%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP126-3.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12:32:44 PM UTC 2026
% Result : Unsatisfiable 4.14s 1.01s
% Output : CNFRefutation 0.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 218
% Syntax : Number of formulae : 797 ( 126 unt; 176 def)
% Number of atoms : 3003 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 3295 (1089 ~;2030 |; 0 &)
% ( 176 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 183 ( 182 usr; 177 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 410 ( 410 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
next(e_0,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
next(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
next(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
greater(e_1,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
greater(e_2,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
greater(e_3,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
greater(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
greater(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
greater(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
greater(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
greater(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y,Z] :
( equalish(Y,Z)
| ~ cycle(X,Z)
| ~ cycle(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X] :
( cycle(X,e_3)
| cycle(X,e_2)
| cycle(X,e_1)
| cycle(X,e_0)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
cycle(e_4,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,W,Z,Z1] :
( equalish(Y,Z1)
| ~ next(Z,Z1)
| ~ greater(Y,e_0)
| ~ next(X,W)
| ~ cycle(W,Z)
| ~ cycle(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Z1,Y,W,Z2] :
( ~ greater(Z1,Z2)
| ~ greater(Y,X)
| ~ next(Y,W)
| ~ cycle(W,Z2)
| ~ cycle(Y,e_0)
| ~ cycle(X,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X,Y] :
( ~ greater(Y,X)
| ~ product(X,e_1,Y)
| ~ cycle(X,e_0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y,Z,X1] :
( equalish(Z,X1)
| ~ next(X,X1)
| ~ greater(Y,e_0)
| ~ product(X,e_1,Z)
| ~ cycle(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,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(f39,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,Y)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,plain,
next(e_0,e_1),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f45,plain,
next(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f46,plain,
next(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f47,plain,
next(e_3,e_4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f48,plain,
greater(e_1,e_0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f49,plain,
greater(e_2,e_0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f50,plain,
greater(e_3,e_0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f52,plain,
greater(e_2,e_1),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f53,plain,
greater(e_3,e_1),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f54,plain,
greater(e_4,e_1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f55,plain,
greater(e_3,e_2),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f56,plain,
greater(e_4,e_2),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f57,plain,
greater(e_4,e_3),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f58,plain,
! [Y,Z] :
( equalish(Y,Z)
| ! [X] :
( ~ cycle(X,Z)
| ~ cycle(X,Y) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f59,plain,
! [X0,X1,X2] :
( equalish(X1,X2)
| ~ cycle(X0,X2)
| ~ cycle(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
! [X0] :
( cycle(X0,e_3)
| cycle(X0,e_2)
| cycle(X0,e_1)
| cycle(X0,e_0)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f61,plain,
cycle(e_4,e_0),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f62,plain,
! [Y,Z1] :
( equalish(Y,Z1)
| ! [Z] :
( ~ next(Z,Z1)
| ~ greater(Y,e_0)
| ! [X,W] :
( ~ next(X,W)
| ~ cycle(W,Z)
| ~ cycle(X,Y) ) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f63,plain,
! [X0,X1,X2,X3,X4] :
( equalish(X1,X4)
| ~ next(X3,X4)
| ~ greater(X1,e_0)
| ~ next(X0,X2)
| ~ cycle(X2,X3)
| ~ cycle(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [Z1,Z2] :
( ~ greater(Z1,Z2)
| ! [X,Y] :
( ~ greater(Y,X)
| ! [W] :
( ~ next(Y,W)
| ~ cycle(W,Z2)
| ~ cycle(Y,e_0)
| ~ cycle(X,Z1) ) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4] :
( ~ greater(X1,X4)
| ~ greater(X2,X0)
| ~ next(X2,X3)
| ~ cycle(X3,X4)
| ~ cycle(X2,e_0)
| ~ cycle(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| ~ product(X0,e_1,X1)
| ~ cycle(X0,e_0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f67,plain,
! [Z,X1] :
( equalish(Z,X1)
| ! [X] :
( ~ next(X,X1)
| ! [Y] :
( ~ greater(Y,e_0)
| ~ product(X,e_1,Z)
| ~ cycle(X,Y) ) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ next(X0,X3)
| ~ greater(X1,e_0)
| ~ product(X0,e_1,X2)
| ~ cycle(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f70,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f71,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f72,plain,
group_element(e_4),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f73,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f74,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f75,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f76,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f77,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f78,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f79,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f80,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f81,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f82,plain,
~ equalish(e_4,e_1),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f83,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f84,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f85,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)],[f38]) ).
fof(f86,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f89,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f90,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f92,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f93,plain,
! [Y,Z1,Z2] :
( product(Z1,Z2,Y)
| ! [X] :
( ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( product(X1,X0,X0)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f92,f94]) ).
fof(f97,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f87,f92]) ).
fof(f99,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[f89,f92]) ).
fof(f101,plain,
! [X0,X1] :
( equalish(X0,X1)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[f91,f92]) ).
fof(f104,plain,
! [X0,X1] :
( equalish(X1,e_0)
| ~ cycle(X0,X1)
| cycle(X0,e_3)
| cycle(X0,e_2)
| cycle(X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f60,f59]) ).
fof(f106,plain,
! [X0,X1,X2,X3] :
( cycle(X2,e_3)
| cycle(X2,e_2)
| cycle(X2,e_1)
| ~ group_element(X2)
| equalish(X1,X3)
| ~ next(e_0,X3)
| ~ greater(X1,e_0)
| ~ next(X0,X2)
| ~ cycle(X0,X1) ),
inference(resolution,[status(thm)],[f63,f60]) ).
fof(f108,plain,
! [X0,X1,X2] :
( equalish(X0,X2)
| ~ next(X1,X2)
| ~ greater(X0,e_0)
| ~ cycle(e_4,X1)
| ~ cycle(e_3,X0) ),
inference(resolution,[status(thm)],[f63,f47]) ).
fof(f113,plain,
! [X0] :
( equalish(X0,e_1)
| ~ greater(X0,e_0)
| ~ cycle(e_1,e_0)
| ~ cycle(e_0,X0) ),
inference(resolution,[status(thm)],[f63,f44]) ).
fof(f136,definition,
( sQ5_spl
<=> cycle(e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ5_spl
| cycle(e_2,e_1) ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f140,definition,
! [X0] :
( sQ6_spl
<=> ( equalish(X0,e_1)
| ~ greater(X0,e_0)
| ~ cycle(e_0,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f141,plain,
! [X0] :
( ~ sQ6_spl
| equalish(X0,e_1)
| ~ greater(X0,e_0)
| ~ cycle(e_0,X0) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,definition,
( sQ7_spl
<=> cycle(e_1,e_0) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( ~ sQ7_spl
| cycle(e_1,e_0) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f145,plain,
( sQ7_spl
| ~ cycle(e_1,e_0) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,plain,
( ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f113,f140,f143]) ).
fof(f149,definition,
( sQ8_spl
<=> equalish(e_0,e_0) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f152,definition,
( sQ9_spl
<=> group_element(e_4) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( sQ9_spl
| ~ group_element(e_4) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f181,plain,
! [X0,X1,X2] :
( ~ greater(X1,X2)
| ~ greater(e_1,X0)
| ~ cycle(e_2,X2)
| ~ cycle(e_1,e_0)
| ~ cycle(X0,X1) ),
inference(resolution,[status(thm)],[f65,f45]) ).
fof(f200,definition,
( sQ18_spl
<=> cycle(e_2,e_0) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f202,plain,
( sQ18_spl
| ~ cycle(e_2,e_0) ),
inference(component_clause,[status(thm)],[f200]) ).
fof(f204,definition,
! [X0,X1,X2] :
( sQ19_spl
<=> ( ~ greater(X1,X2)
| ~ greater(e_1,X0)
| ~ cycle(e_2,X2)
| ~ cycle(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( ~ sQ7_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f181,f204,f143]) ).
fof(f215,plain,
( sQ7_spl
| cycle(e_1,e_3)
| cycle(e_1,e_2)
| cycle(e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f145,f60]) ).
fof(f216,definition,
( sQ22_spl
<=> group_element(e_1) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( sQ22_spl
| ~ group_element(e_1) ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,definition,
( sQ23_spl
<=> cycle(e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( ~ sQ23_spl
| cycle(e_1,e_1) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,definition,
( sQ24_spl
<=> cycle(e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f223,plain,
( ~ sQ24_spl
| cycle(e_1,e_2) ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f225,definition,
( sQ25_spl
<=> cycle(e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( ~ sQ25_spl
| cycle(e_1,e_3) ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f228,plain,
( sQ7_spl
| sQ25_spl
| sQ24_spl
| sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f215,f216,f219,f222,f225,f143]) ).
fof(f229,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f218,f69]) ).
fof(f230,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f229]) ).
fof(f238,definition,
( sQ28_spl
<=> cycle(e_0,e_2) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( ~ sQ28_spl
| cycle(e_0,e_2) ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f245,plain,
( sQ18_spl
| cycle(e_2,e_3)
| cycle(e_2,e_2)
| cycle(e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f202,f60]) ).
fof(f246,definition,
( sQ30_spl
<=> group_element(e_2) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( sQ30_spl
| ~ group_element(e_2) ),
inference(component_clause,[status(thm)],[f246]) ).
fof(f249,definition,
( sQ31_spl
<=> cycle(e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( ~ sQ31_spl
| cycle(e_2,e_2) ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f252,definition,
( sQ32_spl
<=> cycle(e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f253,plain,
( ~ sQ32_spl
| cycle(e_2,e_3) ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,plain,
( sQ18_spl
| sQ32_spl
| sQ31_spl
| sQ5_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f245,f246,f136,f249,f252,f200]) ).
fof(f256,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f248,f70]) ).
fof(f257,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f256]) ).
fof(f259,definition,
( sQ33_spl
<=> group_element(e_3) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f261,plain,
( sQ33_spl
| ~ group_element(e_3) ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f269,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f261,f71]) ).
fof(f270,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f269]) ).
fof(f286,plain,
( ~ greater(e_1,e_1)
| ~ cycle(e_1,e_0) ),
inference(resolution,[status(thm)],[f66,f92]) ).
fof(f287,definition,
( sQ36_spl
<=> greater(e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f290,plain,
( ~ sQ36_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f286,f143,f287]) ).
fof(f331,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f72]) ).
fof(f332,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f331]) ).
fof(f348,plain,
! [X0,X1] :
( equalish(e_1,X1)
| ~ next(e_1,X1)
| ~ greater(X0,e_0)
| ~ cycle(e_1,X0) ),
inference(resolution,[status(thm)],[f68,f92]) ).
fof(f349,definition,
! [X0] :
( sQ37_spl
<=> ( ~ greater(X0,e_0)
| ~ cycle(e_1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f350,plain,
! [X0] :
( ~ sQ37_spl
| ~ greater(X0,e_0)
| ~ cycle(e_1,X0) ),
inference(component_clause,[status(thm)],[f349]) ).
fof(f352,definition,
! [X1] :
( sQ38_spl
<=> ( equalish(e_1,X1)
| ~ next(e_1,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f353,plain,
! [X0] :
( ~ sQ38_spl
| equalish(e_1,X0)
| ~ next(e_1,X0) ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f355,plain,
( sQ38_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f348,f349,f352]) ).
fof(f356,plain,
! [X0,X1,X2] :
( equalish(e_2,X2)
| ~ next(X0,X2)
| ~ greater(X1,e_0)
| ~ cycle(X0,X1)
| product(X0,e_1,e_4)
| product(X0,e_1,e_3)
| product(X0,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f68]) ).
