( ~ sQ33_spl
| ~ sQ59_spl ),
inference(contradiction_clause,[status(thm)],[f1001]) ).
fof(f1005,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f959,f195,f141,f112]) ).
fof(f1006,plain,
( ~ sQ51_spl
| ~ product(e_3,e_4,e_4) ),
inference(resolution,[status(thm)],[f311,f89]) ).
fof(f1012,plain,
( ~ sQ51_spl
| ~ product(e_4,e_4,e_3) ),
inference(resolution,[status(thm)],[f311,f91]) ).
fof(f1021,plain,
( ~ sQ51_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f1006,f323,f310]) ).
fof(f1022,plain,
( ~ sQ51_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f1012,f246,f310]) ).
fof(f1042,plain,
( ~ sQ18_spl
| ~ sQ31_spl
| product(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[f222,f596]) ).
fof(f1051,plain,
( ~ sQ18_spl
| ~ sQ31_spl
| ~ product(e_2,e_1,e_4) ),
inference(resolution,[status(thm)],[f1042,f77]) ).
fof(f1055,plain,
( ~ sQ18_spl
| ~ sQ31_spl
| ~ product(e_3,e_1,e_2) ),
inference(resolution,[status(thm)],[f1042,f82]) ).
fof(f1056,plain,
( ~ sQ18_spl
| ~ sQ31_spl
| ~ product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f1042,f73]) ).
fof(f1061,plain,
( ~ sQ18_spl
| ~ sQ31_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1055,f186,f221,f179]) ).
fof(f1062,plain,
( ~ sQ18_spl
| ~ sQ31_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1056,f122,f221,f179]) ).
fof(f1063,plain,
( ~ sQ56_spl
| ~ sQ18_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f328,f1051]) ).
fof(f1064,plain,
( ~ sQ56_spl
| ~ sQ18_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f1063]) ).
fof(f1076,plain,
( ~ sQ18_spl
| ~ sQ21_spl
| product(e_2,e_4,e_3) ),
inference(resolution,[status(thm)],[f190,f595]) ).
fof(f1082,plain,
! [X0] :
( ~ sQ21_spl
| ~ product(e_2,e_3,X0)
| product(e_2,e_2,X0) ),
inference(resolution,[status(thm)],[f190,f31]) ).
fof(f1085,plain,
( ~ sQ18_spl
| ~ sQ21_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f1076,f272,f189,f179]) ).
fof(f1086,plain,
( ~ sQ58_spl
| ~ sQ21_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f334,f1087]) ).
fof(f1087,plain,
! [X0] :
( ~ sQ21_spl
| ~ product(e_2,e_3,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1082,f78]) ).
fof(f1088,plain,
( ~ sQ58_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f1086]) ).
fof(f1097,plain,
( ~ sQ2_spl
| ~ sQ47_spl
| product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[f286,f432]) ).
fof(f1108,plain,
( ~ sQ2_spl
| ~ sQ47_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f1097,f250,f285,f115]) ).
fof(f1109,plain,
$false,
inference(sat_refutation,[status(thm)],[f121,f134,f147,f160,f166,f167,f168,f185,f198,f211,f224,f229,f230,f231,f232,f249,f275,f288,f294,f296,f313,f339,f352,f357,f358,f359,f360,f365,f366,f367,f368,f373,f375,f376,f381,f382,f383,f384,f398,f403,f404,f405,f406,f415,f425,f436,f438,f440,f442,f444,f446,f448,f450,f461,f469,f471,f482,f489,f499,f511,f512,f513,f526,f535,f541,f543,f544,f546,f547,f548,f556,f557,f558,f559,f560,f569,f579,f585,f586,f597,f598,f599,f600,f601,f611,f613,f623,f638,f639,f641,f655,f657,f658,f678,f680,f681,f682,f695,f700,f701,f702,f707,f709,f710,f711,f713,f714,f715,f717,f718,f736,f743,f744,f745,f747,f748,f749,f750,f760,f762,f763,f773,f774,f788,f790,f792,f806,f807,f809,f810,f811,f814,f815,f817,f818,f832,f833,f834,f836,f838,f839,f840,f841,f842,f844,f845,f860,f862,f863,f880,f881,f893,f894,f896,f926,f928,f930,f932,f982,f983,f984,f986,f988,f1000,f1004,f1005,f1021,f1022,f1061,f1062,f1064,f1085,f1088,f1108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP129-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.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 : Sun Sep 20 20:01:39 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.47 % Refutation found
% 0.13/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.50 % Elapsed time: 0.127002 seconds
% 0.13/0.50 % CPU time: 0.844296 seconds
% 0.13/0.50 % Total memory used: 27.697 MB
% 0.13/0.50 % Net memory used: 26.837 MB
%------------------------------------------------------------------------------