fof(f357,plain,
! [X0] :
( ~ greater(e_2,X0)
| ~ cycle(X0,e_0)
| product(X0,e_1,e_4)
| product(X0,e_1,e_3)
| product(X0,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f66]) ).
fof(f358,plain,
! [X0] :
( equalish(X0,e_2)
| product(X0,e_2,e_4)
| product(X0,e_2,e_3)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f101]) ).
fof(f359,plain,
! [X0,X1,X2] :
( equalish(X2,X0)
| ~ product(X2,X1,e_2)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f91]) ).
fof(f360,plain,
! [X0] :
( equalish(X0,e_2)
| product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f85,f99]) ).
fof(f361,plain,
! [X0,X1,X2] :
( equalish(X2,X1)
| ~ product(X0,X2,e_2)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f89]) ).
fof(f362,plain,
! [X0] :
( equalish(e_2,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f97]) ).
fof(f363,plain,
! [X0,X1,X2] :
( equalish(X2,e_2)
| ~ product(X0,X1,X2)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f87]) ).
fof(f364,plain,
! [X0] :
( product(e_2,X0,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f95]) ).
fof(f365,plain,
! [X0,X1,X2] :
( product(X2,e_2,X0)
| ~ product(X1,X0,X2)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f94]) ).
fof(f366,plain,
! [X0,X1,X2] :
( equalish(e_3,X2)
| ~ next(X0,X2)
| ~ greater(X1,e_0)
| ~ cycle(X0,X1)
| product(X0,e_1,e_4)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f68]) ).
fof(f367,plain,
! [X0] :
( ~ greater(e_3,X0)
| ~ cycle(X0,e_0)
| product(X0,e_1,e_4)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f66]) ).
fof(f368,plain,
! [X0] :
( equalish(X0,e_3)
| product(X0,e_3,e_4)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f101]) ).
fof(f369,plain,
! [X0,X1,X2] :
( equalish(X2,X0)
| ~ product(X2,X1,e_3)
| product(X0,X1,e_4)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f91]) ).
fof(f370,plain,
! [X0] :
( equalish(X0,e_3)
| product(e_3,X0,e_4)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f85,f99]) ).
fof(f371,plain,
! [X0,X1,X2] :
( equalish(X2,X1)
| ~ product(X0,X2,e_3)
| product(X0,X1,e_4)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f89]) ).
fof(f373,plain,
! [X0,X1,X2] :
( equalish(X2,e_3)
| ~ product(X0,X1,X2)
| product(X0,X1,e_4)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f87]) ).
fof(f374,plain,
! [X0] :
( product(e_3,X0,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f95]) ).
fof(f375,plain,
! [X0,X1,X2] :
( product(X2,e_3,X0)
| ~ product(X1,X0,X2)
| product(X0,X1,e_4)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f94]) ).
fof(f376,plain,
! [X0,X1,X2] :
( equalish(e_4,X2)
| ~ next(X0,X2)
| ~ greater(X1,e_0)
| ~ cycle(X0,X1)
| product(X0,e_1,e_3)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f68]) ).
fof(f377,plain,
! [X0] :
( ~ greater(e_4,X0)
| ~ cycle(X0,e_0)
| product(X0,e_1,e_3)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f66]) ).
fof(f378,plain,
! [X0] :
( equalish(X0,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f101]) ).
fof(f379,plain,
! [X0,X1,X2] :
( equalish(X2,X0)
| ~ product(X2,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(resolution,[status(thm)],[f85,f91]) ).
fof(f380,plain,
! [X0] :
( equalish(X0,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[f85,f99]) ).
fof(f381,plain,
! [X0,X1,X2] :
( equalish(X2,X1)
| ~ product(X0,X2,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f89]) ).
fof(f383,plain,
! [X0,X1,X2] :
( equalish(X2,e_4)
| ~ product(X0,X1,X2)
| product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f87]) ).
fof(f384,plain,
! [X0] :
( product(e_4,X0,X0)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f95]) ).
fof(f385,plain,
! [X0,X1,X2] :
( product(X2,e_4,X0)
| ~ product(X1,X0,X2)
| product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f85,f94]) ).
fof(f386,definition,
! [X0,X1,X2] :
( sQ39_spl
<=> ( equalish(e_2,X2)
| ~ next(X0,X2)
| ~ greater(X1,e_0)
| ~ cycle(X0,X1)
| product(X0,e_1,e_4)
| product(X0,e_1,e_3)
| product(X0,e_1,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f389,plain,
( ~ sQ22_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f356,f386,f216]) ).
fof(f390,definition,
! [X0] :
( sQ40_spl
<=> ( ~ greater(e_2,X0)
| ~ cycle(X0,e_0)
| product(X0,e_1,e_4)
| product(X0,e_1,e_3)
| product(X0,e_1,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f393,plain,
( ~ sQ22_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f357,f390,f216]) ).
fof(f394,definition,
! [X0] :
( sQ41_spl
<=> ( equalish(X0,e_2)
| product(X0,e_2,e_4)
| product(X0,e_2,e_3)
| product(X0,e_2,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f397,plain,
( ~ sQ30_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f358,f394,f246]) ).
fof(f398,definition,
! [X0] :
( sQ42_spl
<=> ( equalish(X0,e_2)
| product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( sQ42_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f360,f246,f398]) ).
fof(f402,plain,
! [X0] :
( equalish(e_2,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f362]) ).
fof(f403,plain,
! [X0] :
( product(e_2,X0,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f364]) ).
fof(f404,definition,
! [X0,X1,X2] :
( sQ43_spl
<=> ( equalish(e_3,X2)
| ~ next(X0,X2)
| ~ greater(X1,e_0)
| ~ cycle(X0,X1)
| product(X0,e_1,e_4)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f407,plain,
( ~ sQ22_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f366,f404,f216]) ).
fof(f408,definition,
! [X0] :
( sQ44_spl
<=> ( ~ greater(e_3,X0)
| ~ cycle(X0,e_0)
| product(X0,e_1,e_4)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f411,plain,
( ~ sQ22_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f367,f408,f216]) ).
fof(f412,definition,
! [X0] :
( sQ45_spl
<=> ( equalish(X0,e_3)
| product(X0,e_3,e_4)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f415,plain,
( ~ sQ33_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f368,f412,f259]) ).
fof(f416,definition,
! [X0] :
( sQ46_spl
<=> ( equalish(X0,e_3)
| product(e_3,X0,e_4)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f419,plain,
( sQ46_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f370,f259,f416]) ).
fof(f421,plain,
! [X0] :
( product(e_3,X0,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f374]) ).
fof(f422,definition,
! [X0,X1,X2] :
( sQ47_spl
<=> ( equalish(e_4,X2)
| ~ next(X0,X2)
| ~ greater(X1,e_0)
| ~ cycle(X0,X1)
| product(X0,e_1,e_3)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f425,plain,
( ~ sQ22_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f376,f422,f216]) ).
fof(f426,definition,
! [X0] :
( sQ48_spl
<=> ( ~ greater(e_4,X0)
| ~ cycle(X0,e_0)
| product(X0,e_1,e_3)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f429,plain,
( ~ sQ22_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f377,f426,f216]) ).
fof(f430,definition,
! [X0] :
( sQ49_spl
<=> ( equalish(X0,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( ~ sQ9_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f378,f430,f152]) ).
fof(f434,definition,
! [X0] :
( sQ50_spl
<=> ( equalish(X0,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( sQ50_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f380,f152,f434]) ).
fof(f439,plain,
! [X0] :
( product(e_4,X0,X0)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f384]) ).
fof(f466,plain,
( equalish(e_3,e_3)
| product(e_2,e_3,e_3)
| product(e_3,e_3,e_4)
| product(e_3,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f403,f101]) ).
fof(f476,plain,
( equalish(e_4,e_4)
| product(e_2,e_4,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_1)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[f403,f101]) ).
fof(f488,plain,
( equalish(e_2,e_2)
| product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f403,f99]) ).
fof(f492,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f403,f95]) ).
fof(f494,definition,
( sQ54_spl
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f497,definition,
( sQ55_spl
<=> product(e_1,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( ~ sQ55_spl
| product(e_1,e_1,e_4) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f499,plain,
( sQ55_spl
| ~ product(e_1,e_1,e_4) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f500,definition,
( sQ56_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f501,plain,
( ~ sQ56_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f500]) ).
fof(f503,definition,
! [X1] :
( sQ57_spl
<=> ( equalish(e_3,X1)
| ~ next(e_1,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f504,plain,
! [X0] :
( ~ sQ57_spl
| equalish(e_3,X0)
| ~ next(e_1,X0) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f507,definition,
( sQ58_spl
<=> greater(e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( sQ58_spl
| ~ greater(e_3,e_1) ),
inference(component_clause,[status(thm)],[f507]) ).
fof(f511,definition,
( sQ59_spl
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f512,plain,
( ~ sQ59_spl
| product(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f514,definition,
( sQ60_spl
<=> product(e_3,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f515,plain,
( ~ sQ60_spl
| product(e_3,e_3,e_4) ),
inference(component_clause,[status(thm)],[f514]) ).
fof(f517,definition,
( sQ61_spl
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f518,plain,
( ~ sQ61_spl
| product(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f519,plain,
( sQ61_spl
| ~ product(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f520,definition,
( sQ62_spl
<=> equalish(e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f523,plain,
( sQ62_spl
| sQ61_spl
| sQ60_spl
| sQ59_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f466,f259,f511,f514,f517,f520]) ).
fof(f525,definition,
( sQ63_spl
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f526,plain,
( ~ sQ63_spl
| product(e_1,e_1,e_3) ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f528,definition,
! [X1] :
( sQ64_spl
<=> ( equalish(e_4,X1)
| ~ next(e_1,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f529,plain,
! [X0] :
( ~ sQ64_spl
| equalish(e_4,X0)
| ~ next(e_1,X0) ),
inference(component_clause,[status(thm)],[f528]) ).
fof(f532,definition,
( sQ65_spl
<=> greater(e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f534,plain,
( sQ65_spl
| ~ greater(e_4,e_1) ),
inference(component_clause,[status(thm)],[f532]) ).
fof(f536,definition,
( sQ66_spl
<=> product(e_4,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f537,plain,
( ~ sQ66_spl
| product(e_4,e_4,e_1) ),
inference(component_clause,[status(thm)],[f536]) ).
fof(f539,definition,
( sQ67_spl
<=> product(e_4,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( ~ sQ67_spl
| product(e_4,e_4,e_3) ),
inference(component_clause,[status(thm)],[f539]) ).
fof(f542,definition,
( sQ68_spl
<=> product(e_2,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f543,plain,
( ~ sQ68_spl
| product(e_2,e_4,e_4) ),
inference(component_clause,[status(thm)],[f542]) ).
fof(f544,plain,
( sQ68_spl
| ~ product(e_2,e_4,e_4) ),
inference(component_clause,[status(thm)],[f542]) ).
fof(f545,definition,
( sQ69_spl
<=> equalish(e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f548,plain,
( sQ69_spl
| sQ68_spl
| sQ67_spl
| sQ66_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f476,f152,f536,f539,f542,f545]) ).
fof(f550,definition,
! [X0] :
( sQ70_spl
<=> ( ~ greater(X0,e_0)
| ~ cycle(e_2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f551,plain,
! [X0] :
( ~ sQ70_spl
| ~ greater(X0,e_0)
| ~ cycle(e_2,X0) ),
inference(component_clause,[status(thm)],[f550]) ).
fof(f553,definition,
! [X1] :
( sQ71_spl
<=> ( equalish(e_1,X1)
| ~ next(e_2,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f554,plain,
! [X0] :
( ~ sQ71_spl
| equalish(e_1,X0)
| ~ next(e_2,X0) ),
inference(component_clause,[status(thm)],[f553]) ).
fof(f561,definition,
( sQ73_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f562,plain,
( ~ sQ73_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f561]) ).
fof(f564,definition,
( sQ74_spl
<=> product(e_2,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f565,plain,
( ~ sQ74_spl
| product(e_2,e_2,e_3) ),
inference(component_clause,[status(thm)],[f564]) ).
fof(f567,definition,
( sQ75_spl
<=> product(e_2,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f568,plain,
( ~ sQ75_spl
| product(e_2,e_2,e_4) ),
inference(component_clause,[status(thm)],[f567]) ).
fof(f570,definition,
( sQ76_spl
<=> equalish(e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f573,plain,
( sQ76_spl
| sQ75_spl
| sQ74_spl
| sQ73_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f488,f246,f561,f564,f567,f570]) ).
fof(f575,definition,
( sQ77_spl
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f578,plain,
( sQ77_spl
| sQ75_spl
| sQ74_spl
| sQ73_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f492,f246,f561,f564,f567,f575]) ).
fof(f579,plain,
( sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f534,f54]) ).
fof(f580,plain,
sQ65_spl,
inference(contradiction_clause,[status(thm)],[f579]) ).
fof(f581,plain,
( sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f53]) ).
fof(f582,plain,
sQ58_spl,
inference(contradiction_clause,[status(thm)],[f581]) ).
fof(f587,plain,
( ~ sQ55_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f498,f97]) ).
fof(f593,plain,
( ~ sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f587,f82]) ).
fof(f594,plain,
~ sQ55_spl,
inference(contradiction_clause,[status(thm)],[f593]) ).
fof(f599,plain,
( ~ sQ63_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f526,f97]) ).
fof(f605,plain,
( ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f599,f79]) ).
fof(f606,plain,
~ sQ63_spl,
inference(contradiction_clause,[status(thm)],[f605]) ).
fof(f609,plain,
( ~ sQ56_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f501,f101]) ).
fof(f616,plain,
( ~ sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f609,f76]) ).
fof(f617,plain,
~ sQ56_spl,
inference(contradiction_clause,[status(thm)],[f616]) ).
fof(f620,plain,
( ~ sQ75_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f568,f97]) ).
fof(f624,plain,
( ~ sQ75_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f620,f83]) ).
fof(f625,plain,
~ sQ75_spl,
inference(contradiction_clause,[status(thm)],[f624]) ).
fof(f626,plain,
! [X0] :
( product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| product(X0,e_2,X0)
| product(X0,e_2,e_4)
| product(X0,e_2,e_3)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f365,f403]) ).
fof(f628,plain,
! [X0,X1] :
( product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| product(e_4,e_2,X0)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f365,f85]) ).
fof(f633,definition,
! [X0] :
( sQ78_spl
<=> ( product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| product(X0,e_2,X0)
| product(X0,e_2,e_4)
| product(X0,e_2,e_3)
| product(X0,e_2,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( ~ sQ30_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f626,f633,f246]) ).
fof(f638,plain,
! [X0,X1] :
( product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f628]) ).
fof(f647,plain,
( ~ sQ74_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f565,f97]) ).
fof(f651,definition,
( sQ79_spl
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f652,plain,
( ~ sQ79_spl
| product(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f651]) ).
fof(f655,plain,
( ~ sQ74_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f647,f80]) ).
fof(f656,plain,
~ sQ74_spl,
inference(contradiction_clause,[status(thm)],[f655]) ).
fof(f660,plain,
( ~ sQ73_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f562,f97]) ).
fof(f664,definition,
( sQ80_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f665,plain,
( ~ sQ80_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f664]) ).
fof(f666,plain,
( sQ80_spl
| ~ product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f664]) ).
fof(f668,plain,
( ~ sQ73_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f660,f73]) ).
fof(f669,plain,
~ sQ73_spl,
inference(contradiction_clause,[status(thm)],[f668]) ).
fof(f671,plain,
( ~ sQ68_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f543,f101]) ).
fof(f676,definition,
( sQ81_spl
<=> product(e_4,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f677,plain,
( ~ sQ81_spl
| product(e_4,e_2,e_1) ),
inference(component_clause,[status(thm)],[f676]) ).
fof(f682,definition,
( sQ83_spl
<=> product(e_4,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f683,plain,
( ~ sQ83_spl
| product(e_4,e_2,e_4) ),
inference(component_clause,[status(thm)],[f682]) ).
fof(f684,plain,
( sQ83_spl
| ~ product(e_4,e_2,e_4) ),
inference(component_clause,[status(thm)],[f682]) ).
fof(f686,plain,
( ~ sQ68_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f671,f78]) ).
fof(f687,plain,
~ sQ68_spl,
inference(contradiction_clause,[status(thm)],[f686]) ).
fof(f691,plain,
( ~ sQ67_spl
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[f540,f97]) ).
fof(f695,definition,
( sQ84_spl
<=> product(e_4,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f698,definition,
( sQ85_spl
<=> product(e_3,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f699,plain,
( ~ sQ85_spl
| product(e_3,e_2,e_4) ),
inference(component_clause,[status(thm)],[f698]) ).
fof(f702,plain,
( ~ sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f691,f81]) ).
fof(f703,plain,
~ sQ67_spl,
inference(contradiction_clause,[status(thm)],[f702]) ).
fof(f707,plain,
( ~ sQ66_spl
| equalish(e_1,e_4) ),
inference(resolution,[status(thm)],[f537,f97]) ).
fof(f711,definition,
( sQ86_spl
<=> product(e_1,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f712,plain,
( ~ sQ86_spl
| product(e_1,e_2,e_4) ),
inference(component_clause,[status(thm)],[f711]) ).
fof(f715,plain,
( ~ sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f707,f75]) ).
fof(f716,plain,
~ sQ66_spl,
inference(contradiction_clause,[status(thm)],[f715]) ).
fof(f718,plain,
( ~ sQ61_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f518,f101]) ).
fof(f723,definition,
( sQ87_spl
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f724,plain,
( ~ sQ87_spl
| product(e_3,e_2,e_1) ),
inference(component_clause,[status(thm)],[f723]) ).
fof(f726,definition,
( sQ88_spl
<=> product(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f727,plain,
( ~ sQ88_spl
| product(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f726]) ).
fof(f728,plain,
( sQ88_spl
| ~ product(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f726]) ).
fof(f730,plain,
( ~ sQ61_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f718,f77]) ).
fof(f731,plain,
~ sQ61_spl,
inference(contradiction_clause,[status(thm)],[f730]) ).
fof(f735,plain,
( ~ sQ60_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f515,f97]) ).
fof(f739,definition,
( sQ89_spl
<=> product(e_3,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f743,plain,
( ~ sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f735,f84]) ).
fof(f744,plain,
~ sQ60_spl,
inference(contradiction_clause,[status(thm)],[f743]) ).
fof(f748,plain,
( ~ sQ59_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f512,f97]) ).
fof(f752,definition,
( sQ90_spl
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f753,plain,
( ~ sQ90_spl
| product(e_1,e_2,e_3) ),
inference(component_clause,[status(thm)],[f752]) ).
fof(f756,plain,
( ~ sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f748,f74]) ).
fof(f757,plain,
~ sQ59_spl,
inference(contradiction_clause,[status(thm)],[f756]) ).
fof(f758,plain,
( sQ55_spl
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f499,f403]) ).
fof(f760,plain,
( sQ55_spl
| sQ56_spl
| sQ63_spl
| sQ54_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f758,f216,f494,f525,f500,f497]) ).
fof(f761,definition,
( sQ91_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f762,plain,
( ~ sQ91_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f761]) ).
fof(f775,plain,
( ~ sQ24_spl
| ~ sQ37_spl
| ~ greater(e_2,e_0) ),
inference(resolution,[status(thm)],[f350,f223]) ).
fof(f776,plain,
( ~ sQ37_spl
| cycle(e_1,e_3)
| cycle(e_1,e_2)
| cycle(e_1,e_1)
| ~ group_element(e_1)
| ~ greater(e_0,e_0) ),
inference(resolution,[status(thm)],[f350,f60]) ).
fof(f777,plain,
( ~ sQ24_spl
| ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f775,f49]) ).
fof(f778,plain,
( ~ sQ24_spl
| ~ sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f777]) ).
fof(f779,plain,
( ~ sQ38_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f353,f45]) ).
fof(f780,plain,
( ~ sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f779,f73]) ).
fof(f781,plain,
~ sQ38_spl,
inference(contradiction_clause,[status(thm)],[f780]) ).
fof(f782,definition,
( sQ92_spl
<=> greater(e_0,e_0) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f785,plain,
( ~ sQ37_spl
| sQ25_spl
| sQ24_spl
| sQ23_spl
| ~ sQ22_spl
| ~ sQ92_spl ),
inference(split_clause,[status(thm)],[f776,f782,f216,f219,f222,f225,f349]) ).
fof(f800,plain,
( ~ sQ7_spl
| equalish(e_0,e_0)
| cycle(e_1,e_3)
| cycle(e_1,e_2)
| cycle(e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f144,f104]) ).
fof(f812,plain,
( ~ sQ7_spl
| sQ8_spl
| sQ25_spl
| sQ24_spl
| sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f800,f216,f219,f222,f225,f149,f143]) ).
fof(f820,plain,
( ~ sQ83_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f683,f99]) ).
fof(f824,definition,
( sQ95_spl
<=> product(e_2,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f825,plain,
( ~ sQ95_spl
| product(e_2,e_4,e_1) ),
inference(component_clause,[status(thm)],[f824]) ).
fof(f827,definition,
( sQ96_spl
<=> product(e_2,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f828,plain,
( ~ sQ96_spl
| product(e_2,e_4,e_3) ),
inference(component_clause,[status(thm)],[f827]) ).
fof(f830,definition,
( sQ97_spl
<=> product(e_4,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f831,plain,
( ~ sQ97_spl
| product(e_4,e_2,e_2) ),
inference(component_clause,[status(thm)],[f830]) ).
fof(f832,plain,
( sQ97_spl
| ~ product(e_4,e_2,e_2) ),
inference(component_clause,[status(thm)],[f830]) ).
fof(f834,plain,
( ~ sQ83_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f820,f78]) ).
fof(f835,plain,
~ sQ83_spl,
inference(contradiction_clause,[status(thm)],[f834]) ).
fof(f848,plain,
( sQ68_spl
| product(e_4,e_4,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_1)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[f544,f403]) ).
fof(f849,plain,
( sQ68_spl
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f544,f85]) ).
fof(f850,plain,
( sQ68_spl
| sQ84_spl
| sQ67_spl
| sQ66_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f848,f152,f536,f539,f695,f542]) ).
fof(f851,definition,
( sQ98_spl
<=> product(e_2,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f852,plain,
( ~ sQ98_spl
| product(e_2,e_4,e_2) ),
inference(component_clause,[status(thm)],[f851]) ).
fof(f854,plain,
( sQ68_spl
| sQ96_spl
| sQ98_spl
| sQ95_spl
| ~ sQ9_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f849,f246,f152,f824,f851,f827,f542]) ).
fof(f858,definition,
( sQ99_spl
<=> product(e_4,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f859,plain,
( ~ sQ99_spl
| product(e_4,e_4,e_2) ),
inference(component_clause,[status(thm)],[f858]) ).
fof(f876,plain,
( ~ sQ88_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f727,f99]) ).
fof(f881,plain,
( ~ sQ88_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f876,f77]) ).
fof(f882,plain,
~ sQ88_spl,
inference(contradiction_clause,[status(thm)],[f881]) ).
fof(f889,plain,
! [X0,X1] :
( cycle(e_1,e_3)
| cycle(e_1,e_2)
| cycle(e_1,e_1)
| ~ group_element(e_1)
| equalish(X0,X1)
| ~ next(e_0,X1)
| ~ greater(X0,e_0)
| ~ cycle(e_0,X0) ),
inference(resolution,[status(thm)],[f106,f44]) ).
fof(f904,definition,
! [X0,X1] :
( sQ105_spl
<=> ( equalish(X0,X1)
| ~ next(e_0,X1)
| ~ greater(X0,e_0)
| ~ cycle(e_0,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f907,plain,
( sQ25_spl
| sQ24_spl
| sQ23_spl
| ~ sQ22_spl
| sQ105_spl ),
inference(split_clause,[status(thm)],[f889,f904,f216,f219,f222,f225]) ).
fof(f913,plain,
! [X0] :
( equalish(X0,e_1)
| ~ greater(X0,e_0)
| ~ cycle(e_4,e_0)
| ~ cycle(e_3,X0) ),
inference(resolution,[status(thm)],[f108,f44]) ).
fof(f924,definition,
! [X0] :
( sQ108_spl
<=> ( equalish(X0,e_1)
| ~ greater(X0,e_0)
| ~ cycle(e_3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f927,definition,
( sQ109_spl
<=> cycle(e_4,e_0) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f929,plain,
( sQ109_spl
| ~ cycle(e_4,e_0) ),
inference(component_clause,[status(thm)],[f927]) ).
fof(f930,plain,
( ~ sQ109_spl
| sQ108_spl ),
inference(split_clause,[status(thm)],[f913,f924,f927]) ).
fof(f931,plain,
( sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f929,f61]) ).
fof(f932,plain,
sQ109_spl,
inference(contradiction_clause,[status(thm)],[f931]) ).
fof(f934,plain,
! [X0] :
( ~ sQ87_spl
| equalish(X0,e_3)
| ~ product(X0,e_2,e_1) ),
inference(resolution,[status(thm)],[f724,f91]) ).
fof(f939,plain,
( sQ61_spl
| product(e_3,e_3,e_4)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f519,f403]) ).
fof(f941,plain,
( sQ61_spl
| sQ60_spl
| sQ89_spl
| sQ59_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f939,f259,f511,f739,f514,f517]) ).
fof(f942,definition,
( sQ110_spl
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f943,plain,
( ~ sQ110_spl
| product(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f942]) ).
fof(f949,definition,
( sQ111_spl
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f950,plain,
( ~ sQ111_spl
| product(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f949]) ).
fof(f958,plain,
( ~ sQ91_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f762,f97]) ).
fof(f966,definition,
( sQ113_spl
<=> greater(e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f968,plain,
( sQ113_spl
| ~ greater(e_2,e_1) ),
inference(component_clause,[status(thm)],[f966]) ).
fof(f971,plain,
( ~ sQ91_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f958,f76]) ).
fof(f972,plain,
~ sQ91_spl,
inference(contradiction_clause,[status(thm)],[f971]) ).
fof(f973,plain,
( sQ113_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f968,f52]) ).
fof(f974,plain,
sQ113_spl,
inference(contradiction_clause,[status(thm)],[f973]) ).
fof(f976,plain,
( ~ sQ97_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f831,f101]) ).
fof(f982,plain,
( ~ sQ97_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f976,f83]) ).
fof(f983,plain,
~ sQ97_spl,
inference(contradiction_clause,[status(thm)],[f982]) ).
fof(f984,plain,
! [X0] :
( product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| product(X0,e_3,X0)
| product(X0,e_2,e_4)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f375,f403]) ).
fof(f991,definition,
! [X0] :
( sQ114_spl
<=> ( product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| product(X0,e_3,X0)
| product(X0,e_2,e_4)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f994,plain,
( ~ sQ30_spl
| sQ114_spl ),
inference(split_clause,[status(thm)],[f984,f991,f246]) ).
fof(f1003,plain,
( ~ sQ96_spl
| product(e_3,e_3,e_4)
| product(e_4,e_2,e_4)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[f828,f375]) ).
fof(f1009,plain,
( ~ sQ96_spl
| sQ60_spl
| sQ83_spl
| sQ97_spl
| sQ81_spl
| ~ sQ30_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1003,f152,f246,f676,f830,f682,f514,f827]) ).
fof(f1013,plain,
! [X0] :
( ~ sQ95_spl
| equalish(X0,e_2)
| ~ product(X0,e_4,e_1) ),
inference(resolution,[status(thm)],[f825,f91]) ).
fof(f1026,plain,
( ~ sQ79_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f652,f101]) ).
fof(f1033,plain,
( ~ sQ79_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1026,f80]) ).
fof(f1034,plain,
~ sQ79_spl,
inference(contradiction_clause,[status(thm)],[f1033]) ).
fof(f1037,plain,
( ~ sQ80_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f665,f101]) ).
fof(f1042,definition,
( sQ116_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1043,plain,
( ~ sQ116_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f1042]) ).
fof(f1045,definition,
( sQ117_spl
<=> product(e_2,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1046,plain,
( ~ sQ117_spl
| product(e_2,e_1,e_4) ),
inference(component_clause,[status(thm)],[f1045]) ).
fof(f1053,plain,
( ~ sQ80_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1037,f73]) ).
fof(f1054,plain,
~ sQ80_spl,
inference(contradiction_clause,[status(thm)],[f1053]) ).
fof(f1058,plain,
( ~ sQ98_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f852,f99]) ).
fof(f1064,plain,
( ~ sQ98_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1058,f83]) ).
fof(f1065,plain,
~ sQ98_spl,
inference(contradiction_clause,[status(thm)],[f1064]) ).
fof(f1070,plain,
( ~ sQ99_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f859,f97]) ).
fof(f1076,plain,
( ~ sQ99_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1070,f78]) ).
fof(f1077,plain,
~ sQ99_spl,
inference(contradiction_clause,[status(thm)],[f1076]) ).
fof(f1084,definition,
( sQ119_spl
<=> product(e_4,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f1085,plain,
( ~ sQ119_spl
| product(e_4,e_3,e_3) ),
inference(component_clause,[status(thm)],[f1084]) ).
fof(f1095,definition,
( sQ120_spl
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1096,plain,
( ~ sQ120_spl
| product(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f1095]) ).
fof(f1100,plain,
( sQ88_spl
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f728,f85]) ).
fof(f1101,plain,
( sQ88_spl
| sQ85_spl
| sQ79_spl
| sQ87_spl
| ~ sQ30_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f1100,f259,f246,f723,f651,f698,f726]) ).
fof(f1105,plain,
( ~ sQ110_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f943,f99]) ).
fof(f1111,plain,
( ~ sQ110_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1105,f80]) ).
fof(f1112,plain,
~ sQ110_spl,
inference(contradiction_clause,[status(thm)],[f1111]) ).
fof(f1117,plain,
( ~ sQ111_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f950,f97]) ).
fof(f1123,plain,
( ~ sQ111_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1117,f77]) ).
fof(f1124,plain,
~ sQ111_spl,
inference(contradiction_clause,[status(thm)],[f1123]) ).
fof(f1127,plain,
! [X0] :
( equalish(e_2,X0)
| product(X0,e_2,e_4)
| product(X0,e_2,e_3)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f359,f92]) ).
fof(f1128,definition,
! [X0] :
( sQ121_spl
<=> ( equalish(e_2,X0)
| product(X0,e_2,e_4)
| product(X0,e_2,e_3)
| product(X0,e_2,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1133,plain,
( ~ sQ30_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f1127,f1128,f246]) ).
fof(f1136,plain,
! [X0] :
( equalish(e_2,X0)
| product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f361,f92]) ).
fof(f1137,definition,
! [X0] :
( sQ122_spl
<=> ( equalish(e_2,X0)
| product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1142,plain,
( sQ122_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1136,f246,f1137]) ).
fof(f1174,definition,
( sQ124_spl
<=> product(e_4,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1175,plain,
( ~ sQ124_spl
| product(e_4,e_3,e_2) ),
inference(component_clause,[status(thm)],[f1174]) ).
fof(f1187,plain,
( ~ sQ86_spl
| product(e_4,e_3,e_2)
| product(e_2,e_1,e_4)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f712,f375]) ).
fof(f1189,plain,
! [X0] :
( ~ sQ86_spl
| equalish(X0,e_1)
| ~ product(X0,e_2,e_4) ),
inference(resolution,[status(thm)],[f712,f91]) ).
fof(f1193,plain,
( ~ sQ86_spl
| sQ124_spl
| sQ117_spl
| sQ116_spl
| sQ56_spl
| ~ sQ22_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1187,f246,f216,f500,f1042,f1045,f1174,f711]) ).
fof(f1201,definition,
( sQ125_spl
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1202,plain,
( ~ sQ125_spl
| product(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f1201]) ).
fof(f1211,definition,
( sQ128_spl
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1212,plain,
( ~ sQ128_spl
| product(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f1211]) ).
fof(f1225,plain,
! [X0,X1] :
( ~ sQ117_spl
| equalish(e_4,X1)
| ~ next(e_2,X1)
| ~ greater(X0,e_0)
| ~ cycle(e_2,X0) ),
inference(resolution,[status(thm)],[f1046,f68]) ).
fof(f1226,plain,
( ~ sQ117_spl
| ~ greater(e_4,e_2)
| ~ cycle(e_2,e_0) ),
inference(resolution,[status(thm)],[f1046,f66]) ).
fof(f1233,definition,
! [X1] :
( sQ129_spl
<=> ( equalish(e_4,X1)
| ~ next(e_2,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f1234,plain,
! [X0] :
( ~ sQ129_spl
| equalish(e_4,X0)
| ~ next(e_2,X0) ),
inference(component_clause,[status(thm)],[f1233]) ).
fof(f1236,plain,
( ~ sQ117_spl
| sQ129_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f1225,f550,f1233,f1045]) ).
fof(f1237,definition,
( sQ130_spl
<=> greater(e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1239,plain,
( sQ130_spl
| ~ greater(e_4,e_2) ),
inference(component_clause,[status(thm)],[f1237]) ).
fof(f1240,plain,
( ~ sQ117_spl
| ~ sQ130_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f1226,f200,f1237,f1045]) ).
fof(f1241,definition,
( sQ131_spl
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1242,plain,
( ~ sQ131_spl
| product(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f1241]) ).
fof(f1249,plain,
( sQ130_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1239,f56]) ).
fof(f1250,plain,
sQ130_spl,
inference(contradiction_clause,[status(thm)],[f1249]) ).
fof(f1263,definition,
( sQ134_spl
<=> greater(e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f1265,plain,
( sQ134_spl
| ~ greater(e_3,e_2) ),
inference(component_clause,[status(thm)],[f1263]) ).
fof(f1269,plain,
( sQ134_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1265,f55]) ).
fof(f1270,plain,
sQ134_spl,
inference(contradiction_clause,[status(thm)],[f1269]) ).
fof(f1278,plain,
( ~ sQ116_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f1043,f99]) ).
fof(f1282,definition,
! [X1] :
( sQ135_spl
<=> ( equalish(e_2,X1)
| ~ next(e_2,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f1283,plain,
! [X0] :
( ~ sQ135_spl
| equalish(e_2,X0)
| ~ next(e_2,X0) ),
inference(component_clause,[status(thm)],[f1282]) ).
fof(f1300,plain,
( ~ sQ116_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1278,f73]) ).
fof(f1301,plain,
~ sQ116_spl,
inference(contradiction_clause,[status(thm)],[f1300]) ).
fof(f1302,plain,
( sQ80_spl
| product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f666,f85]) ).
fof(f1303,plain,
( sQ80_spl
| sQ86_spl
| sQ90_spl
| sQ131_spl
| ~ sQ30_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f1302,f216,f246,f1241,f752,f711,f664]) ).
fof(f1371,plain,
( ~ sQ119_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f1085,f101]) ).
fof(f1376,definition,
( sQ149_spl
<=> product(e_3,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1377,plain,
( ~ sQ149_spl
| product(e_3,e_4,e_1) ),
inference(component_clause,[status(thm)],[f1376]) ).
fof(f1382,definition,
( sQ151_spl
<=> product(e_3,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1383,plain,
( ~ sQ151_spl
| product(e_3,e_4,e_4) ),
inference(component_clause,[status(thm)],[f1382]) ).
fof(f1386,definition,
( sQ152_spl
<=> product(e_3,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1387,plain,
( ~ sQ152_spl
| product(e_3,e_4,e_3) ),
inference(component_clause,[status(thm)],[f1386]) ).
fof(f1390,plain,
( ~ sQ119_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1371,f84]) ).
fof(f1391,plain,
~ sQ119_spl,
inference(contradiction_clause,[status(thm)],[f1390]) ).
fof(f1400,plain,
( ~ sQ90_spl
| product(e_3,e_3,e_2)
| product(e_2,e_1,e_4)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f753,f375]) ).
fof(f1406,plain,
( ~ sQ90_spl
| sQ111_spl
| sQ117_spl
| sQ116_spl
| sQ56_spl
| ~ sQ22_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1400,f246,f216,f500,f1042,f1045,f949,f752]) ).
fof(f1410,plain,
( ~ sQ120_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f1096,f101]) ).
fof(f1417,plain,
( ~ sQ120_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1410,f74]) ).
fof(f1418,plain,
~ sQ120_spl,
inference(contradiction_clause,[status(thm)],[f1417]) ).
fof(f1431,plain,
! [X0] :
( product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| product(X0,e_4,X0)
| product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f385,f403]) ).
fof(f1451,definition,
( sQ155_spl
<=> product(e_1,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f1452,plain,
( ~ sQ155_spl
| product(e_1,e_4,e_4) ),
inference(component_clause,[status(thm)],[f1451]) ).
fof(f1455,definition,
! [X0] :
( sQ156_spl
<=> ( product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| product(X0,e_4,X0)
| product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f1458,plain,
( ~ sQ30_spl
| sQ156_spl ),
inference(split_clause,[status(thm)],[f1431,f1455,f246]) ).
fof(f1491,plain,
( ~ sQ124_spl
| product(e_2,e_2,e_3)
| product(e_3,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f1175,f365]) ).
fof(f1506,plain,
( ~ sQ124_spl
| sQ74_spl
| sQ151_spl
| sQ152_spl
| sQ149_spl
| ~ sQ9_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f1491,f259,f152,f1376,f1386,f1382,f564,f1174]) ).
fof(f1523,definition,
( sQ163_spl
<=> greater(e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f1525,plain,
( sQ163_spl
| ~ greater(e_4,e_3) ),
inference(component_clause,[status(thm)],[f1523]) ).
fof(f1527,definition,
( sQ164_spl
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f1528,plain,
( ~ sQ164_spl
| product(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f1527]) ).
fof(f1533,plain,
( sQ163_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1525,f57]) ).
fof(f1534,plain,
sQ163_spl,
inference(contradiction_clause,[status(thm)],[f1533]) ).
fof(f1540,plain,
( ~ sQ125_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f1202,f101]) ).
fof(f1545,definition,
! [X1] :
( sQ165_spl
<=> ( equalish(e_1,X1)
| ~ next(e_3,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f1546,plain,
! [X0] :
( ~ sQ165_spl
| equalish(e_1,X0)
| ~ next(e_3,X0) ),
inference(component_clause,[status(thm)],[f1545]) ).
fof(f1553,definition,
( sQ167_spl
<=> product(e_1,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f1554,plain,
( ~ sQ167_spl
| product(e_1,e_4,e_1) ),
inference(component_clause,[status(thm)],[f1553]) ).
fof(f1559,plain,
( ~ sQ125_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1540,f79]) ).
fof(f1560,plain,
~ sQ125_spl,
inference(contradiction_clause,[status(thm)],[f1559]) ).
fof(f1567,plain,
( ~ sQ128_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f1212,f99]) ).
fof(f1571,definition,
! [X1] :
( sQ168_spl
<=> ( equalish(e_3,X1)
| ~ next(e_3,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f1572,plain,
! [X0] :
( ~ sQ168_spl
| equalish(e_3,X0)
| ~ next(e_3,X0) ),
inference(component_clause,[status(thm)],[f1571]) ).
fof(f1582,plain,
( ~ sQ128_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1567,f74]) ).
fof(f1583,plain,
~ sQ128_spl,
inference(contradiction_clause,[status(thm)],[f1582]) ).
fof(f1595,definition,
! [X1] :
( sQ170_spl
<=> ( equalish(e_2,X1)
| ~ next(e_3,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f1596,plain,
! [X0] :
( ~ sQ170_spl
| equalish(e_2,X0)
| ~ next(e_3,X0) ),
inference(component_clause,[status(thm)],[f1595]) ).
fof(f1618,plain,
( ~ sQ131_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f1242,f99]) ).
fof(f1625,plain,
( ~ sQ131_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1618,f76]) ).
fof(f1626,plain,
~ sQ131_spl,
inference(contradiction_clause,[status(thm)],[f1625]) ).
fof(f1643,plain,
! [X0] :
( product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_2)
| product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f363,f403]) ).
fof(f1644,plain,
! [X0] :
( product(e_2,X0,X0)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(e_4,e_2)
| product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f363,f403]) ).
fof(f1645,plain,
! [X0,X1] :
( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| equalish(e_4,e_2)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f363,f85]) ).
fof(f1646,plain,
! [X0] :
( product(e_2,X0,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(e_3,e_2)
| product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f363,f403]) ).
fof(f1647,plain,
! [X0,X1] :
( product(X0,X1,e_4)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| equalish(e_3,e_2)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f363,f85]) ).
fof(f1651,definition,
( sQ174_spl
<=> equalish(e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f1652,plain,
( ~ sQ174_spl
| equalish(e_1,e_2) ),
inference(component_clause,[status(thm)],[f1651]) ).
fof(f1657,definition,
! [X0] :
( sQ175_spl
<=> ( product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_2)
| product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f1660,plain,
( sQ175_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1643,f246,f1657]) ).
fof(f1661,definition,
! [X0] :
( sQ176_spl
<=> ( product(e_2,X0,X0)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f1664,definition,
( sQ177_spl
<=> equalish(e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f1665,plain,
( ~ sQ177_spl
| equalish(e_4,e_2) ),
inference(component_clause,[status(thm)],[f1664]) ).
fof(f1667,plain,
( sQ177_spl
| sQ176_spl ),
inference(split_clause,[status(thm)],[f1644,f1661,f1664]) ).
fof(f1668,definition,
! [X0,X1] :
( sQ178_spl
<=> ( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f1671,plain,
( sQ177_spl
| sQ178_spl ),
inference(split_clause,[status(thm)],[f1645,f1668,f1664]) ).
fof(f1672,definition,
! [X0] :
( sQ179_spl
<=> ( product(e_2,X0,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_1)
| ~ group_element(X0)
| product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f1675,definition,
( sQ180_spl
<=> equalish(e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f1676,plain,
( ~ sQ180_spl
| equalish(e_3,e_2) ),
inference(component_clause,[status(thm)],[f1675]) ).
fof(f1678,plain,
( sQ180_spl
| sQ179_spl ),
inference(split_clause,[status(thm)],[f1646,f1672,f1675]) ).
fof(f1679,definition,
! [X0,X1] :
( sQ181_spl
<=> ( product(X0,X1,e_4)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f1682,plain,
( sQ180_spl
| sQ181_spl ),
inference(split_clause,[status(thm)],[f1647,f1679,f1675]) ).
fof(f1688,plain,
( ~ sQ180_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1676,f80]) ).
fof(f1689,plain,
~ sQ180_spl,
inference(contradiction_clause,[status(thm)],[f1688]) ).
fof(f1690,plain,
( ~ sQ177_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1665,f83]) ).
fof(f1691,plain,
~ sQ177_spl,
inference(contradiction_clause,[status(thm)],[f1690]) ).
fof(f1701,plain,
! [X0] :
( equalish(e_3,X0)
| product(X0,e_3,e_4)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f369,f92]) ).
fof(f1708,definition,
! [X0] :
( sQ184_spl
<=> ( equalish(e_3,X0)
| product(X0,e_3,e_4)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f1711,plain,
( ~ sQ33_spl
| sQ184_spl ),
inference(split_clause,[status(thm)],[f1701,f1708,f259]) ).
fof(f1723,plain,
( ~ sQ151_spl
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[f1383,f101]) ).
fof(f1730,definition,
( sQ185_spl
<=> product(e_4,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f1731,plain,
( ~ sQ185_spl
| product(e_4,e_3,e_4) ),
inference(component_clause,[status(thm)],[f1730]) ).
fof(f1735,plain,
( ~ sQ151_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1723,f81]) ).
fof(f1736,plain,
~ sQ151_spl,
inference(contradiction_clause,[status(thm)],[f1735]) ).
fof(f1755,plain,
( ~ sQ152_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f1387,f99]) ).
fof(f1767,plain,
( ~ sQ152_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1755,f84]) ).
fof(f1768,plain,
~ sQ152_spl,
inference(contradiction_clause,[status(thm)],[f1767]) ).
fof(f1814,definition,
( sQ191_spl
<=> product(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f1815,plain,
( ~ sQ191_spl
| product(e_4,e_1,e_1) ),
inference(component_clause,[status(thm)],[f1814]) ).
fof(f1824,definition,
( sQ194_spl
<=> product(e_4,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f1825,plain,
( ~ sQ194_spl
| product(e_4,e_1,e_4) ),
inference(component_clause,[status(thm)],[f1824]) ).
fof(f1833,plain,
( ~ sQ155_spl
| equalish(e_1,e_4) ),
inference(resolution,[status(thm)],[f1452,f101]) ).
fof(f1842,plain,
( ~ sQ155_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1833,f75]) ).
fof(f1843,plain,
~ sQ155_spl,
inference(contradiction_clause,[status(thm)],[f1842]) ).
fof(f1866,plain,
( ~ sQ164_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f1528,f99]) ).
fof(f1874,plain,
( ~ sQ164_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1866,f79]) ).
fof(f1875,plain,
~ sQ164_spl,
inference(contradiction_clause,[status(thm)],[f1874]) ).
fof(f1881,plain,
( ~ sQ167_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f1554,f99]) ).
fof(f1889,plain,
( ~ sQ167_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1881,f82]) ).
fof(f1890,plain,
~ sQ167_spl,
inference(contradiction_clause,[status(thm)],[f1889]) ).
fof(f2004,plain,
! [X0] :
( equalish(e_4,e_2)
| product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0)
| product(e_3,X0,X0)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f421,f363]) ).
fof(f2023,plain,
! [X0] :
( equalish(X0,e_2)
| product(e_3,X0,e_4)
| product(e_3,X0,e_3)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_3)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f421,f363]) ).
fof(f2024,plain,
! [X0] :
( product(X0,e_4,X0)
| product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f421,f385]) ).
fof(f2025,plain,
! [X0] :
( product(X0,e_3,X0)
| product(X0,e_3,e_4)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f421,f375]) ).
fof(f2026,plain,
! [X0] :
( product(X0,e_2,X0)
| product(X0,e_3,e_4)
| product(X0,e_3,e_3)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f421,f365]) ).
fof(f2057,definition,
! [X0] :
( sQ198_spl
<=> ( product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0)
| product(e_3,X0,X0)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f2060,plain,
( sQ177_spl
| sQ198_spl ),
inference(split_clause,[status(thm)],[f2004,f2057,f1664]) ).
fof(f2080,definition,
! [X0] :
( sQ201_spl
<=> ( equalish(X0,e_2)
| product(e_3,X0,e_4)
| product(e_3,X0,e_3)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f2083,plain,
( ~ sQ33_spl
| sQ201_spl ),
inference(split_clause,[status(thm)],[f2023,f2080,f259]) ).
fof(f2084,definition,
! [X0] :
( sQ202_spl
<=> ( product(X0,e_4,X0)
| product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f2087,plain,
( ~ sQ33_spl
| sQ202_spl ),
inference(split_clause,[status(thm)],[f2024,f2084,f259]) ).
fof(f2088,definition,
! [X0] :
( sQ203_spl
<=> ( product(X0,e_3,X0)
| product(X0,e_3,e_4)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f2091,plain,
( ~ sQ33_spl
| sQ203_spl ),
inference(split_clause,[status(thm)],[f2025,f2088,f259]) ).
fof(f2092,definition,
! [X0] :
( sQ204_spl
<=> ( product(X0,e_2,X0)
| product(X0,e_3,e_4)
| product(X0,e_3,e_3)
| product(X0,e_3,e_1)
| ~ group_element(X0)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f2095,plain,
( ~ sQ33_spl
| sQ204_spl ),
inference(split_clause,[status(thm)],[f2026,f2092,f259]) ).
fof(f2111,plain,
( ~ sQ185_spl
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[f1731,f99]) ).
fof(f2119,plain,
( ~ sQ185_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2111,f81]) ).
fof(f2120,plain,
~ sQ185_spl,
inference(contradiction_clause,[status(thm)],[f2119]) ).
fof(f2161,plain,
( ~ sQ191_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f1815,f101]) ).
fof(f2181,plain,
( ~ sQ191_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2161,f82]) ).
fof(f2182,plain,
~ sQ191_spl,
inference(contradiction_clause,[status(thm)],[f2181]) ).
fof(f2190,plain,
( ~ sQ194_spl
| equalish(e_1,e_4) ),
inference(resolution,[status(thm)],[f1825,f99]) ).
fof(f2206,plain,
( ~ sQ194_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2190,f75]) ).
fof(f2207,plain,
~ sQ194_spl,
inference(contradiction_clause,[status(thm)],[f2206]) ).
fof(f2272,plain,
! [X0] :
( equalish(e_3,X0)
| product(e_3,X0,e_4)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f371,f92]) ).
fof(f2277,definition,
! [X0] :
( sQ218_spl
<=> ( equalish(e_3,X0)
| product(e_3,X0,e_4)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f2287,plain,
( sQ218_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f2272,f259,f2277]) ).
fof(f2295,plain,
! [X0] :
( product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_3)
| product(e_3,X0,e_4)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f373,f421]) ).
fof(f2298,plain,
! [X0] :
( product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_3)
| product(e_2,X0,e_4)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f373,f403]) ).
fof(f2299,plain,
! [X0] :
( product(e_3,X0,X0)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(e_4,e_3)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f373,f421]) ).
fof(f2300,plain,
! [X0] :
( product(e_2,X0,X0)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(e_4,e_3)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f373,f403]) ).
fof(f2301,plain,
! [X0,X1] :
( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| equalish(e_4,e_3)
| product(X0,X1,e_4)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f373,f85]) ).
fof(f2304,plain,
! [X0] :
( product(e_3,X0,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(e_2,e_3)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f373,f421]) ).
fof(f2307,definition,
( sQ220_spl
<=> equalish(e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f2308,plain,
( ~ sQ220_spl
| equalish(e_4,e_3) ),
inference(component_clause,[status(thm)],[f2307]) ).
fof(f2312,definition,
( sQ221_spl
<=> equalish(e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f2313,plain,
( ~ sQ221_spl
| equalish(e_2,e_3) ),
inference(component_clause,[status(thm)],[f2312]) ).
fof(f2317,definition,
( sQ222_spl
<=> equalish(e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f2318,plain,
( ~ sQ222_spl
| equalish(e_1,e_3) ),
inference(component_clause,[status(thm)],[f2317]) ).
fof(f2323,definition,
! [X0] :
( sQ223_spl
<=> ( product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_3)
| product(e_3,X0,e_4)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f2326,plain,
( sQ223_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f2295,f259,f2323]) ).
fof(f2329,definition,
! [X0] :
( sQ224_spl
<=> ( product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_3)
| product(e_2,X0,e_4)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f2332,plain,
( sQ224_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2298,f246,f2329]) ).
fof(f2333,definition,
! [X0] :
( sQ225_spl
<=> ( product(e_3,X0,X0)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f2336,plain,
( sQ220_spl
| sQ225_spl ),
inference(split_clause,[status(thm)],[f2299,f2333,f2307]) ).
fof(f2337,definition,
! [X0] :
( sQ226_spl
<=> ( product(e_2,X0,X0)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f2340,plain,
( sQ220_spl
| sQ226_spl ),
inference(split_clause,[status(thm)],[f2300,f2337,f2307]) ).
fof(f2341,definition,
! [X0,X1] :
( sQ227_spl
<=> ( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(X0,X1,e_4)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2344,plain,
( sQ220_spl
| sQ227_spl ),
inference(split_clause,[status(thm)],[f2301,f2341,f2307]) ).
fof(f2353,definition,
! [X0] :
( sQ230_spl
<=> ( product(e_3,X0,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_1)
| ~ group_element(X0)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f2356,plain,
( sQ221_spl
| sQ230_spl ),
inference(split_clause,[status(thm)],[f2304,f2353,f2312]) ).
fof(f2359,plain,
( ~ sQ220_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2308,f84]) ).
fof(f2360,plain,
~ sQ220_spl,
inference(contradiction_clause,[status(thm)],[f2359]) ).
fof(f2361,plain,
( ~ sQ221_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2313,f77]) ).
fof(f2362,plain,
~ sQ221_spl,
inference(contradiction_clause,[status(thm)],[f2361]) ).
fof(f2534,plain,
( ~ sQ28_spl
| ~ sQ6_spl
| equalish(e_2,e_1)
| ~ greater(e_2,e_0) ),
inference(resolution,[status(thm)],[f141,f239]) ).
fof(f2536,definition,
( sQ236_spl
<=> greater(e_2,e_0) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f2538,plain,
( sQ236_spl
| ~ greater(e_2,e_0) ),
inference(component_clause,[status(thm)],[f2536]) ).
fof(f2539,definition,
( sQ237_spl
<=> equalish(e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f2540,plain,
( ~ sQ237_spl
| equalish(e_2,e_1) ),
inference(component_clause,[status(thm)],[f2539]) ).
fof(f2542,plain,
( ~ sQ28_spl
| ~ sQ6_spl
| sQ237_spl
| ~ sQ236_spl ),
inference(split_clause,[status(thm)],[f2534,f2536,f2539,f140,f238]) ).
fof(f2547,plain,
( ~ sQ237_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2540,f76]) ).
fof(f2548,plain,
~ sQ237_spl,
inference(contradiction_clause,[status(thm)],[f2547]) ).
fof(f2549,plain,
( sQ236_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2538,f49]) ).
fof(f2550,plain,
sQ236_spl,
inference(contradiction_clause,[status(thm)],[f2549]) ).
fof(f2554,definition,
( sQ239_spl
<=> greater(e_1,e_0) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f2556,plain,
( sQ239_spl
| ~ greater(e_1,e_0) ),
inference(component_clause,[status(thm)],[f2554]) ).
fof(f2560,plain,
( sQ239_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2556,f48]) ).
fof(f2561,plain,
sQ239_spl,
inference(contradiction_clause,[status(thm)],[f2560]) ).
fof(f2562,plain,
( ~ sQ174_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1652,f73]) ).
fof(f2563,plain,
~ sQ174_spl,
inference(contradiction_clause,[status(thm)],[f2562]) ).
fof(f2584,plain,
( ~ sQ71_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f554,f46]) ).
fof(f2585,plain,
( ~ sQ71_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2584,f74]) ).
fof(f2586,plain,
~ sQ71_spl,
inference(contradiction_clause,[status(thm)],[f2585]) ).
fof(f2589,plain,
( ~ sQ64_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f529,f45]) ).
fof(f2590,plain,
( ~ sQ64_spl
| sQ177_spl ),
inference(split_clause,[status(thm)],[f2589,f1664,f528]) ).
fof(f2591,plain,
( ~ sQ57_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f504,f45]) ).
fof(f2592,plain,
( ~ sQ57_spl
| sQ180_spl ),
inference(split_clause,[status(thm)],[f2591,f1675,f503]) ).
fof(f2621,plain,
! [X0] :
( equalish(e_3,e_2)
| product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0)
| product(e_4,X0,X0)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f439,f363]) ).
fof(f2642,plain,
! [X0] :
( equalish(X0,e_3)
| product(e_4,X0,e_4)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f439,f373]) ).
fof(f2643,plain,
! [X0] :
( equalish(X0,e_2)
| product(e_4,X0,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f439,f363]) ).
fof(f2644,plain,
! [X0] :
( product(X0,e_4,X0)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X0)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f439,f385]) ).
fof(f2645,plain,
! [X0] :
( product(X0,e_3,X0)
| product(X0,e_4,e_4)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X0)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f439,f375]) ).
fof(f2646,plain,
! [X0] :
( product(X0,e_2,X0)
| product(X0,e_4,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X0)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f439,f365]) ).
fof(f2662,definition,
! [X0] :
( sQ240_spl
<=> ( product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0)
| product(e_4,X0,X0)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f2687,plain,
( sQ180_spl
| sQ240_spl ),
inference(split_clause,[status(thm)],[f2621,f2662,f1675]) ).
fof(f2715,definition,
! [X0] :
( sQ247_spl
<=> ( equalish(X0,e_3)
| product(e_4,X0,e_4)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f2718,plain,
( ~ sQ9_spl
| sQ247_spl ),
inference(split_clause,[status(thm)],[f2642,f2715,f152]) ).
fof(f2719,definition,
! [X0] :
( sQ248_spl
<=> ( equalish(X0,e_2)
| product(e_4,X0,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_1)
| ~ group_element(X0)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f2722,plain,
( ~ sQ9_spl
| sQ248_spl ),
inference(split_clause,[status(thm)],[f2643,f2719,f152]) ).
fof(f2723,definition,
! [X0] :
( sQ249_spl
<=> ( product(X0,e_4,X0)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(X0)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f2726,plain,
( ~ sQ9_spl
| sQ249_spl ),
inference(split_clause,[status(thm)],[f2644,f2723,f152]) ).
fof(f2727,definition,
! [X0] :
( sQ250_spl
<=> ( product(X0,e_3,X0)
| product(X0,e_4,e_4)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(X0)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f2730,plain,
( ~ sQ9_spl
| sQ250_spl ),
inference(split_clause,[status(thm)],[f2645,f2727,f152]) ).
fof(f2731,definition,
! [X0] :
( sQ251_spl
<=> ( product(X0,e_2,X0)
| product(X0,e_4,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_1)
| ~ group_element(X0)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f2734,plain,
( ~ sQ9_spl
| sQ251_spl ),
inference(split_clause,[status(thm)],[f2646,f2731,f152]) ).
fof(f2752,plain,
( ~ sQ129_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f1234,f46]) ).
fof(f2753,plain,
( ~ sQ129_spl
| sQ220_spl ),
inference(split_clause,[status(thm)],[f2752,f2307,f1233]) ).
fof(f2777,plain,
( ~ sQ135_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f1283,f46]) ).
fof(f2778,plain,
( ~ sQ135_spl
| sQ221_spl ),
inference(split_clause,[status(thm)],[f2777,f2312,f1282]) ).
fof(f2784,plain,
( ~ sQ165_spl
| equalish(e_1,e_4) ),
inference(resolution,[status(thm)],[f1546,f47]) ).
fof(f2785,plain,
( ~ sQ165_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2784,f75]) ).
fof(f2786,plain,
~ sQ165_spl,
inference(contradiction_clause,[status(thm)],[f2785]) ).
fof(f2787,plain,
( ~ sQ168_spl
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[f1572,f47]) ).
fof(f2788,plain,
( ~ sQ168_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2787,f81]) ).
fof(f2789,plain,
~ sQ168_spl,
inference(contradiction_clause,[status(thm)],[f2788]) ).
fof(f2799,plain,
! [X0] :
( equalish(e_4,X0)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f379,f92]) ).
fof(f2808,definition,
! [X0] :
( sQ254_spl
<=> ( equalish(e_4,X0)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f2827,plain,
( ~ sQ9_spl
| sQ254_spl ),
inference(split_clause,[status(thm)],[f2799,f2808,f152]) ).
fof(f2837,plain,
! [X0] :
( equalish(e_4,X0)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[f381,f92]) ).
fof(f2846,definition,
! [X0] :
( sQ260_spl
<=> ( equalish(e_4,X0)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f2865,plain,
( sQ260_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2837,f152,f2846]) ).
fof(f2866,plain,
( ~ sQ37_spl
| ~ sQ25_spl
| ~ greater(e_3,e_0) ),
inference(resolution,[status(thm)],[f226,f350]) ).
fof(f2872,plain,
( ~ sQ37_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2866,f50]) ).
fof(f2873,plain,
( ~ sQ37_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f2872]) ).
fof(f2882,plain,
( ~ sQ37_spl
| ~ sQ23_spl
| ~ greater(e_1,e_0) ),
inference(resolution,[status(thm)],[f220,f350]) ).
fof(f2888,plain,
( ~ sQ37_spl
| ~ sQ23_spl
| ~ sQ239_spl ),
inference(split_clause,[status(thm)],[f2882,f2554,f219,f349]) ).
fof(f2909,plain,
( ~ sQ70_spl
| ~ sQ5_spl
| ~ greater(e_1,e_0) ),
inference(resolution,[status(thm)],[f137,f551]) ).
fof(f2915,plain,
( ~ sQ70_spl
| ~ sQ5_spl
| ~ sQ239_spl ),
inference(split_clause,[status(thm)],[f2909,f2554,f136,f550]) ).
fof(f2925,plain,
( ~ sQ70_spl
| ~ sQ31_spl
| ~ greater(e_2,e_0) ),
inference(resolution,[status(thm)],[f250,f551]) ).
fof(f2931,plain,
( ~ sQ70_spl
| ~ sQ31_spl
| ~ sQ236_spl ),
inference(split_clause,[status(thm)],[f2925,f2536,f249,f550]) ).
fof(f2951,plain,
( ~ sQ170_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f1596,f47]) ).
fof(f2952,plain,
( ~ sQ170_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2951,f78]) ).
fof(f2953,plain,
~ sQ170_spl,
inference(contradiction_clause,[status(thm)],[f2952]) ).
fof(f2957,plain,
( ~ sQ149_spl
| ~ sQ95_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f1013,f1377]) ).
fof(f2959,plain,
( ~ sQ149_spl
| ~ sQ95_spl
| sQ180_spl ),
inference(split_clause,[status(thm)],[f2957,f1675,f824,f1376]) ).
fof(f2993,plain,
! [X0,X1,X2] :
( equalish(e_3,X2)
| ~ next(X0,X2)
| ~ greater(X1,e_0)
| ~ cycle(X0,X1)
| product(e_1,X0,e_3)
| product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,e_1,e_4)
| product(X0,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f638,f68]) ).
fof(f2995,plain,
! [X0] :
( ~ greater(e_3,X0)
| ~ cycle(X0,e_0)
| product(e_1,X0,e_3)
| product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,e_1,e_4)
| product(X0,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f638,f66]) ).
fof(f3002,plain,
! [X0] :
( equalish(e_3,e_2)
| product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f638,f363]) ).
fof(f3003,plain,
! [X0,X1] :
( equalish(e_3,e_2)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,X1,e_4)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f638,f363]) ).
fof(f3011,plain,
! [X0] :
( equalish(X0,e_3)
| product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,e_3,e_4)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f638,f101]) ).
fof(f3037,plain,
! [X0,X1,X2] :
( equalish(e_4,X2)
| ~ next(X0,X2)
| ~ greater(X1,e_0)
| ~ cycle(X0,X1)
| product(e_1,X0,e_3)
| product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,e_1,e_3)
| product(X0,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f638,f68]) ).
fof(f3038,plain,
! [X0] :
( ~ greater(e_4,X0)
| ~ cycle(X0,e_0)
| product(e_1,X0,e_3)
| product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,e_1,e_3)
| product(X0,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f638,f66]) ).
fof(f3044,plain,
! [X0,X1] :
( equalish(e_4,e_3)
| product(X0,X1,e_4)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f638,f373]) ).
fof(f3046,plain,
! [X0,X1] :
( equalish(e_4,e_2)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f638,f363]) ).
fof(f3053,plain,
! [X0] :
( equalish(X0,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,e_4,e_3)
| product(X0,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f638,f101]) ).
fof(f3057,plain,
! [X0] :
( equalish(X0,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| product(e_4,e_2,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[f638,f99]) ).
fof(f3067,plain,
! [X0] :
( sQ97_spl
| product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f638,f832]) ).
fof(f3068,plain,
! [X0] :
( sQ83_spl
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| product(e_4,X0,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[f638,f684]) ).
fof(f3110,plain,
! [X0,X1] :
( equalish(e_1,e_3)
| product(X1,X0,e_4)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(e_4,e_2,X0)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f638,f373]) ).
fof(f3111,plain,
! [X0,X1] :
( equalish(e_1,e_2)
| product(X1,X0,e_4)
| product(X1,X0,e_3)
| product(X1,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(e_4,e_2,X0)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f638,f363]) ).
fof(f3117,plain,
! [X0] :
( equalish(X0,e_1)
| product(e_1,X0,e_3)
| product(e_1,X0,e_2)
| product(e_4,e_2,X0)
| product(X0,e_1,e_4)
| product(X0,e_1,e_3)
| product(X0,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f638,f99]) ).
fof(f3143,plain,
! [X0] :
( equalish(X0,e_2)
| product(X0,e_2,e_3)
| product(X0,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f638,f101]) ).
fof(f3145,plain,
! [X0] :
( equalish(X0,e_2)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,e_2,e_4)
| product(X0,e_2,e_3)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f638,f99]) ).
fof(f3167,plain,
! [X0,X1] :
( equalish(e_3,e_2)
| product(X1,X0,e_4)
| product(X1,X0,e_3)
| product(X1,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f638,f363]) ).
fof(f3173,plain,
! [X0] :
( equalish(X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,e_3,e_4)
| product(X0,e_3,e_3)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f638,f99]) ).
fof(f3194,definition,
! [X0,X1,X2] :
( sQ269_spl
<=> ( equalish(e_3,X2)
| ~ next(X0,X2)
| ~ greater(X1,e_0)
| ~ cycle(X0,X1)
| product(e_1,X0,e_3)
| product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,e_1,e_4)
| product(X0,e_1,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f3197,plain,
( ~ sQ22_spl
| sQ269_spl ),
inference(split_clause,[status(thm)],[f2993,f3194,f216]) ).
fof(f3199,definition,
! [X0] :
( sQ270_spl
<=> ( ~ greater(e_3,X0)
| ~ cycle(X0,e_0)
| product(e_1,X0,e_3)
| product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,e_1,e_4)
| product(X0,e_1,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f3202,plain,
( ~ sQ22_spl
| sQ270_spl ),
inference(split_clause,[status(thm)],[f2995,f3199,f216]) ).
fof(f3215,definition,
! [X0] :
( sQ273_spl
<=> ( product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f3218,plain,
( sQ180_spl
| sQ273_spl ),
inference(split_clause,[status(thm)],[f3002,f3215,f1675]) ).
fof(f3219,definition,
! [X0,X1] :
( sQ274_spl
<=> ( product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,X1,e_4)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f3222,plain,
( sQ180_spl
| sQ274_spl ),
inference(split_clause,[status(thm)],[f3003,f3219,f1675]) ).
fof(f3230,definition,
! [X0] :
( sQ275_spl
<=> ( equalish(X0,e_3)
| product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,e_3,e_4)
| product(X0,e_3,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f3233,plain,
( ~ sQ33_spl
| sQ275_spl ),
inference(split_clause,[status(thm)],[f3011,f3230,f259]) ).
fof(f3259,definition,
! [X0,X1,X2] :
( sQ277_spl
<=> ( equalish(e_4,X2)
| ~ next(X0,X2)
| ~ greater(X1,e_0)
| ~ cycle(X0,X1)
| product(e_1,X0,e_3)
| product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,e_1,e_3)
| product(X0,e_1,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f3262,plain,
( ~ sQ22_spl
| sQ277_spl ),
inference(split_clause,[status(thm)],[f3037,f3259,f216]) ).
fof(f3263,definition,
! [X0] :
( sQ278_spl
<=> ( ~ greater(e_4,X0)
| ~ cycle(X0,e_0)
| product(e_1,X0,e_3)
| product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,e_1,e_3)
| product(X0,e_1,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f3266,plain,
( ~ sQ22_spl
| sQ278_spl ),
inference(split_clause,[status(thm)],[f3038,f3263,f216]) ).
fof(f3278,definition,
! [X0,X1] :
( sQ281_spl
<=> ( product(X0,X1,e_4)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f3281,plain,
( sQ220_spl
| sQ281_spl ),
inference(split_clause,[status(thm)],[f3044,f3278,f2307]) ).
fof(f3283,definition,
! [X0,X1] :
( sQ282_spl
<=> ( product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f3286,plain,
( sQ177_spl
| sQ282_spl ),
inference(split_clause,[status(thm)],[f3046,f3283,f1664]) ).
fof(f3293,definition,
! [X0] :
( sQ283_spl
<=> ( equalish(X0,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,e_4,e_3)
| product(X0,e_4,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f3296,plain,
( ~ sQ9_spl
| sQ283_spl ),
inference(split_clause,[status(thm)],[f3053,f3293,f152]) ).
fof(f3301,definition,
( sQ285_spl
<=> equalish(e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f3302,plain,
( ~ sQ285_spl
| equalish(e_2,e_4) ),
inference(component_clause,[status(thm)],[f3301]) ).
fof(f3305,definition,
! [X0] :
( sQ286_spl
<=> ( equalish(X0,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| product(e_4,X0,e_3)
| product(e_4,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f3308,plain,
( sQ83_spl
| sQ286_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3057,f152,f3305,f682]) ).
fof(f3324,definition,
! [X0] :
( sQ290_spl
<=> ( product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f3327,plain,
( sQ97_spl
| sQ290_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f3067,f246,f3324,f830]) ).
fof(f3328,definition,
! [X0] :
( sQ291_spl
<=> ( product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| product(e_4,X0,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f3331,plain,
( sQ83_spl
| sQ291_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3068,f152,f3328,f682]) ).
fof(f3405,definition,
! [X0,X1] :
( sQ304_spl
<=> ( product(X1,X0,e_4)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(e_4,e_2,X0)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f3408,plain,
( sQ222_spl
| sQ304_spl ),
inference(split_clause,[status(thm)],[f3110,f3405,f2317]) ).
fof(f3409,definition,
! [X0,X1] :
( sQ305_spl
<=> ( product(X1,X0,e_4)
| product(X1,X0,e_3)
| product(X1,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(e_4,e_2,X0)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f3412,plain,
( sQ174_spl
| sQ305_spl ),
inference(split_clause,[status(thm)],[f3111,f3409,f1651]) ).
fof(f3420,definition,
! [X0] :
( sQ307_spl
<=> ( equalish(X0,e_1)
| product(e_1,X0,e_3)
| product(e_1,X0,e_2)
| product(e_4,e_2,X0)
| product(X0,e_1,e_4)
| product(X0,e_1,e_3)
| product(X0,e_1,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f3423,plain,
( ~ sQ22_spl
| sQ307_spl ),
inference(split_clause,[status(thm)],[f3117,f3420,f216]) ).
fof(f3449,definition,
! [X0,X1] :
( sQ310_spl
<=> ( product(X1,X0,e_4)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| product(X1,X0,e_3)
| product(X1,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f3460,definition,
! [X0] :
( sQ312_spl
<=> ( equalish(X0,e_2)
| product(X0,e_2,e_3)
| product(X0,e_2,e_1)
| product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f3463,plain,
( sQ97_spl
| sQ312_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f3143,f246,f3460,f830]) ).
fof(f3464,definition,
! [X0] :
( sQ313_spl
<=> ( equalish(X0,e_2)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,e_2,e_4)
| product(X0,e_2,e_3)
| product(X0,e_2,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f3467,plain,
( ~ sQ30_spl
| sQ313_spl ),
inference(split_clause,[status(thm)],[f3145,f3464,f246]) ).
fof(f3495,plain,
( sQ180_spl
| sQ310_spl ),
inference(split_clause,[status(thm)],[f3167,f3449,f1675]) ).
fof(f3503,definition,
! [X0] :
( sQ318_spl
<=> ( equalish(X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,e_3,e_4)
| product(X0,e_3,e_3)
| product(X0,e_3,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f3506,plain,
( ~ sQ33_spl
| sQ318_spl ),
inference(split_clause,[status(thm)],[f3173,f3503,f259]) ).
fof(f3511,plain,
( ~ sQ285_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3302,f78]) ).
fof(f3512,plain,
~ sQ285_spl,
inference(contradiction_clause,[status(thm)],[f3511]) ).
fof(f3593,plain,
( ~ sQ81_spl
| ~ sQ87_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f934,f677]) ).
fof(f3597,plain,
( ~ sQ81_spl
| ~ sQ87_spl
| sQ220_spl ),
inference(split_clause,[status(thm)],[f3593,f2307,f723,f676]) ).
fof(f3626,plain,
( ~ sQ222_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2318,f74]) ).
fof(f3627,plain,
~ sQ222_spl,
inference(contradiction_clause,[status(thm)],[f3626]) ).
fof(f3664,plain,
! [X0] :
( product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[f383,f439]) ).
fof(f3668,plain,
! [X0] :
( product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_4)
| product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f383,f421]) ).
fof(f3672,plain,
! [X0] :
( product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f383,f403]) ).
fof(f3679,plain,
! [X0] :
( product(X0,X0,e_2)
| product(X0,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0)
| equalish(e_3,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f383,f638]) ).
fof(f3680,plain,
! [X0,X1] :
( product(X0,X1,e_2)
| product(X0,X1,e_1)
| product(e_4,e_2,X1)
| product(X1,X0,e_4)
| product(X1,X0,e_3)
| product(X1,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| equalish(e_3,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f383,f638]) ).
fof(f3683,plain,
! [X0] :
( product(e_4,X0,X0)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(e_3,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f383,f439]) ).
fof(f3687,plain,
! [X0,X1] :
( product(X0,X1,e_3)
| product(X0,X1,e_1)
| product(e_4,e_2,X1)
| product(X1,X0,e_4)
| product(X1,X0,e_3)
| product(X1,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| equalish(e_2,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f383,f638]) ).
fof(f3688,plain,
! [X0] :
( product(e_4,X0,X0)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(e_2,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f383,f439]) ).
fof(f3693,definition,
( sQ330_spl
<=> equalish(e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f3694,plain,
( ~ sQ330_spl
| equalish(e_3,e_4) ),
inference(component_clause,[status(thm)],[f3693]) ).
fof(f3709,definition,
! [X0] :
( sQ333_spl
<=> ( product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f3712,plain,
( sQ333_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3664,f152,f3709]) ).
fof(f3716,definition,
! [X0] :
( sQ334_spl
<=> ( product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_4)
| product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f3719,plain,
( sQ334_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f3668,f259,f3716]) ).
fof(f3723,definition,
! [X0] :
( sQ335_spl
<=> ( product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f3726,plain,
( sQ335_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f3672,f246,f3723]) ).
fof(f3748,definition,
! [X0] :
( sQ341_spl
<=> ( product(X0,X0,e_2)
| product(X0,X0,e_1)
| product(e_4,e_2,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ341_spl])],[split_symbol_definition]) ).
fof(f3751,plain,
( sQ330_spl
| sQ341_spl ),
inference(split_clause,[status(thm)],[f3679,f3748,f3693]) ).
fof(f3752,definition,
! [X0,X1] :
( sQ342_spl
<=> ( product(X0,X1,e_2)
| product(X0,X1,e_1)
| product(e_4,e_2,X1)
| product(X1,X0,e_4)
| product(X1,X0,e_3)
| product(X1,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ342_spl])],[split_symbol_definition]) ).
fof(f3755,plain,
( sQ330_spl
| sQ342_spl ),
inference(split_clause,[status(thm)],[f3680,f3752,f3693]) ).
fof(f3758,definition,
! [X0] :
( sQ343_spl
<=> ( product(e_4,X0,X0)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ343_spl])],[split_symbol_definition]) ).
fof(f3761,plain,
( sQ330_spl
| sQ343_spl ),
inference(split_clause,[status(thm)],[f3683,f3758,f3693]) ).
fof(f3765,definition,
! [X0,X1] :
( sQ344_spl
<=> ( product(X0,X1,e_3)
| product(X0,X1,e_1)
| product(e_4,e_2,X1)
| product(X1,X0,e_4)
| product(X1,X0,e_3)
| product(X1,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ344_spl])],[split_symbol_definition]) ).
fof(f3768,plain,
( sQ285_spl
| sQ344_spl ),
inference(split_clause,[status(thm)],[f3687,f3765,f3301]) ).
fof(f3769,definition,
! [X0] :
( sQ345_spl
<=> ( product(e_4,X0,X0)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f3772,plain,
( sQ285_spl
| sQ345_spl ),
inference(split_clause,[status(thm)],[f3688,f3769,f3301]) ).
fof(f3776,plain,
( ~ sQ330_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3694,f81]) ).
fof(f3777,plain,
~ sQ330_spl,
inference(contradiction_clause,[status(thm)],[f3776]) ).
fof(f3796,plain,
! [X0] :
( equalish(e_3,e_2)
| product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0)
| equalish(e_2,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f402,f363]) ).
fof(f3816,plain,
! [X0] :
( equalish(e_4,e_3)
| product(X0,X0,e_4)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0)
| equalish(e_2,X0)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f402,f373]) ).
fof(f3817,plain,
! [X0] :
( equalish(e_4,e_2)
| product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0)
| equalish(e_2,X0)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f402,f363]) ).
fof(f3836,definition,
! [X0] :
( sQ346_spl
<=> ( product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0)
| equalish(e_2,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f3844,definition,
! [X0] :
( sQ348_spl
<=> ( product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0)
| equalish(e_2,X0)
| product(X0,X0,e_4)
| product(X0,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f3847,plain,
( sQ180_spl
| sQ348_spl ),
inference(split_clause,[status(thm)],[f3796,f3844,f1675]) ).
fof(f3865,plain,
( sQ220_spl
| sQ346_spl ),
inference(split_clause,[status(thm)],[f3816,f3836,f2307]) ).
fof(f3866,definition,
! [X0] :
( sQ350_spl
<=> ( product(X0,X0,e_4)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X0)
| equalish(e_2,X0)
| product(X0,X0,e_3)
| product(X0,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f3869,plain,
( sQ177_spl
| sQ350_spl ),
inference(split_clause,[status(thm)],[f3817,f3866,f1664]) ).
fof(f3879,plain,
( ~ sQ70_spl
| ~ sQ32_spl
| ~ greater(e_3,e_0) ),
inference(resolution,[status(thm)],[f253,f551]) ).
fof(f3886,plain,
( ~ sQ70_spl
| ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3879,f50]) ).
fof(f3887,plain,
( ~ sQ70_spl
| ~ sQ32_spl ),
inference(contradiction_clause,[status(thm)],[f3886]) ).
fof(f3971,plain,
( ~ sQ85_spl
| ~ sQ86_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f1189,f699]) ).
fof(f3980,plain,
( ~ sQ85_spl
| ~ sQ86_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3971,f79]) ).
fof(f3981,plain,
( ~ sQ85_spl
| ~ sQ86_spl ),
inference(contradiction_clause,[status(thm)],[f3980]) ).
fof(f3982,plain,
$false,
inference(sat_refutation,[status(thm)],[f146,f207,f228,f230,f255,f257,f270,f290,f332,f355,f389,f393,f397,f401,f407,f411,f415,f419,f425,f429,f433,f437,f523,f548,f573,f578,f580,f582,f594,f606,f617,f625,f636,f656,f669,f687,f703,f716,f731,f744,f757,f760,f778,f781,f785,f812,f835,f850,f854,f882,f907,f930,f932,f941,f972,f974,f983,f994,f1009,f1034,f1054,f1065,f1077,f1101,f1112,f1124,f1133,f1142,f1193,f1236,f1240,f1250,f1270,f1301,f1303,f1391,f1406,f1418,f1458,f1506,f1534,f1560,f1583,f1626,f1660,f1667,f1671,f1678,f1682,f1689,f1691,f1711,f1736,f1768,f1843,f1875,f1890,f2060,f2083,f2087,f2091,f2095,f2120,f2182,f2207,f2287,f2326,f2332,f2336,f2340,f2344,f2356,f2360,f2362,f2542,f2548,f2550,f2561,f2563,f2586,f2590,f2592,f2687,f2718,f2722,f2726,f2730,f2734,f2753,f2778,f2786,f2789,f2827,f2865,f2873,f2888,f2915,f2931,f2953,f2959,f3197,f3202,f3218,f3222,f3233,f3262,f3266,f3281,f3286,f3296,f3308,f3327,f3331,f3408,f3412,f3423,f3463,f3467,f3495,f3506,f3512,f3597,f3627,f3712,f3719,f3726,f3751,f3755,f3761,f3768,f3772,f3777,f3847,f3865,f3869,f3887,f3981]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP126-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n002.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 20:02:18 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.14/0.36 % Drodi V4.1.1
% 4.14/1.01 % Refutation found
% 4.14/1.01 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.14/1.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.97/1.04 % Elapsed time: 0.669246 seconds
% 0.97/1.04 % CPU time: 4.980078 seconds
% 0.97/1.04 % Total memory used: 32.260 MB
% 0.97/1.04 % Net memory used: 30.197 MB
%------------------------------------------------------------------------------